Spectroscopy and Dynamics of Single Molecules: Methods and Applications 0128164638, 9780128164631

Table of contents :
Cover
Spectroscopy and
Dynamics of Single
Molecules:

Methods and Applications
Copyright
Contributors
Section 1
Introduction
Historical overview
Beyond intensity: Expanding techniques
New applications
Topics covered in this book
References
Section 2
1
Photophysics of single-molecule probes
Introduction
Potential artifacts from surfaces and the use of extrinsic probes
Potential artifacts due to the generation of dark states
Photophysical processes and the generation of dark states
Absorption of light
Fluorescence
Intersystem crossing and the triplet state
Energy transfer
Quenching
The dynamic behavior of dark states
Nanosecond dynamics of the S0/S1 system
Dynamics of the S0/S1/T1 system
Understanding the various contributions to the measured fluorescence intensities
Photophysical considerations in the calculation of accurate FRET efficiencies
Photophysical properties of common single-molecule fluorescent probes
Rhodamines and carborhodamines
Oxazines
Carbocyanines
Concluding remarks
Appendix
Acknowledgments
References
2
Probing dynamics in single molecules
Introduction and overview
Single molecule FRET microscopy
Fluorescence
Förster resonance energy transfer (FRET)
Widefield - Total internal reflection fluorescence (WF-TIRF) microscopy
Total internal reflection
Prism-based TIRF (pTIRF) microscopy
Objective-based TIRF (oTIRF) microscopy
Alternating laser excitation (ALEX)
Camera-based detection
Electron-multiplying CCD-based cameras
CMOS-based cameras
The quantum efficiency of emCCD and sCMOS cameras
Surface and sample preparation for smFRET on surface-immobilized molecules
Practical considerations regarding smTIRF microscopy
Illumination
Detection
Sample channels for TIRF microscopy
Experimental aspects
Single molecule TIRF data evaluation
Camera mapping
Particle localization and pair finding
Intensity trace extraction and background subtraction
Trace evaluation and categorization
FRET efficiency correction and distance calculation
Direct excitation correction
Spectral crosstalk or leakage correction
Detection efficiency and quantum yield correction
Summary FRET efficiency correction
Frame- and trace-wise FRET histograms
Analyzing dynamics using hidden Markov modeling (HMM)
Markovian processes, Markovian chains and transition probability matrices
Hidden Markov models, emission functions and likelihood
The Baum-Welch forward-backward algorithm
Viterbi algorithm
Information theory and likelihood estimators
HMM analysis of smTIRF FRET data
Global and trace-wise HMM
Transition density plots
Dwell-time histograms and transition rate calculation
HMM analysis of NC2-mediated TATA box-binding protein dynamics on DNA
Future applications
Summary
References
3
Single molecule spectroscopy at interfaces
Introduction
Historical overview of single molecule spectroscopy at interfaces
Instrumentation and analysis
Sample considerations for single molecule fluorescence at interfaces
Instrumentation - Total internal reflection fluorescence (TIRF) microscopy
Instrumentation - Confocal microscopy
Analysis - Single molecule localization methods for super-resolution imaging
Analysis - Kinetic analysis of adsorption or turnover rates
Analysis - Single molecule tracking to quantify diffusion
Analysis - Correlation techniques for diffusion and super-resolution information
Advancements in three-dimensional single molecule imaging techniques and analysis at interfaces
Imaging single molecule interfacial dynamics with engineered point spread functions
Biophysical interfaces
Live cell lipid membranes
Membraneless interfaces through liquid/liquid phase separation
Improving single molecule fluorescent protein localization at biointerfaces
Soft material interfaces used in separations
Interfacial catalysis
Sample considerations to achieve single molecule detection at heterogeneous catalytic interfaces
Resolving spatiotemporal heterogeneity at catalytic solid/liquid interfaces
Other applications of single molecule spectroscopy to interfaces
Outlook
Acknowledgements
References
4
Quantum dots in single molecule spectroscopy
Introduction
Synthesis, shelling and functionalization of colloidal QDs
Colloidal CdE (E=S, Se, Te) QD synthesis
QD shelling
QD functionalization
Cd-free QDs
Electronic structure and photophysics of single QDs
Electronic structure of QDs
Single QD photophysics
QDs as single-molecule fluorescent probes and single photon sources
Single particle tracking (SPT)
Fluorescence/image correlation spectroscopy (FCS/ICS)
Single molecule FRET
Super-resolution microscopy
Blinking dynamics as a probe of local environment and chemical reactions
Fluorescence lifetime imaging and time-gated imaging (FLIM/TGI)
Single photon sources
Acknowledgments
References
Further reading
5
Three-dimensional single-molecule tracking in living cells
Historical background
Uses of 3D single-molecule tracking
Alternatives to 3D molecular tracking
Theoretical background
Single-particle localization
Experimental design
PSF engineering
Multi-plane imaging
Confocal tracking
Light-sheet microscopy
Interference methods
Labeling strategies
Precautions
Data analysis
Applications
Location
Stoichiometry
Kinetics and dynamics
Future prospects
Acknowledgments
References
Further reading
6
Multiparameter fluorescence spectroscopy of single molecules
Outline
Multiparameter fluorescence spectroscopy
Data acquisition with time-correlated single-photon counting
Burst-integrated fluorescence lifetime
Spectral information
Quantum yield
Stoichiometry and brightness
Fluorescence lifetime
Inter-fluorophore distance and Förster resonance energy transfer
Steady-state FRET
Time-resolved FRET
FRET network design
Time-resolved anisotropy
Fluorescence correlation spectroscopy
Accuracy of MFS with FRET
Spatial accuracy
Temporal accuracy
Temporal accuracy of FCS
Sample preparation for MFS with FRET
Summary and workflow of MFS
Applications of MFS: Examples
Benchmark and DNA standards
Monitoring transient conformational states along enzymatic reactions
Monitoring weak interdomain interactions
Discussion and conclusion
Acknowledgments
References
7
Single molecule analysis in nanofluidic devices
Introduction
Unique physical phenomena in confined environments with nanometer critical dimensions
Nanoslits (1D), nanochannels (2D) and nanopores (3D)
Sense-of-scale
Surface charge effects
Electroosmotic flow (EOF) and the electric double layer (EDL)
Electrokinetic versus hydrodynamic pumping at the nanometer scale
Nanometer confinement and stretching of single DNA molecules
Shaping electrical fields
Concentration polarization
Fabrication of nanochannel devices
Fabrication techniques of nanofluidic devices
Bonding strategies for nanofluidic devices
Fabrication of thermoplastic nanofluidic devices
Applications of single molecule detection in nanofluidic devices
DNA stretching
Effects of channel dimensions
Effects of ionic strength
Optical mapping in nanochannels
Enzymatic labeling
Affinity labeling
DNA methylation detection using nanochannels
Genomic mapping for sequence variation maps using nanofluidic devices
Nanoscale electrophoresis
Conclusions
References
Index
A
B
C
D
E
F
G
H
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J
K
L
M
N
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P
Q
R
S
T
U
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W
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Back Cover

Citation preview

Spectroscopy and Dynamics of Single Molecules

Developments in Physical & Theoretical Chemistry Series Editor James E. House

With the new series Developments in Physical & Theoretical Chemistry, Elsevier introduces a collection of volumes that highlight timely and important developments in this interdisciplinary field. The series aims to present useful and timely reference works dealing with significant areas of research in which there is rapid growth. Through the contributions of specialists, these volumes will provide essential background on appropriate and relevant topics and provide surveys of the literature at a level to be useful to advanced students and researchers. In this way, the volumes will address the underlying theoretical and experimental background on the topics for researchers entering the topic fields and function as useful reference works of lasting value. A primary goal for the volumes in the series is to provide a strong educational thrust for advanced study in particular fields. Each volume will have an editor who is intimately involved in work constituting the topic of the volume. Although contributions to volumes in the series will include those of established scholars, contributions from those who are rising in prominence will also be included. 2018 2019 2019

Physical Chemistry of Gas–Liquid Interfaces Jennifer A. Faust and James E. House, Editors Mathematical Physics in Theoretical Chemistry S.M. Blinder and J.E. House, Editors Spectroscopy and Dynamics of Single Molecules Carey K. Johnson, Editor

Developments in Physical & Theoretical Chemistry James E. House, Series Editor

Spectroscopy and Dynamics of Single Molecules Methods and Applications

Edited by Carey K. Johnson Department of Chemistry, University of Kansas, Lawrence, KS, United States

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States © 2019 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-816463-1 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Susan Dennis Acquisition Editor: Anneka Hess Editorial Project Manager: Devlin Person Production Project Manager: Prem Kumar Kaliamoorthi Cover Designer: Greg Harris Typeset by SPi Global, India

Contributors Charuni A. Amarasekara Department of Chemistry and the Bioengineering Program, University of Kansas, Lawrence, KS, United States Peter M. Goodwin Center for Integrated Nanotechnologies, Materials Physics and Applications, Los Alamos National Laboratory, Los Alamos, NM, United States George Hamilton Department of Physics, Clemson University, Clemson, SC, United States Colin D. Heyes Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, AR, United States Carey K. Johnson Department of Chemistry, University of Kansas, Lawrence, KS, United States Daniel M. Kalb Center for Integrated Nanotechnologies, Materials Physics and Applications, Los Alamos National Laboratory, Los Alamos, NM, United States Lydia Kisley Department of Physics, Case Western Reserve University, Cleveland, OH, United States Don C. Lamb Department of Chemistry, Center for NanoScience, Nanosystems Initiative Munich (NIM), and Center for Integrated Protein Science Munich (CIPSM), Ludwig Maximilian University of Munich, Munich, Germany Marcia Levitus School of Molecular Sciences; The Biodesign Institute, Arizona State University, Tempe, AZ, United States Demosthenes P. Morales Center for Integrated Nanotechnologies, Materials Physics and Applications, Los Alamos National Laboratory, Los Alamos, NM, United States Evelyn Ploetz Department of Chemistry, Center for NanoScience, Nanosystems Initiative Munich (NIM), and Center for Integrated Protein Science Munich (CIPSM), Ludwig Maximilian University of Munich, Munich, Germany Duncan P. Ryan Center for Integrated Nanotechnologies, Materials Physics and Applications, Los Alamos National Laboratory, Los Alamos, NM, United States

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Clemens-B€ assem Salem Department of Chemistry, Center for NanoScience, Nanosystems Initiative Munich (NIM), and Center for Integrated Protein Science Munich (CIPSM), Ludwig Maximilian University of Munich, Munich, Germany Hugo Sanabria Department of Physics, Clemson University, Clemson, SC, United States Steven A. Soper Department of Chemistry and the Bioengineering Program, University of Kansas, Lawrence, KS, United States Swarnagowri Vaidyanathan Department of Chemistry and the Bioengineering Program, University of Kansas, Lawrence, KS, United States Kumuditha M. Weerakoon-Ratnayake Department of Chemistry and the Bioengineering Program, University of Kansas, Lawrence, KS, United States James H. Werner Center for Integrated Nanotechnologies, Materials Physics and Applications, Los Alamos National Laboratory, Los Alamos, NM, United States

CHAPTER

Introduction

Carey K. Johnson Department of Chemistry, University of Kansas, Lawrence, KS, United States

It has been thirty years since the detection of single molecules was first reported.1 In the intervening decades the field has grown explosively. Applications vary widely, from materials to cellular biology, and the field has spawned new and fruitful research directions and methods, highlighted by super-resolution microscopy2,3—a growing array of methods for peering into cells with unprecedented precision. The goal of this volume is to provide a concise introduction to new techniques and applications of single-molecule spectroscopy. My hope is that experimentalists will value the volume as an introduction to new techniques they may wish to implement, while theoretical and computational chemists will find a description of techniques and applications that may be potential candidates for theoretical treatment. A further aim is to provide graduate students with a concise introduction to singlemolecule experimental techniques and methods of data analysis. The added information gained by probing single molecules is well rehearsed in the literature: removing the ensemble average to access the full distribution; circumventing the need for synchronization in studies of dynamics; the possibility to observe rare events; and accessibility to new photophysical and photochemical phenomena. In addition, single-molecule approaches have allowed researchers to ask and begin to answer new questions: How does the behavior of individual molecules lead to the overall properties observed in complex systems? How do molecular machines work, step-by-step? What molecular interactions and events are important for chemical catalysis or separations? How do molecular conformations interchange?

Historical overview Single-molecule spectroscopy emerged from three independent streams of research in the early 1990s, each leading to detection at the single-molecule level. The first was low-temperature spectroscopy in solids. In an effort to resolve the homogeneous linewidth of molecules within an inhomogeneous broadened band, researchers investigated the spectroscopy of guest molecules in host matrices at low temperature by Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.10000-8 # 2019 Elsevier Inc. All rights reserved.

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methods such as hole-burning spectroscopy.4,5 With lower and lower dopant concentration, statistical fine structure could be detected in the dopant absorption band by frequency-modulation spectroscopy.6,7 Spurred by the detection of structure traceable to statistical fluctuations in the numbers of absorbing molecules, Moerner and Kador1,8 reported single-molecule absorption of pentacene molecules in a host p-terphenyl crystal. Although the detection of light absorption by single-molecules was a tour-deforce of sensitive detection of a small signal riding on a large background, it soon became clear that laser-induced fluorescence would be much more sensitive and versatile for detection of single molecules. To detect fluorescence from single molecules, it is necessary that the molecule have a high absorption cross section and that it emit photons at a high rate compared to the rates of other photophysical processes such as intersystem crossing or photochemical processes such as photobleaching. In addition, a high-efficiency optical setup is required to collect fluorescence photons over a large solid angle, and these photons must be sensitively registered by a detector with low dark noise. In 1990, Orrit and Bernard reported singlemolecule detection of pentacene in p-terphenyl by fluorescence at low temperature,9 and in 1991 Ambrose and Moerner reported spectral jumps in the excitation band of pentacene detected by fluorescence at low temperature.10 A second research stream leading to single-molecule detection had its source in ultra-sensitive fluorescence detection of molecules in room-temperature liquids for applications such as flow cytometry, DNA sequencing, immunofluorescence assays,11 and fluorescence correlation spectroscopy (FCS). As early as 1976, Hirschfeld reported detection of polyethyleneimine conjugated with 80 to 100 fluorescein dye molecules.12 The Keller group in 1987 and the Mathies group in 1989 reported the detection of single molecules of phycoerythrin (containing 34 bilin chromophores) in flowing liquid.13,14 Detection of single molecules of rhodamine 6G dye molecules in solution was achieved initially with pulsed laser excitation and timegated detection to reduce background from Rayleigh, Raman, and specular scattering,15 and soon after with CW excitation.16 It soon became possible to observe fluorescence bursts from single molecule in real time17,18 and to measure singlemolecule fluorescence lifetimes.19,20 FCS was first introduced in the 1970s,21–23 but applications surged in the 1990s with the availability of sensitive photoncounting detectors such as avalanche photodiodes and the application of confocal microscopy to reduce probe volumes in the labs of Rudolf Rigler and Elliot Elson.24–27 Although not strictly a single-molecule technique—the correlation in FCS is taken over contributions from many molecules—the raw data stream in FCS when applied at sufficiently low concentrations contains photon bursts from molecules diffusing through the probe volume.27,28 The third research stream contributing to single-molecule detection was scanningprobe microscopy. Although single-molecules had been detected at low temperature, it was not immediately obvious that single-molecules could be imaged at room temperature. After all, the oscillator strength of molecules at room temperature is spread over a broad absorption band, so that the absorption cross section and therefore

Beyond intensity: expanding techniques

the brightness of a single molecule at a given excitation wavelength are lower than in a low-temperature solid. The fleeting passage of single molecules in solutions was detected by 1990, as described above, but extended observation of single molecules at room temperature was not reported until 1994 by scanning probe microscopy. Scanning tunneling microscopy29 and atomic force microscopy30 had been developed in the 1980s. With the goal of imaging single fluorophores with sub-diffraction spatial resolution at interfaces at room temperature, Betzig and Chichester coupled scanning– probe microscopy with near-field optics, a technique known as near-field scanning optical microscopy (NSOM).31 Fluorophores were excited by the evanescent field emerging from an aperture or tip in near-field, i.e. at distances much less than the wavelength of the excitation light. Scanning of the tip allows resolution down to a few nanometers. The method was applied to detection of the emission spectrum of a carbocyanine dye with near-field excitation,32 fluctuations in the fluorescence intensity of single sulforhodamine dye molecules,33 and measurement of single-molecule fluorescence lifetimes.34 Subsequent applications demonstrated imaging of photosynthetic light harvesting complexes35 and allophycocyanin trimers.36

Beyond intensity: Expanding techniques Far-field single-molecule imaging at room temperature was reported in 199637 setting the stage for new applications of single-molecule fluorescence spectroscopy. Far-field excitation quickly became the norm for single-molecule detection. Most current implementations of single-molecule spectroscopy use far-field imaging at room temperature. Researchers attracted by the advantages of probing single molecules—resolving distributions, tracking dynamics, detecting rare events or interactions—soon sought additional dimensions of information from single-molecule experiments. Methods well known from ensemble fluorescence were applied or adapted to single-molecule detection. Fluorescence decays of single molecules were measured early.19,33 The added information was used to identify molecules in solution,38 probe electron transfer kinetics,39 and to detect conformational changes of RNA40 and DNA.41 Polarization methods were also brought into play. The polarization of the excitation beam can be modulated to probe the orientation31,33 or orientational mobility42 of single molecules. Selection of fluorescence polarization permits detection of fluorescence anisotropy43,44 and anisotropy decay.45 One of the most powerful fluorescence techniques at the single-molecule level is F€ orster resonance energy transfer (FRET). FRET with a single donor-acceptor pair was introduced by Ha et al.46 coupled with NSOM. Since that time, single-pair FRET coupled with wide-field imaging or confocal microscopy47,48 has become one of the most widely used single-molecule methods.49–51 Methods were also developed to track single molecules in space. Inherent in single-molecule tracking is localization of single molecules to a precision better than the resolution limit.52–55 Localization techniques developed for single-

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molecule applications are intrinsic to methods of super-resolution fluorescence microscopy,56–59 the development of which led to the 2014 Nobel Prize in Chemistry.2,3

New applications Whereas initial publications in single-molecule spectroscopy demonstrated feasibility and introduced basic techniques, subsequent work expanded to an increasingly wide range of applications. Single-molecule spectroscopy has by now been applied in many fields of research (see Fig. 1). Its biggest impact has perhaps been felt in molecular and cellular biology. (Among reviews too numerous to cite comprehensively, see Refs. 60–64.) To cite a few additional examples, it has also been applied to polymers,65,66 catalysis,67 and optoelectronics.68 Single-molecule spectroscopy is now a mature field, one where the technology and methodology are largely established. Single-molecule methods have become a resource in studies of physical, chemical, and biological systems, one very powerful tool among many. Advances involve applications to more and more complex systems—living cells or chromatographic systems are two examples—and, by and large, refinements of existing methods. One is now as likely to find singlemolecule spectroscopy mentioned in a conference session on enzyme function or solar energy conversion as in a specialized session on single molecule spectroscopy. In this way, the method will impact a broad and multidisciplinary array of systems and fields.

FIG. 1 Distribution of papers in single-molecule fluorescence since 1989. Applications in chemistry and molecular biology/biochemistry dominate, with significant activity in biophysics and cell biology. Single-molecule fluorescence has also had important impacts in physics, materials, and nanoscience. A topic search for “single-molecule fluorescence” was carried out in Web of Science.

Topics covered in this book

Single-molecule spectroscopy has been the topic of numerous reviews. Only a handful can be mentioned here, with apologies for the many excellent review articles that are not mentioned. A retrospective review of the origins of single-molecule detection can be found in Ref. 69. Other reviews include Refs. 50, 62, 63, 70–72.

Topics covered in this book No book could comprehensively cover the field of single-molecule spectroscopy at the depth the field deserves. This volume focuses on basic techniques and their applications in chemistry and molecular and cellular biology. Important topics not covered in this volume include single-molecule techniques other than fluorescence (single-molecule absorption or Raman spectroscopy) and applications in fields such as condensed matter physics or nanophotonics. In Chapter 1, Marcia Levitus examines the photophysics of single-molecule probes and methods to understand the role of probe photophysics in applications. One of the earliest single-molecule observations was “blinking.”73 Professor Levitus describes how blinking and other photophysical phenomena can be characterized and taken into account in interpreting single-molecule results. In Chapter 2, Clemens-B€assem Salem, Evelyn Ploetz, and Don C. Lamb describe the application of FRET to probe dynamics in immobilized single molecules. FRET has become one of the most powerful probes in the single-molecule toolkit. Salem et al. describe methods to carry out single-molecule FRET experiments by wide-field imaging and approaches to analyze results. In Chapter 3, Lydia Kisley reviews single-molecule methods to find new information about interactions and catalysis at interfaces. Professor Kisley shows that single-molecule spectroscopy is particularly well suited to probing interfaces and describes techniques and examples. In Chapter 4, Colin D. Heyes introduces quantum dots as fluorophores for single-molecule spectroscopy. While dyes and autofluorescent proteins are the most common single-molecule fluorophores, Professor Heyes describes the fluorescent properties and the advantages (and disadvantages) of quantum dots for singlemolecule spectroscopy. In Chapter 5, Daniel M. Kalb, Duncan P. Ryan, Demosthenes P. Morales, Peter M. Goodwin, and James H. Werner describes experimental approaches and methods of analysis for three-dimensional single-molecule tracking in complex environments such as living cells. Single-molecule fluorescence has made a particularly strong impact in characterizing the translational mobility of molecules, first in two dimensions and now in three dimensions. In Chapter 6, George Hamilton and Hugo Sanabria describes the current state-ofthe-art in multi-parameter single-molecule fluorescence burst measurements. The techniques developed for the detection of fluorescence bursts from single molecules

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in solution have led to a rich and fruitful set of methods to characterize molecules in solution by detection of single molecules bursts. Chapter 7 by Kumuditha M. Weerakoon-Ratnayake, Swarnagowri Vaidyanathan, Charuni A. Amarasekara, Carey K. Johnson, and Steven A. Soper describes the application of single-molecule spectroscopy to detection and analysis of DNA in nanofluidic devices. Professor Soper and coworkers show how single-molecule detection of DNA confined in nanochannels opens new dimensions for optical mapping and diagnostic applications.

References 1. Moerner, W. E.; Kador, L. Optical Detection and Spectroscopy of Single Molecules in a Solid. Phys. Rev. Lett. 1989, 62, 2535–2538. 2. Moerner, W. E. Single-Molecule Spectroscopy, Imaging, and Photocontrol: Foundations for Super-Resolution Microscopy (Nobel Lecture). Angew. Chem. Int. Ed. 2015, 54, 8067–8093. 3. Betzig, E. Single Molecules, Cells, and Super-Resolution Optics (Nobel Lecture). Angew. Chem. Int. Ed. 2015, 54, 8034–8053. 4. Jankowiak, R.; Small, G. J. Hole-Burning Spectroscopy and Relaxation Dynamics of Amorphous Solids at Low Temperatures. Science 1987, 237, 618–625. 5. Skinner, J. L.; Moerner, W. E. Structure and Dynamics in Solids as Probed by Optical Spectroscopy. J. Phys. Chem. 1996, 100, 13251–13262. 6. Moerner, W. E.; Carter, T. P. Statistical Fine Structure of Inhomogeneously Broadened Absorption Lines. Phys. Rev. Lett. 1987, 59, 2705–2708. 7. Carter, T. P.; Manavi, M.; Moerner, W. E. Statistical Fine Structure in the Inhomogeneously Broadened Electronic Origin of Pentacene in p-Terphenyl. J. Chem. Phys. 1988, 89, 1768–1779. 8. Kador, L.; Horne, D. E.; Moerner, W. E. Optical Detection and Probing of Single Dopant Molecules of Pentacene in a p-Terphenyl Host Crystal by Means of Absorption Spectroscopy. J. Phys. Chem. 1990, 94, 1237–1248. 9. Orrit, M.; Bernard, J. Single Pentacene Molecules Detected by Fluorescence Excitation in a p-Terphenyl Crystal. Phys. Rev. Lett. 1990, 65, 2716–2719. 10. Ambrose, W. P.; Moerner, W. E. Fluorescence Spectroscopy and Spectral Diffusion of Single Impurity Molecules in a Crystal. Nature 1991, 349, 225–227. 11. Jett, J. H.; Keller, R. A.; Martin, J. C.; Marrone, B. L.; Moyzis, R. K.; Ratliff, R. L.; Seitzinger, N. K.; Shera, E. B.; Stewart, C. C. High-Speed DNA Sequencing: An Approach Based Upon Fluorescence Detection of Single Molecules. J. Biomol. Struct. Dyn. 1989, 7, 301–309. 12. Hirschfeld, T. Optical Microscopic Observation of Single Small Molecules. Appl. Optics 1976, 15, 2965–2966. 13. Nguyen, D. C.; Keller, R. A.; Jett, J. H.; Martin, J. C. Detection of Single Molecules of Phycoerythrin in Hydrodynamically Focused Flows by Laser-Induced Fluorescence. Anal. Chem. 1987, 59, 2158–2161. 14. Peck, K.; Stryer, L.; Glazer, A. N.; Mathies, R. A. Single-Molecule Fluorescence Detection: Autocorrelation Criterion and Experimental Realization With Phycoerythrin. Proc. Natl. Acad. Sci. 1989, 86, 4087–4091.

References

15. Shera, E. B.; Seitzinger, N. K.; Davis, L. M.; Keller, R. A.; Soper, S. A. Detection of Single Fluorescent Molecules. Chem. Phys. Lett. 1990, 174, 553–557. 16. Soper, S. A.; Shera, E. B.; Martin, J. C.; Jett, J. H.; Hahn, J. H.; Nutter, H. L.; Keller, R. A. Single-Molecule Detection of Rhodamine 6G in Ethanolic Solutions Using Continuous Wave Laser Excitation. Anal. Chem. 1991, 63, 432–437. 17. Goodwin, P. M.; Wilkerson, C. W., Jr.; Ambrose, W. P.; Keller, R. A. Ultrasensitive Detection of Single Molecules in Flowing Sample Streams by Laser-Induced Fluorescence. Proceedings of SPIE—The International Society for Optical Engineering;1993; Vol. 1895, pp 79–89. 18. Nie, S.; Chiu, D. T.; Zare, R. N. Probing Individual Molecules With Confocal Fluorescence Microscopy. Science 1994, 266, 1018–1021. 19. Soper, S. A.; Davis, L. M.; Shera, E. B. Detection and Identification of Single Molecules in Solution. J. Opt. Soc. Am. B 1992, 9, 1761–1769. 20. Wilkerson, C. W.; Goodwin, P. M.; Ambrose, W. P.; Martin, J. C.; Keller, R. A. Detection and Lifetime Measurement of Single Molecules in Flowing Sample Streams by LaserInduced Fluorescence. Appl. Phys. Lett. 1993, 62, 2030–2032. 21. Magde, D.; Elson, E.; Webb, W. W. Thermodynamic Fluctuations in a Reacting System— Measurement by Fluorescence Correlation Spectroscopy. Phys. Rev. Lett. 1972, 29, 705–708. 22. Magde, D.; Elson, E. L.; Webb, W. W. Fluorescence Correlation Spectroscopy. II. An Experimental Realization. Biopolymers 1974, 13, 29–61. 23. Magde, D.; Webb, W. W.; Elson, E. L. Fluorescence Correlation Spectroscopy. III. Uniform Translation and Laminar Flow. Biopolymers 1978, 17, 361–376. 24. Rigler, R. Ultrasensitive Detection of Single Molecules by Fluorescence Correlation Spectroscopy. Bioscience 1990, ;180–183. 25. Qian, H.; Elson, E. L. Analysis of Confocal Laser-Microscope Optics for 3-D Fluorescence Correlation Spectroscopy. Appl. Optics 1991, 30, 1185–1195. € Widengren, J.; Kask, P. Fluorescence Correlation Spectroscopy With 26. Rigler, R.; Mets, U.; High Count Rate and Low Background: Analysis of Translational Diffusion. Eur. Biophys. J. 1993, 22, 169–175. 27. Rigler, R.; Mets, U. Diffusion of Single Molecules Through a Gaussian Laser Beam. Proc. SPIE-Int. Soc. Opt. Eng. 1993, 1921, 239–248. 28. Mets, U.; Rigler, R. Submillisecond Detection of Single Rhodamine Molecules in Water. J. Fluoresc. 1994, 4, 259–264. 29. Binnig, G.; Rohrer, H. Scanning Tunneling Microscopy—From Birth to Adolescence. Rev. Mod. Phys. 1987, 59, 615–625. 30. Binnig, G.; Quate, C. F.; Gerber, C. Atomic Force Microscope. Phys. Rev. Lett. 1986, 56, 930–933. 31. Betzig, E.; Chichester, R. J. Single Molecules Observed by Near-Field Scanning Optical Microscopy. Science 1993, 262, 1422–1425. 32. Trautman, J. K.; Macklin, J. J.; Brus, L. E.; Betzig, E. Near-Field Spectroscopy of Single Molecules at Room Temperature. Nature 1994, 369, 40–42. 33. Xie, X. S.; Dunn, R. C. Probing Single Molecule Dynamics. Science 1994, 265, 361–364. 34. Ambrose, W. P.; Goodwin, P. M.; Martin, J. C.; Keller, R. A. Alterations of Single Molecule Fluorescence Lifetimes in Near-Field Optical Microscopy. Science 1994, 265, 364–367. 35. Dunn, R. C.; Holtom, G. R.; Mets, L.; Xie, X. S. Near-Field Fluorescence Imaging and Fluorescence Lifetime Measurement of Light Harvesting Complexes in Intact Photosynthetic Membranes. J. Phys. Chem. 1994, 98, 3094–3098.

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36. Dunn, R. C.; Allen, E. V.; Joyce, S. A.; Anderson, G. A.; Xie, X. S. Near-Field Fluorescent Imaging of Single Proteins. Ultramicroscopy 1995, 57, 113–117. 37. Macklin, J. J.; Trautman, J. K.; Harris, T. D.; Brus, L. E. Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface. Science 1996, 272, 255–258. 38. Zander, C.; Sauer, M.; Drexhage, K. H.; Ko, D. S.; Schulz, A.; Wolfrum, J.; Brand, L.; Eggeling, C.; Seidel, C. A. M. Detection and Characterization of Single Molecules in Aqueous Solution. Applied Physics B: Lasers and Optics 1996, 63, 517–523. 39. Lu, H. P.; Xie, X. S. Single-Molecule Kinetics of Interfacial Electron Transfer. J. Phys. Chem. B 1997, 101, 2753–2757. 40. Jia, Y.; Sytnik, A.; Li, L.; Vladimirov, S.; Cooperman, B. S.; Hochstrasser, R. M. Nonexponential Kinetics of a Single tRNAPhe Molecule under Physiological Conditions. Proc. Natl. Acad. Sci. 1997, 94, 7932–7936. 41. Edman, L.; Mets, U.; Rigler, R. Conformational Transitions Monitored for Single Molecules in Solution. Proc. Natl. Acad. Sci. 1996, 93, 6710–6715. 42. Ha, T.; Glass, J.; Enderle, T.; Chemla, D. S.; Weiss, S. Hindered Rotational Diffusion and Rotational Jumps of Single Molecules. Phys. Rev. Lett. 1998, 80, 2093–2096. 43. Ha, T.; Ting, A. Y.; Liang, J.; Caldwell, W. B.; Deniz, A. A.; Chemla, D. S.; Schultz, P. G.; Weiss, S. Single-Molecule Fluorescence Spectroscopy of Enzyme Conformational Dynamics and Cleavage Mechanism. Proc. Natl. Acad. Sci. 1999, 96, 893–898. 44. Harms, G. S.; Sonnleitner, M.; Sch€ utz, G. J.; Gruber, H. J.; Schmidt, T. Single-Molecule Anisotropy Imaging. Biophys. J. 1999, 77, 2864–2870. 45. Schaffer, J.; Volkmer, A.; Eggeling, C.; Subramaniam, V.; Striker, G.; Seidel, C. A. M. Identification of Single Molecules in Aqueous Solution by Time-Resolved Fluorescence Anisotropy. J. Phys. Chem. A 1999, 103, 331–336. 46. Ha, T.; Enderle, T.; Ogletree, D. F.; Chemla, D. S.; Selvin, P. R.; Weiss, S. Probing the Interaction Between Two Single Molecules: Fluorescence Resonance Energy Transfer Between a Single Donor and a Single Acceptor. Proc. Natl. Acad. Sci. 1996, 93, 6264–6268. 47. Sch€utz, G. J.; Trabesinger, W.; Schmidt, T. Direct Observation of Ligand Colocalization on Individual Receptor Molecules. Biophys. J. 1998, 74, 2223–2226. 48. Deniz, A. A.; Dahan, M.; Grunwell, J. R.; Ha, T.; Faulhaber, A. E.; Chemla, D. S.; Weiss, S.; Schultz, P. G. Single-Pair Fluorescence Resonance Energy Transfer on Freely Diffusing Molecules: Observation of Forster Distance Dependence and Subpopulations. Proc. Natl. Acad. Sci. 1999, 96, 3670–3675. 49. Roy, R.; Hohng, S.; Ha, T. A Practical Guide to Single-Molecule FRET. Nat. Methods 2008, 5, 507–516. 50. Lerner, E.; Cordes, T.; Ingargiola, A.; Alhadid, Y.; Chung, S.; Michalet, X.; Weiss, S. Toward Dynamic Structural Biology: Two Decades of Single-Molecule F€ orster Resonance Energy Transfer. Science 2018, 359, eaan1133. 51. Hellenkamp, B.; Schmid, S.; Doroshenko, O.; Opanasyuk, O.; K€ uhnemuth, R.; Rezaei Adariani, S.; Ambrose, B.; Aznauryan, M.; Barth, A.; Birkedal, V.; Bowen, M. E.; Chen, H.; Cordes, T.; Eilert, T.; Fijen, C.; Gebhardt, C.; G€ otz, M.; Gouridis, G.; Gratton, E.; Ha, T.; Hao, P.; Hanke, C. A.; Hartmann, A.; Hendrix, J.; Hildebrandt, L. L.; Hirschfeld, V.; Hohlbein, J.; Hua, B.; H€ ubner, C. G.; Kallis, E.; Kapanidis, A. N.; Kim, J.-Y.; Krainer, G.; Lamb, D. C.; Lee, N. K.; Lemke, E. A.; Levesque, B.; Levitus, M.; McCann, J. J.; Naredi-Rainer, N.; Nettels, D.; Ngo, T.; Qiu, R.; Robb, N. C.; R€ocker, C.; Sanabria, H.; Schlierf, M.; Schr€ oder, T.; Schuler, B.; Seidel, H.; Streit, L.; Thurn, J.; Tinnefeld, P.; Tyagi, S.; Vandenberk, N.; Vera, A. M.;

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Weninger, K. R.; W€unsch, B.; Yanez-Orozco, I. S.; Michaelis, J.; Seidel, C. A. M.; Craggs, T. D.; Hugel, T. Precision and Accuracy of Single-Molecule FRET Measurements—A Multi-Laboratory Benchmark Study. Nat. Methods 2018, 15, 669–676. Gelles, J.; Schnapp, B. J.; Sheetz, M. P. Tracking Kinesin-Driven Movements With Nanometer-Scale Precision. Nature 1988, 331, 450–453. Schmidt, T.; Schuetz, G. J.; Baumgartner, W.; Gruber, H. J.; Schindler, H. Characterization of Photophysics and Mobility of Single Molecules in a Fluid Lipid Membrane. J. Phys. Chem. 1995, 99, 17662–17668. Thompson, R. E.; Larson, D. R.; Webb, W. W. Precise Nanometer Localization Analysis for Individual Fluorescent Probes. Biophys. J. 2002, 82, 2775–2783. Yildiz, A.; Forkey, J. N.; McKinney, S. A.; Ha, T.; Goldman, Y. E.; Selvin, P. R. Myosin V Walks Hand-Over-Hand: Single Fluorophore Imaging With 1.5-nm Localization. Science 2003, 300, 2061–2065. Rust, M. J.; Bates, M.; Zhuang, X. Sub-Diffraction-Limit Imaging by Stochastic Optical Reconstruction Microscopy (STORM). Nat. Methods 2006, 3, 793–795. Betzig, E.; Patterson, G. H.; Sougrat, R.; Lindwasser, O. W.; Olenych, S.; Bonifacino, J. S.; Davidson, M. W.; Lippincott-Schwartz, J.; Hess, H. F. Imaging Intracellular Fluorescent Proteins at Nanometer Resolution. Science 2006, 313, 1642–1645. Hess, S. T.; Girirajan, T. P. K.; Mason, M. D. Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy. Biophys. J. 2006, 91, 4258–4272. Sharonov, A.; Hochstrasser, R. M. Wide-Field Subdiffraction Imaging by Accumulated Binding of Diffusing Probes. Proc. Natl. Acad. Sci. 2006, 103, 18911–18916. Axmann, M.; Madl, J.; Schuetz, G. J. Single-Molecule Microscopy in the Life Sciences; Wiley-VCH Verlag GmbH & Co. KGaA, 2017; pp 365–404. Widom, J. R.; Dhakal, S.; Heinicke, L. A.; Walter, N. G. Single-Molecule Tools for Enzymology, Structural Biology, Systems Biology and Nanotechnology: An Update. Arch. Toxicol. 2014, 88, 1965–1985. Juette, M. F.; Terry, D. S.; Wasserman, M. R.; Zhou, Z.; Altman, R. B.; Zheng, Q.; Blanchard, S. C. The Bright Future of Single-Molecule Fluorescence Imaging. Curr. Opin. Chem. Biol. 2014, 20, 103–111. Gust, A.; Zander, A.; Gietl, A.; Holzmeister, P.; Schulz, S.; Lalkens, B.; Tinnefeld, P.; Grohmann, D. A Starting Point for Fluorescence-Based Single-Molecule Measurements in Biomolecular Research. Molecules 2014, 19, 15824–15865. 42 pp. Lord, S. J.; Lee, H.-l.D.; Moerner, W. E. Single-Molecule Spectroscopy and Imaging of Biomolecules in Living Cells. Anal. Chem. 2010, 82, 2192–2203. Yu, J.; Hu, D. H.; Barbara, P. F. Photophysics of Conjugated Polymers Unmasked by Single Molecule Spectroscopy. Vol. 67; Springer-Verlag, 2001; pp. 114–129. Walter, M. J.; Lupton, J. M. Energy Transfer in Single Conjugated Polymer Chains; Wiley-VCH Verlag GmbH & Co. KGaA, 2010; pp. 243–279. Roeffaers, M. B. J.; De Cremer, G.; Sels, B. F.; De Vos, D. E.; Hofkens, J. Reactions at the Single-Molecule Level. Wiley-VCH Verlag GmbH & Co. KGaA, 2010; pp. 281–308. Laquai, F.; Park, Y.-S.; Kim, J.-J.; Basche, T. Excitation Energy Transfer in Organic Materials: From Fundamentals to Optoelectronic Devices. Macromol. Rapid Commun. 2009, 30, 1203–1231. Moerner, W. E. Single-Molecule Optical Spectroscopy and Imaging: From Early Steps to Recent Advances. Vol. 96; Springer GmbH, 2010; pp. 25–60.

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70. von Diezmann, A.; Shechtman, Y.; Moerner, W. E. Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking. Chem. Rev. 2017, 117, 7244–7275. 71. Aggarwal, V.; Ha, T. Single-Molecule Fluorescence Microscopy of Native Macromolecular Complexes. Curr. Opin. Struct. Biol. 2016, 41, 225–232. 72. Gahlmann, A.; Moerner, W. E. Exploring Bacterial Cell Biology With Single-Molecule Tracking and Super-Resolution Imaging. Nat. Rev. Microbiol. 2014, 12, 9–22. 73. Moerner, W. E. Those Blinking Single Molecules. Science 1997, 277, 1059–1060.

CHAPTER

Photophysics of singlemolecule probes

1 Marcia Levitus*,†

*School of Molecular Sciences, Arizona State University, Tempe, AZ, United States † The Biodesign Institute, Arizona State University, Tempe, AZ, United States

1.1 Introduction Researchers entering the field of single-molecule fluorescence face important decisions that can potentially affect the outcome of the study, from selecting dyes, linker types and labeling positions, to making decisions on whether and how to immobilize molecules to surfaces, which buffers to use, etc. There are many variables that need to be taken into account when designing and analyzing a single-molecule FRET (smFRET) experiment, and new investigators are often disappointed to learn that there is not always a consensus regarding optimal fluorescent probes and protocols. A successful single-molecule fluorescence experiment requires a careful experimental design to minimize artifacts and to ensure that the measured fluorescence signals can be interpreted in terms of the biophysical or biochemical phenomena of interest. Most commonly, smFRET experiments are performed to identify subpopulations of molecules adopting different conformations within a sample,1–5 or to investigate a dynamic process that changes the distance between two segments of a biomolecule or between two interacting partners.6–12 A large number of smFRET studies to date have focused on obtaining kinetic parameters for the interconversion between different conformations that can be distinguished by their different FRET efficiencies (Fig.1.1). Kinetic information is typically obtained from the analysis of time-dependent changes in fluorescence intensity (fluorescence trajectories) obtained by acquiring the photons emitted by many individual molecules over long times (usually seconds to minutes).14,15 A schematic example is given in Fig. 1.1, which shows simulated donor and acceptor fluorescence trajectories (panel B) for a hypothetical two-state system (panel A). Panel C shows the ratio of the acceptor intensity to the sum of both intensities; a quantity usually referred to as the proximity factor or the raw FRET efficiency (Eraw). In this scenario, the FRET efficiencies are only used to distinguish between a small number of states with significantly different donor-acceptor distances.16–20 Precise knowledge of the donoracceptor distances is not needed because the experiment is designed with sufficient Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.00001-8 # 2019 Elsevier Inc. All rights reserved.

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CHAPTER 1 Photophysics of single-molecule probes

FIG. 1.1 A- Hypothetical protein labeled with a donor (D) and acceptor (A) pair that can exist in two conformations with donor-acceptor separations of R1 and R2. The two distances are assumed to lead to clearly distinguishable FRET efficiencies. B- Hypothetical donor-acceptor singlemolecule traces (trajectories) for this protein. The traces were simulated assuming that the laser excites preferentially the donor, so acceptor fluorescence arises exclusively from energy transfer. The last transition is due to photobleaching of the acceptor, which leads to a recovery of donor fluorescence. C- Raw energy transfer efficiency calculated as the ratio of the acceptor intensity to the sum of the acceptor and donor intensities. For this assumed twostate system, the value denoted by * is due to the conformation in which the inter-dye distance is R1, and ** denotes the conformation in which the inter-dye distance is R2. The reader should note that although the figure was constructed around known structures of phosphoglycerate kinase, the labeling positions and simulated traces are hypothetical and not necessarily consistent with the behavior of this protein.

prior structural knowledge of the system to allow assignment of the observed FRET states to expected conformations of the proteins and nucleic acids (e.g. low FRET for an open conformation and high FRET for a closed conformation, see Fig. 1.1). In fact, such an experiment often does not require precise determinations of the FRET efficiencies as long as the measurement can yield approximated values that can be used to distinguish the different populations. This type of smFRET approach is extremely powerful, but limited and even potentially misleading if the researcher does not have sufficient knowledge of the possible conformations being probed in the experiment. With sufficient corrections and ancillary experiments, smFRET experiments can yield accurate FRET efficiencies (i.e. the true quantum efficiency of energy transfer, see Section 1.2.4), which can in turn be used to estimate donor-acceptor distances with remarkable precision.22,23 These FRET-derived distances can be used as constraints in the determination of structural models in conjunction with computational methods and other experimental biophysical techniques.23–27 As will be discussed in detail in this chapter, the determination of a precise FRET efficiency and donoracceptor distance requires a thorough characterization of the photophysical properties of the fluorophores used to probe the system.

1.1 Introduction

There are many variables that need to be taken into account when designing a single-molecule experiment. The choice of fluorescent dye, immobilization protocol, and even the buffer composition can affect the outcome of the experiment. Once data is acquired, the correct interpretation of the fluorescence intensities in terms of FRET efficiencies and ultimately in terms of distances, requires a profound understanding of the variables that affect the measured signals. The goal of this chapter is to bring attention to the considerations and control experiments that are important to avoid artifacts or misinterpretations of the data, while maximizing the accuracy of the kinetic and structural information obtained from the experiment. This chapter will focus on the critical role of fluorophore photophysics on the design and interpretation of single-molecule experiments. Emphasis will be placed on understanding how to prevent or account for contributions to the fluorescence signals that originate from confounding photoinduced transitions between different electronic states of the molecule (photophysical processes). Other variables such as surface effects or artifacts introduced by attachment of the extrinsic probe will be discussed only briefly (Section 1.1.1). To motivate the need for this discussion, we will start by describing two published examples of single-molecule experiments whose correct interpretation relies on considering the photophysical behavior of the probes (Section 1.1.2). This will be followed by an introductory summary of photophysical concepts and terms (Section 1.2), which will facilitate a rigorous quantitative discussion of how the events that follow photoexcitation ultimately contribute to the measured fluorescence signals (Sections 1.3 and 1.4). Section 1.5 will then focus on different aspects of how photophysical processes impact the interpretation of single-molecule FRET experiments, and to conclude, the chapter will end with an overview of the properties of the most common families of fluorophores used in single-molecule research (Section 1.6).

1.1.1 Potential artifacts from surfaces and the use of extrinsic probes Proteins and nucleic acids are often immobilized on microscope slides to acquire single-molecule trajectories over long timescales (seconds to minutes). It is critical, however, to ensure that immobilization itself does not alter the conformation of the biopolymer or its interactions with ligands and cofactors. Suggested protocols for passivating surfaces and immobilizing proteins and nucleic acids exist in the literature.14,28,29 Yet, researchers should always perform their own control experiments to ensure that results are not affected by surface interactions. In many cases, the same experiment can be carried out in a traditional cuvette-type fluorescence experiment to determine an average property (e.g. an average FRET efficiency, or an average enzymatic reaction rate). This average should be consistent with the average measured for many single-molecules on a surface provided that the surface treatment does not affect the biochemical and biophysical properties of the system under study. In addition, and as with any other fluorescence-based experiment, control experiments need to be performed to ensure that the outcome is not affected by the

17

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CHAPTER 1 Photophysics of single-molecule probes

fluorophore used to probe a structure, an interaction, or a conformational change. There is limited information on this important subject because negative results are unfortunately rarely shared in publications. Yet, a few studies have been published that highlight the potentially distorting effects of fluorescent labels on protein conformation,30,31 protein-protein interactions,32,33 peptide-membrane interactions,34 DNA hairpin dynamics,35,36 and DNA duplex stability.37,38 Researchers should characterize the labeled materials as thoroughly as possible to ensure that labeled proteins and nucleic acids have the same properties of their unlabeled counterparts. This may involve measuring enzymatic activities, binding constants between interacting partners, CD spectra, melting temperatures, and NMR or crystallographic structures whenever possible. Ideally, single-molecule experiments with more than one fluorescent probe should be performed to demonstrate that results do not depend on the particular choice of fluorophore. Careful experiments with different FRET pairs, for example, allowed, DeVore et al. to recognize that one particular FRET acceptor (Texas Red) altered the conformational landscape and dynamics of the protein calmodulin (CaM).31 In this work, the authors performed identical smFRET experiments with CaM labeled with one donor and three different acceptors (Alexa Fluor 594, ATTO594, and Texas Red). The FRET distributions computed from the measured data were consistent with the presence of multiple conformations of the protein, but surprisingly, the authors found that the dye Texas Red stabilized a high FRET state consistent with a compact conformation of CaM. The three dyes used as acceptors are all rhodamine dyes (see Fig. 1.9 for representative examples of rhodamine dyes), but they bear different substitutions that result in different net charges. Alexa Fluor 594 and ATTO594 carry a net negative electrical charge, while Texas Red has a net neutral charge. This difference could explain why Texas Red interacts with the protein more strongly, biasing its conformational landscape to stabilize a compact conformation that is not as populated when the system is probed with the Alexa dyes. Artifacts due to probe interference or surface effects are somewhat unsurprising in the sense that it is hardly surprising that adding a relatively bulky probe or attaching a biomolecule to a surface can potentially modify its biochemical and biophysical properties. Yet, there is nothing trivial about avoiding or even identifying these artifacts. In particular, the issue of probe interference does not often receive the attention it deserves, as judged from often missing control experiments that should be carried out to ease concerns about the potential impact of the fluorescent probe in the biophysical properties of the system of interest.

1.1.2 Potential artifacts due to the generation of dark states What other types of considerations should a researcher take into account when choosing labels, linkers, and sites of attachment? What sorts of control experiments can be designed to exclude other potential artifacts, or to obtain complementary information to properly analyze the measured signals? Addressing these questions will be the focus of the remainder of the chapter. To motivate the discussion, let us consider an early report of sm-FRET measurements on DNA duplexes by Meller et al.21 Fig. 1.2 shows single-molecule fluorescence trajectories for a donor (TMR,

1.1 Introduction

FIG. 1.2 Fluorescence trajectories for a single dsDNA molecule labeled with TMR (donor, green) and Cy5 (acceptor, red) as shown in the top figures. The fluorescence traces were obtained by alternating a green and a red laser at a rate much faster than the transitions observed in the figures. A- Donor (green) and acceptor (red) single molecule traces during green excitation. B- Donor (green) and acceptor (red) single molecule traces during red excitation. The acceptor intensity fluctuates between a high and a low intensity level corresponding to the fluorescent state and a dark state, respectively. Comparison with the trace measured during green excitation shows the exact same fluctuations for the acceptor, demonstrating that loss of FRET under green excitation is due to acceptor blinking, and not to a change in donor-acceptor distance. Sm-FRET traces reprinted with permission from Sabanayagam, C. R.; Eid, J. S.; Meller, A. Long Time Scale Blinking Kinetics of Cyanine Fluorophores Conjugated to DNA and Its Effect on Forster Resonance Energy Transfer. J. Chem. Phys. 2005, 123, 224708, with the permission of AIP Publishing.

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CHAPTER 1 Photophysics of single-molecule probes

green) and acceptor (Cy5, red) pair bound covalently to a DNA duplex. The dyes are covalently bound to the nucleic acid at positions separated by 14 nucleotides ˚ ), and given the rigidity of duplex DNA at these short length-scales, changes (
48 A in distance are not expected beyond what results from the rapid diffusion of the linkers used to attach the dyes to the DNA. Therefore, the donor and acceptor trajectories for this system were expected to be constant (except for noise) with average ˚ separation intensities consistent with the FRET efficiency expected for the 48 A between donor and acceptor. Instead, the measured traces suggest the existence of two states with FRET efficiencies E1
0.6 and E2
0.1 interconverting in the second-timescale. These large changes in FRET would be consistent with a change ˚ , which would indicate a significant conforin donor-acceptor distance of about 30 A mational change. Have the authors discovered a new DNA conformation? Have they defied everything we know about DNA flexibility? Given the simplicity of the system (duplex DNA), it is reasonable to consider a different origin for the observed changes in FRET. Indeed, a carefully executed experiment shed light on the origin of these fluctuations; as seen in Fig. 1.2B, the same fluctuations are observed when the system is illuminated with a laser that excites the acceptor directly, but not the donor. To obtain these data, the laser used to excite the donor (a 514 nm laser) was alternated with a laser used to excite the acceptor directly (a 640 nm laser) at a rate much faster than the timescale of the fluctuations observed in the figure. In this way, the same state of the system could be probed with green and red excitation to produce the two traces shown in the figure (that is, fluorescence from the donor and acceptor under either green or red excitation). The results of Fig. 1.2A are indeed consistent with changes in FRET due to changes in the donor-acceptor distance. However, if this were the case, the fluorescence intensity of the acceptor when excited directly with the red laser should have remained constant during the experiment. In contrast, the results of Fig. 1.2B show that fluctuations are intrinsic to the acceptor, indicating that the Cy5 molecule makes excursions to a nonemissive (dark) state that persists for several seconds. This is an example of discrete reversible fluctuations in fluorescence intensity that originate from transitions between dark and bright states of the fluorophore, a phenomenon commonly called ‘blinking’. The example discussed above shows how fluorescence fluctuations of photophysical origin could be easily misinterpreted as changes in donor-acceptor distance if the researcher is not aware of this common artifact and thus does not design appropriate control experiments. In the previous example, the researchers had enough knowledge of the system (short dsDNA) to suspect that the observed signals were not due to conformational changes. However, as the next example illustrates, much greater care should be taken when the system is expected to display conformational dynamics. The trajectories shown in Fig. 1.3A were obtained with fluorescently labeled nucleosomes immobilized on a coverslip by Koopmans et al.13 In this experiment, nucleosomal DNA was labeled with a donor (Cy3) and an acceptor (Cy5) FRET pair to monitor the spontaneous unwrapping of the DNA from the protein core, a phenomenon that had been previously described using fluorescence correlation spectroscopy (FCS).39 In the closed conformation, the donor and

1.1 Introduction

FIG. 1.3 A and B- Observed fluorescence trajectories of single nucleosome particles labeled with Cy3 (donor, green trace) and Cy5 (acceptor, red trace) under green laser excitation and calculated FRET efficiency. The transition around 16 s is due to photobleaching of the acceptor. C- A mechanism consistent with the measured trajectories shown in the top panel. The close proximity between the two dyes in the closed conformation of the nucleosome results in low donor emission and high acceptor emission. Loss of FRET and a concomitant increase in donor emission occurs if a portion of the DNA unwraps from the protein core. D- Hypothetical fluorescence trajectories under red excitation consistent with this proposed mechanism. E- Another mechanism consistent with the measured trajectories shown in the top panel. Loss of FRET and a concomitant increase in donor emission occurs when the acceptor undergoes a transition to a nonemissive state. F- Fluorescence trajectories measured under red excitation. The acceptor intensity fluctuates between two values indicating transitions between a fluorescent and a nonemissive state. Comparison with the trace measured during green excitation shows the same fluctuations for the acceptor, demonstrating that loss of FRET under green excitation is due to acceptor blinking, and not to a change in donor-acceptor distance. The data for panels A, B, and F were generously provided by Prof. John van Noort (Leiden University) and were published in Ref. 13. The traces in panel D are simulated (not measured).

acceptor are expected to be in close proximity, which would lead to efficient FRET. If significant unwrapping of the DNA occurred as suggested by the published FCS results, the increase in distance would result in a state with low FRET efficiency (Fig. 1.3C). Experimentally, this would be consistent with a simultaneous decrease

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CHAPTER 1 Photophysics of single-molecule probes

and increase in the acceptor and donor intensities under green excitation, respectively, which is in fact what the authors observed (Fig. 1.3A). Acceptor photobleaching at approximately 15 s results in the recovery of the donor signal due to permanent loss of FRET. The calculation of the FRET efficiency from these data gives the trajectory shown in the figure, from which the researchers could have obtained, in principle, the kinetic rates of the DNA opening and closing reactions. Of course, this analysis results in the intended information only if the observed fluctuations were indeed due to DNA unwrapping; if this were the case, however, the intensity of the acceptor under direct (red) excitation should have remained constant as sketched in Fig. 1.3D. In contrast, direct excitation of the acceptor was shown to result in the same fluctuations observed under green excitation (Fig. 1.3F). This indicates that the apparent FRET changes are not due to conformational fluctuations (mechanism 1) but rather to excursions of the acceptor (Cy5) to a dark state (acceptor blinking, mechanism 2). Without the trajectory measured under red excitation, it would have been easy to misinterpret the trajectories obtained under green excitation in terms of the conformational fluctuations sketched in the figure (proposed mechanism 1). Two other pieces of evidence further support the interpretation of these data in terms of acceptor blinking (proposed mechanism 2). First, the authors point out that very similar dynamics was reported by another laboratory in experiments that were virtually identical except for the location of the probes.40 In this other study, the authors labeled the DNA at positions where unwrapping events are expected to be very rare when compared to the positions used by Koopmans et al. Yet, both labeling schemes yielded the same FRET dynamics, suggesting that the signals were not due to changes in donor-acceptor distance. In addition, Koopmans et al. reported that the observed dynamics was nearly abolished when β-mercaptoethanol, which was added to the buffer for its properties as a triplet quencher, was replaced by Trolox (another triplet quencher). This result is consistent with the formation of a thiol-induced dark state of Cy5, which resulted in the observed fluorescence fluctuations in the presence of β-mercaptoethanol, but not Trolox. The nature of this dark state remained a mystery until Dempsey et al. provided evidence of the formation of an adduct between the thiol and the cyanine (see Section 1.6.3).41 Regardless of the nature of the dark state, Koopmans’ results clearly indicate that most of the fluctuations observed in the FRET trajectories are the result of thiol-induced Cy5 blinking and not DNA breathing. Yet, it should be stressed that DNA breathing (Fig. 1.3C) was indeed detected in some traces thanks to the careful control experiments and additional measurements that allowed the researchers to remove the artifactual fluctuations (acceptor blinking) from the true changes in donor-acceptor distance. The two examples discussed in this section illustrate examples of control experiments that a researcher should plan to avoid misinterpreting the data, and the types of considerations that should guide the selection of dyes and buffers. As it will become evident from the many examples described in this chapter, a basic understanding of the variables that affect the photophysical properties of the fluorescent probes used in the experiment is essential to anticipate potential problems.

1.2 Photophysical processes and the generation of dark states

Section 1.6 of this chapter summarizes some known properties of the most common chemical families of dyes used in single-molecule research, but it is important to stress that our current understanding of how the environment of a fluorescent probe within a biological polymer affects its photophysical properties is still incomplete. The next sections focus on defining the concepts needed to discuss the photophysics of single-molecule dyes and on how these properties influence the measured fluorescence intensities, from which FRET efficiencies are measured. Before moving on, however, it is important to stress that although fluorophore blinking was presented as a potential source of artifacts in the preceding discussion, the on-off fluctuations caused by transitions to dark states are the basis of many ground-breaking super-resolution microscopy approaches. The ability to transiently switch fluorescent molecules ‘off’ is the basis of a family of super-resolution methods based on stochastic readout. Examples include the techniques known as STORM (stochastic optical reconstruction microscopy),42 PALM (photoactivated localization microscopy),43 blink microscopy (BM),44 and related methods.45–47 A common feature of these approaches is that only one emitter is allowed to be in the ‘on’ state within a diffraction limited area at any given time, so that its position can be determined with high precision. Fluorophores are then switched back to the dark state or photobleached permanently so another subset of fluorophores can be activated and imaged. The temporal and spatial resolution that can be achieved in these methods depends critically on the lifetimes of the ‘on’ and ‘off’ states. Therefore, designing fluorophores and strategies for superresolution microscopy requires a thorough understanding of the nature of the dark states that are generated upon photoexciation, and how the kinetic rate constants that connect these states can be manipulated to achieve ‘on-off’ rates suitable to achieve the needed resolution. This chapter focuses on understanding the variables that affect the nature and dynamics of the dark states that are commonly populated upon photoexcitation of organic dyes commonly used in single molecule work. Although the chapter focuses on singlemolecule FRET and related approaches, the discussion and information presented here will also interest readers with interest in superresolution technologies.

1.2 Photophysical processes and the generation of dark states State diagrams such as the one shown in Fig. 1.4 (frequently called Perrin-Jablonski diagrams) are commonly used to depict molecular states and photophysical processes. Thick horizontal lines represent molecular electronic states while thin lines represent vibrational states. Note that only a few vibrational states are shown for clarity within each electronic state, but importantly, higher vibrational levels of S0 overlap in energy with vibrational levels of S1 and T1. The vertical axis represents relative energy, while the horizontal axis has no physical connotation and is merely used to group states of the same multiplicity (i.e. singlet states, triplet states) in different columns. Solid arrows are used to indicate radiative processes (absorption and

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CHAPTER 1 Photophysics of single-molecule probes

FIG. 1.4 Perrin-Jablonski diagram depicting molecular states and photophysical processes for a donor (D) and acceptor (A) FRET pair. Only the singlet excited state of the acceptor (S1) is shown for clarity. Thick horizontal lines represent molecular electronic states and thin lines represent vibrational states (only a few vibrational states are shown for each electronic state). Radiative process (absorption and emission) are represented with solid vertical lines. Wavy lines indicate nonradiative transitions (see text for details).

emission), and wavy arrows indicate nonradiative transitions. In Fig. 1.4, D and A represent a donor and acceptor pair in the context of FRET. Absorption of light, depicted as ①, originates from the lowest vibrational state of the lowest-energy singlet state (S0). A notable exception is molecular oxygen, O2, which is a triplet in the ground state. In a typical single-molecule experiment, a laser with output in the visible region of the spectrum is used to excite the molecule to the first electronic excited state (S1). The transitions depicted in Fig. 1.4 are called vibronic transitions because they involve a change in both the electronic and vibrational quantum numbers. Transitions to singlet electronic states of higher energy (Sn, n > 1) are also possible (not shown), but these states are rarely fluorescent because molecules usually relax rapidly (in picoseconds) to the lowest singlet excited state (S1). Direct excitation to the triplet state involves a change in spin and is therefore considered forbidden (i.e. it occurs with a negligible probability). In solution, excess vibrational energy is transferred to the solvent molecules through collisions within a few picoseconds, a process commonly known as vibrational relaxation (②). This process deactivates the excited state to its lowest vibrational level (thick line of S1 in Fig. 1.4), which is further deactivated by several possible mechanisms including fluorescence emission (③), internal conversion to S0 (see below), intersystem crossing to the triplet state (⑤), energy transfer to an acceptor molecule (⑧), and other nonradiative processes not depicted in Fig. 1.4 that will be discussed later in this chapter. Internal conversion is an isoenergetic

1.2 Photophysical processes and the generation of dark states

nonradiative transition between two electronic states of the same multiplicity48 that occurs when there is good overlap between the wavefunctions of two vibrational levels of different electronic states (e.g. S1 and S0). Internal conversion from S1 to S0 therefore results in a vibrationally excited molecule in the lowest electronic state, a process that is followed by vibrational relaxation to the lowest vibrational level of S0. The combination of internal conversion from S1 to S0 (an isoenergetic transition not shown in the figure) and vibrational relaxation within S0 is indicated as ④ in Fig. 1.4. Similarly, intersystem crossing from the triplet to S0 (an isoenergetic transition not shown explicitly in the figure) followed by vibrational relaxation within S0 are depicted together as ⑦. Phosphorescence (photon emission involving a change in spin multiplicity, ⑥) is rarely observed in solution at room temperature, and will not be discussed in this chapter. Understanding the various processes that occur after photon absorption is crucial because the efficiency of fluorescence emission, which ultimately determines the number of photons emitted by the molecule, depends critically on the relative rates of all the competing processes that originate from the lowest vibrational state of S1 (i.e. the fluorescent state). Of particular importance is the fact that these rates can depend strongly on environmental factors such as solvent polarity and viscosity, and on the presence of other solutes such as molecular oxygen, ions, and other molecules. Furthermore, transitions to nonemissive states may result in discrete fluctuations in fluorescence intensity (blinking), which often complicate the analysis of single-molecule data. Dark states also contribute to the saturation of fluorescence signals (Section 1.3.2), which may introduce additional challenges in the analysis of the measured intensities in terms of accurate FRET efficiencies.

1.2.1 Absorption of light The probability that a molecule will absorb a photon of a given wavelength is determined by its absorption cross section (σ(λ)), which is directly proportional to the molar extinction coefficient (ε(λ) ¼ σ(λ)Nav/1000. ln 10, where σ is expressed in cm2, Nav is Avogadro’s number, and ε is expressed in cm1 M1). The latter is usually used in the context of the Lambert-Beer law, but the cross section is more convenient conceptually when absorption is considered at a molecular level. The rate of light absorption (a) is given by a ¼ I0 σ 1

(1.1) 1

where a is in units of s , and I0 is the intensity of the incident light in units of s cm2. The quantity I0 is formally known as the photon fluence rate, defined as the number of photons incident from all directions on a small sphere divided by the cross-sectional area of the sphere per unit time.48 The quantity a can be thought of as the kinetic rate constant for the reaction S0 + hν ! S1 (k12, Fig. 1.6A), and as with any other rate constant, it can be interpreted as the probability per unit time that the reaction will occur (in this case, that a photon will be absorbed by the ground state).49

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CHAPTER 1 Photophysics of single-molecule probes

1.2.2 Fluorescence Photon absorption will usually result in an excited state with an energy higher than the lowest vibrational state of S1 (① in Fig. 1.4). Relaxation toward the lowest vibrational state of S1 typically occurs in  1012 s, while the rates of the processes that depopulate S1 (③, ④, ⑤ and ⑧ in Fig. 1.4) are usually at least two orders of magnitude slower. As a consequence, fluorescence emission usually occurs from the lowest vibrational state of the first singlet excited state (S1), and its spectrum is shifted toward longer wavelengths (lower energies) compared to absorption. The lifetime of the excited state (which from now on will be assumed to be the lowest vibrational state of S1) is determined by the sum of the rates of all the process that depopulate the state, and is usually in the nanosecond timescale for the dyes and conditions used in single-molecule research:  X 1 τ ¼ kf + knr

(1.2)

P Here, kf is the rate constant for emission of fluorescence, and knr represents the sum of the rate constants for all the nonradiative processes that deactivate S1 (e.g. internal conversion, intersystem crossing, energy transfer, etc). The lifetime of the excited state (τ) is often referred to as the lifetime of fluorescence, but it is critical to keep in mind that it depends on all rates, and can actually be defined for a molecule with negligible fluorescence efficiency. The lifetime of the excited state, as defined in Eq. (1.2), is the average amount of time that a molecule spends in the excited state before deactivating to the ground state. This quantity represents the average of the actual times elapsed between the formation and the deactivation of the excited state. This can be interpreted in two ways. If a large number of identical fluorophores is excited simultaneously with a short pulse of light (e.g. in a cuvette-type experiment), each individual molecule will decay with a random lifetime τi. When analyzed statistically by means of a histogram, the distribution of lifetimes will be exponential with an average of τ (p(τi) ¼ τ1e τi/τ,where p(τi) is a probability density function). Alternatively, for a single fluorophore under continuous excitation, each absorptionemission cycle will yield a random lifetime τi from the same exponential distribution function (p(τi)) with mean τ. The probability that an excited state will deactivateP by emission of a photon (vs a knr, a quantity known as the nonradiative process) is given by the ratio of kf to kf + fluorescence quantum yield (ϕf): ϕf ¼

kf X ¼ kf τ kf + knr

(1.3)

While the absorption extinction coefficient is defined for a particular excitation wavelength, the fluorescence quantum yield is an integrated quantity that takes into account all emitted photons in a given spectral band (i.e. for a given electronic transition). For a molecule under continuous excitation, ϕf can be thought of as the fraction of the photons absorbed that result in emission of a photon. For each absorbed

1.2 Photophysical processes and the generation of dark states

photon, ϕf can be interpreted as the probability that the excited molecule will return to the ground state by emitting a photon. Fluorescence quantum yields are commonly determined experimentally as the ratio of the number of photons emitted to the number of photons absorbed by a solution of fluorophores. For a detailed discussion of how to properly determine fluorescence quantum yields experimentally see Ref. 50. It should be noted that although the intensity of fluorescence is proportional to ϕf, the brightness of the dye (defined as the number of photons emitted per molecule per unit of time) also depends on the absorption cross section. A high probability of fluorescence emission is not useful if the dye has a low probability of photon absorption. For this reason, the product ε. ϕf (often referred to as the fluorophore brightness) is usually used to compare the relative brightness of two dyes. The fluorescence quantum yield is an important variable in the analysis of singlemolecule data because it is directly related to the number of photons that can be possibly detected in an experiment. The measured emission intensity (number of detected photons in a given acquisition interval) is proportional to the fluorescence quantum yield of the dye, so understanding the variables that affect ϕf is critical to properly design and analyze single-molecule fluorescence signals. A change in ϕf during an experiment will result in a fluctuation in fluorescence intensity that can be easily misinterpreted if the origin of the change in ϕf is not understood. Conversely, a thorough understanding of the sensitivity of ϕf to the environment can be taken advantage of to analyze fluorescence fluctuations in terms of changes in the environment of the probe. An example that illustrates these important points is discussed in Section 1.6.3.

1.2.3 Intersystem crossing and the triplet state Selection rules state that spin must not change during an electronic transition and, consequently, transitions between singlet and triplet states are said to be forbidden.51 These simple selection rules are derived by disregarding possible interactions between the spin and the orbital angular momenta of the molecule (spin-orbit coupling), so if these interactions exist, transitions involving changes in spin may occur with measurable probabilities. For instance, transitions between singlet and triplet states are more efficient in the presence of high atomic number (‘heavy’) or paramagnetic atoms,52,53 and by collisions with species that can participate in an electronexchange mechanism (e.g. O2).54,55 Triplet radiative lifetimes are many orders of magnitude longer than the corresponding values for singlet excited states (usually seconds to minutes vs. nanoseconds). Consequently, triplet states are very efficiently deactivated in solution by collisions with solvent molecules, oxygen, and other solutes dissolved in the buffer, which results in measured triplet lifetimes that are typically in the microsecond timescale (for instance, the measured triplet lifetime of Rhodamine 6G in water is 2 μs).56 Triplet states are often considered a nuisance in single-molecule fluorescence because their generation reduces the fraction of molecules in the bright (fluorescent) state, which in turn reduces the acquired

27

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CHAPTER 1 Photophysics of single-molecule probes

fluorescence signals. Importantly, the extent to which this occurs depends strongly on laser power (see Section 1.3). In addition, triplet states are common intermediates in the reactions that lead to photobleaching. For instance, millimolar concentrations of divalent manganese (a paramagnetic ion) were shown to increase the intersystem crossing rate of a rhodamine bound to DNA, causing a significant increase in the photobleaching rate.57 The same phenomenon was observed with the cyanines Cy3, Cy5 and Cy3B.58 As discussed in detail in Section 1.3.2, the generation of significant populations of triplet states is unavoidable even when using dyes with low intersystem crossing efficiencies. For this reason, a variety of strategies have been developed to minimize triplet lifetimes in order to mitigate photobleaching and blinking.59–61 It is important to note that some buffer additives used to quench the triplet state (e.g. β-mercaptoethanol) can donate an electron to the triplet state of many fluorophores, generating radical anions that also contribute to bleaching and blinking.62,63 The lifetimes of the radical ions of organic dyes depend strongly on the concentration of oxygen in solution, and are usually in the μs-ms timescale for solutions equilibrated with atmospheric oxygen.64–66 Because oxygen is usually depleted in single-molecule experiments to minimize bleaching, the lifetime of the radical anions generated from the triplet state can persist for much longer in singlemolecule conditions, resulting in severe blinking. For instance, the radical anions of oxazines with high reduction potentials have been shown to persist for minutes in the presence of reducing agents and low oxygen concentrations (see Section 1.6.2).67,68 For this reason, a common and more universal strategy to eliminate blinking is the use of reducing and oxidizing systems (ROXS),60,69 which rapidly depopulate radical anionic and radical cationic states to regenerate the ground state.

1.2.4 Energy transfer This term refers to the process in which the excited state of a molecule (the donor) deactivates to a lower-lying state by transferring energy to a second molecule (the acceptor). The mechanism of energy transfer depends strongly on the separation between the two molecules. In the context of single-molecule research, where the donor and the acceptor are typically separated by distances considerably larger than their van der Waals radii, energy transfer is the consequence of a nonradiative process in which weak interactions between the transition dipole moments of the two molecules result in the transfer of electronic excitation. This mechanism is commonly known as F€ orster-resonance energy transfer (FRET, represented as ⑧ in Fig. 1.4), and often as fluorescence-resonance energy transfer although this term is discouraged to avoid the misconception that energy transfer involves the emission of radiation.48 Readers interested in learning more about F€orster’s theory and other transfer mechanisms are encouraged to read the chapters written by Valeur,70 Meer,71,72 and Clegg.73,74 The rate constant for energy transfer (kE) depends strongly on the donor-acceptor distance (r), making FRET an ideal tool for probing dynamic changes in the conformation of biomolecules:

1.2 Photophysical processes and the generation of dark states

kE ¼

  1 R0 6 τ0D r

(1.4)

Here, τ0D is the excited state lifetime of the donor in the absence of energy transfer, and R0 is a critical distance known as F€ orster’s radius. The probability that the donor will deactivate by FRET (vs fluorescence, internal conversion, etc) is given by the quantum yield of energy transfer (ϕFRET), commonly known as the efficiency of FRET, E: ϕFRET ¼ E ¼

kE kE + kf +

kE X ¼ knr kE + 1=τ0D

(1.5)

P The term knr includes all the nonradiative processes that deactivate the excited state of the donor other than energy transfer. Combining Eqs. (1.4), (1.5) we obtain: E¼

1  6 r 1+ R0

(1.6)

Eq. (1.6) provides a straightforward interpretation for the critical distance R0: the F€ orster radius is the donor-acceptor distance at which E ¼ ½, or in other words, the distance at which the probability of energy transfer equals the probability that the donor will deactivate through another mechanism (fluorescence, internal conversion, etc). The parameter R0 can be expressed in terms of spectroscopic variables and solvent properties as70: R60 ¼

ð 9ð ln10Þκ 2 ϕ0D FD ðλÞεA ðλÞλ4 dλ 128 π 5 NAv n4

(1.7)

where κ 2is the orientation factor, ϕ0D is the fluorescence quantum yield of the donor in the absence of transfer, n is the refractive index of the medium, and NAv is Avogadro’s number. The integral describes the overlap between the normalized emission spectrum of the donor (FD(λ)) and the extinction coefficient of the acceptor (εA(λ)). Eq. (1.7) highlights the challenges of using measured FRET efficiencies to obtain distances because the accuracy with which r can be measured depends critically on the precision with which R0 can be evaluated. The spectroscopic quantities (ϕ0D and the overlap integral) should be evaluated experimentally using the substrates of interest. Naively, one could think that these quantities can be determined using the same donor and acceptor dyes in different contexts (e.g. using the free dyes), but this ignores the fact that ϕ0D can be significantly sensitive to the local environment of the donor (polarity, viscosity, specific interactions with nucleobases or amino acids). The position (and sometimes shape) of the absorption and emission spectra may change once the dyes are bound to macromolecules, and this should be evaluated for precise determinations of r. Extinction coefficients are less likely to vary, but the reality is that if they do, evaluating these changes is not straightforward.

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CHAPTER 1 Photophysics of single-molecule probes

The parameter κ2 in Eq. (1.7) is often called the orientation factor, or kappasquare factor, and takes into account the fact that the efficiency of transfer depends on the relative orientation between the transition dipole moments of the donor and acceptor.75–77 The value κ2 ¼ 2/3 that is often used in FRET calculations is derived by averaging all possible angles for freely rotating donor and acceptor molecules. Free rotation, however, may not be achieved due to steric restrictions and specific interactions between the dyes and nucleotides or amino acids. This makes the exact treatment of the kappa-square factor a particularly difficult task. Many authors have discussed the impact of the orientation factor on the accuracy with which distances can be determined from FRET measurements, and the reader is encouraged to read Refs. 76–79 for a detailed treatment of the subject. A dramatic example for which the κ2 ¼ 2/3 approximation does not hold has been reported by Lilley and coworkers in measurements of the FRET efficiency of DNA terminally labeled with Cy3 and Cy5.80–83 In this case, dye-DNA interactions result in transition moments with almost fixed orientations (Fig. 1.5). As it will be discussed in detail in Section 1.6.3, these interactions do not only create uncertainties in the κ2 factor, but also affect the spectroscopic and photophysical parameters of Eq. (1.7). In general, the uncertainty in κ2 can be reduced if structural information or computational simulations are available to exclude certain orientations.27,78,84,85 In addition, knowledge of the depolarization factors (obtained from fluorescence anisotropy measurements) can also reduce the uncertainty in the orientation factor.75,78,86,87 Time-resolved fluorescence anisotropy experiments are critical for a rigorous analysis of the κ2 factor. A common misconception, however, is that fluorescence anisotropy measurements are enough to compute κ2. Instead, these values can be used to remove some, but not all of the uncertainty.78 For instance, the use of anisotropy data to analyze FRET distance measurements on an HIV-1 integrase complex using Cy3 and Cy5 resulted in about 25% uncertainty in the measured distances largely due to the uncertainty in the κ2 factor.87

1.2.5 Quenching A quencher is a molecule (or ion) whose presence decreases the fractional population of an excited-state. If that state is S1, the quencher results in loss of fluorescence (lower intensity and a decreased ϕf).70,89 The term static quenching is used when loss of fluorescence occurs without changing the excited state lifetime. A typical case is the formation of a ground-state nonfluorescent complex; for instance, fluorescein and many rhodamines form nonfluorescent dimers with a plane-to-plane stacking geometry (H-dimers).90–92 The fluorescence intensity of the solution will be proportional to the concentration of uncomplexed fluorophores, which decreases with increasing quencher concentration, but the fluorescence lifetime is not affected because fluorescence arises from fluorophores that do not interact with the quencher. Other examples of static quenching are the interactions of the oxazine derivatives MR121 and JA242 and the rhodamine derivatives R6G and TMR with

1.2 Photophysical processes and the generation of dark states

FIG. 1.5 A molecular model generated from NMR structures of Cy3 and Cy5 attached to duplex DNA.81,88 The dyes are mostly stacked at the end of the helix. Courtesy of Prof. D. Lilley, University of Dundee.

deoxyguanosine monophosphate (dGMP).93 In the opposite limit, the interaction between the quencher and the fluorophore decreases the lifetime of the excited state, and this decrease parallels the decrease in fluorescence quantum yield (dynamic quenching). Dynamic quenching is often called collisional quenching because loss of fluorescence is due to collisions between the fluorophore and the quencher. One important example of this mechanism is quenching by molecular oxygen, which causes the fluorophore to undergo intersystem crossing to the triplet state.89 Quenching by oxygen is more pronounced for dyes with long lifetimes (e.g. pyrene) because for collisional quenching to be efficient, the quencher needs to encounter the fluorophore during its excited state. Other examples of dynamic quenching are the interaction of the dye Alexa 488 with tyrosine94 and the quenching of the coumarin

31

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CHAPTER 1 Photophysics of single-molecule probes

dye C—120 by deoxycytidine (dC).95 More generally, however, static and dynamic quenching occur simultaneously, resulting in a decrease in fluorescence lifetime that is less pronounced than the corresponding decrease in quantum yield. This is the case, for instance, of the quenching of Alexa Fluor 488 by tryptophan and histidine.94 A common mechanism of fluorescence quenching by nucleobases and amino acids is photo induced electron transfer (PET), a process in which the excited state of the fluorophore accepts or donates an electron from the quencher. This process results in the formation of a semi-reduced (radical anion) or semi-oxidized (radical cation) dye molecule. For instance, the nucleoside guanosine and the amino acid tryptophan are good electron donors,95–98 and are efficient quenchers of fluorescein, many rhodamines, and oxazines.93–95,99–102 The quenching of many dyes by guanosine in DNA and RNA is a well-known phenomenon that results in a significant reduction of the fluorescence quantum yield of the dye when it is bound in close proximity to a G-base. Notably, the cyanine dyes such as Cy3 and Cy5 have lower electron acceptor tendencies and are not efficiently quenched by nucleobases or amino acids.101,102 The examples above involve the oxidation of the quencher, and the efficiency of the process therefore correlates with the oxidation potentials of the nucleobases and amino acids. In the case of the DNA bases, guanine has the lowest redox potential (G < A < C < T) and is therefore most easily oxidized.95,103 PET reactions involving nucleobase reduction have also been observed, but are efficient only for dyes with low excited state oxidation potentials such as some amino-substituted coumarins that emit in the blue edge of the visible spectrum.95

1.3 The dynamic behavior of dark states As already discussed, the generation of dark states is a crucial factor in the interpretation of single-molecule fluorescence signals. Depending on timescales, dark states may lead to noticeable blinking or noisier signals, and generally result in lower fluorescence intensity averages. The focus of this section will be on the important role of the excitation rate (related to the laser power) in determining the dynamic behavior of dark states. An important conclusion of this section is that laser power is an important variable that can be used to assess the contributions of dark states to fluorescence signals.

1.3.1 Nanosecond dynamics of the S0 /S1 system Let us consider a fluorophore that is being continuously excited by a laser source. Initially, suppose that the excited state deactivates exclusively to S0. The kinetics of this simple two-state system (Fig. 1.6A) can be modeled as a reversible chemical reaction with a forward rate r12 ¼ k12[S0] and a backward rate r21 ¼ k21[S1], where [S0] and [S1] are the concentrations of molecules in the ground and the excited state, respectively. The rate constant that describes the transition from S0 to S1 (a in

1.3 The dynamic behavior of dark states

0.07

S1

0.06

100 m W

fss (S1) t = 4 ns

k12

f(S1)

0.05

k21

0.04 0.03 0.02

0.00 0.00

(A)

(B)

1.0

0.03

0.04

0.05

time (ms)

t = 4 ns t = 1 ns

0.6 0.4

0.2

0.2

0.0 0.01

0.0 0.01

(C)

0.02

0.8

lf /I0 (A.U.)

fss(S0),fss(S1)

0.4

0.01

1.0

0.8 0.6

fss (S1) t = 1 ns

0.01

S0

0.1

1

10

(D)

P (mW)

t = 4 ns t = 1 ns 0.1

1

10

P (mW)

FIG. 1.6 Dynamics of the two state system S0/S1 (A). B- Fractional concentration of molecules in the excited state (S1) as a function of time for k12 ¼ 1.5  107 s1 and k21 ¼ 1/τ (k21 ¼ 109 s1 in blue, k21 ¼ 2.5  108 s1 in black). C- Fractional concentration of molecules in the ground state (dotted lines) and in the excited state (solid lines) in photostationary conditions as a function of laser power. D- Ratio of the intensity of fluorescence to the excitation intensity (in arbitrary units) as a function of laser power. The flat slope at low laser powers indicates that laser intensity is directly proportional to laser power.

Eq. 1.1) can be expressed in terms of the absorption cross-section for excitation (σ, expressed in cm2) and the incident photon fluence rate (I0 in s1 cm2). To express k12 in terms of laser power (P, expressed in Watts), which can be measured experimentally, we will take into account that the energy of a photon is hc/λ, and we will assume that the beam is focused to an area πω2r : k12 ¼ σ

P λ π:ω2r h:c

(1.8)

where h is Plank’s constant, c is the speed of light, and λ is the wavelength of the laser. For instance, for rhodamine 6G in water (σ ¼ 1.7  1016 cm2)56 excited with a 500 nm-laser focused to a radius of 0.3 μm, Eq. (1.8) gives k12 ¼ 1.5  107 s1 for P ¼ 100 μW. This assumes that the laser has constant intensity over the area πω2r ,

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CHAPTER 1 Photophysics of single-molecule probes

and that the rate of excitation is constant throughout the sample (i.e. the shape of the point-spread-function is ignored). These simplifications are good enough for the purpose of this discussion. For the transition from S1 to S0, k21 is the reciprocal of the fluorophore’s lifetime (e.g. for a fluorophore with τ ¼ 4 ns, k21 is 2.5  108 s1). For this assumed twostate system [S0] + [S1] ¼ [S0](t ¼ 0), and therefore r12 decreases and r21 increases as the ground state is depleted to form S1. Eventually, the rate at which S1 is generated by absorption of light will equal the rate at which it decays to the ground state (r12 ¼ r21), and the system is said to have reached a photostationary state. This is depicted in Fig. 1.6B, which shows the predicted fractional concentration of S1 ( f(S1) ¼ [S1](t)/[S0](t ¼ 0)) as a function of time for k12 ¼ 1.5  107 s1 and two values of k21 corresponding to τ ¼ 4 ns (black line) and τ ¼ 1 ns (blue line). The equations used to obtain these curves are summarized in Appendix. As expected, this fraction increases initially until it reaches a steady state value ( fss(S1)). This result indicates that under these excitation conditions, the photostationary state is established within a few nanoseconds and that the probability that a molecule is found in the excited state after this short lag time remains constant at about 5% for τ ¼ 4 ns and 1.5% for τ ¼ 1 ns. A key result of this analysis is the fact that this steady-state fraction increases with laser power (Fig. 1.6C). This is true because k12 is proportional to P (Eq. 1.8), resulting in a higher rate of formation of the excited state (r12). In contrast, k21 does not depend on laser power, so a higher concentration of excited states needs to build up until r21 (which is proportional to [S1]) matches r12 in the photostationary state. In addition, the steady-state fraction of molecules in the excited state at a given laser power increases with increasing fluorescence lifetime (i.e. decreasing k21). Another important consequence of this analysis is the concept of saturation. From Eq. (1.1), the rate of light absorption (in s1) is given by I0σ, so a molecule under continuous illumination would experience I0σ excitation events per unit time on average. This, however, assumes that the molecule is always available in the ground state to absorb an incident photon. From the discussion above, the probability that an incident photon will strike a molecule in the ground state decreases with increasing laser power and with increasing excited state lifetime. The actual rate of light absorption under continuous excitation is then fss(S0)I0σ, where fss(S0) is the fraction of the time that the molecule spends in the ground state. Because ϕf (the quantum yield, Eq. 1.3) is the probability that the excited state will decay by fluorescence emission, the intensity of fluorescence can be expressed as: If ¼ I0 σfss ðS0 Þϕf 1

2

(1.9)

where I0 (units of s cm ) is proportional to the laser power, and If is expressed in units of s1. The reader should note that I0 and If in Eq. (1.9) are expressed in different units, and the apparent inconsistency arises from the fact that the term ‘intensity’ is traditionally used to refer to different physical variables such as photon flux, radiant intensity, etc. Formally, If in Eq. (1.9) is a photon flux (number of photons per unit time), whereas I0 is a photon fluence rate.48 Eq. (1.9) shows that under

1.3 The dynamic behavior of dark states

photostationary conditions, If/I0 is proportional to the fractional concentration of molecules in the ground state, fss(S0), which decreases with increasing laser power (Fig. 1.6C, fss(S0) ¼ 1  fss(S1)). The shape of the ratio If/I0 (in arbitrary units) is shown in Fig. 1.6D as a function of laser power for the same photophysical parameters used to generate Fig. 1.6B. The intensity of fluorescence is approximately proportional to the incident intensity (If/I0 is constant) at low laser powers, because at small excitation rates the average time between two absorption events (1/k12) is significantly longer than the lifetime of the excited state. This ensures that the molecule is predominantly in the ground state and available to absorb an incident photon. At higher laser powers, in contrast, a fraction of the incident photons is unused because they strike the molecule while in its excited state. This phenomenon is known as saturation because molecules are not able to relax to the ground state fast enough to keep up with the high excitation rates. As a result, fluorescence intensity is no longer proportional to laser power, and it is only a fraction of what it would be for a hypothetical fluorophore with negligible excited state lifetime.

1.3.2 Dynamics of the S0/S1/T1 system Next, let us consider a third state, which will be assumed to be nonemissive (Fig. 1.7A). Diagrams like these are useful to analyze the effects of triplet states and non-fluorescent isomers on the amplitude and dynamics of fluorescence fluctuations.56,104 In the case of a triplet state, k23 is the rate constant for intersystem crossing from S1 to T1, and k31 is the rate constant for intersystem crossing from T1 to S0. For the triplet transitions of rhodamine 6G in water, k23 ¼ 1.1  106 s1 and k31 ¼ 4.9  105 s1.56 The value of k31 will be affected by oxygen concentration and triplet quenchers added to the buffer, so the reader should keep in mind that the results described in Fig. 1.7 correspond to aqueous solutions equilibrated with atmospheric oxygen. Obtaining expressions that describe the time evolution of the three states involved in this scheme requires solving a system of linear differential equations (Appendix) and can be easily achieved using mathematical software such as Mathematica. It is highly recommended that the reader takes the time to set up these equations and modify the different kinetic parameters to appreciate the impact of the different rate constants on the steady-state concentration of the dark state (here assumed to be a triplet) and on the timescale at which the photostationary state is established. The rate of excitation (k12) is the only rate that depends on laser intensity, but because the generation of T1 occurs at a rate proportional to the concentration of S1, a higher laser power results in a higher photostationary fraction of triplet states as well (Fig. 1.7C). Fig. 1.7B shows the fractional populations of S1 and T1 (f(S1) ¼ [S1](t)/[S0] (t ¼ 0) and f(T1) ¼ [T1](t)/[S0] (t ¼ 0)) with a logarithmic time axis to facilitate visualization from nanoseconds to microseconds. Because k23 ≪ k21 (intersystem crossing is a forbidden transition), the fraction of molecules in S1 reaches almost the same value calculated for the two-state system before it starts decreasing in the microsecond timescale as the triplet state is populated. A higher laser power increases the rate of formation of S1 and

35

CHAPTER 1 Photophysics of single-molecule probes

0.12

S1

k23

k21

f (S1),f (T1)

k12

100 µW fss (T1)

0.10

T1

k31

0.08 0.06 0.04

fss (S1)

0.02

S0

0.00

(A)

0.001

0.01

(B) 1.0 0.8

T1

0.6 0.4

(C)

1

10

100

0.8

S1

0.2 0.0 0.01

0.1

time (µs) 1.0

S0

If /I0(A.U.)

fss (S0),fss (S1),fss (T1)

36

0.1

1

P (mW)

0.6 0.4 0.2 0.0 0.01

10

(D)

0.1

1

10

P (mW)

FIG. 1.7 Dynamics of the three-state system S0/S1/T1 (A). The values of the rate constants are assumed to be k12 ¼ 1.5  107 s1, k21 ¼ 2.5  108 s1, k23 ¼ 1.1  106 s1, and k31 ¼ 4.9  105 s1. B- Fractional concentration of molecules in the excited singlet and triplet states (S1 and T1, respectively) as a function of time for P ¼ 100 μW. C- Fractional concentration of molecules in the ground state (dotted line) and in the excited singlet and triplet states (solid lines) in photostationary conditions as a function of laser power. D- Ratio of the intensity of fluorescence to the excitation intensity (in arbitrary units) as a function of laser power. The flat slope at low laser powers indicates that laser intensity is directly proportional to laser power.

therefore T1, which results in higher populations of these transient entities in the photostationary state (Fig. 1.7C). Fig. 1.7D shows the predicted shape for the ratio of the intensity of fluorescence to the incident intensity. Not surprisingly, the presence of considerable populations of triplet states results in saturation effects that are more significant than in the case of the two-state system discussed previously. A remarkable conclusion of this exercise is that the triplet steady-state population can be quite significant under typical single-molecule illumination conditions even when the quantum efficiency for intersystem crossing is quite low 1 for the rhodamine used in this example). Similar consid(ϕISC ¼ k23 =ðk23 + k21 Þ
250 erations can be used to evaluate the fractional populations of other dark states such as

1.4 Understanding the various contributions? to the measured fluorescence intensities the cis photoisomer of cyanine dyes (Section 1.6.3). For instance, for the cyanine dye Cy5, the photostationary fraction of cis states is close to 50% even at relatively low laser powers (
1 kW/cm2).104 These results have important consequences for the analysis of single-molecule data. How and if single-molecule signals will be affected by the presence of nonemissive states will depend on how the timescales for the generation and decay of the dark states compare to the relevant timescales of the experiment. To illustrate this point, let us consider the results of Fig. 1.7 in the context of an experiment where photons from a single-molecule are collected continuously with 10 ms resolution (i.e. the intensity of fluorescence is measured as the sum of all photons detected in a 10 ms period). This timescale is orders of magnitude longer than the rates of interconversion between the three states (Fig. 1.7B), and consequently any fluctuations due to the interconversion between bright and dark states will be averaged out during the much longer acquisition time. A situation like this does not lead to blinking, but the measured fluorescence intensity will be a fraction of what it would be in the absence of the dark state. Importantly, this fraction will decrease with increasing laser power. As seen in Fig. 1.7C, the contribution of triplet states is significant only at high laser powers, but as stated above, the steady-state fractional contribution of the cis nonemissive isomer of Cy5 can be as high as
50% even at low-to-moderate laser powers. This has important consequences when these signals are used to determine accurate FRET efficiencies (see Section 1.5). From the discussion above, it follows that the generation of dark states will result in blinking if the rates of interconversion between bright and dark states are such that the dark state persists at timescales that are longer than the acquisition time. Because one of these rates (k12) is proportional to laser power (Eq. 1.8), the temporal behavior of the observed fluorescence fluctuations depends on laser power. This distinctive property can be in fact used to distinguish between fluctuations of photophysical origin (i.e. photoinduced processes) and fluctuations that arise from other sources such an intramolecular conformational change that affects a FRET efficiency. An example of long-lived dark states that result in blinking was already presented in Figs. 1.2 and 1.3, which point to the formation of dark states of Cy5 with lifetimes much longer than that of the triplet state or cis isomer (see Section 1.6.3 for a discussion of the nature of this dark state). The radical ions of many commonly used dyes are also known to persist for long times (compared to typical acquisition timescales). For example, the triplet state of rhodamine dyes such as Alexa Fluor 488 can be reduced by thiols present in the buffer to form a stable radical anion that can persist for minutes and up to hours.67

1.4 Understanding the various contributions to the measured fluorescence intensities Let us now discuss the various contributions to the measured fluorescence signals. Eq. (1.9) represents the number of photons emitted by a molecule per unit time under continuous irradiation, but only a fraction of these photons will be detected by the

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instrument. In addition, in the case of FRET, fluorescence may arise from excited states that were not produced by direct absorption of a photon, but from energy transfer from an excited donor to an acceptor. The goal of this section is to write expressions for the signals measured in the donor and acceptor detectors, which will eventually be used to calculate the desired FRET efficiencies. Understanding the variables and factors that contribute to the measured signals is critical to avoid misinterpretations of the data, and to identify what complementary spectroscopic or photophysical data may be necessary to calculate accurate FRET efficiencies. The discussion in the introduction highlighted the importance of measuring donor and acceptor fluorescence intensities using alternating lasers that excite the donor or the acceptor directly,105 so in this section we will assume that molecules labeled with a donor-acceptor pair are continuously illuminated by alternating green and red excitation (ExG and ExR, Fig. 1.8). Here, the colors green and red are merely used to denote wavelengths used to excite the donor and the acceptor, respectively, but the analysis is not restricted to any particular choice of dyes. As is typical in these experiments, the emission of the sample is collected, and passed through a dichroic mirror that preferentially transmits the longer-wavelength photons (primarily from the acceptor) and reflects the shorter-wavelength ones (primarily from the donor). The transmitted light is passed through a filter that preferentially transmits photons emitted by the acceptor (EmR, Fig. 1.8), which are then detected with an efficiency that depends on the wavelength of the incident photons. The reflected photons are passed through a filter that preferentially transmits photons emitted by the donor (EmG, Fig. 1.8) and focused on an independent detector. There are four measured signals: FGG and FRG are the intensities measured in the donor detector (“green detector”) under green and red laser excitation, respectively, and FGR and FRR are

FIG. 1.8 Absorption (dotted lines) and emission (solid lines) spectra of hypothetical donor (green) and acceptor (red) dyes. The arrows denoted with ExG and ExR point to the wavelengths of the lasers used to excite the donor (ExG) and the acceptor (ExR). The black horizontal lines indicate ranges of wavelengths that are transmitted by the filters placed in front of the donor and acceptor detectors (EmG and EmR, respectively).

1.4 Understanding the various contributions? to the measured fluorescence intensities the intensities measured in the acceptor detector (“red detector”) under green and red laser excitation, respectively. All intensities are assumed to be already corrected for background. To start, let us consider a donor-only sample. As discussed in Section 1.2.1, the quantity a ¼ I0σ is the rate of light absorption in units of s1. If every photon absorbed by the donor resulted in fluorescence, and if every emitted photon could reach the detector and trigger a response, then a would also represent the fluorescence intensity in units of s1. The measured intensities (FGG, FGR, FRG, and FRR), however, are only a small fraction of the excitation rates because of a combination of photophysical and instrumental factors that limit the number of photons that are emitted and detected. The calculation of FGG, FGR, FRG, and FRR can be understood by considering a series of sequential steps, each of which decreases the excitation rate by a given fraction. The excitation rates for the donor under green 0 D 0 0 and red excitation are I0Gσ D G and IRσ R , respectively, where IG and IR are the incident intensities under green and red excitation (formally photon fluence rates, see D Section 1.2.1), and σ D G and σ R are the donor cross-sections at those wavelengths (G ¼ green excitation, R ¼ red excitation). The absorption spectra of all common dyes used in single-molecule work are asymmetric in shape and decrease sharply on the red-side of the spectrum (Fig. 1.8). For this reason, it is usually possible to avoid direct excitation of the donor when using the red laser (σ D R  0, Fig. 1.8). However, avoiding direct excitation of the acceptor at the wavelength used to excite the donor is usually not possible (σ AG 6¼ 0, Fig. 1.8). Once a molecule is in the excited state, the probability that it will decay by emitting a photon is given by its quantum yield (ϕD, ϕA). Therefore, for the donor under green excitation, the rate of photon emission (in units of s1) in the absence of FRET D and ignoring saturation (Section 1.3.2) is I0Gσ D Gϕ . Finally, a small fraction of these photons will reach the detectors, and only a fraction of these will trigger a detector response. The number of photons that reach each detector depends on the geometry of the instrument, and on the wavelength-dependent transmission and reflection properties of all optical components (polarization effects will be ignored in this analysis). The probability that a photon emitted by the donor will reach the green (or red) detector and trigger a response that is recorded as a photon arrival will be denoted by ηDG (or ηDR), respectively. Although instruments are designed to minimize ηDR, a fraction of the donor photons is often leaked into the acceptor detector (Fig. 1.8). Similarly, ηAGand ηAR are the fractions of photons emitted by the acceptor detected in the green and red detectors, respectively. Therefore, for the donor only sample. D DG FGG ¼ IG0 σ D Gϕ η

(1.10a)

D DR FGR ¼ IG0 σ D Gϕ η

(1.10b)

D DR FRR ¼ IR0 σ D 0 Rϕ η

(1.10c)

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D DG FRG ¼ IR0 σ D 0 Rϕ η

(1.10d)

σD R

The values of FRR and FRG are negligible because  0 (see above). For a biomolecule containing a donor-acceptor pair within FRET distance (i.e. E 6¼ 0), the fraction of photons emitted by the donor is further reduced by (1  E), where E is the FRET efficiency (the fraction of photons absorbed by the donor that result in the generation of the acceptor excited state). Correspondingly, (1  E) represents the fraction of excited states that do not undergo energy transfer. With this in mind, Eqs. (1.10a)–(1.10d) can be re-written as: D DG A AG D DG FGG ¼ IG0 σ D + IG0 σ D + IG0 σ AG ϕA ηAG  IG0 σ D G ð1  EÞϕ η G Eϕ η G ð1  EÞϕ η

(1.11a)

D DR A AR FGR ¼ IG0 σ D + IG0 σ D + IG0 σ AG ϕA ηAR G ð1  EÞϕ η G Eϕ η

(1.11b)

D DR FRR ¼ IR0 σ D + IR0 σ AR ϕA ηAR  IR0 σ AR ϕA ηAR Rϕ η

(1.11c)

D DG + IR0 σ AR ϕA ηAG  0 FRG ¼ IR0 σ D Rϕ η

(1.11d)

Eq. (1.11a) describes the intensity measured in the green detector under green excitation. The first term represents the photons emitted by the donor, which are detected by the green detector with a probability ηDG. The second term in Eq. (1.11a) represents photons emitted by the acceptor due to FRET. The quantity I0Gσ D G is the rate of E is the rate of formation of excitation for the donor under green excitation, I0Gσ D G A Eϕ is the rate of emission of acceptor acceptor excited states due to FRET, I0Gσ D G photons from excited states created through energy transfer, and ηAG is the fraction of those photons that are detected in the green detector. Fluorescence spectra are usually approximately mirror images of their corresponding excitation spectra, and therefore fluorescence intensity decreases steeply at wavelengths lower than the emission maximum. Consequently, it is not difficult to choose filters that prevent leakage of the acceptor into the donor channel, and ηAG is usually negligible. The third term describes the emission of acceptor photons due to direct excitation with the green laser. Here, I0Gσ AG is the rate of formation of acceptor excited states under green excitation and I0Gσ AGϕA is the rate of photon emission from excited states that were created by direct excitation. As before, the probability that these photons are detected in the green channel is small (ηAG  0). Eq. (1.11b) describes photons detected in the red channel upon green excitation. Here, the first term represents the fraction of green photons that are leaked into the red detector (ηAR 6¼ 0), and the second and third terms represent acceptor photons detected in the red channel with a probability ηAR. The only contribution to FRR (Eq. 1.11c) is direct excitation of the acceptor under red excitation because σ D R  0, and the two AG are negligible. terms in Eq. (1.11d) are negligible because both σ D R and η This exercise highlights the role of important photophysical parameters in determining the measured fluorescence intensities from which investigators typically

1.5 Photophysical considerations? in the calculation of accurate FRET efficiencies calculate FRET efficiencies. The role of saturation was ignored for simplicity, but readers interested in determining very precise FRET efficiencies should take the time to evaluate how saturation affects the different terms in Eqs. (1.11a)–(1.11d). Simply replacing fluorescence quantum yields by effective quantum yields is not as straightforward as it was for the case discussed in Section 1.3. For example, donor saturation will likely be negligible in Eq. (1.11c) due to the small excitation rate in the red (small cross-section), but not in Eq. (1.11a) (green excitation). Therefore, the effective donor quantum yields are different in these equations. The next section focuses on how these intensities are usually manipulated to determine FRET efficiencies, and which types of spectroscopic and photophysical considerations are critical to maximize accuracy.

1.5 Photophysical considerations in the calculation of accurate FRET efficiencies Arithmetic manipulation of Eqs. (1.11a)–(1.11d) allows the calculation of E from the four measured intensities59,106: E¼

FGR  βFGG  αFRR FGR  βFGG  αFRR + γFGG

(1.12)

where β ¼ ηAG/ηDG, α ¼ I0Gσ AG/I0Rσ AR and γ ¼ ϕAηAR/ϕDηDG. The precision with which E can be determined from single-molecule experiments depends critically on the investigator’s ability to determine the correction factors α, β, and γ. Rough estimates may be enough in many cases, but precise values are more critical if FRET is used as a structural tool to determine absolute distances. It should be stressed that an accurate distance determination requires both accurate estimates of E and R0, and as discussed previously, the latter depends on the orientation factor and therefore its determination carries its own complications. Here, the focus will be on important photophysical considerations for the determination of accurate FRET efficiencies from Eq. (1.12). Initially it may appear that knowledge of all extinction coefficients (or crosssections), quantum yields and detector efficiencies is a prerequisite to calculate E, but the values of α and β can be measured experimentally using donor- and acceptor-only samples. For example, from Eqs. (1.11a), (1.11b), β ¼ FGR/FGG for a donor-only sample. A similar analysis for acceptor-only samples yields α ¼ FGR/FRR. Donor-only and acceptor-only species may be already present in the sample due to incomplete labeling, so the measurements needed to calculate α and β are often obtained in the same experiment designed to calculate E. Once again, these equations assume that the effects of saturation are negligible, or in other words, that the probability that a molecule is in the excited state is small so all photons can be assumed to strike the molecule in the ground state. Yet, the fractional concentration of dark states can be more than 50% for common acceptors such as Cy5 or Alexa 647 (cyanine dyes, see Section 1.6.3), and this number depends on the excitation rate and

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therefore on the wavelength of the laser. For instance, saturation will be more prominent for the acceptor under red excitation than under green excitation due to the different cross-sections of the dyes at those wavelengths. The effective fluorescence quantum yield of the acceptor in Eq. (1.11b) (green excitation) is therefore likely larger than the corresponding value in Eq. (1.11c) (red excitation), and the ratio FGR/FRR will not equal α ¼ I0Gσ AG/I0Rσ AR as it is the case when saturation is ignored. The measurement of the parameter γ from the measured fluorescence intensities is less straightforward even when saturation is ignored, and different approaches exist for its determination and analysis. One common approach for the determination of the correction factor γ relies on measuring at least two different FRET samples with the same donor-acceptor pair.105,106 The actual procedure is somewhat convoluted and readers are encouraged to read details in the original references. Alternatively, for TIRF measurements, the γ-factor can be calculated for each individual trace from the intensities before and after acceptor photobleaching.107,108 The γ-factor depends on the quantum yields of the donor and acceptor, which depend on several environmental factors such as quenching, viscosity, polarity, etc. If saturation is considered, these values will also depend on laser power and excitation wavelength. Regardless of the method, researchers should keep in mind the definition of γ and evaluate whether the method chosen to measure this factor provides a true measurement of the ratio ϕAηAR/ϕDηDG. For instance, if two or more different samples are used to calculate γ as described by Lee et al.,106 the investigator should critically evaluate if the values of ϕA and ϕD are the same in all samples used in the procedure, and identical to the values for the fluorophores in the sample of unknown FRET. For example, the cyanine Cy3, commonly used as a donor in sm-FRET, displays a fluorescent quantum yield that can change dramatically (by more than a factor of 2) depending on DNA sequence and other environmental variables (see Section 1.6.3). Harvey et al. reported fluorescence quantum yields in the range ϕ ¼ 0.18–0.39 for Cy3 covalently bound to the 50 terminus of oligonucleotides of the same length but different sequence.109 Rasnik et al. reported fluorescence quantum yields of Cy3 covalently bound to a helicase complexed with DNA, and observed values that depended strongly on the amino acid used for labeling (see Section 1.6.3).110 Notably, Sabanayagam et al. reported significant variability in the γ-factors measured for many identical Cy3/Cy5-labeled DNA molecules, and concluded that the quantum yield of Cy3 has a large variability even among molecules that are expected to be identical.111 It is therefore hard to imagine that different Cy3-labeled nucleic acids or proteins could be used to calculate a unique γ-factor. Lee et al. suggested that a situation like this could be circumvented by measuring the fluorescence quantum yields of the donor and acceptors in all samples, and using these values to correct for possible differences.106 However, this does not take into account the formation of dark states, which can be quite significant for Cy3 due to the formation of a nonemissive cis isomer (Section 1.6.3) that may result in significant saturation of the fluorescence signal at the high excitation rates used in singlemolecule experiments. The previous discussion highlights challenges that are often overlooked in the analysis of smFRET data, especially when accuracy in the measured FRET

1.6 Photophysical properties? of common single-molecule fluorescent probes efficiencies is important (e.g. to derive structural models). Fluorescence saturation due to the formation of dark states is a problem that has not received enough attention. It is often assumed that this is taken into account when measuring fluorescence quantum yields, but it is critical to keep in mind that the fraction of molecules in the excited state increases steeply with increasing laser power, and may be negligible in the cuvette-type measurements typically used to measure ϕD. Acceptor dark states may create additional challenges because, depending on their nature, they may or may not be able to accept energy from a nearby excited donor. The impact of this would need to be evaluated on an individual basis by researchers wishing to use sm-FRET for accurate determinations of FRET efficiencies. This chapter opened with a sentence cautioning the reader about the many variables that need to be taken into account when selecting dyes, performing measurements, and analyzing data. As it is hopefully apparent by now, the relative importance of the different issues discussed so far in this chapter depends strongly on the objectives of the investigator. For example, while Cy3 can be problematic as a donor for accurate measurements of distance from FRET, it would be unwise to conclude that Cy3 is not a good choice for any sm-FRET experiment. In fact, this dye has been extensively used by Ha and co-workers in hundreds of influential publications that have inspired the whole community. It should be clear, therefore, that there is no undisputed candidate for the role of “best single-molecule dye”, and that choices need to be made judiciously based on the particular characteristics of the system and the objectives of the experiment.

1.6 Photophysical properties of common single-molecule fluorescent probes This final section aims to give the reader an overview of the photophysical properties of the different families of fluorophores commonly used in single-molecule research. The reader is also encouraged to read other reviews and chapters on the topic.112–115 In most cases, single-molecule fluorescence experiments rely on the use of extrinsic fluorophores, i.e. fluorophores that are not native to the biopolymer of interest. The fluorescence quantum yield of the DNA bases is negligible,116 and the fluorescent amino acids (mainly tryptophan and tyrosine) absorb and emit in the UV region of the spectrum.117 Instead, organic fluorophores or fluorescent proteins that absorb and emit in the visible are preferred to minimize contributions from Raman scattering and autofluorescence.113,115 The photophysical properties of fluorescent proteins will not be reviewed here explicitly, but many of the considerations that will be discussed in the context of organic fluorescent molecules still apply when designing and interpreting experiments that use those probes. Even though hundreds of different organic fluorescent dyes are available commercially, most dyes used in singlemolecule research belong to a handful of chemical classes: rhodamines, carbocyanines, oxazines and carborhodamines.114,115 Examples are shown in Figs. 1.9 and 1.11. It is worth noting that the terms “Alexa dyes” or “ATTO dyes” are trademarks

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that identify many different dyes commercialized by Thermo Fisher Scientific and ATTO-TEC GmbH, respectively, but these groups of dyes do not necessarily have a shared chemical structure or common photophysical properties. Even among the same family of dyes, fluorophores with similar chromophores may differ in their hydrophobicity and net charge due to the presence of various substituents that may have little impact in the fundamental fluorescence properties of the free dye (spectra, quantum yield, and lifetime), but can greatly affect the nature and strength of their interactions with the building blocks of the biomolecules being investigated. The preceding sections already offered examples of how interactions with nucleobases and amino acids can greatly affect the photophysical properties of the dye, and even alter the conformation of the system being probed. However, it would be a mistake to conclude that changes in photophysical properties due to proximity to a biomolecule are always detrimental. In fact, the next sections will highlight examples of how changes in fluorescence quantum yield and lifetime can inform on interactions that can help the researcher gain information about the conformation of a biopolymer, the oligomeric state of a protein, or the proximity of a protein to a particular location on DNA (as in PIFE, see Section 1.6.3).

1.6.1 Rhodamines and carborhodamines Most rhodamine dyes absorb in the 520–570 nm range of the spectrum. Examples of commercially available rhodamine derivatives commonly used in single-molecule studies are TAMRA (carboxy tetramethylrhodmine), Alexa Fluor 488, Alexa Fluor 532, Alexa Fluor 546 (Thermo Fisher Scientific), and ATTO532, ATTO565 and ATTO590 (ATTO-tec Inc). Some examples are shown in Fig. 1.9. All Alexa and some ATTO derivatives contain sulfonate groups to increase water solubility and to reduce dye aggregation. Indeed, while TAMRA dimerizes at concentrations as low as 10 μM, Alexa Fluor 546 and Alexa Fluor 488 do not show signs of aggregation even at mM concentrations.92 The sulfonate groups in the Alexa dyes also reduce interactions between the dyes and DNA and proteins. For instance, while TAMRA has been shown to associate with the DNA nucleotide monophosphates (dNMPs) in solution, interactions between dNMPs and Alexa Fluor 546 are negligible.118 Similar differences were also reported in studies of DNA labeled with rhodamine dyes. For example, NMR and smFRET studies of DNA terminally labeled with Rhodamine 6G (a non-sulfonated rhodamine) indicated that the dye can stack on the terminal base pair.119 In contrast, Alexa Fluor 488 appears to have rather free mobility when attached to DNA.120 Time-resolved fluorescence anisotropy measurements of the E. coli β subunit of DNA polyerase III labeled with either TAMRA or Alexa Fluor 488 also showed nearly unrestricted mobility for Alexa Fluor 488, but not for TAMRA. In addition, while the fluorescence intensity decay of the Alexa 488labeled protein was nearly monoexponential, the corresponding decay for the TAMRA-labeled sample required an additional exponential term consistent with protein-fluorophore interactions. As already discussed in the introduction, dyeprotein interactions not only can affect the photophysical properties of the dye,

Chemical structures of representative rhodamine derivatives used in sm-fluorescence. Alexa Fluor is a registered trademark of Thermo Fisher Scientific. ATTO dyes are products of ATTO-TEC GmbH. The numbers in the Alexa and Atto dyes indicate optimal excitation wavelengths.

1.6 Photophysical properties? of common single-molecule fluorescent probes

FIG. 1.9

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but perhaps more importantly, can alter the conformational landscape of the protein. As mentioned earlier, DeVore et al. reported FRET distributions obtained from experiments with fluorescently labeled calmodulin, which indicated that the dye Texas Red (a rhodamine with no net electrical charge, Fig. 1.9) stabilized a compact conformation of the protein.31 In contrast, Alexa Fluor 594 and ATTO594 (sulfonated rhodamines with a net charge of 2 and 1, respectively) did not appear to bias the conformational landscape of the protein. The photophysical properties of rhodamine dyes depend greatly on the nature of the substituents bound to the amino groups (Fig. 1.9). Rhodamines with amino groups fully substituted with alkyl groups (e.g. TAMRA) have fluorescence quantum yields that depend strongly on temperature and viscosity. In contrast, rhodamines in which the amino groups are part of aliphatic rigidized rings (e.g. Texas Red), or that are only partially alkylated (e.g. ATTO532), have quantum yields close to unity.114,121 Derivatives containing fused rings often have improved phtosability and brightness (e.g. Alexa Fluor 594), and replacing the N,N-dimethylamino groups in tetramethylrhodamine (TMR) with a four-membered azetidine ring results in a dye with substantially improved photostability and greater extinction coefficient and fluorescence quantum yield (Janelia Fluor 549).122 This last example is one of several current efforts to improve the photostability and brightness of rhodamines to satisfy the requirements of the most demanding fluorescence-based applications such as superresolution imaging and single-particle tracking.122 Most rhodamines are efficiently quenched by guanosine and tryptophan.93–95,102 For example, the fluorescence quantum yield of Rhodamine 6G decreases from 0.95 for the free dye to 0.15 for the dye covalently bound to a cytosine at the 50 terminus of dsDNA (which is base paired to a guanine).119 Time-resolved measurements on this sample revealed a distribution of lifetimes with mean values 1.3 ns and 4.1 ns, consistent with a dynamically quenched population of fluorophores (shorter lifetime) and a population of fluorophores with less favorable interactions with guanine (longer lifetime, similar to the free dye). In addition, rhodamine dyes self-quench when in close proximity.90–92,123,124 The dimerization of rhodamine dyes in aqueous solution results in a non-fluorescent (quenched) dimer with a plane-to-plane stacking geometry (H-dimers) and a characteristic absorption band that overlaps with the first vibronic shoulder of the monomer.90,92,121,125–128 Therefore, rhodamine dimerization gives the illusion of an enhanced shoulder in the spectrum of the monomer, although this is merely a consequence of the spectral overlap of the two species (monomer and dimer). The properties of the dimers of xanthene dyes (rhodamines and fluorescein derivatives) have been used to probe the conformation and dynamics of proteins and nucleic acids.91,123,124,129–145 For instance, Hamman et al. used the spectroscopic characteristics of the dimer of TMR as a probe to assess the proximity between two residues in a protein dimer.137 The self-quenching properties of rhodamine dyes were used to investigate diverse aspects of the biochemistry and biophysics of DNA sliding clamps and their interactions with clamp loaders,129–133 and to produce profluorescent protease substrates for the in vivo determination of protease activities.91,123,138

1.6 Photophysical properties? of common single-molecule fluorescent probes A recent study of the self-quenching properties of rhodamine dyes conjugated to proteins showed the efficient formation of dimers of TMR when the dyes were conju˚ ).92 These efficient interactions gated to amino acids in very close proximity (
5 A gave rise to the characteristic blue shoulder in the UV-VIS spectrum of the dye, and a ca. 40-fold decrease in fluorescence intensity. Changes in the fluorescence lifetime were significantly smaller, indicating that the decrease in fluorescence intensity was predominantly due to a static quenching mechanism (formation of H-dimers). In contrast, H-dimers did not form when the same protein was labeled with Alexa 488 or Alexa 546. Yet, the fluorescence emission of these dyes was still quenched through a dynamic mechanism that resulted in a ca. six-fold decrease in both intensity and average lifetime. A large number of rhodamine dyes, including Alexa Fluor 488, Alexa Fluor 532, Alexa Fluor 568, ATTO488, ATTO532, and ATTO565, were found to form stable radical anions upon irradiation in the presence of thiol compounds such as β-mercaptoethylamine (MEA).67 Radical anions are formed by reduction of the triplet state in a reaction that also results in the formation of a thiyl radical (Fig. 1.10). The resulting thiyl radicals further react with molecular oxygen, so the continuous irradiation of an aqueous solution of a rhodamine dye containing MEA results both in significant concentrations of the radical anion and depletion of dissolved oxygen. The formation of stable radicals that persist for over an hour was unambiguously demonstrated by means of electron paramagnetic resonance spectroscopy (EPR).67 Re-dissolution of oxygen results in the oxidation of the radical anion and the concomitant recovery of fluorescence. Interestingly, excitation of the radical anion at a wavelength that matches its absorption spectrum (typically 380–430 nm) also recovers the fluorescent state even in the absence of oxygen. Therefore, the dye

FIG. 1.10 Formation of the triplet excited state (3F) occurs spontaneously from the singlet excited state (1F). The triplet state reacts with dissolved oxygen (3O2) to repopulate the singlet ground state and produce singlet oxygen (1O2). The triplet state can also react with thiols dissolved in the • • buffer (RSH) to generate a semireduced dye radical (F ) and a thiyl radical (RS ). The semireduced dye radical can react with oxygen to repopulate the singlet ground state. State diagram adapted from van de Linde, S.; Krstic, I.; Prisner, T.; Doose, S.; Heilemann, M.; Sauer, M. Photoinduced Formation of Reversible Dye Radicals and Their Impact on Super-Resolution Imaging. Photochem. Photobiol. Sci. 2011, 10, 499–506 to describe the formation of stable rhodamine radicals.

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can be switched on and off by alternating between a laser that excites the ground state (e.g. 488 nm for Alexa Fluor 488) and a laser that excites the radical anion (e.g. 405 nm for the same dye).67 Replacing the xanthene oxygen of a rhodamine with a quaternary carbon results in a class of compounds known as carbopyronins (or carborhodamines), which absorb ca. 50-nm to the red with respect to the corresponding rhodamine compound.146,147 The dye known as ATTO647N (Fig. 1.9), for example, is a popular red-absorbing carbopyronin commonly used in superresolution microscopy and as acceptor in sm-FRET experiments.148 This dye is quite hydrophobic, and has been found to label proteins nonspecifically and stick to microscope cover slides and tubes, and to cell membranes.149–151 Moreover, conjugation of ATTO647N to antibodies has been shown to sometimes result in a nonemissive species with an absorption band shifted ca. 30 nm to the blue with respect to the dye’s absorption maximum,151 and single-molecule experiments showed evidence of spectral jumps that led to fluctuations in the fluorescence intensity of the dye.152

1.6.2 Oxazines Oxazines absorb in the red region of the spectrum (
600–700 nm). Examples of commercially available oxazines used in single-molecule work include ATTO655, ATTO680 and ATTO700 (Fig. 1.11).67,68,153 Oxazines generally have higher electron affinities and higher ionization energies than do rhodamine or cyanine derivatives. This results in a lower oxidation tendency, making these dyes more resistant to photobleaching in aerated conditions.68 Most other fluorophores show effectively no blinking in buffers containing both an oxidant (such as N,N-methylviologen, MV) and a reductant (e.g. ascorbic acid, AA) because this combination recovers all triplet and ionized states quickly to the ground state.69 In contrast, single-molecule traces of the oxazine dye ATTO655 in a buffer containing both AA and MV and an enzymatic system to remove oxygen showed frequent transitions to an off (nonfluorescent) state that persisted for hundreds of milliseconds.154 The dark state has been proposed to be the semi-reduced (radical anion) oxazine molecule that is formed by reduction of the triplet state by AA. While MV oxidizes the semi-reduced species of most other fluorophores efficiently, its reaction with the radical anion of ATTO655 is thermodynamically unfavorable. In fact, the radical anion of this and other oxazines is so stable that it has been shown to persist for minutes in the absence of oxidants (e.g. when oxygen is removed using an enzymatic scavenging system).68 These properties can be exploited in the context of superresolution imaging, as it is possible to control the kinetics of switching between on and off states by adjusting the concentrations of oxidizing and reducing agents.44,68 Interestingly, the dye ATTO655 appears to interact strongly with DNA (as judged from the relatively high fluorescence anisotropy measured for an ATTO655-DNA construct), and this interaction shields the dye from redox active agents in solution. This results in on-off blinking kinetics that depends on the position of the label within the DNA.154

1.6 Photophysical properties? of common single-molecule fluorescent probes

FIG. 1.11 Chemical structures of representative oxazine and carbocyanines derivatives used in sm-fluorescence. Alexa Fluor is a registered trademark of Thermo Fisher Scientific. ATTO dyes are products of ATTO-TEC GmbH. The numbers in the Alexa and ATTO dyes indicate optimal excitation wavelengths. The structures of ATTO655 and ATTO680 were obtained from PubChem (PubChem CID: 16218786 and PubChem CID: 16218508).

While the radical ions of rhodamine dyes can persist for hours in solutions containing thiols (Section 1.6.1), oxazine dyes such as ATTO 655 can accept a second electron to form a colorless fully reduced state (the so-called leuco form). The oxidation of the radical anion of ATTO 655 by molecular oxygen is not thermodynamically favorable, so further reduction to a long-lived leuco form is possible.67 This reaction was proposed to proceed via an intermediate consisting of a covalent adduct between the thiol compound and the dye.155

1.6.3 Carbocyanines Cyanine dyes are characterized by two nitrogen atoms linked by a conjugated polymethine chain containing an odd number of carbon atoms. Heterocyclic groups at both ends of the chain are needed for these compounds to be stable.112,156 The most widely used cyanine dyes in biophysical research are Cy3 and Cy5, two indocarbocyanines that differ in the length of the polymethine chain (Fig. 1.11). The longer chain in Cy5 is responsible for the red shift in absorption and emission spectra, making it an ideal acceptor in FRET applications that use Cy3 or other green-absorbing dyes as donors. Other examples of cyanines used in sm-fluorescence are Cy3B, Cy5.5 and Cy7 (GE Healthcare Inc) and Alexa 647 (Thermo Fisher Scientific).

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Unfortunately, the terms Cy3 and Cy5 (which are trademarks of GE Healthcare) are often used indiscriminately to describe related but not identical compounds that differ in hydrophobicity and net charge. For instance, Cy3-type dyes with varying numbers of sulfonate substituents are available from Dyomics (Dyomics GmbH, Germany) under the names DY-547P1, DY-548P1 and DY-549P1, and the phosphoramidite commercialized by Glen Research (Glen Research Corporation, VA) that is used to synthesize end-labeled oligonucleotides is a non-sulfonated version of the dye. The maleimide derivative commercialized by GE Healthcare is sulfonated, but the maleimide commercialized by Abcam (Abcam, MA) as Cyanine3 maleimide is not. These distinctions are often underappreciated and have potentially important consequences in biophysical research. As discussed below, the photophysical properties of these dyes are particularly sensitive to interactions with the DNA nucleotides and proteins, and these interactions in turn depend strongly on the hydrophobicity and net charge of the dye. Cyanine dyes have been extremely popular since the early days of sm-FRET due to their photostability and due to their commercial availability as succinimidyl esters and maleimides in the late 1990s and early 2000s, when the catalog of reactive fluorescent dyes suitable for single-molecule experiments was not as extensive as it is today. The photophysics of cyanine dyes is dominated by a nonradiative transition that originates from the singlet excited state of the thermodynamically stable alltrans isomer and leads to the formation of a ground state nonemissive isomer (cis isomer, Fig. 1.12).112 This process is very efficient for the trimethine cyanines (e.g. Cy3) in fluid solution, resulting in a low fluorescence lifetime and quantum yield.157,158 Values for the trimethine cyanine diIC2(3), a dye with the same chromophore as Cy3 that just lacks the sulfonate moieties, are ϕf ¼ 0.042 and τ ¼ 162 ps in ethanol.158,159 Similar values have been reported for the succinimidyl ester of Cy3 in aqueous buffer.160,161 The fluorescence quantum yield and lifetime of Cy3 do not show a strong dependence on solvent polarity,162,163 but increase strongly with solvent viscosity because a higher viscous drag results in a lower rate of isomerization (kiso, Fig. 1.12).157,158,164,165 Because photoisomerization is a nonradiative process that originates from the singlet excited state, and therefore competes with fluorescence emission, a lower photoisomerization rate due to higher viscosity leads to a higher fluorescence quantum yield and lifetime. As discussed below in detail, the efficiency of fluorescence of Cy3 also increases significantly when bond rotation is sterically hindered by interactions with biomolecules. In addition, rotation is eliminated altogether by chemical rigidization of the polymethine chain, as in the commercially available compound Cy3B (Fig. 1.11).161 Although Cy3 and Cy3B share a common chromophore, the chemical structure of Cy3B eliminates the efficient decay channel that reduces the brightness of Cy3, resulting in significantly higher fluorescence quantum yields and lifetimes (ϕf ¼ 0.68 and τ ¼ 2.8 ns in aqueous buffer).161 The synthesis of a “Cy5B”-type rigidized pentamethine cyanine has been reported,166 but it is not commercially available to date. Isomerization to the cis state is not efficient in the ground state due to the high activation energy for thermal isomerization. Therefore, describing the polymethine

1.6 Photophysical properties? of common single-molecule fluorescent probes

FIG. 1.12 Left- Structures of the trans and cis isomers of Cy3 bound covalently to the 50 terminus of DNA. The red arrow indicates the torsional coordinate that leads to the formation of the isomer. Right- Potential energy diagram for cyanine photoisomerization. The energies of the ground and first singlet excited states are represented as a function of torsion angle (θ). The ground state is present as an all-trans conformation. Following light absorption, the singlet excited state deactivates by competing processes, the most efficient being fluorescence emission (green arrow), internal conversion (not shown) and rotation around a CdC bond of the polymethine chain (kiso). Isomerization from the excited singlet state occurs via a nonspectroscopic partially twisted intermediate (θ ¼ 90°), which deactivates rapidly to the ground state hypersurface to yield the ground state photoisomer (cis), or to return back to the thermodynamically stable all-trans ground state. Once formed, the photoisomer undergoes a thermal back-isomerization reaction to yield the thermodynamically stable all-trans isomer (kthermal). The cis isomer absorbs about 20 nm shifted to the red with respect to the trans isomer and is not fluorescent. Excitation of the cis isomer can also result in photoinduced back-isomerization (kbiso).

chain of cyanine dyes as “highly flexible”, as has been stated in several publications, is a misconception. Instead, bond rotation occurs in the excited state surface due to the significantly lower activation energy for bond twisting compared to the ground state. This process results in a twisted intermediate (θ ¼ 90°) that relaxes into either the trans or cis ground state (Fig. 1.12). The probability that one or the other isomer is formed varies greatly among different cyanines.118 The cis isomer is not fluorescent, and eventually reverts to the trans isomer in a thermal reaction in the ground-state surface (kthermal). This process is typically in the μs-ms timescale, depending on viscosity and steric restraints.118 The absorption spectrum of the cis isomer is shifted only about 20 nm to the red with respect to the trans isomer, and it can therefore also undergo photoinduced isomerization back to the trans isomer (kbiso). All these factors contribute to the relative amounts of trans and cis isomers in photostationary conditions. The effect of viscosity and proximity to biomolecules on fluorescence efficiency has also been observed with the pentamethine dyes such as Cy5 and Alexa 647,

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although to a lesser extent. The fluorescence quantum yield and lifetime of diIC2(5), a dye with the same chromophore as Cy5 and Alexa 647, were reported as ϕf ¼ 0.21 and τ ¼ 0.98 ns in ethanol.167 The higher fluorescence efficiency of diIC2(5) compared to diIC2(3) is due to the higher activation energy for the excited state rotation of the double bond that leads to the formation of the cis isomer. This higher activation energy is also responsible for the reduced sensitivity to viscosity and steric interactions when compared to the trimethine counterparts. Binding of cyanines to biomolecules lowers the efficiency of photoisomerization, resulting in a large increase in fluorescence quantum yield and lifetime. This effect is generally more pronounced in the trimethine cyanines due to their lower energy of activation for photoisomerization in the unbound states. For example, the fluorescence quantum yield of Cy3 conjugated to immunoglobulin G increases by about five-fold with respect to the value of the free dye in aqueous buffer,168 while the lifetime of Cy5 bound to the same protein increases by only 1.5-fold.169,170 The fluorescence quantum yield of Cy3 attached to a helicase-DNA complex was observed to vary in the range 0.27–0.48 depending on the amino acid used for labeling the protein.110 This represents an approximately 5 to 10-fold increase compared to the free dye. Interestingly, the lowest quantum yield values were measured for Cy3 bound to two sites in a flexible domain of the protein, where isomerization is presumably less hindered, while the highest values were determined for residues in closer contact to the DNA. In contrast, the fluorescence quantum yield of Cy5 bound to the γ-subunit of F1-ATPase is practically the same as the free dye.171 The cyanines Cy3, Cy3B and Cy5 have been shown to interact with the DNA bases in a sequence–dependent manner.80,81,83,88,109,118,172–174 Interactions between Cy3 and the DNA bases were shown to decrease the efficiency of photoisomerization, resulting in higher fluorescence quantum yields and lifetimes. Reported values vary widely depending on DNA sequence, secondary structure, linker type and length, and attachment position (50 ,30 , or internal).111,160,175 In the case of Cy3B, which cannot isomerize, these interactions do not lead to significant changes in the fluorescence properties of the dye, but are still relevant to FRET studies in the context of the kappa-square problem because they reduce the mobility of the dye. The pronounced sensitivity of Cy3’s fluorescence to interactions with biomolecules can be a nuisance in many single-molecule experiments because it translates into fluctuations in the fluorescence intensity of the dye that may confound fluctuations due to other sources. At the same time, this sensitivity can be rationally used to probe changes in the local environment of the fluorophore during a biochemical process. This concept is the basis of the approach known as PIFE (protein-induced fluorescence enhancement),176 where the increase in the fluorescence quantum yield of Cy3 is used to monitor the proximity of a protein to a Cy3-labeled DNA (or RNA) base.177–182 The correlation between fluorescence enhancement and reduced photoisomerization efficiency has been demonstrated experimentally using complexes of DNA bound to the Klenow fragment by means of time-resolved fluorescence and transient spectroscopy techniques.183 The authors were able to monitor the formation of the cis isomer directly, proving that the enhancement of Cy3 fluorescence

1.6 Photophysical properties? of common single-molecule fluorescent probes correlates with a decrease in the efficiency of photoisomerization, and occurs in conditions where the dye is sterically constrained by the protein.183 PIFE is an attractive approach because it provides proximity information at short distances where FRET is not sensitive without the need of labeling the protein. As an example, Fig. 1.13 shows data obtained by Myong et al.,179 who coined the term PIFE to refer to this type of proximity-induced fluctuations in fluorescence.177 Dramatic fluctuations in fluorescence intensity were observed during single-molecule fluorescence experiments investigating the protein RIGh complexed with dsRNA. The nucleic acid was labeled with DY547 (a trimethine cyanine similar to Cy3) as shown in the figure. Importantly, these fluctuations were not observed in control experiments without RIGh or in the absence of ATP, allowing the investigators to conclude that the observed fluctuations were due to a newly-discovered ATP-powered dsRNA translocation activity that resulted in a repetitive movement of the enzyme on the RNA molecule. FRET experiments with fluorescently labeled RNA and RIGh confirmed that the fluctuations in DY547 fluorescence correlated with the changes in enzymeDY547 distance. Eq. (1.10a) provides a way to rationalize these observations in terms of changes in the effective quantum yield of the dye due to interactions with the protein. On one hand, and as demonstrated with other proteins,177,183 the fluorescence quantum yield of the dye increases when in close proximity to the protein. In addition, it is possible that fssA(S0), the fractional concentration of molecules in the

FIG. 1.13 PIFE visualization of RIG-I translocation on dsRNA.179 A 25mer dsRNA containing a DY547 fluorophore was bound to a surface for single-molecule visualization. Addition of the protein RIG-I (blue) resulted in abrupt fluctuations in the fluorescence intensity of the dye in the presence of ATP, consistent with a previously unknown ATP-powered dsRNA translocation activity. The data for the figure was generously provided by Prof. Sua Myong (Johns Hopkins University).

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ground state, increases as well because the lower efficiency of photoisomerization leads to a lower fractional concentration of cis (nonemissive) states. As already mentioned in the introduction, the formation of long-lived dark states of Cy5 in thiol-containing buffers was one of the first observations of persistent blinking in single-molecule fluorescence. Additional research led to the observation that the red-absorbing cyanine dyes Cy5, Cy5.5, Alexa 647 and Cy7 can be photoconverted into a dark state by illumination with red light in the presence of primary thiols and in the absence of oxygen.184,185 As an example, a Cy5 molecule bound to DNA can be switched ‘on’ and ‘off’ in a buffer containing β-mercaptoethylamine by alternating the excitation between 633 nm and 488 nm.184 Intriguingly, switching of these red-emitting dyes is facilitated by direct excitation of a secondary chromophore (an ‘activator’) such as Alexa 405, Cy2, TMR,186 although the exact mechanism for the activation process is still unknown. Photoswitching occurs in the presence of a primary thiol, and was initially thought to be related to the quenching of the triplet state. However, it was quickly recognized that other triplet quenchers did not yield the same results, and subsequent studies identified the formation of an adduct between the primary thiol compound and the cyanine that interrupts conjugation, and is therefore believed to be responsible for the observed loss of fluorescence.41 Yet, there are still some unanswered questions regarding this mechanism. For example, it is not entirely clear how the system is switched back to the fluorescent state, and how activators allow the switching to the off state to be performed at relatively low laser powers. As discussed in Section 1.6.2, the formation of a thiol-oxazine adduct was proposed to be an intermediate in the reduction of ATTO655 by 2-mercapthoethanol.155 The redox reaction between flavin and thiols was also shown to proceed via a covalent adduct which then breaks down to produce a reduced flavin and a disulfide compound.187,188 In the case of ATTO655, reduction to the leuco form occurs via further reduction of the semi-reduced oxazine, and consistent with this mechanism, fluorescence is partially restored upon excitation at 405 nm (absorption maximum of the radical anion). The fluorescence of Cy5 can be restored by illuminating at ca. 500 nm, where the radical anions of related cyanines have been shown to absorb.189 Therefore, it is possible that the radical anion of the cyanine is involved in the photoswitching mechanism of these dyes, and that the thiol adduct observed by mass spectrometry41 is formed by reaction of the thiol with the radical anion of the dye.67

1.7 Concluding remarks At this point, it would be tempting to recommend particular probes for different applications. Yet, the fact that well-established research labs around the world have different preferred probes for seemingly similar applications reflects the many considerations that go into choosing probes for single molecule experiments. A nonexhaustive survey of recent publications shows that the following FRET pairs are popular choices for in vitro single-molecule FRET applications with labeled nucleic

1.7 Concluding remarks

acids and proteins: Cy3/Cy5,190–195 Cy3B/ATTO647N,196,197 Alexa Fluor 488/ Alexa Fluor 594,198–200 ATTO550/ATTO 647N,22,201–203 ATTO550/Alexa 647,22,204 ATTO 488/Alexa 647,149 ATTO 488/ATTO647N,205 and Alexa Fluor 555/Alexa Fluor 647.206 It is clear, therefore, that many FRET pairs can be successfully used in single molecule research as long as researchers understand what the critical variables are for the success of their own experiments. No dye outperforms the rest in every aspect. For example, while Alexa Fluor 647 is often preferred over ATTO647N due to the hydrophobicity of the latter, a recent multi-laboratory study comparing the precision and accuracy of distances inferred from single-molecule experiments concluded that ATTO 647N was a better choice. This is likely because the photophysics of Alexa Fluor 647 (a cyanine) is complex, and as discussed in this chapter in detail, relating single molecule fluorescence intensities to the true efficiencies of FRET is not straightforward. Some applications require only rough estimates of the FRET efficiencies to determine the kinetics of interconversion between a limited number of conformational states (Fig. 1.1), so issues such as how labeling restricts the dye’s mobility or perturbs the dye’s quantum yield are not usually a source of concern. Therefore, although Cy3-DNA interactions complicate the treatment of the kappa-square factor (see Section 1.2.4), and alter the dye’s fluorescence quantum yield (see Section 1.6.3), this dye is still an excellent choice for experiments that do not require precise determinations of the FRET efficiency. On the other hand, Alexa 488 (see Section 1.6.1) appears to be a better choice when restricted mobility is a problem (e.g. for the treatment of the kappa-square factor), but unlike Cy3, Alexa 488 is known to be quenched by guanosine and the aromatic amino acids (see Section 1.2.5). ATTO555 was also successfully used as a donor in studies of dsDNA aimed to illustrate the use of single molecule FRET as a tool to determine distances with atomic-scale resolution.22 However, more research is needed to demonstrate if the same precision can be achieved in studies with proteins. In addition, choosing dyes is not necessarily the only important decision in the successful design of a single-molecule experiment. Immobilization and passivation strategies, buffers, and technical aspects of the acquisition and analysis of the signals play an equally important role. We refer the reader to the excellent article by Gust et al.152 for a discussion on buffers that can be used to minimize blinking and photobleaching, guidelines on immobilization and passivation strategies, and for a summary of spectroscopic properties of common probes. Readers should keep in mind that some of these spectroscopic properties depend strongly on the environment, and may change when dyes are conjugated to biomolecules. The characterization of all labeled materials and the design of proper control experiments is always crucial. Finally, the importance of planning and executing experiments to address potential detrimental effects of the fluorescent labels must not be understated. There are no systematic studies addressing the problem of potential probe interference, so researchers should approach projects with a healthy dose of cautious skepticism and design control experiments to ease concerns. Experiments with the protein

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calmodulin labeled with different FRET acceptors paired with the same donor suggest that the net electrical charge of the dye is an important variable to rationalize dye-protein interactions and how they may affect the protein conformational landscape.31 Still, it would be premature to assume that the conclusions of this particular research can be used as universal guidelines for probe selection. For instance, while a dye with zero net charge affected the conformational landscape of calmodulin,31 combinations of dyes with net negative, zero or positive charges yielded the same results in studies of the interaction of the linker histone H1 with a highly negatively charged intrinsically disordered protein.200 The latter is an excellent example of how carefully executed control experiments using dyes with different net charges eased concerns about potential perturbations of the protein-protein interactions that were the subject of the research.

Appendix The kinetics of the two state system can be modeled as a simple reversible chemical reaction that follows first order kinetics in both directions: k12

S0 > S1 k21

The rate law for the reaction is: d ½S0  ¼ k12 ½S0  + k21 ½S1  dt

(1.A1)

and [S1] ¼ [S0]0  [S0] (mass balance). Here, [S0]0 is the initial (t ¼ 0) concentration of S0, and the initial concentration of S1 is taken as [S1]0 ¼ 0. Eq. (1.A1) is a separable ordinary differential equation that can be readily solved to give:   ½S0 0 k21 + k12 eðk12 + k21 Þt ½S0  ¼ k12 + k21

(1.A2)

The time-dependent concentration of [S1] is then [S1] ¼ [S0]0  [S0], where [S0] is given by Eq. (1.A2). In the photostationary state (t ! ∞): ½S0 eq ¼

½S0 0 k21 k12 + k21

(1.A3a)

½S1 eq ¼

½S0 0 k12 k12 + k21

(1.A3b)

And the fractional concentrations of S0 and S1 in equilibrium can be expressed as fss ðS0 Þ ¼

½S0 eq k21 ¼ ½S0 0 k12 + k21

fss ðS1 Þ ¼ ½S1 eq =½S0 0 ¼

k12 k12 + k21

(1.A4a)

(1.A4b)

References

For the 2-state system discussed in Section 1.3.1, k12 is defined in Eq. (1.8), and k21 is 1/τ, where τ is the lifetime of the excited state. Eq. (1.A2) can be then used to generate the traces shown in Fig. 1.6B (f(S1) ¼ [S1]/[S0]0) and Eqs. (1.A4a), (1.A4b) can be used to obtain Fig. 1.6C. Note that the concept of chemical equilibrium does not apply to the situations described in Section 1.6, but the mathematical description of the photostationary state (the state at which the rates of formation and disappearance of each transient entity are equal) is mathematically analogous. The 3-state system of Fig. 1.7A can be modeled as: k12

S0 > S1 k21

k23

S1 ! T1 k31

T1 ! S0

and the differential equations that describe the dynamics of the system are d ½S0  ¼ k12 ½S0  + k21 ½S1  + k31 ½T1  dt

(1.A5a)

d ½S1  ¼ k12 ½S0   k21 ½S1   k23 ½S1  dt

(1.A5b)

d ½T1  ¼ k23 ½S1   k31 ½T1  dt

(1.A5c)

This system of linear ordinary differential equations can be solved exactly with initial conditions[S0](t ¼ 0) ¼ [S0]0, [S1](t ¼ 0) ¼ [T1](t ¼ 0) ¼ 0. However, for the purpose of this exercise, numerical solutions can be readily obtained using any mathematical software to generate the lines of Fig. 1.7B–D.

Acknowledgments The author thanks professors Amit Meller, John van Noort, Sua Myong and David Lilley for their generosity in sharing data to create several of the figures presented in this chapter. Mr. Gabriel Salmon, Ms. Nikita Kumari and Mr. Christopher Dilli proofread the manuscript and provided valuable feedback.

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Probing dynamics in single molecules

2

Clemens-B€ assem Salem, Evelyn Ploetz, Don C. Lamb Department of Chemistry, Center for NanoScience, Nanosystems Initiative Munich (NIM), and Center for Integrated Protein Science Munich (CIPSM), Ludwig Maximilian University of Munich, Munich, Germany

2.1 Introduction and overview The combination of F€ orster Resonance Energy Transfer (FRET) spectroscopy with single molecule experiments has opened a new window to uncover the biological pathways and conformational dynamics of biological systems under native conditions. While methods such as electron microscopy or X-ray scattering can give important insights into the structure and composition of proteins, there is limited information regarding dynamics. Since the function of proteins is intimately linked to their structure via dynamics, it is important to investigate these sensitive complexes nondestructively under native conditions. The interactions of biological compounds are often strongly heterogeneous. Hence, experiments with single molecule sensitivity are essential for detecting and investigating these heterogeneities. Since its first application in 1990,1,2 single molecule fluorescence microscopy has become a powerful tool for studying the function of biomolecules.3 In 1996, the first singlemolecule FRET (smFRET) experiments were performed.4 FRET exploits the distance-related quenching probability of a fluorescent donor molecule’s emission in proximity to an acceptor molecule due to nonradiative energy transfer with max˚ .5–8 Depending on the biological question at hand, imum sensitivity around 40 to 70 A various FRET-based methods were developed to quantify intramolecular distance fluctuations between fluorescently labeled molecules over a wide range of time scales (for an overview of time and size scales, see Fig. 2.1). The rotation of sidechains and short-lived interactions between polypeptides happen on the nanosecond timescale and often govern the structural dynamics of intrinsically disordered proteins (IDFs).9 Protein folding processes occur on the micro- to millisecond time range and are being extensively investigated. Slower conformational dynamics starting from minutes and hours are often observed in misfolding and oligomerization that lead to, for example, prion formation, which is linked to many neurodegenerative diseases in animals and humans. Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.00002-X # 2019 Elsevier Inc. All rights reserved.

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FIG. 2.1 Time scales and methods for following single molecule dynamics. Intramolecular dynamics cover a wide range of time scales that define the necessary experimental methods for their investigation. Molecular rotations occur on the picosecond time range, while conformational changes take place in microseconds as in peptide dynamics of disordered proteins to milliseconds for protein folding. Transitions along energetically unfavored pathways can take hours to years, as in prionic misfolding. Picosecond to microsecond processes require fast time-correlated detectors and are typically examined in solution with confocal methods such as Fluorescence Correlation Spectroscopy (FCS) and Multiparameter Fluorescence Detection with Pulsed Interleaved Excitation (MFD-PIE) (A). Conformational states are identified in the FRET efficiency distribution of many single-molecule events (B). Experiments at far-from equilibrium concentrations over extended periods of time can be performed with microfluidic mixing chambers (C) or by immobilizing individual molecules using trapping methods or on the surface, e.g. in vesicles (D). Surface-immobilization permits the application of array-detectors to investigate multiple individual molecules inside their field of view. In contrast to freely-diffusing solution experiments, information is gained from the very same molecules and only limited by fluorophore photobleaching instead of averaging across many momentary snapshots of molecules. The analysis can be hence focused onto small heterogeneous fractions otherwise hidden in bulk distributions (E). For more information, see the main text. Reprint with permission from Schuler, B.; Hofmann, H. Single-Molecule Spectroscopy of Protein Folding Dynamics—Expanding Scope and Timescales. Curr. Opin. Struct. Biol. 2013, 23 (1), 36–47.

2.1 Introduction and overview

There are two approaches for studying biological molecules with smFRET: either data are collected from individual molecules freely diffusing in solution or measurements are performed on molecules that are immobilized. For solution-based measurements, a confocal microscope is used and the FRET efficiency is determined from the photons collected as the molecule diffuses through the probe volume. Hence, one typically obtains a snapshot of the conformation of the protein. However, fast dynamics can be extracted from solution-based measurements using, for example, nanosecond fluorescence correlation spectroscopy (ns-FCS, Fig. 2.1A),10 pulsed interleaved excitation combined with fluorescence cross-correlation spectroscopy (PIE-FCCS)11,12 and multiparameter fluorescence detection (MFD) with burst analysis (MFD-PIE).13,14 Structural and dynamic information can be gained from the smFRET distribution measured from thousands of single molecules (Fig. 2.1B). Dynamics can also be investigated on the millisecond to second timescale with the aid of microfluidic devices (Fig. 2.1C). For more information on smFRET experiments in solution, we refer to Chapter 6 by Hugo Sanabria. When extended time trajectories from individual molecules are desired, the molecules need to be somehow contained within the observation volume. This can be done, for example, using optical tweezers,15 atomic force microscopy (AFM)16 or electro-kinetic feedback traps.17 The standard approach to measure surfaceimmobilized molecules using fluorescence is with total-internal reflection fluorescence (TIRF) microscopy for excitation and widefield (WF) detection using a sensitive imaging pixel array detector or camera. Total internal reflection illumination is preferred to WF-excitation due to the reduced background signal from the smaller illumination volume, leading to an increase in the signal-to-noise ratio (SNR).18 Molecules can be immobilized by tethering them to a previously passivated surface via linker molecules such as biotin to (strept-)avidin on the surface,19 encapsulating them in liposomes (Fig. 2.1D)20–22 or attaching them to DNA-origami scaffolds that are already immobilized on the passivated microscope slide.23 The FRET signal can then be followed continuously or intermittently for the same molecule from seconds to hours (Fig. 2.1E), the timescale being limited by the desired time resolution and the stability of the fluorophore. Alternating excitation schemes can be used to gain additional information about labeling stoichiometry of the complex and the photophysical state of the acceptor fluorophore.24 Due to the sequential readout process required for imaging, cameras have slower sampling rates compared to point detectors (e.g. avalanche photodiodes or photomultiplier tubes). Typical integration times start from milliseconds, posing a lower limit to the time resolution of conformational dynamics. In this chapter, we will focus on surface-immobilized molecules measured with TIRF microscopy. We begin with insights into the methodology of FRET, the required instrumentation in the form of a widefield fluorescence microscope with total internal reflection illumination and immobilization techniques. Upon collection of the data and extraction of the smFRET traces, we will and discuss the application of advanced data analysis using Hidden Markov Modeling (HMM) to recover states and transition kinetics hidden within the data. We end the chapter with an example of

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a smFRET study on the interaction of TATA-box binding protein with DNA in the presence of the negative cofactor 2.25

2.2 Single molecule FRET microscopy 2.2.1 Fluorescence Fluorescence is often used for single molecule investigations as it can be measured in small volumes with high sensitivity. It provides specificity by the fluorescent label and does not require contact with the sample. Fluorescence describes the phenomenon of light emission from a molecule during relaxation from a higher excited electronic singlet state to the ground state when the excited state is populated via absorption of light (shown schematically in the Jablonski diagram in Fig. 2.2A). It is also possible for molecules to be de-excited via other, potentially non-radiative pathways leading to a decrease in fluorescence signal. The emission efficiency, i.e.the ratio of absorbed to emitted photons is given by the fluorophore’s quantum yield Φ. Electronic transitions occur on the time-scale of femtoseconds, quasi instantaneous in comparison to nucleic motion. Upon the absorption of a photon with sufficient energy, an electron is transferred to a new vibrational level in the electronic excited state. The most probable transitions are those with the highest overlap between the vibrational wave functions of the electronic ground state and excited state, giving rise to the shape of the absorption spectrum (Franck-Condon principle). This typically results in the excitation to higher-order vibrational states, which quickly relax to the lowest energy level of the electronic excited state (see Fig. 2.2A). Fluorescence emission then occurs from lowest energy level of the electronic excited state (Kasha’s rule,26 typically S1) to the electronic ground state via photon emission. Hence, the fluorescence emission spectrum is independent of the excitation wavelength. In the electronic excited state, the surrounding solvent reorganizes, which leads to a decrease in the energy of the electronic excited state. As during excitation, the most likely transitions leading to fluorescence emission occur where the vibrational states have the highest overlap, which again is typically not the vibrational ground state. As the vibrational energy levels of the singlet ground and excited states are similar, the emission spectrum of the S1 ! S0 transition often mirrors the absorption spectrum (S0 ! S1, see Fig. 2.2B). Taken together, these factors lead to a spectral shift between the maxima of absorption and emission spectra, referred to as the Stokes shift. While the emission spectrum is discrete in the gaseous phase, it is heterogeneously broadened to a continuous spectrum in the liquid phase. The lifetime of the excited states in fluorophores is typically on the nanosecond scale. Molecules in the singlet state S1 can interconvert to the triplet state T1 via spin conversion. A direct return to the singlet ground state S0 is then quantummechanically forbidden and leads to long lifetimes of triplet states in the μs to ms time scale. When a photon is emitted during the transition from the triplet state

2.2 Single molecule FRET microscopy

FIG. 2.2 Mechanism of fluorescence, phosphorescence and FRET. (A) Jablonsky energy diagrams. After absorption of a photon, the molecule transits from the electronic ground state S0 to the first or higher electronic singlet state Sn. After direct excitation to the first excited electronic state respectively internal conversion from e.g. S2 – followed by vibrational relaxation into the vibrational ground state, the molecule can de-excite by three pathways: (i) fluorescence, (ii) non-radiatively to S0 via internal conversion and (iii) phosphorescence after intersystem crossing into the first triplet state T1. In the presence of an acceptor, energy can also be transferred via F€orster resonance energy transfer. (B) Spectra of commonly employed fluorophores suitable for 3-color FRET. Excitation spectrum (dashed lines) and emission spectrum (solid lines) of fluorophores Atto488, Atto565 and Atto647N dissolved in PBS. Fluorescent emission is usually detected within spectral detection windows (solid areas) defined by the chosen emission filters. (C) Distance relationship of FRET. The transfer efficiency between donor and acceptor follows a sigmoidal shape and is proportional to the inverse 6th power of the interdye-distance. The F€orster radius R0 denotes the distance at which the FRET transfer efficiency equals 50%. FRET is most sensitive in a range of 20 A˚ around R0. Fo€rster radii of common FRET pairs are found between 40 and 70 A˚.

T1 to the singlet ground state S0, the processes is referred to as phosphorescence. During the time the molecule is in a triplet state, it is not emitting photons and the molecule is dark. In smFRET applications, these “dark” states are undesired. Hence, stabilizing and triplet quenching agents are often added to the imaging buffer to minimize the time a molecule spends in the triplet state.27,28

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2.2.2 F€ orster resonance energy transfer (FRET) A powerful method for determining distances on the molecular scale is FRET, a phenomenon first described correctly by T. F€orster in 1946.5 Briefly, FRET describes the effect of the distance-dependent transfer of energy between two molecules via dipole-dipole interactions. More specifically, the electromagnetic field formed around a dipole emitter can be discriminated into a far-field component, whose amplitude decreases with 1/R, and an evanescent near-field component with higher power-decays. At distances shorter than one oscillation wavelength, the near-field typically dominates. In contrast to the far-field, the near-field possesses phase-related non-radiative components that are either fed back into the dipole or can couple to a nearby receiver. Contrary to radiation emitted in the far-field, energy absorbed in the near-field has direct feedback on the emitter, an effect that is exploited in resonant energy transfer and other near-field optical microscopy methods.29,30 The efficiency of FRET between a donor molecule and a nearby acceptor molecule depends on the respective fluorescence emission and absorption spectra of the molecules, their relative orientation and the distance between them. The rate of energy transfer between both dyes is inverse proportional to the lifetime of the donor τD in absence of the acceptor and the distance between both to the 6th power. It is given by: kFRET ¼

R60 9000  ln10  κ 2  ΦD ¼  J ðλ Þ 6 τD  R 128  π 5  NA  n4  τD  R6

(2.1)

Here, the F€ orster Radius R0 refers to the distance at which the energy transfer efficiency is 50%. It is defined as: R60 ¼

9000  ln10  κ 2 ΦD  J ðλ Þ 128  πð5  NA  n4

(2.2)

with J ðλÞ ¼ fD ðλÞEA ðλÞλ4 dλ

The F€ orster radius R0 is specific to the donor-acceptor-pair used for FRET and dependent on the relative spatial orientation of donor and acceptor dipole moments, described by the orientation factor κ. It is further proportional to the donor quantum yield ΦD, refractive index n of the medium, Avogadro’s number NA and the spectral overlap integral J(λ), in particular the normalized donor emission fD and the molar acceptor extinction EA. The FRET efficiency, i.e. the quantum yield of the energy transfer is usually expressed as the ratio between the rate of energy transfer kFRET and the intrinsic excited state decay rate kD of the donor (Eq. 2.3). By employing the inverse relation between rates and lifetimes, the FRET efficiency can be linked to a distance. This distance relationship of FRET efficiency follows an inverse 6th-power law and is calculated as: R60 kFRET R6 1 τD  R6 EFRET ¼ ¼ ¼ 6 0 6¼  6 6 kD + kFRET 1 R0 + R R0 R + 1+ τD τD  R6 R60

(2.3)

Acceptor quenching of the donor reduces the fluorescence emission of the donor. Comparing emission rates from experiments with and without an acceptor allows

2.2 Single molecule FRET microscopy

calculation of the transfer efficiency and distance using the equations below. For detection methods that cannot resolve the fluorescence decay times in the range of nanoseconds, which is the case for most camera-based methods, the same relationship holds true for the ratio of averaged intensities. EFRET ¼ 1 

τDðAÞ IDðAÞ ¼1 τDð0Þ IDð0Þ

(2.4)

Here, the fluorescence lifetime of the donor in the presence and absence of the acceptor are denoted as τD(A) and τD(0), respectively; the corresponding intensities as ID(A) and ID(0). When the acceptor is fluorescent, the FRET efficiency can be calculated from the enhanced fluorescence of the acceptor. When measuring FRET on a single molecule, we can take advantage of knowing that the molecule contains a single donor and a single acceptor fluorophore (i.e. the sample of one molecule has a labeling efficiency of 100%) and the FRET efficiency can be determined from the ratio of average acceptor fluorescence intensity to total fluorescence intensity of acceptor and donor after donor excitation as: EFRET ¼

IDA IDA + IDD

(2.5)

The intensities IDD and IDA refer to the donor and acceptor emission after donor excitation, respectively. Provided the donor and acceptor molecules (and thus dipole moments) are free to rotate on a timescale much faster  than the fluorescence lifetime of the donor, an average orientation factor of κ 2 ¼ 2 3 can be assumed.5,31 With restricted rotational freedom, i.e. due to steric hindrance, the value for κ2 deviates and should be determined by polarization-sensitive spectroscopy.32 Experimentally, donor and acceptor fluorescence emission are spectrally separated using suitable dichroic mirrors and emission filters and individually measured with photosensitive detectors. The FRET efficiency is calculated from the ratio of acceptor fluorescence intensity to total intensity of acceptor and donor channel using Eq. (2.5) along with a few correction factors. More details regarding the experimental aspects of the measurements can be found in Sections 2.2.3 through 2.2.7.

2.2.3 Widefield – Total internal reflection fluorescence (WF-TIRF) microscopy The initial single-molecule experiments on immobilized molecules were performed using near-field microscopy to minimize background contributions.30 In contrast to probing single molecules separately, WF microscopy allows imaging of an entire field of view on a camera, and hence the simultaneous investigation of hundreds of single molecules. To decrease background signal, the depth of the excited volume is typically reduced by using the evanescent wave field formed during total internal reflection illumination at the prism-buffer interface or objective-type TIRF microscopy where a high numerical objective allows illumination of the sample at angles larger than the critical angle (see Fig. 2.3 for particulars of our setup).

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FIG. 2.3 (See figure legend on opposite page)

2.2 Single molecule FRET microscopy

Total internal reflection When crossing the boundary between two media of different indices of refraction, n1 and n2, light is refracted according to Snell’s Law (Eq. 2.6). When the refractive index of the first medium is greater than that of the entered medium, the angle of refraction increases with respect to the surface normal. When applied for microscopy, this interface is typically between a glass or quartz coverslip and an aqueous sample solution. sinθ2 n1 ¼ sinθ1 n2

(2.6)

When the incoming angle θ1 reaches the critical angle θC, the refracted angle is 90°, meaning that the light travels along the interface.   n2  θC ¼ arcsin n1 θ2 ¼90°

(2.7)

At angles beyond the critical angle, the incident light cannot be transmitted into the second medium and is totally reflected at the interface. At the interface, an evanescent wave forms with an exponentially decaying penetration depth. The wavelengthdependent penetration depth d is given by d¼

  1  λ  2 2 n1 sin θ  n22 2  4π θθC

(2.8)

FIG. 2.3, CONT’D Camera-based single molecule FRET imaging. (A) A widefield setup for prism- and objective-type TIRF microscopy equipped with ALEX. Excitation light is alternated with an AOTF and selectively coupled into a single-mode fiber for either objective- or prism-type TIRF illumination. In pTIRF (upper right panel), light is focused through the prism onto the interface with the sample volume above the critical angle to achieve TIRF. For oTIRF (middle right panel), light is focused onto the back-focal plane of an oil-immersion objective while being shifted parallel to the optical axis to hit the coverslip with immobilized molecules above the critical angle for TIRF illumination. For both excitation types, sample slides feature channels for stopped-flow experiments. The slides and quartz-prism are silanized and surfacepassivated with PEG/PEG-Biotin for exclusive immobilization of biotinylated sample molecules via streptavidin. Emission of the sample is spectrally separated by dichroic mirrors and filters suitable for three-color FRET and detected by emCCD cameras. The camera detection and sample exposure to millisecond alternated laser excitation are synchronized via a micro controller, such as an FPGA. Legend: AOTF: acousto-optical tunable filter, C: collimator, D: dichroic mirror, F: optical filter, M: mirror, Obj: microscope objective, SM: switchable mirror. (B) Data extraction from smFRET TIRF movies. (left) A calibration pattern is used to match the field of view of all cameras and create a coordinate transformation map. (mid) Data movies are loaded, molecule PSFs are localized and matched across cameras to identify FRET partners. (right) Intensity traces of pixels inside a particle mask are extracted. FRET efficiencies are calculated per FRET pair.

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Here, λ denotes the wavelength of the incident light. In TIRF microscopy, the penetration depth is typically on the order of 100–200 nm. Further information can be found in Ref. 33. The low penetration depth of TIRF illumination is utilized in TIRF microscopy to confine the excitation light to a thin layer near the surface where the molecules of interest are immobilized. TIRF illumination has the advantage that the surface immobilized molecules are well excited and the emitted fluorescence is detected with high sensitivity, but the background is reduced due to the smaller illumination volume. Typical sources of background in fluorescence spectroscopy are fluorescent impurities in the buffer, elastically scattered light and Raman scattering. By reducing the excitation volume, these types of background signals are also reduced and thus an increased signal to noise ratio (SNR) is obtained with respect to classic WF excitation. The most common experimental realizations are described in the following two sections.

Prism-based TIRF (pTIRF) microscopy In prism-based TIRF (pTIRF) microscopy, total internal reflection is achieved by directing the excitation light externally onto one side of a fused silica prism to strike the boundary to the sample medium sandwiched between the prism and the coverslip at an angle above the critical angle (see Fig. 2.3A top right). This approach has the advantage that a dichroic mirror separating excitation and emission light is not required. It also simplifies the alignment of the excitation beams when exciting with multiple wavelengths compared to objective-based TIRF (oTIRF) microscopy described below. The excitation spot is focused manually and centered in the microscope objective’s field of view for optimal excitation power density. Due to the distance of the prism surface from the microscope coverslip (100 μm), a water immersion objective is typically used. Using a higher numerical aperture oil immersion objective to focus through such a distance of buffer leads to a distorted point-spread-function and a decrease in the collection efficiency.

Objective-based TIRF (oTIRF) microscopy In oTIRF microscopy, the excitation light is focused onto the microscope objective’s back focal plane as in widefield excitation but laterally shifted from the optical axis. The amount of displacement from the center axis determines the angle at which the light exits the objective and impinges on the coverslip/buffer interface. When the numerical aperture of the objective is sufficiently large (above 1.40), the angle between the excitation beam and normal to the coverslip can exceed the critical angle and total internal reflection occurs inside the microscope coverslip at the boundary to the sample medium. Contrary to pTIRF microscopy, access to the sample volume from above is unrestricted and it is thus comparatively easy to install additions such as microfluidic systems for stopped flow and mixing experiments.34 Compared to pTIRF microscopy, oTIRF microscopy typically has a higher amount of background signal from auto-fluorescence and internal scattering in the

2.2 Single molecule FRET microscopy

microscope objective and microscope coverslip. These disadvantages are largely compensated for by the increased number of collected photons in oTIRF due to the higher numerical aperture of the used objectives.35 In addition, the radiation pattern of fluorescence coming from fluorophores close to the glass surface do not follow the normal dipole pattern but preferentially emit into the coverslip.35,36 An alternative approach to pTIRF microscopy or oTIRF microscopy is lightguide based (LG) TIRF microscopy.37 Here, the excitation light is coupled into the thin edge of a microscopy coverslip to achieve total internal reflection inside the coverslip. The beam is repeatedly reflected between upper and lower surface of the slide, producing an evanescent wave-field at each interface. LG-TIRF microscopy that employs an inverted microscope has the same advantage as oTIRF microscopy: the sample is accessible from the top so that other types of sample manipulations can be performed in parallel.

2.2.4 Alternating laser excitation (ALEX) Single-pair FRET measurements can be performed using a single excitation wavelength and two detection channels. However, in practice, samples are never 100% labeled with a 1:1 stoichiometry of photoactive donor and acceptor molecule. There is always a mixture consisting of double-labeled, “donor only” and “acceptor only” labeled molecules or complexes. Signal from a donor only molecule can often be difficult to distinguish from a low FRET signal. In addition, temporary nonfluorescent (“dark”) states of the acceptor can raise the false impression of dynamic state transitions from the FRET traces. These difficulties can be circumvented by performing millisecond alternating laser excitation (msALEX) in combination with TIRF microscopy. In ALEX, excitation of fluorophores is modulated by cycling between donor and acceptor excitation.38 With msALEX, it is possible to monitor the photophysical state of the acceptor fluorophore independently from the donor signal and to directly determine labeling efficiency and stoichiometry. When performing three- or four-color FRET experiments where a dye can act simultaneously both as an acceptor and donor, multicolor ALEX is essential to extract separate FRET efficiencies for each acceptor.39–41 When using ALEX, it is possible to quantify the intensity contributions from direct excitation of the acceptor by the donor excitation laser and spectral crosstalk of the donor fluorophore into the acceptor channel (as described below). This comes at the cost of a reduced time resolution of the FRET measurements. Alternatively, one can vary the number of frames with donor excitation between acceptor excitation, an approach referred to as duty cycle optimized ALEX (DCO-ALEX).42 If acceptor blinking can be neglected due to a proper choice of fluorophores and/or photostabilizing agents in the imaging buffer, a good strategy might consist of direct acceptor excitation for a low number of frames before continuous donor excitation. This facilitates detection of properly labeled donor-acceptor compounds during data evaluation while maintaining a maximum time resolution for more precise investigation of dynamic FRET state transitions.

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The duration of a smFRET measurement is limited by photobleaching and -blinking of either the donor or acceptor fluorophore. The time-resolution is determined by the frame rate and number of detected photons. By increasing laser power and reducing the applied exposure time, one can increase the time resolution at the cost of the duration, since the total number of photons is limited via photobleaching. Various classes of fluorophores such as xanthenes (Atto488, Atto532, TMR), oxazines (Atto655), carbopyronines (Atto647n) or cyanines (Cy3(B), Cy5, Alexa647) are employed for smFRET experiments. As these fluorophores have different demands in terms of photostability,43 certain dye pairs like Cy3/Cy5 or TMR/ Alexa647 are frequently employed for smFRET.27,44,45 To increase their overall photostability, oxygen scavenging systems are important. The triplet state plays an important role with respect to photobleaching and blinking. Continuous excitation of the fluorophore renders intersystem crossing to the triplet state possible. Since the triplet state lives on the micro- to millisecond time scale, molecules that cycle to the triplet state will appear dimmer or off. They will return to the electronic ground state primarily by quenching with oxygen under the creation of singlet oxygen, which is responsible for irreversible photodamage of fluorophores. Enzymatic oxygen removal systems prevent the formation of singlet-oxygen and thereby protect the chromophore. To quench the resulting triplet-state, various strategies for photostabilization based on geminate recombination,45 Dexter energy transfer46 or reducing and oxidizing systems (ROXS)46 have been developed extending the fluorophores lifetime e.g. for Cy5 from seconds to several minutes. Of course, the chemical components of the buffer need to be compatible with the system measured (i.e. biological sample). This is particularly important when using ROXS, but other factors such as pH and salt content need to considered as well. When long-term FRET experiments are desired, photostability of the fluorophore can be further supported by interrupting the illumination beam to extend average survival times before photobleaching.

2.2.5 Camera-based detection In addition to the reduced background when using total internal reflection excitation, smTIRF experiments have the advantage of detecting many individual molecules in a single measurement since wide-field detection can be used. Movies containing hundreds of immobilized molecules within the field of view are recorded on highly sensitive CCD or CMOS cameras and electronics. For optimal signal and data quality, it is important to have a basic understanding of the operational principles and individual characteristics of the camera used – especially when a conversion to approximate photon number is desired. This would be useful, for example when determining the shot noise contribution and camera noise in the analysis.47 Simply put, the cameras convert photons arriving on their sensitive semiconductor chips into electric charges (one electron per photon) and amplify the signal by charge multiplication (gain) registers. During exposure, the charges in the pixel bins are accumulated and afterwards amplified and sent through shift registers for readout

2.2 Single molecule FRET microscopy

and analog-to-digital (A-to-D) conversion into intensity values. The resulting intensity array images are collected into image stacks and stored for evaluation.

Electron-multiplying CCD-based cameras CCD array sensor chips are comprised of multiple layers. The exposed top layer acts as pixel-sized capacitors that store the charge generated by the incident light. Underneath the exposure layer is a shift register that incrementally shifts the charges into a readout and amplification register. It is not desirable to expose the camera further during the readout process, which commonly takes several tens of milliseconds on a typically sized chip with 512 or 1024 pixels in each dimension. To reduce this dead time in favor of increased frame rates, some cameras feature a frame transfer array (a region on the chip with the same size as the photosensitive array, which is permanently isolated from light). In between exposures, the full frame is quickly transferred into this frame transfer array and readout while the photosensitive array is being used to collect the next frame. The time to transfer the image to the frame transfer array is mainly determined by the camera’s row-shift clock rate, which is usually on the order of microseconds per row. In total, the frame transfer therefore occurs on the millisecond timescale. To readout the signal, the pixel charges are shifted one row at a time into a singlerow readout register and then readout pixel by pixel and amplified. In electronmultiplying CCD (emCCD) cameras, a pre-gain amplification and additional gain are performed on the chip before readout. In this way, the weak signal from single fluorophores can be multiplied by several fold before being converted into camera counts, which leads to negligible readout noise when converting the number of electrons into an intensity value via an A-to-D converter. After a complete readout, the readout register is flushed and the next row is shifted in and read out. Hence, it is the clock of the A-to-D converter that limits the full frame rate of data collection. EmCCD camera chips are cooled to reduce dark counts caused by thermal noise that would cover up the weak signal from single photons. It is important to note that secondary charge generation is a stochastic process. The high-voltage gain registers generate secondary electrons by impact ionization. The probability of generating a secondary electron depends on the gain. However, as the generation of additional electrons is stochastic, the average gain can be determined but the exact gain factor is not known. It should be noted that the optimal gain is not necessarily the highest gain. The SNR reaches a limit and does not increase further with higher gains. In addition, high gain levels in combination with high pixel intensities increase chip aging by electromigration. Special care is advised considering the high cost of emCCD cameras.47,48

CMOS-based cameras When faster data collection is desired, CMOS cameras can be used that feature an active on-chip amplification circuitry – i.e. transistors – for each pixel. This circuit takes up part of the available photosensitive area and thereby reduces the overall detection efficiency. This issue can be mitigated with the introduction of back-

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illuminated sensors or micro-lens arrays. Compared to emCCD cameras, scientific CMOS (sCMOS) cameras have much faster image readout rates that can reach up to several kHz while maintaining similar quantum efficiencies. On the downside, sCMOS cameras have the disadvantage of a rolling shutter effect (as illumination and readout are not totally decoupled) and pixel-to-pixel variations in sensitivity because each pixel has an individual amplification circuit with manufacturing inhomogeneities. At least up until now, these factors have severely hampered the use of sCMOS cameras for image correlation analysis methods.

The quantum efficiency of emCCD and sCMOS cameras The quantum efficiency (QE) of a detector is defined as the ratio of detected photons to total arriving photons. As the circuitry blocks some of the incident light, the QE is reduced in comparison to what is obtainable from the photosensitive material. To get around this problem, the design of the detector can be inverted and the supporting silicon wafer thinned such that the CCD chip can be illuminated from the back. The QE of modern, back-illuminated cameras averages over 90% in the visible region of the spectra. It is wavelength dependent and reaches a maximum of 95% around 590 nm both for emCCD and sCMOS cameras.49,50 In summary, when a fast sampling rate and high number of pixels are desired, sCMOS cameras are advantageous. When homogenous pixel sensitivity, well-defined noise characteristics and a true global shutter is required, emCCD cameras are preferable.

2.2.6 Surface and sample preparation for smFRET on surfaceimmobilized molecules To follow the FRET efficiency of a single molecule over time, it is necessary for the sample molecules to remain stationary within the excited volume of the evanescent wave field in the camera field of view. There are a number of approaches for immobilizing the molecules on the surface. In addition, measures need to be taken to prevent non-specific surface adsorption, particularly when working with proteins. Surface interactions can lead to a partial denaturation of the protein or the protein can stick in a particular conformation, leading to alterations in the function and/ or conformation of the protein. In addition, non-specific binding can lead to the accumulation of undesired particles within the field of view. Common methods involve a combination of surface passivation and specific immobilization. Surface passivation can be achieved by bovine serum albumin (BSA, for measurements on nucleic acids) or polyethylene glycol (PEG, for measurements with proteins). Specific immobilization is realized by addition of groups for targeted binding e.g. via biotin/avidin,19,51 polyHistidine/Ni2+ or antibody/His tag52 based linkage (see “Sample channels for TIRF microscopy” section for details). More recently, improvements to passivation by addition of (DDS-)Tween-20 have been reported.53–55 Another elegant method of immobilization is encapsulation of target molecules in surface-tethered vesicles. This allows investigation of weakly interacting confined molecules and membrane proteins while maintaining the advantages of TIRF microscopy.21

2.2 Single molecule FRET microscopy

Adjusting the fraction of linker-functionalized passivation agents allows control of the sample surface density for the experiment. The sample concentration should be low enough to minimize overlapping point spread functions (PSFs) from the individual molecules but high enough to achieve sufficient statistical information. Sample concentrations used for sample loading are typically in the picomolar range but need to be determined empirically.

2.2.7 Practical considerations regarding smTIRF microscopy In this section, we describe some of the practical improvements and tweaks we have applied to enhance the quality of our measurements and the data acquired. Our selfconstructed smTIRF setup offers both pTIRF and oTIRF illumination modes that can be modulated via an acousto-optic tunable filter (AOTF) for msALEX with up to three lasers (see Fig. 2.3).

Illumination Due to the typically inhomogeneous laser beam profile used for oTIRF illumination, illumination power density and hence fluorophore brightness is not equal across the measured field of view. This effect broadens the intensity distribution and can impede later analysis. Compensation is possible by measuring the intensity gradient in a dye solution and using it for correction of the TIRF image data during analysis. Alternatively, the intensity gradient can be decreased to a few percent by enlarging the beam diameter and overfilling the excitation optics. For this approach, only the peak of the Gaussian profile is used for uniform illumination, however, it requires a higher overall laser power. Another way is to couple the excitation through a multimode fiber and a speckle reducer for a near top-hat flat shaped beam profile.56

Detection

We have chosen a two-step magnification combining 60  apochromatic objectives (Nikon Inc.) with an additional two-fold magnification in the detection pathway to achieve magnifications around 100 nm per pixel such that the PSF of a single molecule is spread over 9 pixels. This value was found to yield sufficient detail of the PSF shape while maintaining a field of view large enough for 300–500 molecules with good separation using separate 512  512 px2 emCCD cameras (Andor Inc.) for each detection channel. The camera detectors have “blind” periods during image readout or charge cleanup at which they are unable to detect photons. For example, the frame-transfer performed on CCD cameras takes 2–3 ms and can easily take up 20% of the total frame cycle time at faster frame rates of 15 ms. Hence, fluorophore survival times can be prolonged when excitation is turned off when detection is not possible. We achieve this by using a real-time field-programmable gate array (FPGA) control system granting us free choice of excitation schemes for the experiment at hand. The use of a real-time controller is strongly encouraged for this purpose, as small time-jitter common in ordinary computer systems and interfaces can introduce additional noise.

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Sample channels for TIRF microscopy For both pTIRF and oTIRF modalities, we have modified our system with flow channels for simple in-situ sample immobilization and assembly. For pTIRF, sample molecules are directly immobilized on the prism bottom surface to avoid the hassle of coupling the prism to a slide. We have designed asymmetrically cut prisms for our setup such that the excitation beam enters the prism normal to the front face, which is cut at 72°, such that the excitation beam is totally reflected at the bottom surface. In this way, we avoid refraction upon entering the prism, which would lead to different wavelengths being reflected at different positions on the bottom surface of the prism. The back surface of the prism is cut at 45° to avoid direct reflections and interference in the field of view from the opposite surface. The sample chamber is formed using a laser-cut sealing polymer gasket (NescoFilm), 100 μm in thickness, sandwiched between the prism and the coverslip. Inlet and outlet holes have been drilled through the prism to allow on-the-fly sample injection and buffer exchange during experiments (See Fig. 2.3A top right). We have developed an intensive cleaning protocol to refresh and prepare the prisms for reuse, described below. Over time, surface scratches accumulate and can deteriorate image quality, which can be almost entirely recovered by professional repolishing. For oTIRF, we use flow cells with a single channel formed by a polymer film gasket and a cover slide with two holes to attach the polyethylene tubes for the inlet and outlet (See Fig. 2.3A mid right). The channel is sealed off using two-component adhesive or other clear polymers such as nail polish. Prior to covering the channel with the cover slide, photobleaching the sample surface with a UV lamp is recommended. Furthermore, an undistorted and planar surface is important to avoid refractive deterioration of the image and maintain a homogenous evanescent excitation without variations in TIRF angle. Therefore, the properties of the adhesive should be evaluated, as it can bend the cover slide unfavorably after curing. During our measurements, we have observed a significant background contribution from the totally reflected excitation beam emerging from the microscope objective. These could be substantially reduced by blocking the reflection with the introduction of a small object close to the focal plane. Another fundamental requirement for high-quality measurements are molecularly clean microscope slides with a near-zero background fluorescence in the spectral regions of the fluorophore emission. The surface should be free of dust and contaminants. The coverslips should also be checked that they do not show a significant amount of autofluorescence, especially at UV and blue excitation wavelengths.33 Additional background can also arise from Raman scattering in SiO2-based coverslips (520 cm1) and aqueous buffer (3200–3600 cm1). When setting up a new microscope system, special care needs to be taken to choose the appropriate emission filters of optimized width. They should be broad enough to optimize the photons collected from the fluorophore, but need to be narrow enough, to exclude spontaneous Raman scattered photons caused by the excitation laser from the detection window. However, due to the reduced excitation volume in TIRF microscopy, the contribution of Raman from the buffer to the background is not as problematic as in confocal microscopy.

2.2 Single molecule FRET microscopy

The coverslips used for oTIRF and prism sealing for pTIRF are thoroughly rid of any potentially fluorescent impurities using a step-wise, solvent-based cleaning procedure with a range of polar and non-polar solvents.19 A combination with nitrogen drying and plasma-cleaning steps has proven effective in minimizing background fluorescence. Solvent cleaning includes step-wise washing with 2% Hellmanex solution (Hellma GmbH), ethanol, acetone and 1 M KOH. Optionally, one can bleach the prisms with HCl. As mentioned above, various protocols for surface passivation and linkage of molecules with biotin-avidin interaction have been developed.54,55 Usually, they involve the passivation with polyethylene glycol (PEG) or bovine serum albumin (BSA) functionalized by biotin linker sites. Depending on the precise smFRET application, two different passivation strategies can be employed: (i) glass cleaning in combination with assembly of the flow cell and subsequent passivation or (ii) passivation of the glass substrate prior to flow cell assembly. In the first case, cleaned, but chemically unmodified flow cells are created. The passivation is achieved by incubating the flow chamber on the TIRF microscope with either BSA/BSA-Biotin or PEG-/PEG-Biotin-Lysine. In the second case, glass surfaces are passivated prior to flow cell assembly. The passivation can be carried out in a two-step process. At first, the glass surface is functionalized with amino groups using e.g. 3-aminopropyl(diethoxy)methylsilane (APDMES) or (3-aminopropyl)triethoxysilane (APTES) for the silanization process. Afterwards, the functionalized glass surface is PEGylated using click-chemistry between the amino groups and PEG-/PEG-Biotin-NHS-Esters. More details can be found e.g. in Refs. 19, 51. In the last step, the designed flow channels for pTIRF or oTIRF are immobilized onto the smTIRF setup. After filling the flow system with imaging buffer, the biotinylated surfaces are exposed at 0.1 mg/mL streptavidin or neutravidin for 10 min and extensively washed with imaging buffer thereafter. Labeled molecules are surface-immobilized just before the measurement by exposing the functionalized glass surface with a 5–10 pM solution until 300–400 immobile molecules per field of view are observed. The quality of surface passivation needs to be evaluated prior to every single-molecule experiment. We test for unspecific stickiness by incubating the surface with 5–10 nM of labeled molecules without the addition of streptavidin or neutravidin as anchor molecule. Surfaces with less than 10–50 molecules in the field of view can be employed for smTIRF imaging.

Experimental aspects The typical workflow in smTIRF measurements involves a cycle of moving the microscope stage to a new field of view, refocusing the sample and recording a movie with a fixed duration and number of frames per field of view. The movie length depends on the photobleaching rate of the sample. A sufficiently high number of movies should be acquired to ensure sufficient statistics for robust data analysis. This number depends on the sample density and survival time of the fluorophores. Exposure times and camera gain factors should be chosen on grounds of fluorophore brightness and excitation strategy for optimal SNR. In our case, we use separate emCCD cameras for each detection channel. This facilitates the alignment of the

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detection channels and allows more statistics to be collected in a single measurement compared to dividing the fluorescence signal on different locations on a single chip. However, it then becomes necessary to synchronize the cameras for simultaneous exposure by trigger pulses from a common external source. Here again, the FPGA is very useful in synchronizing the cameras as well as the excitation lasers. The exact camera behavior should be verified by comparison of exposure and excitation trigger cycles using an oscilloscope. Inappropriate settings for exposure times or trigger sequences can lead to unexpected effects such as dropped frames. Due to the large data rates that can exceed 100 Mbytes per second per camera, consistently fast storage devices such as solid-state drives (SSDs) are recommended.

2.3 Single molecule TIRF data evaluation Movies collected by WF-TIRF microscopy can easily reach sizes of tens of gigabytes and require a complex protocol to extract the contained information and prepare it for further analysis. The first step is to create a transformation map for the different detection channels to allow the donor and acceptor fluorophores from the same molecule to be analyzed. The mapping allows for compensation of relative shifts, rotations and magnification differences between the detection channels as well as optical imperfections such as chromatic and spherical aberrations present despite careful adjustment of the optical setup (Section 2.3.1). Afterwards, the molecules are localized in each channel followed by assignment of donor and acceptor FRET pairs in their respective field of view (Section 2.3.2). Next, intensity traces are extracted (Section 2.3.3) and the background is subtracted to isolate the FRET signal (see Fig. 2.3B for an example of this process). Then, the traces have to be sorted by their qualitative behavior such as the presence and order of photobleaching steps or visible anticorrelated intensity fluctuations suggesting conformational dynamics (Section 2.3.4). Intensity correction factors for accurate calculation of FRET efficiency and inter-dye distance can be acquired during this process (Section 2.3.5). Although many of the tasks can be automated to some extent by software, it is strongly advised to go through the data manually to get a “feeling” for the data and see potentially unexpected effects.

2.3.1 Camera mapping The first step in extracting the smFRET information in a movie is the accurate localization and correct linking of same-molecule emitters across the detection channels. As high-sensitivity, multicolor cameras are not yet available, the donor and acceptor channels are imaged separately. To compensate the effects from aberrations and imperfect alignment, a coordinate transformation map is required. To determine a good map, the coordinates from the same objects in the different channels distributed throughout the field of view needs to be obtained. In some cases, this can be performed on the data itself. In our case, we use a calibration pattern that is visible in all detection channels to derive a precise transformation function. Specifically,

2.3 Single molecule TIRF data evaluation

we use the equally spaced grid of diffraction-limited spots on a zero-mode waveguide (ZMW) illuminated from above using the wide-field lamp of the microscope. First, a coarse alignment function is generated using the 2D image correlation function. Next, the coordinates of the ZMW apertures are located and linked via a pair finding method usually looking in the local neighborhood of the referenced position on the second camera channel. After image correlation, the positions should typically not deviate by more than three pixels. From the coordinates, a 2D multipolynomial function is calculated to represent the distortion of PSF-pairs between the cameras. Using this function, coordinates can be converted back and forth for any pixel coordinate. When using more than two cameras, it is beneficial to calculate transformation functions toward one common reference camera. Although it is possible to use the transformation functions to reimage the data, we use the mapping to find the coordinates of the donor and acceptor signal from the same molecule in the different detection channels. All further analyses are performed on the raw data directly.

2.3.2 Particle localization and pair finding The first step in accessing the intensity changes lies in the accurate localization of the single-molecule emitters and correct linking of same-molecule emitters across detection channels. Multiple methods are available, many of which were adapted from astronomy for the localization of diffraction-limited point spread functions (PSFs) from distant stellar objects. In microscopy, the 2D PSF is typically a first-order Bessel function, known as the Airy disk, which can be well approximated by a 2D Gaussian function. While the subpixel localization of the emitter such as used in super resolution microscopy is not required for the extraction of intensity traces, the quality of the camera mapping function benefits from accurate localizations. When localizing particles from real single-molecule experiments, it is important to exclude regions with overlapping or intersecting particles as well as particles that are cropped by the chip border. Due to the lower SNR of single-molecule emitters and the low photon counts per frame at fast acquisition rates as well as different fluorophore survival times before photobleaching, a global mean or frame-wise localization would miss dark or short-lived fluorophores. Hence, a maximum intensity projection with a sliding window average has proven useful to maximize particle-wise contrast even for short-lived fluorophores and optimal localization results. Preparatory steps before localization can involve denoising steps such as Gaussian deconvolution, wavelet decomposition or morphological opening methods.57 Several particle localization algorithms exist ranging from basic thresholding and center-ofmass calculation to 2D-Gaussian function58 and radial symmetry fitting,59 k-means clustering and regional maximum determination.60 The best combination of applied techniques and optimal parameters will vary depending on the measurement and sample conditions. In our experience, a two-step approach involving a coarse localization step using wavelet-decomposition filtering and thresholding followed by a refined localization step using radial symmetry fitting proved the most robust over a wide range of signal-to-noise ratios.57,60 Using the maps, localized particles are matched

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across cameras. Particles found in all detection channels indicate correctly labeled particles and are marked for trace extraction during the next step. Molecules with less than the desired number of fluorophores, i.e. double-labeled molecules in a three-color system can still be useful for the determination of correction factors.

2.3.3 Intensity trace extraction and background subtraction To obtain FRET efficiencies from smTIRF movie data, frame-wise trace intensities must be extracted for each particle in every detection channel. To avoid heterogeneities from different background signal levels and camera-related bias, the background signal is typically subtracted from the accumulated intensity within a particle mask. The size and shape of the particle mask and the method of background determination have significant impact on the SNR and quality of the traces. Background intensity decreases during measurement time due to photobleaching, raw intensity traces hence often exhibit an exponentially decreasing behavior. Additionally, illumination is not homogenous across the field of view due to the Gaussian beam profile. Hence, particle-wise local determination of the background level is advised over the assignment of a global value. One approach is to use individual background assignment from local background masks pixels surrounding the particles.60 Frame-wise background subtraction can potentially introduce additional noise or artifacts to the extracted traces. Therefore, it is desirable to optimize the number of background pixels used for background correction in both, the spatial and temporal dimension. Neighboring particles inside the background mask can lead to exaggerated values and decrease the overall SNR. This issue can be addressed by excluding overly bright pixels or calculating the median brightness instead of a mean value. Needless to say, several approaches for background signal correction have been developed.61 We subtract the median value of the pixel intensities inside a ring-shaped mask around the particle averaged over a five-frame sliding window from the frame-wise pixel intensities inside a circular mask that covers the PSF (Fig. 2.3B, middle panel). This method has proven to be robust to offsets caused by neighboring particles inside the background mask. Mask shapes and sizes can be varied depending on the setup’s total magnification and the shape of the PSF intensity profile. For the PSF mask, square areas of about 1 μm2 have been used in literature, although it can be useful to experiment with different sizes and shapes for the optimal SNR.19 The sum of background-subtracted particle intensities is calculated for each frame of the recorded movie for all cameras. The resulting traces are then displayed for inspection and manual or automatic trace evaluation and FRET calculation.

2.3.4 Trace evaluation and categorization The individual fluorophore intensity traces extracted from smTIRF movies exhibit a wide variety of heterogenic behaviors due to labeling efficiency, blinking or photobleaching. Hence, they need to be sorted and categorized based on their qualitative characteristics. For FRET efficiency evaluation, only sample molecules featuring a full set of donor/acceptor fluorophores are relevant. Out of those, only the trajectories

2.3 Single molecule TIRF data evaluation

containing dynamic FRET state transitions are of interest for further HMM analysis. Traces from incompletely labeled and static species can be used to calculate the intensity correction factors required for accurate distance estimates based on the photobleaching order. In general, trace evaluation can be assisted by software algorithms but their results should always be verified by manual inspection to avoid artifacts and misinterpretations in the following analysis steps.19 Some basic aspects of trace quality to be considered during trace assessment are listed below: •

•

•

•

•

Single-molecule fluorophore traces should have comparable intensities in absence of a FRET partner. Total intensity should remain constant regardless of step transitions for intensity-corrected traces. To get a feeling for the intensities to be expected from a single-molecule FRET pair, the intensity distribution across all traces should be compared. Foreign PSFs inside the background mask can have detrimental effects on the background subtraction and introduce additional noise. Hence, verification by looking at the local particle neighborhood and PSF profile in the image data is advised. Traces from blinking fluorophores should be carefully inspected and ideally completely excluded, as dynamic transitions during dark phases would be missed. ALEX is helpful to distinguish artifacts coming from acceptor photophysics. Photobleaching steps are needed for the derivation of intensity correction factors as described in the next section. In addition, traces with single photobleaching events ascertain that the data was indeed collected from single molecules. Intensity traces from a FRET pair undergoing dynamic distance fluctuations exhibit a strongly anti-correlated behavior of donor and acceptor intensity during state transitions resulting in steps in the calculated FRET efficiency trace. In contrast, the FRET efficiency trace of a system persisting in a single state remains constant.

2.3.5 FRET efficiency correction and distance calculation Measured, raw intensities of donor or acceptor fluorophores, do not reflect the emission of the employed dyes alone, but also show signatures of additional sources such as background from fluorescent impurities in the buffer, spectral crosstalk from the donor in the acceptor channel24,62 or direct excitation of the acceptor fluorophore during donor excitation. In addition, the detection efficiency is wavelength dependent.63 We denote fully corrected intensity traces as Ixy, while raw intensity traces after background subtraction are written as I∗xy (compare Section 2.3.3). Here, x stands for the excitation source and y for the emission channel, meaning that I∗DA represents the background corrected emission within the acceptor channel (A) after donor excitation (D). Without further correction steps, the FRET efficiency (Eq. 2.5) calculated from these pre-corrected, raw intensity values can only give a so-called proximity ratio, not an accurate distance. In order to acquire precise

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distances using the F€ orster equation (Eq. 2.5), corrections have to be applied to separate the fluorophore signals from each other. These correction factors can be obtained directly from traces that exhibit the correct order of photobleaching steps or dark states. Fluorophore quantum yield, setup detection efficiency and excitation power density are dependent on spectral properties of the fluorophores as well as the setup illumination and should thus be compensated for data evaluation. In WF-TIRF data, these can be derived from the absolute intensity differences caused by photobleaching of one or more FRET partners. An important parameter to satisfy is the total intensity from the sum of fluorophore intensities after donor excitation. If relative detection efficiencies and quantum yields are correctly compensated, the total intensity should remain constant regardless of any dynamics and hence fluctuation between donor and acceptor channels. It is important to note that the dye quantum yield can change during measurement by influence of the local environment as in protein induced fluorescence enhancement or quenching effects. If possible, individually calculated correction factors should be applied to traces when available instead of using averaged values. Please see Fig. 2.4 for examples of the various correction factors and comparisons between before and after intensity correction. A comparison of FRET efficiencies determined for the same sample across multiple research groups can be found in Ref. 64.

Direct excitation correction The first spurious contribution that needs to be accounted for is acceptor fluorescence caused by direct excitation of the acceptor by the donor excitation laser. Calculation from data is only possible when alternating excitation with direct acceptor excitation is used. In that case, the correction factor for direct excitation α, is calculated as:  ∗  IDA  α¼  I∗ 

(2.9)

AA no donor

∗ is the difference in mean acceptor emission after direct acceptor excitation Here, IAA ∗ is the difference in mean intensity in the acceptor detection channel after and IDA donor excitation in absence of the donor (Fig. 2.4A top). The difference in signal is obtained for values before and after the photobleaching of the donor fluorophore.

Spectral crosstalk or leakage correction When performing FRET experiments with spectrally close fluorophores, the emission of one dye within the detection window of the other dyes can be significant. The donor’s emission detected in the acceptor channel causes an offset in total intensity and needs to be subtracted from the acceptor signature. Determination of the so-called leakage correction factor β can be calculated from traces where the acceptor photobleaches before the donor as:  ∗  IDA  β¼  I∗ 

DD no acceptor

(2.10)

2.3 Single molecule TIRF data evaluation

FIG. 2.4 Data correction for accurate FRET determination. Example of smTIRF data of a DNA origami double-labeled with Atto488 and Alexa 568 at an interdye distance of 50 A˚. Data was recorded by objective-based TIRF microscopy with ALEX between 488 and 561 nm excitation in TRIS based buffer with Trolox and oxygen removal. (A) Determination of correction factors. Distance information from single-pair FRET experiments can be obtained after correcting the background-corrected, raw intensities I∗DD, I∗DA and I∗AA against the following contributions: (i) direct excitation of acceptor (α), (ii) spectral crosstalk from donor emission into acceptor channel (β) and (iii) differences in dye-dependent detection efficiency and quantum yield (γ). α is available when ALEX is used. It is determined from the ratio between ∗ and the intensity in the acceptor channel in absence of the donor after donor excitation ΔIDA ∗ acceptor emission after direct acceptor excitation ΔIAA . β is determined from background (Continued)

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∗ denotes mean donor intensity after donor excitation in the absence of an acceptor IDD ∗ denotes the mean signal in the acceptor detection channel after donor excitation dye, IDA equal to the crosstalk from donor emission without an acceptor (Fig. 2.4A bottom).

Detection efficiency and quantum yield correction After correction for direct excitation of the acceptor (α) and leakage of donor emission into the acceptor channel (β), a last contribution needs to be corrected for: the detection efficiency is wavelength dependent. The detection efficiency correction factor γ, can be determined from the ratio of changes in acceptor and donor emission after donor excitation when the acceptor photobleaches (Fig. 2.4A bottom). There can be significant differences between γ-factors within the same field of view, thus determination of individual γ-factors for each trace is advised instead of applying an averaged value globally. After correction, the total intensity should exhibit a constant behavior regardless of photobleaching steps or conformational transitions (see Fig. 2.4A bottom for an example). The γ-factor is calculated as:  ηA ϕA ΔIDA  γ¼ ¼  ∗  ηD ϕD ΔIDD

A photo bleaches

 ∗  αΔI ∗  βΔI ∗  ΔIDA DD  AA ¼   ΔI ∗ DD

(2.11) A photo bleaches

Here, η denominates the setup detection efficiency within the donor and acceptor channel and Φ denominates the quantum yield of donor and acceptor ∗ ∗ refer to intensity difference for the mean donor and and ΔIDA fluorophore. ΔIDD acceptor emission after donor excitation, before and after acceptor photobleaching, ∗ denotes the intensity difference of the mean acceptor emission respectively. ΔIAA after acceptor excitation. An alternative method to derive the γ-value for an individual trace is to employ dynamic transitions. In this case, γ is calculated as the ratio of intensity changes between sensitized emission and donor emission before and after a conformational change. In both scenarios, it is advised to average multiple intensity values before and after the transition to increase the accuracy of the calculated value.

Summary FRET efficiency correction For analyzing dynamics, the apparent FRET efficiency, or proximity ratio, is sufficient. However, it is usually interesting to also calculate distances. Calculation of the corrected FRET efficiency based on the correction factors introduced before is FIG. 2.4, CONT’D differences in the acceptor channel after donor photobleaching. γ is calculated from relative intensity differences after acceptor photobleaching. Experimental data is shown before (left) and after data correction (right). (B) Gaussian-fitted distributions of γ and β values. Both factors are heterogeneous between individual FRET traces. Individual corrections for each trace should be preferred to global application of averaged values. (C) Apparent vs. accurate FRET efficiency and derived distances. SmFRET histograms for trace-wise (dashed lines) averaged and frame-wise determined FRET efficiencies (solid lines) with Gaussian fits, respectively. The distance calculated from the peak mean corrected FRET efficiency is 48.7 A˚, in good agreement with the expected separation of 50 A˚.

2.3 Single molecule TIRF data evaluation

necessary for accurate distance estimations. Combining Eqs. (2.8)–(2.10), one can write a single equation to obtain the corrected FRET efficiency: EFRET ¼

IDA I ∗  αI ∗  βI∗ ¼ ∗ DA ∗ AA ∗ DD ∗ IDA + IDD IDA  αIAA  βIDD + γIDD

(2.12)

Usually, not all correction factors can be extracted from the same trace, as detection efficiency γ and leakage β require a donor-only trace section, whereas direct excitation α needs an acceptor-only trace segment. Accordingly, the mean or median value for α and β can be taken from the statistics obtained from other traces. Since values for γ factors vary a lot experimentally, only traces, for which γ can be determined, should be employed. Often, an alternative gamma factor γ’ is determined without first correcting the acceptor intensity for crosstalk and direct excitation. This is possible, but γ’ does not equal Eq. (2.11), i.e. is not equal to the ratio of quantum yields and detection efficiency of acceptor and donor channel. Eq. (2.12) hence needs to be modified accordingly. In the case of multicolor FRET with multiple acceptors that can act as donors of their own, full correction of intensities and FRET efficiency becomes increasingly difficult. Alternating excitation becomes mandatory to measure each donor fluorophore separately, before acceptor intensities are successively corrected.40 Distances can be calculated from the corrected FRET efficiency using Eq. (2.1) provided the F€ orster radius, R0, for the dye pair is known. Ideally, this should be determined specifically for the individual measurements, because the donor quantum yield, solvent refractive index and relative dipole orientation factors can be influenced by the experimental conditions. Literature values determined using standardized conditions are often used, but at the cost  of reduced accuracy. As an example, an average dipole orientation factor of κ2 ¼ 2 3 is often assumed, although real values can deviate due to rotational and steric restraints from the fluorophore environment.14,65,66

2.3.6 Frame- and trace-wise FRET histograms Every extracted smFRET pair yields the associated intensity traces from which the FRET efficiency can be calculated as a function of time for an individual molecule. The conformational state of the molecular species is inferred from the FRET value and can be evaluated in different ways: for example, a histogram of the FRET values determined in each frame of the movie for all molecules included in the analysis can be generated (a so called frame-wise histogram) or we can determine an averaged FRET value for each molecule and plot a histogram of the molecule-wise averaged FRET efficiencies (referred to as a molecule-wise or trace-wise histogram) (Fig. 2.4C). A frame-wise histogram is useful when molecules undergo conformational changes during the measurement but are broadly distributed due to the limited number of photons detected per frame. The trace-wise histograms are generally narrower due to the better statistics. Direct comparison of the frame-wise and moleculewise histograms can give a good hint on the presence of dynamic conformational transitions, as the averaged FRET value over a system switching between two FRET efficiencies will lead to FRET efficiency values not present in the frame-wise

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distribution. In a static system, the peak values of the FRET states visible in the frame-wise and molecule-wise histograms should be the same. These assumptions should always be confirmed by direct inspection of the individual intensity traces. Single- or multicomponent Gaussian fits can provide a first estimate for the number of states and their relative mean distances for training of a HMM.

2.4 Analyzing dynamics using hidden Markov modeling (HMM) Single-molecule FRET is a powerful method for measuring dynamics in molecular systems as has been demonstrated previously for dynamic DNA origami,67 hairpins68 or Holliday junction structures.39,69 Since transitions between different conformational states are typically much faster than the resolution of the smFRET measurement,70 one might expect FRET traces to exhibit jumps between discrete FRET values. However, many noise sources such as instrumental noise, photophysical effects or temporal coarse graining, result in a distribution of FRET values and a broadening of the distribution, making individual transitions difficult to detect.48,71 This holds especially true for dynamic biological systems with more than two states. To reveal the underlying dynamics of the FRET traces obscured by experimental noise, an objective data analysis is desirable. Before the introduction of HMM to smFRET data analysis in 2003, different techniques such as thresholding algorithms were applied.72 In the following section, we will first introduce the theoretical concepts of a Markovian process, likelihood, estimation maximization and the mechanism of hidden Markov modeling.25,73,74 Later, we will demonstrate the application of an HMM for the analysis of conformational dynamics in smTIRF data.

2.4.1 Markovian processes, Markovian chains and transition probability matrices Named after the Russian mathematician, Andrey Markov,75 a Markovian process is a system with a finite set of discrete states and fixed probabilities for undergoing transitions into the other states or remaining in their original state (see Fig. 2.5A for an exemplary system with three states). A Markovian process is memoryless, meaning that the transition probabilities are constant over the trajectory and the state transition probability during each time step solely depends on the previous state. The chronological sequence of transitions undergone by a Markovian process is called a Markovian chain.76 For a Markov process with transitions between a set of states S ¼ {1, … , s, … S}2 ℕ, there are S2 possible independent transition probabilities kij of going from state i to j that can be written in a quadratic probability matrix K of size S  S as 2

3 k11 ⋯ k1S 4 K¼ ⋮ ⋱ ⋮ 5 kS1 ⋯ kSS

(2.13)

2.4 Analyzing dynamics using hidden markov modeling (HMM)

FIG. 2.5 Hidden Markov Modeling. (A) Three state Markov chain. A Markov chain is a system of discrete states s with fixed transition probabilities kij between two states per time step. Transition probabilities only depend on the current emitting state of the system. (B) Role of emission states in Hidden Markov Modeling. In real-world scenarios, neither actual states nor transition probabilities kij are directly accessible. Observed values from the hidden states become continuously distributed as determined by the transition probabilities of the prior states and the emission functions fs. HMM allows inference of the hidden system’s configuration from the observed data.

The Markovian property requires that the row-wise sum of all transition probabilities for each emitting state must be equal to one: S X

kij ¼ 1

(2.14)

j¼1

The transition rate matrix R is related to the transition probability matrices via: R ¼ ðK  I Þ  Δt1

(2.15)

where I denotes the identity matrix and Δt is the time interval for which the rates are calculated. The transition rate matrix is then calculated as: 2 6 R¼4

k11 

XS ⋮ kS1

k j¼1 1j

3 ⋯ k1S 7 ⋱ ⋮ 5  Δt1 X S ⋯ kSS  k j¼1 Sj

(2.16)

2.4.2 Hidden Markov models, emission functions and likelihood A hidden Markov model (HMM) represents a Markovian chain where the exact state trajectory is unknown and hidden due to noise. The Markovian process generates observation values, which are related to the current state by emission functions. HMM allows the inference of the hidden transition probabilities and original state sequence from the observed trajectory or trajectories emitted by the underlying Markovian process. Originally, HMM was developed by Leonard E. Baum in 1966 for dynamic voice recognition. It has since evolved into a wide field of applications such as machine

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learning and temporal pattern recognition of audio,77 visual78 and abstract data.79,80 In 2003, Andrec et al. first applied the HMM analysis to single molecule FRET data.72 In the meantime, several implementations of HMM on smFRET data have been published.73,81–84 Here, we give a short introduction to HMM modeling of smFRET data from TIRF microscopy experiments. Mathematically put, the S discrete Markov states and their transition probabilities are only indirectly accessible. They can be accessed via observations X ¼ {x} from a continuous sample space of possible observations x 2  (where  represents the space of all possible observations) that follows a statistical model defined by emission functions fs(Xj θs). The emission functions give the probability of observing a value x 2 X for the given model parameters θs and state s (see Fig. 2.5B). The model parameters θs define the HMM, namely the transition probability matrix, the initial state probabilities and the emission functions. P For S states with relative occurrence probabilities W ¼ ðω1 , … , ωS Þ where Ss¼1 ωs ¼ 1, the combined emission functions give the continuous probability distribution function F ðXj W, ΘÞ with Θ ¼ {θ1, … , θS} as: F ðXj W, ΘÞ ¼

S X

ωs  fs ðXj θs Þ

(2.17)

s¼1

An example of a F ðXj W, ΘÞ function is plotted at the bottom of Fig. 2.5B. Consequently, observables from states with overlapping emission functions cannot be directly back-referenced to a single emitting state s. For example, in Fig. 2.6A, a measurement with a FRET efficiency of 0.5 cannot be clearly assigned to state 1 or 2. Often, the parameters for a hidden Markov model are not known; neither the transition probabilities, the initial state probability nor the emission functions. Hence, there are three steps to be taken in the hidden Markov model approach: 1)

2)

3)

What we typically have is our set of observables X and either an idea of the functional form of the emission functions or a model for the emission functions is chosen. A first step is then to determine how likely a given set of parameters can produce the measured data. This is typically done using a Maximum Likelihood approach. Once we have a measure for the quality of the parameters in describing the data, we wish to optimize the parameter set to give the maximum likelihood. This is done using an expectation maximization algorithm. A very effective approach is the Baum-Welch forward-backward algorithm. This needs to be done iteratively. Once the optimal parameters for the emission functions and transition probability matrix are known, it is then possible to convert the observed smFRET traces into the most probably underlying sequence of states, and thereby discretize the data. This is done using the Viterbi path.

After the parameters have been optimized, there are also methods to evaluate the quality of the HMM. Each of these steps are described in more detail below.

2.4 Analyzing dynamics using hidden markov modeling (HMM)

FIG. 2.6 HMM analysis. (A) HMM inference on simulated smFRET data from a three-state dynamic system. SmFRET data is simulated for a three-state Markov chain with known transition probabilities and emission functions. The probability density distributions for FRET efficiencies from the observed simulated data (black line) and a fit with three Gaussian distributions (green line), where the individual Gaussian components are shown in green, red and blue. The three states returned by the local HMM performed on the individual traces are plotted as red bars and a global HMM as blue, dotted bars. Despite broadening by noise, global HMM recovers the hidden input. (B) Effects of under- and overfitting. Viterbi-paths from HMMs trained for less (yellow dashed line) or more states (red dashed line) than the original input (green dashed line) on observation data (gray solid line). The 2-state HMM fails to reproduce the original states while the 4-state HMM overestimate states not present in the hidden system. (C) Viterbi-algorithm. The Viterbi-path generates the most likely hidden state sequence for an observation time series. At each time step, the posterior probability for the (Continued)

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The first step is to calculate the probability of measuring a series of T data points, X ¼ (x1, … , xt, … , xT) given the model parameters Θ. Following the argumentation of Fraser,85 we first begin with the joint probability P(X, S j Θ) of a state sequence S ¼ {s1, … , si, … , sT} giving rise to the measured observables X: PðX, Sj ΘÞ ¼ Pðs1 j ΘÞ  PðSj ΘÞ  PðXj S, ΘÞ T T Y Y ¼ Pðs1 j ΘÞ  Pðst j st1 Þ  Pðxt0 j st0 Þ t¼2

(2.18)

t0 ¼1

The terms in the expression describe the probability of the initial state P(s1 j Θ), the state evolution probability P(S j Θ) and the probability P(Xj S, Θ) for the emission of a specific observation trajectory. P(st j st1) denotes the probability of being in state st at timepoint t given one was in state st1 at timepoint t  1 and P(xt0 j st0 ) is the emission probability, i.e. the probability of state st0 yielding the observed data xt0 . For a given Θ, we can directly determine the probability of the measured observable X. Experimentally, however, we only have access to the observable X and not the modeling parameter Θ that describe our data best. Hence, we need to determine the parameter Θ0 that makes the observable data most likely, i.e. we need to maximize the so-called likelihood function LðΘj XÞ LðΘj XÞ  PðXj ΘÞ

(2.19)

that is a function yielding the likelihood of the model parameters Θ producing the given data set X and is linearly proportional to our joint probability. In order to derive the maximum likelihood from L, one usually maximizes the log LðΘj X Þ, since the logarithm of a function has the same extrema as the function itself and it circumvents the danger of precision underflow errors from the consecutive multiplication of small probabilities. The maximum log-likelihood is related to the expectation value of log FIG. 2.6, CONT’D next observed value is calculated using the prior state transition probability and the emission probability values. The transition with the highest total probability is selected as the prior for the data point. Individual probabilities and likelihoods for two proposed sequences P1 (light gray) and P2 (dark gray) are compared. While the proposed sequence P1 is purely based on emission probabilities (plot background) and appears visually more fitting, P2 has a higher total likelihood when considering the prior transition probabilities found by HMM. (D) Transition density plot (TDP). TDPs are bivariate histograms of dynamic transitions found by HMM. Clusters indicate frequently occurring transitions between two states. Vertically aligned clusters show transitions from a single state to multiple likely states, populations connectable by increasing diagonals (gray or red circles) indicate chronologically associated state sequences (left). Dwell time histograms of the durations spent within a stationary state allow calculation of the transition rates. Transitions missed by the chosen HMM model cause deviations from a single exponential decay line (mid). A comparison of the transition probability matrice from the hidden input with those found by local and global HMM analysis. The values found by the global HMM analysis are in excellent agreement with the hidden input (right).

2.4 Analyzing dynamics using hidden markov modeling (HMM)

P(X, Sj Θ) over all states or state combinations and is often referred to as the Baum auxiliary function, Q. Thus, the most likely parameter set, Θ0 , given the current estimate, Θ, can be calculated by summing over all possible hidden trajectories using: X

QðΘ0 j ΘÞ ¼

PðX, Sj ΘÞ  logPðX, Sj Θ0 Þ

(2.20)

S2

where  represents the space of all possible trajectories. This equation can be written out into three terms; one describing the probability of the initial state, one term that describes the probability of a transition between states and the third that gives the probability of the measured data given a particular trajectories (i.e., state sequence): QðΘ0 j ΘÞ ¼ Qinitial ðΘ0 j ΘÞ + Qtransition ðΘ0 j ΘÞ + Qobservable ðΘ0 j ΘÞ " X 0 Pðs1 , θÞ  logPðs1 , θ0 Þ Q ðΘ j ΘÞ ¼ S2

+

T1 X w0 ðst + 1 , st , θÞ  logPðst + 1 j st , θ0 Þ t¼1

T X + wðst , θÞ  log Pðxt j st , θ0 Þ

(2.21)

#

t¼1

where w(st, θ) represents the conditional probability, given the data, of being in state st at time t and w0 (st, st+1, θ) represents the conditional probability, given the data, of being in state st at time t and state st+1 at time t + 1. Each term in the sum can then be optimized individually. The first and last terms depend only on the parameters of the emission functions. ωst  fst ðxt j θst Þ F ðxt j W, ΘÞ

(2.22)

Pðxt j st , θst Þ ¼ fst ðxt j θst Þ

(2.23)

wðst , θÞ ¼

and The initial state probability can be approximated by the relative occurrences of the states, ωs. For estimating the emission functions, we maximize the term of the Baum Auxiliary function that includes the contribution of the emission functions: QðΘ0 j ΘÞ ¼

S X T X

wðst Þ  log ðfst ðxt j θst ÞÞ

(2.24)

s¼1 t¼1

^ maximizing the Baum Auxiliary term and thus the likeThe optimal parameter set Θ lihood for the given data is given by ^¼ Θ



arg max QðΘ0 j ΘÞ θ2Θ



(2.25)

and called the maximum likelihood estimate (MLE). The Baum Auxiliary Function takes the log of the probability (i.e. it is a log likelihood function). In the case of fully independent observation values, the parameters that maximize the likelihood

101

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CHAPTER 2 Probing dynamics in single molecules

function can be found by setting the partial derivatives of the Baum Auxiliary Function with respect to emission parameters to zero.25 ∂ logQðΘ0 j ΘÞ ≝0 ∂θs

(2.26)

By solving these equations, a first guess of the optimal parameters is obtained, referred to as estimators. As the parameters are often interdependent, the optimal parameters have to be determined iteratively. In addition, we have not yet optimized the transition probabilities that contribute to the total Baum Auxiliary Function. This is accomplished using expectation maximization algorithms. An important factor to note when performing a computational MLE is the time cost or computational complexity O of the system, especially when a large number of parameters and large data sets are involved. For a smFRET experiment with Gaussian emission functions, T data points and S populations or states, the computational complexity of the naı¨ve approach above would pose a highly expensive computational cost of O ðST Þ. Fortunately, several faster-converging algorithms for the MLE and computational likelihood optimization exist such as the Brent’s or Baum-Welch forward-backward algorithm (BWA) introduced in 1970 by Leonard E. Baum for real-time speech processing.86 Being one of the fastest HMM implementations using expectation maximization, the BWA (described in Section 2.4.4) decreases computational time cost to a much more manageable range of O ðT  S2 Þ:86

2.4.3 The Baum-Welch forward-backward algorithm The next step of the HMM analysis is to determine the optimal parameters that describe the data. This is performed by using an expectation maximization algorithm that iteratively modifies the hidden parameters to maximize the log-likelihood for a given data trajectory or set of trajectories.87 During the expectation (E) step, the log-likelihood of the observed data is calculated for a set of hidden system parameters. The initial set of parameters are either randomly chosen or guessed. During the maximization (M) step, the parameters maximizing the log-likelihood for the given data are optimized using the MLE, which then become the new priors for the next expectation step. The algorithm ends when the log-likelihood change between two cycles is lower than a predefined threshold. It is important to note that the convergence time can be vastly reduced by good initial parameter guesses. Using a single- or multicomponent Gaussian fit to the frame-wise smFRET histograms often provides a good first estimate for the number of states and their relative mean distances for training of an HMM. Repeating the procedure with different initial parameter sets reduces the potential risk of being trapped in local maxima with limited overall relevance. The Baum-Welch forward-backward algorithm, applies the expectation maximization algorithm for HMM parameter optimization. It exploits the Markov condition in that the current state of a Markovian process is only determined by the transition probabilities from the previous state. Instead of calculating a total likelihood for all possible state sequences, the forward-backward algorithm conveniently calculates

2.4 Analyzing dynamics using hidden markov modeling (HMM)

the posterior probabilities for transitions from the potential emitting states st at time point t to state st+1 at the next time point starting from the beginning (forward, αt+1(st+1)) and to the previous time point starting from the end of the trajectory (backward, βt1(st1)). α t + 1 ðst + 1 Þ ¼

S X

αt ðr Þkrst + 1 fst + 1 ðxt + 1 j θst + 1 Þ

(2.27)

βt ðrÞkrst1 fst1 ðxt1 j θst1 Þ

(2.28)

r¼1

βt1 ðst1 Þ ¼

S X r¼1

At each time step, the transition contributing the highest increase to the total likelihood is accepted. In the end, we take the product to calculate a combined probability: wðst , θÞ ¼

αt ðst Þβt ðst Þ S X αt ðr Þβt ðr Þ

(2.29)

r¼1

and w0 ðst + 1 , st , ΘÞ ¼

αt ðst Þkst st + 1 fst + 1 ðxt + 1 j θst + 1 Þβt + 1 ðst + 1 Þ Pðxt + 1 j xt ,… ,x1 ,ΘÞ

(2.30)

where the denominator of Eq. (2.30) is the probability of observing xt+1 given the parameters and data observed up to time point t. Optimization of the Baum Auxiliary Function term for transitions yields a new estimate for the transition probability matrix: T1 X

k^sr ¼

wðs, r, tÞ

t¼1 S X T1 X

(2.31) wðs, r, tÞ

r¼1 t¼1

The forward-backward algorithm along with the maximum likelihood estimation are then used iteratively to find the system parameters that maximize the posterior likelihood for a given data set.86

2.4.4 Viterbi algorithm

^ has been determined, the last step is to Once the most likely set of parameters, Θ, determine the most likely hidden state sequence for a particular observed trajectory. For this purpose, the Viterbi algorithm, named after American engineer Andrew J. Viterbi,88 is commonly used. At each time step t, the transition probabilities from the previously proposed prior state st1 to proposed states st are calculated. Hence, the ^ for all available S transitions are determined given emission probabilities fst xt jΘ ^ and the observable xt. The transition with the maxithe most likely prior state st1 ^ ðxt j θs Þ becomes the assumed state for the next time mum total log-likelihood log L t

103

104

CHAPTER 2 Probing dynamics in single molecules   ^ generated with the highest total likelihood found step t + 1. The state sequence X Θ by this incremental algorithm is called the Viterbi path. It is important to keep in mind that the Viterbi path does not provide a metric of absolute probabilities to compare between different emission models. A demonstration of the method can be seen in Fig. 2.6A and B. SmFRET data of a dynamic system with three states was simulated using a three state Markov chain with known transition probabilities and emission functions (Fig. 2.6A and B). The effects of HMMs that under- or overestimate the original number of states can be seen by overlaying the retrieved Viterbi paths (Fig. 2.6B) in comparison with the simulated path and an HMM with the correct number of states. The Viterbi algorithm is demonstrated in Fig. 2.6C.

2.4.5 Information theory and likelihood estimators While HMM allows the optimization of the stochastic model parameters for a set of observations, it does not directly provide the optimal number of states for the model. Naively stated, increasing the number of variable parameters indefinitely would continuously increase the goodness of the fit without any additional gain in information about the hidden system. Estimating more than the original number of fit components is called overfitting while estimating a lower number is called underfitting (see Fig. 2.6C). Hence, a metric, such as the Bayesian information criterion (BIC) or the related Akaike information criterion (AIC), is required to compare the quality of different stochastic models and number of states. Both BIC and AIC favor models with less complexity by the addition of a penalty term for the number of free parameters and are calculated as

 ^ + S  logT BIC ¼ 2  log L

(2.32)

 ^ +2S AIC ¼ 2  log L

(2.33)

One can see that the penalty term for BIC incorporates the number of observations T and is higher at large sample sizes than for AIC. The model with the lowest BIC or AIC value is preferred. Although the AIC value is theoretically independent of the sample size, one should be careful when drawing conclusions based upon the absolute log-likelihood, as the AIC tends to overfit at low sample sizes.89 Multiple approaches such as variational74 and empirical Bayes models90 have been used to apply Bayesian estimation maximization to HMM. Several published, open-source software packages utilizing various approaches for HMM smFRET data analysis are meanwhile available.73,74,83,90,91

2.5 HMM analysis of smTIRF FRET data Up to this point, the concept of HMM was introduced from a general, universally valid perspective. Here, we describe the specifics of an HMM analysis applied to smTIRF FRET data. The distribution of FRET efficiencies typically follows a beta

2.5 HMM analysis of smTIRF FRET data

distribution at shot-noise dominated levels, but can be well-approximated by a Gaussian emission model with a mean value μ and standard deviation σ for count rates typically achieved in smTIRF experiments.92 Consequently, the probability density function (PDF) for the FRET efficiencies calculated from the measured donor and acceptor intensities is a product of the Gaussian PDFs. The product of Gaussian functions is itself a Gaussian distribution and the emission functions for assumed conformational states s 2 S can be written as: ðxs μs Þ 1  2 fs ðxs j θs ¼ fμs , σ s gÞ ¼ pffiffiffiffiffi  e 2σ s 2π σ 2s

2

(2.34)

An example of three overlapping Gaussian emission functions is shown in Fig. 2.6A. The ratio of the integrals of the individual components represents the relative occupancy of the FRET states. For low photon counts in the presence of background and when using the electron gain of an emCCD cameras, additional shot noise broadening parameters need to be introduced.48 However, as discussed above, no information regarding the dynamic transitions between the states can be derived from the emission functions.

2.5.1 Global and trace-wise HMM To calculate the transition state matrix, the HMM has to be trained on the time series. There are two main approaches to train an HMM on smFRET data. Either, one can independently refine the transition probabilities and emission parameters individually per FRET trace (trace-wise HMM), or one uses a common transition probability matrix and emission function parameters for the whole set of observed data (a global HMM). Depending on the amount of intensity heterogeneities between traces due to local environmental effects on the fluorophores and optical properties of the setup, a global HMM might not suitably represent the values observed in the individual data series and may even wrongly assign the values. This is especially the case when working with apparent FRET efficiency distributions. Hence, a global HMM approach is predominantly advised for FRET data from corrected FRET traces. A trace-wise HMM will yield one transition probability matrix and emission parameter set per FRET pair. Conformational transitions with low rates and probabilities that do not show up in all traces can reduce the overall confidence in the HMM. When performing a trace-wise HMM, it is recommended to look at the distributions of the transition and emission parameters to exclude outliers from the sample. A comparison of a global HMM and trace-wise HMM for simulated data is shown in Fig. 2.6A.

2.5.2 Transition density plots One way to visualize the transition probabilities found by HMM is via the transition density plots (TDPs). TDPs are bivariate histograms of the state transitions identified by an HMM where the FRET efficiency values prior to a transition

105

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CHAPTER 2 Probing dynamics in single molecules

(EFRET(t)) and after a transition (EFRET(t + 1)) are plotted. Most commonly, the Gaussian mean values before and after each identified transition are plotted as point coordinates in a 2D plot. Instead of building up the TDP from the individual point contributions, using multivariate Gaussians that include the full emission function parameters for the identified states can be plotted for a cleaner appearance with better population separation. Often, color maps are used to indicate the population density and thus the cumulative probability of a transition (see Fig. 2.6D for an exemplary TDP plot of a simulated smFRET system with dynamic transitions between 3 states). Multiple populations aligned vertically indicate the possible transitions from a common starting state whereas a single population indicates that only one transition is possible. Similarly, multiple populations in a horizontal line indicate that the particular FRET state can be reached from several initial states. Hence, the connectivity of the different states can be read out from the TDP plot.

2.5.3 Dwell-time histograms and transition rate calculation Once the discrete states within the FRET efficiency traces have been identified by HMM, dwell times and transition kinetics can be investigated. Although the state transition rates can be directly calculated from the transition probability matrices, it can be very useful to look at the distribution of dwell-times determined from the Viterbi path. For smFRET traces, the Viterbi path provides a means of “digitalizing” the traces and providing the sequence of states hidden within the data. For a correctly identified state configuration, the state-wise plotted dwell time distribution following the transition from state si to sj should satisfy a mono-exponential decay (see Fig. 2.6D) with the rate parameter λij ¼ k1 ij . Fluorophore blinking or state conversions missed by HMM can cause deviations from an ideal curve. By fitting the dwell time histograms with an exponential, the transition rates can also be directly calculated.

2.6 HMM analysis of NC2-mediated TATA box-binding protein dynamics on DNA There are many publications demonstrating the power of HMM when applied to investigate dynamic interactions (see for example, Refs. 40,93–95). One example from our laboratory is the specific interaction of the TATA-box binding protein (TBP) with the core-promotor TATA-box, which is present in a significant fraction of eukaryote genes.25,96 TBP is part of the general transcription factor TFIID and aids in forming the RNA polymerase (RNAp) preinitiation complex (PIC). This is done, in part, by bending the DNA upon association by angles between 80° and 100° and recruiting other factors involved in formation of the PIC.97–100 Negative Cofactor 2 (NC2) is a transcription cofactor that attaches to TBP-DNA complexes from the bent side to form a ring-like structure with TBP that sterically occludes the association of TFIIA and TFIIB.101 FRET experiments on labeled TBP using the Adenovirus Major-Late (AdML) promoter site shows the induction of rapid conformational

FIG. 2.7 Demonstration of HMM analysis on TBP-AdMLp DNA complexes undergoing NC2-mediated dynamic conformational transitions. Yeast TATA box binding protein (TBP) from S. cerevisiae bound to the AdML DNA promoter with TATA consensus sequence bends the DNA by 80° 93–96 . The complex undergoes dynamic conformational transitions upon addition of Negative Cofactor 2 (NC2). (A) NC2-induced TBP-DNA dynamics. Sample trace from smTIRF data of TBP-DNA complexes with and without NC2 (donor intensity: green, acceptor intensity: red, total intensity: purple, FRET efficiency: blue). (Left) smTIRF data shows static FRET efficiency (blue line) without Negative Cofactor 2 (NC2). (Right) After the addition of NC2, the system becomes dynamic. The Viterbi path derived from a globally trained HMM (orange) shows prominent states at FRET efficiencies of 0.83 and 0.2 with short intermediate excursions to 0.64 and 0.4. (B) FRET histograms of TBP-DNA with and without NC2. After addition of NC2 (blue curve), the framewise FRET efficiency distribution clearly splits from a single into at least two distinct states when compared to the plot curve without NC2 (red). (C) TDP of 4-state global HMM. A detailed analysis revealed the presence of 4 states with FRET efficiencies of 0.20, 0.40, 0.64 and 0.83. The TDP from the HMM is plotted revealing the interconnections between the different states of the complex. (D) Dwell times vs FRET efficiency. Dwell times plotted against observed FRET efficiencies during continued states assigned by molecule-wise HMM. (E) Proposed Model. Schematic structures of the identified states and associated FRET efficiencies. Transitions between the most probable states are indicated with arrows. NC2 is not shown for clarity. Initially, the DNA is fully bent with stably attached TBP (40% FRET efficiency). After addition of NC2, the complex fluctuates between the 60% and 80% states, whereas the 20% FRET efficiency state represents motion along the DNA. Adapted from Zarrabi, N.; et al. Analyzing the Dynamics of Single TBP-DNA-NC2 Complexes Using Hidden Markov Models. Biophys. J. 2018, 115 (12), 2310–2326.

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CHAPTER 2 Probing dynamics in single molecules

changes in the TBP-DNA complex between distinct FRET states after the addition of NC2 (Fig. 2.7A).25,96 Upon addition of NC2, the resulting FRET efficiency distribution splits up from a single state at 40% FRET efficiency into at least two populations around 40 and 80% FRET efficiency, respectively (see Fig. 2.7B). An HMM analysis revealed a total of four states in the data with FRET efficiencies of 0.20, 0.40, 0.64 and 0.83. Beginning from the 40% FRET state corresponding with the bent AdML promoter (AdMLp) DNA configuration of the DNA-TBP complex, transitions occurred to either the 20% FRET state associated with NC2-TBP motion along the DNA or, via an intermediate 64% FRET efficiency state to the 83% FRET efficiency population (see Fig. 2.7C and D). The two high FRET states fluctuate rapidly between each other. A close inspection of the TDP indicates that the four states are connected by a linear 4-well model. Transitions to the low, mobile population at a FRET efficiency of 0.20 are only possible via the initial 0.40 FRET efficiency state (Fig. 2.7E). Transitions from the 0.40 FRET state to higher FRET values goes mainly to the 0.64 FRET state. Rare transitions directly to the 0.83 FRET efficiency state are observed when an additional transition from 0.64 to 0.83 occurred too quickly to be detected by the HMM. The results from these experiments suggest that the transitions between the 0.40, 0.64 and the 0.83 FRET states involve conformational changes of the DNA whereas the transition to the 0.20 FRET state involves motion of the TBP-NC2 complex along the DNA.25

2.7 Future applications Although much information has been gained regarding the dynamics of biological systems using smFRET, there are several new developments that can further improve smFRET and allow additional information to be extracted. First, the FRET system can be expanded by labeling the sample of interest with additional fluorophores and monitoring multiple distances simultaneously. Such information is highly desirable for many questions in biology and chemistry. With careful correction of fluorophore intensities and illumination with msALEX, two or more intermolecular distances can be obtained in parallel.40,102 By combining smFRET with selective plane illumination microscopy (SPIM), also known as light sheet microscopy,103 single-molecule FRET measurements could be performed with axial resolution in cells under in-vivo conditions. Generally, fluorophores with improved brightness and photostability are in high demand for enhanced data quality. In addition to the continued search for better fluorophores, fluorescence enhancement using metallic nanoparticles may be an option. One manifestation of fluorescence enhancement uses self-assembled DNA origami with attached metallic nanoparticles.102,104–106 In addition to fluorescence emission enhancement, surface-plasmons have been shown to enhance acceptor quenching efficiency, and hence increase the distance sensitivity and range in FRET as well as reduce background.107 Due to the small confinement of enhancement within the hot spot of the antenna, it becomes possible to perform single molecule experiments at much higher concentrations of the labeled species. Another approach for measuring smFRET at high concentrations of labeled sample is zero-mode waveguides (ZMW).108

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An additional area where experimental developments would be useful is the development of better immobilization strategies for smTIRF. New surface-immobilization methods can facilitate the investigation of previously inaccessible sample molecules such as intrinsically disordered proteins (IDFs) by reducing surface interactions.109 In addition, better surface passivation methods will help to decrease artifacts from foreign or non-specifically sticking molecules. Immobilization can also be combined with microfluidic systems made of polymer flow chips to permit in-situ sample assembly and precise real-time control over sample compounds. Another future development for smFRET experiments would be to increase the time-resolution of imaged-based systems. Currently, emCCD and sCMOS cameras are being continuously improved for higher sensitivity and faster imaging rates. Another approach would be to use single-photon avalanche photo diode (SPAD) detector arrays, which are becoming large enough for imaging applications and enable scanning-free fluorescence lifetime microscopy (FLIM). Recently, detector arrays were demonstrated with up to 128 pixels per dimension.8,110,111 Moreover, the development of small, fully integrated fluorescence widefield microscopes as smartphone attachments or the use of CMOS sensors built into consumer appliances could allow new lab-free and costeffective FRET applications in diagnostics and environmental research. As smFRET becomes easier to perform, it is also possible to utilize it to investigate other parameters than only distance. Recently, fluorescence-based smFRET has been used for measuring forces on dynamically interacting complexes of DNA and TBP. The molecules were clamped into an origami scaffold at variable tension forces determined by linker length.23 At higher tension forces, the binding affinity of TBP to the DNA was incrementally reduced. In contrast to previous methods, all molecules immobilized within one field of view could be investigated separately and in parallel, yielding more statistics.

2.8 Summary In this chapter, we have provided the toolbox to perform and analyze single molecule experiments using widefield-TIRF smFRET microscopy. We have demonstrated how to identify intramolecular distance configurations and how to quantify conformational transitions between them by training of a hidden Markov model. With this knowledge, it should be possible to gain new insights into relevant dynamic processes such as protein-folding and molecular interactions in biology. We anticipate further developments to lower the entry barriers to this proven technology and firmly establish the method as a molecular diagnostics platform in both research and commercial applications.

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84. K€onig, S. L. B.; et al. BOBA FRET: Bootstrap-Based Analysis of Single-Molecule FRET Data. PLoS One 2013, 8 (12), e84157. 85. Fraser, A. M. Hidden Markov Models and Dynamical Systems; Society for Industrial and Applied Mathematics, 2008. 86. Baum, L. E.; et al. A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains. Ann. Math. Stat. 1970, 41 (1), 164–171. 87. Dempster, A. P. P.; Laird, N. M.; Rubin, D. B. Maximum Likelihood From Incomplete Data via the EM Algorithm. J. R. Stat. Soc. Ser. B Methodol. 1977, 39, 1–38. 88. Viterbi, A. J. A Personal History of the Viterbi Algorithm. IEEE Signal Process. Mag. 2006, 23 (4), 120–142. 89. Claeskens, G.; Hjort, N. L. Model Selection and Model Averaging; Cambridge University Press, 2008. 90. van de Meent, J. W.; et al. Empirical Bayes Methods Enable Advanced Population-Level Analyses of Single-Molecule FRET Experiments. Biophys. J. 2014, 106 (6), 1327–1337. 91. Shuang, B.; et al. Fast Step Transition and State Identification (STaSI) for Discrete Single-Molecule Data Analysis. J Phys Chem Lett 2014, 5 (18), 3157–3161. 92. Gopich, I.; Szabo, A. Theory of Photon Statistics in Single-Molecule Forster Resonance Energy Transfer. J. Chem. Phys. 2005, 122 (1), 14707. 93. Keller, B. G.; et al. Complex RNA Folding Kinetics Revealed by Single-Molecule FRET and Hidden Markov Models. J. Am. Chem. Soc. 2014, 136 (12), 4534–4543. 94. Ratzke, C.; Hellenkamp, B.; Hugel, T. Four-Colour FRET Reveals Directionality in the Hsp90 Multicomponent Machinery. Nat. Commun. 2014, 5, 4192. 95. R€ohl, A.; et al. Hsp90 Regulates the Dynamics of its Cochaperone Sti1 and the Transfer of Hsp70 Between Modules. Nat. Commun. 2015, 6 (1), 6655. 96. Schluesche, P.; et al. NC2 Mobilizes TBP on Core Promoter TATA Boxes. Nat. Struct. Mol. Biol. 2007, 14 (12), 1196–1201. 97. Parkhurst, K. M.; Brenowitz, M.; Parkhurst, L. J. Simultaneous Binding and Bending of Promoter DNA by the TATA Binding Protein: Real Time Kinetic Measurements. Biochemistry 1996, 35 (23), 7459–7465. 98. Schluesche, P.; et al. Dynamics of TBP Binding to the TATA Box. In Single Molecule Spectroscopy and Imaging, Enderlein, J., Gryczynski, Z. K., Erdmann, R., Eds; SPIE, 2008, pp 68620–68628. 99. Blair, R. H.; Goodrich, J. A.; Kugel, J. F. Single-Molecule Fluorescence Resonance Energy Transfer Shows Uniformity in TATA Binding Protein-Induced DNA Bending and Heterogeneity in Bending Kinetics. Biochemistry 2012, 51 (38), 7444–7455. 100. Robinson, P. J.; et al. Structure of a Complete Mediator-RNA Polymerase II PreInitiation Complex. Cell 2016, 166 (6), 1411–1422. 101. Albert, T. K.; et al. Global Distribution of Negative Cofactor 2 Subunit-Alpha on Human Promoters. Proc. Natl. Acad. Sci. U. S. A. 2007, 104 (24), 10000–10005. 102. Stein, I. H.; Steinhauer, C.; Tinnefeld, P. Single-Molecule Four-Color FRET Visualizes Energy-Transfer Paths on DNA Origami. J. Am. Chem. Soc. 2011, 133 (12), 4193–4195. 103. Weber, M.; Mickoleit, M.; Huisken, J. Light Sheet Microscopy. Methods Cell Biol. 2014, 123, 193–215. 104. Chung, H. S.; et al. Single-Molecule Fluorescence Experiments Determine Protein Folding Transition Path Times. Science 2012, 335 (6071), 981–984. 105. Ochmann, S. E.; et al. Optical Nanoantenna for Single Molecule-Based Detection of Zika Virus Nucleic Acids Without Molecular Multiplication. Anal. Chem. 2017, 89 (23), 13000–13007.

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Single molecule spectroscopy at interfaces

3 Lydia Kisley

Department of Physics, Case Western Reserve University, Cleveland, OH, United States

3.1 Introduction The states of matter – solid, liquid, gas – are one of the first concepts of physical science we are aware of. For elementary school-aged children, the states of matter is one of the first physical science lessons in the classroom1 and even by the age of six months infants have depth perception that make them aware of solid/air interfaces that prevent them from crawling off a “cliff.”2 An interface is where two states of matter come into contact, forming a two-dimensional boundary between the two phases (e.g. solid1/solid2, solid/liquid, solid/gas, liquid1/liquid2, liquid/gas interfaces). Historically, the study of interfaces has been of interest to scientists and engineers from Benjamin Franklin’s experiments of an oil droplet covering the surface of a pond to the quantitative development of surface physics by Young, Laplace, Gauss, Gibbs and Poisson in the 18th century.3 Interfacial chemistry and physics then developed both scientifically and for industrial applications in the 19th and early 20th centuries, with notable contributions by Langmuir, Sabatier, and Haber. Written qualitative descriptions of oil/water interfaces have even been found in Babylonian texts dating back to the 16th century B.C.4 The current importance of interfaces spans interdisciplinary problems in biology, medicine, engineering, industry, chemistry, and physics. In nature, interfaces in living cells help organize organelles, isolate the cell from surroundings, and form barriers that signals can be transmitted across to induce specific biological responses. Physiologically, examples of interfacial phenomenon include joint lubrication, liquid transport within blood capillaries, and respiration. In industry, it has been estimated that 90% of all industrial processes depend on heterogeneous catalysis at solid/liquid or solid/gas interfaces.5 In the pharmaceutical industry, separating mixtures of molecules at solid/liquid chromatographic interfaces can account for 50% of the $2.6 billion dollar cost in bringing a drug to market.6 Beyond these examples, interfaces are important in pressing challenges in water purification, transportation, pollution, and health. Therefore, studying interfacial phenomenon can impact a wide range of problems in society. Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.00003-1 # 2019 Elsevier Inc. All rights reserved.

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Our understanding of interfaces is complicated by the unique, heterogeneous phenomena that occur on the nanoscale. The nature of an interface is complex due to it being comprised of multiple phases of materials. Forces acting on molecules at the interface occur from both bulk phases and are asymmetric. The length scale of these forces spans nanometers, resulting in orientation of molecules one to several layers thick, which defines the interface. The molecular dimension of the interfacial region is then Angstrom to nanometers thick axially. Chemical complexity (defects in crystallinity, mixtures of molecules, stochastic processes, curvature, etc.) also leads to nanoscale heterogeneity laterally. These variations within the plane of the interface also lead to asymmetric forces. The dynamics of molecules – their diffusion, conformation, organization, and reactive rates – therefore change at interfaces as compared to their dynamics in the three-dimensional bulk of one of the phases or the other. Truly understanding the molecular phenomena that are important for interfacial systems requires experimental techniques that can access these dimensions and dynamics. Single molecule fluorescence spectroscopy is a useful tool to understand the spatiotemporal nanoscale heterogeneity at interfaces due to advantages over conventional imaging techniques. Scanning probe techniques (AFM, STM, SECM) can achieve atomic resolutions, but in situ imaging of multiple molecules simultaneously is not possible with conventional scan rates. The need for an invasive tip can also perturb the sample. Electron microscopies (SEM, TEM) often are operated in ex situ conditions to achieve high resolutions and do not have molecular specificity in imaging unless rather large nanoparticle/antibody probes are used as labels.7 Ellipsometry, X-ray and neutron scattering can achieve nanoscale axial information, but average data over a micro- to macroscale dimensions laterally. In contrast, single molecule fluorescence imaging can monitor millisecond-resolved dynamics at resolutions of
10 nm in situ under ambient conditions.8–13 Chemical specificity is achieved with targeted labeling or selection of specific fluorogenic reactions.14 While single molecule spectroscopy can study molecules within the bulk of materials, selection of appropriate microscopes and sample conditions can isolate dynamics specifically at interfaces. This chapter focuses on single molecule fluorescence techniques to study interfaces. In Section 3.2, a brief history of the development of single molecule spectroscopy at interfaces is presented. The different instrumentation and analysis to understand the spatial organization, adsorption or turnover kinetics, and diffusion in two- and three-dimensions at interfaces is then introduced in Section 3.3. Example applications of these single molecule spectroscopic techniques at a variety of interfaces: fundamental three-dimensional dynamics of single molecules at solid/liquid and liquid/liquid interfaces achieved with recent developments in microscopy hardware, liquid/liquid interfaces important for biophysical cellular organization with and without membranes, solid/liquid interfaces modified with soft synthetic materials used for separations, and solid/liquid interfaces used for heterogeneous catalysis are presented in Sections 3.4–3.7. The highlighted literature focuses on recent exciting work spanning from 2015 to 2018. This chapter is not intended to be an

3.2 Historical overview of single molecule spectroscopy at interfaces

exhaustive treatment of all aspects of single molecule techniques at interfaces. Monitoring molecular conformation by single molecule fluorescence resonance energy transfer (FRET) and other non-fluorescence single molecule techniques (AFM, nanopores, optical tweezers) will not be covered in this chapter, along with other interfaces discussed in Section 3.8. Finally, an outlook on possible directions the field can head by studying more complex interfacial materials and utilizing advances in single molecule instrumentation is discussed in Section 3.9.

3.2 Historical overview of single molecule spectroscopy at interfaces Single molecule spectroscopy allows for studies at the fundamental concentration detection limit of an individual molecule. Therefore molecular parameters and statistical distributions can be accessed that are obscured in typical ensemble techniques used to characterize interfaces. Almost 30 years ago, the first reports of single molecule detection of individual pentacene molecules doped in p-terphenyl crystals at cryogenic temperatures were reported using absorption by Moerner and Kador at IBM15 and fluorescence by Orrit and Bernard.16 Quickly, fluorescence became the method of choice, as high signals (
105 photons/s) can be achieved with practical instrumentation, sample preparation, and strategic selection of high quantum yield fluorophores compared to alternative spectroscopic phenomena such as absorption, Raman, or Rayleigh scattering. Detecting single molecules at interfaces was important in the development of single molecule fluorescence imaging at room temperature in the far-field. The first reports of detecting single molecules at interfaces were immobile organic fluorophores at solid/air interfaces. In 1993, Betzig and Chichester at Bell Labs used near-field scanning optical microscopy of carbocyanine dyes on polymethylmethacrylate films (Fig. 3.1A).17 The polymer improved the quantum yield and adhesion of the molecules. Dipole-dependent emission patterns were observed as a way to determine the angular orientation of the individual molecules. Xie and Dunn at Pacific Northwest National Laboratory then observed time-resolved processes in single sulforhodamine 101 molecules absorbed on borosilicate glass surfaces in the near-field (Fig. 3.1B).18 The work continued, as Brus et al. in 1996 and Xie et al. in 1997 expanded to detecting similar samples with one- and two-photon far-field microscopy (Fig. 3.1C–E).19,20 Far-field imaging avoids perturbation of any molecular properties by the metallized near-field scanning probe used in the earlier reports. Single molecule detection at liquid/liquid and solid/liquid interfaces were achieved around the same time as solid/air interfaces, but required technological advancements in detector quantum yield and temporal resolution. This was needed as the dynamic diffusion of molecules spreads the photon emission spatially over a larger area compared to static, immobile molecules at solid/gas interfaces. Improvements in cameras, excitation geometry, and sample preparation were needed to achieve continuous imaging at adequate signal-to-noise ratios for single molecule

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FIG. 3.1 Historical observations of single molecules at the solid/gas interface. (A) Near-field scanning optical microscopy of carbocyanine dyes on a PMMA coated-substrate with random polarization.17 (B) Near-field time-resolved dependent emission of a single sulforhodamine 101 molecule on a glass surface as polarizers are switched from parallel to perpendicular as indicated by the inset.18 (C) Far-field two-photon excitation of rhodamine B dye molecules on a glass surface.12 (D, E) Far-field imaging of carbocyanine dyes at PMMA/air interface with orthogonal excitation polarizations indicated by arrows in the upper-left corners.19,20 From Betzig, E.; Chichester, R. J. Single Molecules Observed by Near-Field Scanning Optical Microscopy. Science 1993, 262, 1422–1425. Reprinted with permission from AAAS. From Xie, X. S.; Dunn, R. C. Probing Single Molecule Dynamics. Science 1994, 265, 361–364. Reprinted with permission from AAAS. Figures reprinted with permission from Sa´nchez, E. J.; Novotny, L.; Holtom, G. R.; Xie, X. S. Room-Temperature Fluorescence Imaging and Spectroscopy of Single Molecules by Two-Photon Excitation. J. Phys. Chem. A 1997, 101, 7019–7023. Copyright 1997 American Chemical Society. From Macklin, J. J.; Trautman, J. K.; Harris, T. D.; Brus, L. E. Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface. Science 1996, 272, 255–258. Reprinted with permission from AAAS.

identification. These included using intensified CCD cameras, total internal reflection fluorescence (TIRF) excitation geometry (discussed in Section 3.3), and larger sample molecules (DNA, proteins) that diffuse more slowly than small, organic fluorophores. Studies at liquid/liquid interfaces were achieved by Schindler et al. by imaging a fluorescently-labelled lipid in a fluid lipid membrane with a liquidnitrogen cooled CCD in 1996.21 Xu and Yeung22,23 were able to monitor millisecond dynamics of individual rhodamine 6G, fluorescently-tagged single-stranded DNA, and proteins at glass/water interfaces in 1997.

3.3 Instrumentation and analysis Design and selection of the sample geometry and labeling, instrumentation, and analysis techniques are key to implementing far-field single molecule fluorescence techniques to interfaces. Here, an overview of common methods is presented. Readers are encouraged to refer to the citations for more details, as entire reviews have been dedicated to the instrumentation and analyses covered.

3.3 Instrumentation and analysis

3.3.1 Sample considerations for single molecule fluorescence at interfaces Utilizing appropriate sample conditions allows for single molecule detection at interfaces by fluorescence microscopy. By using fluorescence, the resulting photons are red-shifted from the laser excitation, allowing the emission to be separated from the excitation for detection using filters. But first the sample must be as free as possible from contamination, as autofluorescence from impurities decreases the signal-to-background ratio when detecting individual molecules. Care in cleaning microscope coverslips to remove contamination, purchasing high-purity reagents, and using far-red or near-infrared fluorophores24,25 can help avoid autofluorescence. Raman scattering from the sample itself can also decrease the signal-to-background ratio. Next, typically a low fluorescent dye concentration, usually in the pM–nM range, is required to ensure only one molecule is detected at a time within an area of
100s of nm. Expanding the dynamic range of single molecule experiments to mM concentrations has been recently demonstrated using creative waveguide excitation geometries, energy transfer of the analytes, or advanced analysis techniques.26,27 Additionally, the chemistry and size of the fluorescent probe must be appropriate to the system of interest. For example, small organic fluorophores such as rhodamine 6G, BODIPY, or Alexa dyes are cationic, neutral, or anionic, respectively, and their charged properties can influence their behavior at interfaces.28 Biological molecules can be labeled with organic fluorophores. Nucleic acids can be labeled at terminal 30 or 50 ends with amino-linkers, internal sites can be postsynthetically labeled through enzymatic techniques or dyes that undergo intercalation into the base pair stack or bind to the minor grove,29 and single-stranded nucleic acids can be hybridized with fluorescently-labeled complementary sequences. Proteins can be labeled with amine- or thiol-chemistry on native amino acids or mutated to contain a site-specific amino acid. Alternatively, fluorescent proteins, such as the thoroughly-studied green fluorescent protein (GFP), can be used. Fluorescent proteins have the benefit of being able to be genetically engineered to be expressed in cells directly attached to the protein of interest when studying biological interfaces. But fluorescent proteins are also larger than their organic counterparts (for example, the hydrodynamic radius, Rh
3.5 nm for GFP vs. Rh
0.7 nm for rhodamine) For either label type, it is important to reduce as much as possible the perturbations the label has on the biomolecular function. Finally, the fluorophore must have a high enough quantum yield and photostability to emit enough photons to be detected at the single molecule level over the course of an experiment.

3.3.2 Instrumentation – Total internal reflection fluorescence (TIRF) microscopy TIRF microscopy30,31 is ideal for performing single molecule fluorescence measurements at interfaces. The axial focal volume is limited to be within
100 nm of the solid/liquid or gas sample interface by evanescent wave excitation. This excitation decays exponentially with distance from the interface and reduces background from

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FIG. 3.2 Single molecule fluorescence microscopy excitation geometries. (A) objective-based TIRF and (B) confocal focal volumes.

out of focus fluorophores above the interface (Fig. 3.2A). The formation of the evanescent excitation wave is achieved by total internal reflection where the excitation light is passed at a high angle, θ, at the interface relative to the critical angle, θc, as defined by Snell’s law: θc ¼ arcsin


 η2 η1

(3.1)

where η1 and η2 are the refractive indices of the two phases. High excitation angles can be achieved by passing the excitation at the edge of a high numerical aperture objective in an epifluorescence geometry (Fig. 3.2A) or using a prism in a transillumination fluorescence geometry. The totally internally reflected beam creates an evanescent wave that passes normal to the interface and its penetration depth, dp, the depth at which the intensity is reduced to 1/e of the initial intensity at the interface, is determined according to: dp ¼ λ=4π

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi η21 sin 2 θ  η22

(3.2)

where λ is the wavelength of the incident excitation. In typical TIRF measurements, dp
100 nm. A wide field, typically
50  50 μm laterally, is excited in TIRF

3.3 Instrumentation and analysis

allowing for a large area to be excited simultaneously. The resulting wide field of emission can be detected on a two-dimensional array detector, such as a scientific CMOS or EMCCD detector. The resulting output is a movie comprised of a series of two-dimensional images that can be obtained at time scales of
10–100s of Hz. The ms-dynamics of many molecules can be imaged simultaneously. Common analysis of the images can be performed by single particle tracking and super-resolution imaging, as discussed later.

3.3.3 Instrumentation – Confocal microscopy Alternatively, confocal microscopy has been used to study single molecules at interfaces. In confocal microscopy, the focal volume is focused to the diffraction limit by overfilling the back of a high numerical aperture objective with the excitation beam (Fig. 3.2B). This leads to a 1/e2 intensity lateral beam radius, r0, of
250 nm and axial beam radius, z0, of
500 nm for green light. Therefore, confocal microscopy can detect molecules well above a solid/liquid or gas sample interface compared to TIRF microscopy. A high degree of control and calibration of the focal volume axial position with piezocontrol is therefore important when using confocal microscopy at interfaces.28 The objective/sample stage can be scanned to obtain spatial information or the focal volume can be held stationary as molecules are detected as they diffuse through. Emitted photons are detected versus time on a single-element detector, usually a semiconductor-based avalanche photodiode, although historically photomultiplier tubes have also been used.32 The intensity transient signal detected in confocal microscopy reveals single molecule dynamics through several routes of analysis. In the scanning geometry the resulting output from the single channel detector can be reconstructed into an image based on the location of the objective versus the sample stage at a given time. The areas of the image with bright spots reveal the spatial locations of adsorbed molecules. The frequency at which an image can be obtained is lower,
30 mHz for a 15  15 μm image, compared to TIRF, due to limitations in the timescale required to scan the objective or sample relative to the other. Blip analysis, i.e. counting the number of events where increases in intensity are observed, can also be applied when the focal volume is in a fixed location. The blips indicate that a molecule has passed through the focal volume and the total number can be used to quantify the affinity between the probe molecule and the interface. Further analysis of intensity trajectories by correlation is discussed in further detail below.

3.3.4 Analysis – Single molecule localization methods for super-resolution imaging Location-based super-resolution imaging analysis of TIRF data can obtain spatial resolutions on the order of
10s of nm. Since the general principles were introduced,33–37 super-resolution methods have become near routine in biophysics to image cellular structures with commercially-available instrumentation, but the

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techniques are finding increased application at interfaces. In the most commonly used localization-based super-resolution imaging techniques, fluorophores stochastically turn on and off through the image series such that only a few fluorophores are “on” at a time within a single frame (Fig. 3.3A). An alphabet soup worth of acronymed super-resolution techniques are available (STORM, PALM, PAINT, FIONA, FPALM, RESOLFT, NASCA, SHRImP)8–13 and are based on controlling the number of fluorophores that are “on” within a given area. This can be controlled by photophysical switching,34,35 adsorption/desorption/diffusion properties,38,39 photobleaching,12 or environmental37 or chemical reaction13 spectral changes in the fluorophore. Individual diffraction-limited spots (
250 nm) are isolated (Fig. 3.3A) so that the centers can be localized with precision on the order of 10s of nm by fitting to a two-dimensional Gaussian or related point spread function model (Fig. 3.3C)40,41; a statistical buildup of the locations of multiple “on” events (Fig. 3.3D) leads to an image below the diffraction limit (Fig. 3.3E). Ex situ microscopy techniques confirm super-resolution results observed by single molecule fluorescence techniques. Structural features at the interface are often imaged by SEM, TEM, or AFM and correlated to the corresponding features in the reconstructed single molecule super-resolution maps.42 The spatial capabilities of these ex situ techniques are comparable or better than super-resolution fluorescence techniques, so that nanoscale physical features at the interface, such as defects, crystallographic planes, or aggregates, can be identified at the interface to give insight into the resulting super-resolution maps.14 Correlative imaging requires the samples to be indexed, patterned, or marked so that the same nanoscale areas of the samples are imaged by the single molecule fluorescence and ex situ techniques.43 Elemental properties of the sample can further be obtained by X-ray

FIG. 3.3 Localization-based data analysis to obtain super-resolution information. (A) Cartoon of excited dye adsorbed at an interface (red circle) compared to diffusing “dark” molecule (yellow circle). The emission from the fluorescent dye is only observable when it is adsorbed to the surface. The dye is not observed when it is freely diffusing in the bulk due to being outside the near-interface TIRF focal volume or motion blur of the signal compared to the integration time of the detector. The signal from the adsorbed dye is observed as (B) a diffraction-limited point spread function. (C) The data from the point spread function emission (white dots) is fit to a two-dimensional Gaussian (surface) to obtain the centroid location (white x). (D) Centroids from
100 adsorption events (black dots overlaid the diffraction limited image) localize the adsorption site to
30 nm, shown in (E), the final super-resolution image. Scale bar ¼ 200 nm.

3.3 Instrumentation and analysis

absorption, Raman, or wavelength-dispersive techniques. Due to the requirement for samples to be measured in vacuum or dry for many of these techniques, ex situ correlation is often performed for interfaces that have a solid material only.

3.3.5 Analysis – Kinetic analysis of adsorption or turnover rates Kinetic information is contained in super-resolution spatial information for techniques that use the repetitive adsorption, desorption, or reactions of fluorophores at interfaces. Instead of synchronizing reactions and measuring concentration changes as in classical ensemble experiments, kinetics are directly measured in single molecule spectroscopy by monitoring the turnover of stochastic events and describing reactions by probabilities and statistical mechanical models.44 In these studies, commonly the fluorophore is “off” and unobservable either by being in a non-fluorescent state or by motion blur when freely diffusing even near the interface due to their rapid diffusion (D
150 μm2/s)45 in a bulk solution phase compared to the detector temporal resolution (10–100s Hz). The fluorophores is then “on” when stochastic, low-density reversible adsorption or reaction of a single fluorescent molecule occurs at the interface.38 Adsorption kinetics of the identified specific adsorption sites are calculated by counting the number and length of events from frame-to-frame to obtain the desorption time (i.e. dwell time of an individual molecule) and adsorption time (i.e. the waiting time between one molecule leaving and a new molecule adsorbing to the same site) (Fig. 3.4A). Similarly, for fluorogenic reactions the times between “on” or “off” events can be related to the turnover frequency.44 Cumulative distributions of the adsorption or turnover times are commonly used, as they have been shown to be more sensitive to rare populations than commonly-used histograms/probability distributions,46 and are obtained by 100

td

ta

(A)

Time

P(t’>t)

Intensity

10–1 10–2 10–3

(B)

Time

FIG. 3.4 Kinetic information obtained from single molecule experiments. (A) Desorption (td) and adsorption (ta) times of individual events at a single location at the interface. (B) Example semilog plot of cumulative distribution of desorption times for all adsorption sites at an interface. The data follow a multiexponential decay due to heterogeneity between adsorption sites (example three-component fit, N ¼ 3 in Eq. 3.3, shown as a solid line with dashed lines representing 95% confidence intervals of the fit).

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an integration of the number of counts of the times at all locations (Fig. 3.4B). Kinetic information can be obtained from fitting exponential decays to the cumulative distributions, according to, Pðt0 > tÞ ¼

N X

AN exp ½t=τN 

(3.3)

i¼1

where P(t0 > t) is the probability of observing a desorption or adsorption event that is t long or longer, N is the number of components, AN is the amplitude contribution, and τN is the desorption or adsorption decay time. Alternatively, quantifying the decays as a stretched exponential through Weibull analysis can quantify deviation from monoexponential kinetics and the degree of heterogeneity without requiring a user-defined N in Eq. (3.3).47

3.3.6 Analysis – Single molecule tracking to quantify diffusion Particle tracking analysis quantifies the diffusion dynamics of individual molecules at interfaces. In particle tracking, molecules are identified in each frame of the resulting movie output of either TIRF or scanning confocal microscopy, their locations are found and recorded, and the trajectories of the motion of the molecules from frameto-frame are constructed by connecting molecule locations between frames (Fig. 3.5D). The single molecule trajectories can be further analyzed to understand the rate, nature, and distribution of diffusion (Brownian, anomalous, etc.) through mean square displacement analysis.53–58 Commonly for two-dimensional Brownian diffusion at a flat interface, a linear fit to the mean square displacement (hr2i) vs. the time lag (t) can obtain the diffusion coefficient for two-dimension Brownian diffusion constant, D, according to:  2 r ¼ 4Dt:

(3.4) 59–61

62,63

Cumulative step size and Van Hove distributions or radius of gyration analyses are alternative methods that can distinguish periods of immobilization versus diffusion for trajectories that deviate from two-dimensional Brownian diffusion at interfaces.64,65 Compared to correlation analysis of confocal microscopy data taken with a stationary focal volume (discussed below), the diffusion dynamics in particle tracking can be found for each individual molecule instead of requiring many individual events to calculate quantitative information.

3.3.7 Analysis – Correlation techniques for diffusion and superresolution information Correlation analysis can provide diffusion and spatial details at interfaces. Fluorescence correlation spectroscopy (FCS) analysis quantifies diffusion properties of molecules through the correlation of the signal of many single molecule events over time. Through not truly a single molecule technique as with single molecule tracking, the

3.3 Instrumentation and analysis

(B)

y (nm)

(A)

Cumulative Probability

7000

6000

(C) 5000 (D) 2000

10

NH2–100%

0.5

NH2–75% NH2–50% FS Simulated Browninan Motion

0.0 3000

4000

x (nm)

(F)

0.5 1.0 1.5 Return Time (s)

(E) FIG. 3.5 Three-dimensional single molecule tracking of interfacial hopping diffusion. (A–C) Example experimental data of Fourier optical imaging of engineered point spread functions that encode axial information including (A) double helix,48 (B) tetrapod,49 and (C) trispot.50,51 Scale bars, 1 μm. (D–F) Application of the double helix point spread function to three-dimensional imaging of protein diffusion.52 (D) Example two-dimensional trajectory that can be (E) realized in three-dimensions showing flights in the bulk liquid phase in red squares. (F) Flight length depends on the long-range electrostatic forces between the molecule and the surface. As cationic surface content increases with the mole percent of an amine-terminated silane (notated as “NH2 – X%,” where X is the mole percent), the more the diffusion of the anionic protein deviates from Brownian behavior. In contrast, the diffusion over anionic fused silica surface (FS) is similar to Brownian diffusion simulated by kinetic Monte Carlo methods. Figures reprinted with permission from Thompson, M. A.; Lew, M. D.; Badieirostami, M.; Moerner, W. E. Localizing and Tracking Single Nanoscale Emitters in Three Dimensions With High Spatiotemporal Resolution Using a Double-Helix Point Spread Function. Nano Lett. 2009, 10, 211–218. Copyright 2010 American Chemical Society; Shechtman, Y.; Sahl, S. J.; Backer, A. S.; Moerner, W. E. Optimal Point Spread Function Design for 3D Imaging. Phys. Rev. Lett. 2014, 113, 133902. Copyright 2014 by the American Physical Society; Ding, T.; Lu, J.; Mazidi, H.; Lew, M. D.; Zhang, O. Measuring 3D Molecular Orientation and Rotational Mobility Using a Tri-Spot Point Spread Function. In Single Molecule Spectroscopy and Superresolution Imaging XI; Enderlein, J., Gregor, I., Gryczynski, Z. K., Erdmann, R., Koberling, F., Eds.; SPIE, 2018; Vol. 10500, p 12. Copyright 2018 SPIE; Wang, D.; Wu, H.; Schwartz, D. K. Three-Dimensional Tracking of Interfacial Hopping Diffusion. Phys. Rev. Lett. 2017, 119, 268001. Copyright 2017 by the American Physical Society.

results provide a bridge between the classical ensemble averaged and single molecule levels.66 From the intensity signal over time, F(t), the fluctuations of the signal, δF(t) are calculated by subtracting the average signal, hFi, from all points: δFðtÞ ¼ FðtÞ  hFi

(3.5)

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The self-similarity of the signal is then calculated by autocorrelation: G ðτ Þ ¼

hδFðtÞδFðt + τÞi hFðtÞi2

(3.6)

where the resulting response, G(τ), is a result of the overlap of the original signal, δF(t), with the signal shifted, δF(t + τ), for a given lag time, τ. The resulting autocorrelation decay calculated in Eq. (3.6) can then be related to the diffusion dynamics of the molecules in confocal microscopy by fitting to: 2

3

2
!1=2 τ r0 τ 4 5 1+ GðτÞ ¼ 1= Veff hCi 1 + z0 τD τD

(3.7)

where Veff is the size of the effective focal volume, hCi is the concentration of fluorescent probe used, τ is the correlation lag time, τD is the characteristic diffusion time, and r0 and z0 are the focal beam radius and height, respectively (Fig. 3.2B). Eq. (3.7), derived by Elson and Madge, is based on the StokesEinstein relationship for Brownian diffusion67–69 and τD can be related to the diffusion coefficient, D, by: D¼

r2 : 4τD

(3.8)

Other fitting equations for additional types of diffusion have also been derived.70,71 If various types of diffusion are present, a multiple component fit can be used to resolve heterogeneous behavior.72 Further advancement of unique confocal microscopy setups with two photon73,74 or stimulated emission depletion (STED) excitation,33,75 scanning geometries,76–78 or use of wide field imaging with pixelby-pixel correlation79–81 have been developed to circumvent temporal and spatial limitations in traditional confocal FCS setups to study diffusion at liquid/liquid membrane interfaces and solid/liquid interfaces. Super-resolution Optical Fluctuation Imaging (SOFI)82,83 uses correlation analysis to achieve spatial resolutions below the diffraction limit. SOFI correlates optical fluctuations from individual switching emitters either due to photoblinking or photoswitchable fluorophores. The intensity signal over time for individual pixels in a wide-field image is analyzed by autocorrelation. Pixels with isolated emitters have a highly correlated signal compared to areas with mixed signal from multiple emitters. While the original reports of SOFI used blinking or photoswitchable fluctuations from stationary fluorophores labeling biomolecular

3.3 Instrumentation and analysis

structures of interest, FCS has also been combined with SOFI where fluctuations are produced from diffusing probes to produce super-resolution spatial maps of diffusion coefficients.84 This has been applied to understand diffusion and spatial properties of porous materials. SOFI offers advantages over the previously discussed localization-based super-resolution techniques because it has a broader tolerance for emitter density, signal-to-background ratio, point spread function shape, and user-input requirements.83 While SOFI’s objectivity is beneficial, the super-resolution capabilities are around
100 nm for second-order correlation, which is about an order of magnitude less than localization-based analysis.

3.3.8 Advancements in three-dimensional single molecule imaging techniques and analysis at interfaces Advancements in point spread function engineering have expanded the spatial and temporal resolutions of studying single molecule dynamics at interfaces. By introducing an optical astigmatism that aberrates the emission pattern, the axial position, the orientation, or the sub-frame arrival time of a molecule can be achieved. A simple cylindrical lens placed in the detection path will lead to resolvable axial information to
50 nm,85,86 but using phase masks in the Fourier domain that produce engineered point spread functions such as double-helix (Fig. 3.5A),48,87,88 tetrapod (Fig. 3.5B),49 tri-spot (Fig. 3.5C),50,51 self-bending,89 diamond,90 or phase-ramp,91 patterns can determine three-dimensional molecular position at higher precisions or through thick samples. Alternatively, hardware changes with light sheet excitation92 or detection with multi-plane collection geometries93–97 using multiple detectors placed at different focal planes can image distinct axial locations in the sample. Finally, using intensity-based analysis methods,98 such as calculating the radial distribution of the probability of photon arrivals within emission patterns can determine the axial position of single molecules over a range of 600 nm without requiring hardware changes.99 These new detection patterns and geometries have then led to development of new single molecule analysis techniques that extract the three-dimensional locations at high precision, reaching the theoretical limits defined by the Cramer-Rao lower bound.100 Given, the μm-scale dimensions of cells in the axial direction, many of these developments in instrumentation and analysis have been utilized by the biophysics community to study molecular organization in cellular environments. In addition, the use of the engineered point-spread function developments in single molecule instrumentation at interfaces have revealed fundamental properties about the adsorption and diffusion of molecules at solid/liquid and liquid/ liquid interfaces (Section 3.4).

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3.4 Imaging single molecule interfacial dynamics with engineered point spread functions With the advancements in engineered point spread functions as described in the previous paragraph, new diffusion dynamics of single molecules at fundamental solid/ liquid interfaces have been achieved. Utilizing the double helix point spread function, the Schwartz group directly imaged the three-dimensional motion of molecules at a solid/liquid interface for the first time.52,101 While diffusion in bulk liquids has long been well described by Brownian diffusion models, the two-dimensional behavior of molecules at interfaces is not as simple. Two-dimensional single molecule imaging of diffusion at solid/liquid interfaces (Fig. 3.5D) fail to be described by two-dimensional random walk models.64,65 These deviations can be accounted for with Levy-models of diffusion that have “flights” of the molecule away from the solid surface into the bulk liquid before reencountering the surface.101,102 Schwartz et al. directly observed these flights (Fig. 3.5E).52 Fluorescently-labeled anionic human serum albumin at the solid/liquid interface of fused silica and water/glycerol liquid phase was imaged. The effect of long-range electrostatic forces was studied by modifying the anionic silica surfaces with cationic amine-terminated silanes mixed at different mole percents with oligo(ethylene glycol) silanes. A comprehensive quantitative analysis of the mean square displacement, diffusion coefficients, sticking coefficients, hop length, hop height, hop duration, and return time between hops was performed and compared to kinetic Monte Carlo simulations. Importantly, weak long-range electrostatic interactions were shown to control the surface dynamics. At electrostatically-repulsive anionic fused silica surfaces,
3 times as many collisions with the surface occur before the molecule re-adsorbed compared to electrostatically-attractive cationic surfaces, resulting in larger flight lengths and longer return times to the surface (Fig. 3.5F). Dynamics of single molecules at liquid/liquid interfaces can also be imaged in three dimensions with engineered point spread functions. Due to surface tension properties many liquid/liquid interfaces are spherical and have high-curvature, such as vesicles and membraneless organelles in biology or emulsions in the oil and paint industries. Zhong and Wang, et al. used a diamond-shaped point spread function to track the diffusion of 100 nm polystyrene spheres at the curved interfaces between oil droplets and an aqueous solution.103 The droplet size was varied from 390 nm to 4900 nm to vary surface curvature. The diffusion constant of the particles decreased as droplet size decreased and was attributed to the particle deforming and rearranging the interface and causing an increase in friction. The results show further development of models for hydrodynamic friction at liquid/liquid interfaces is needed. Landes et al. creatively used a phase mask to improve the temporal resolution of single molecule measurements to extract adsorption kinetics of proteins at

3.4 Imaging single molecule interfacial dynamics with engineered point spread functions interfaces below the integration time of the camera, achieving “super temporalresolved microscopy (STReM)” (Fig. 3.6).104 Traditionally, processes occurring faster than the collection time of an individual frame are integrated and appear as an identical shape (Fig. 3.6B). In STReM, a double-helix phase mask is rotated at a rate that is synchronized to have a 180 degree rotation during the integration time of an individual frame (Fig. 3.6A). When a molecule initially adsorbs, the orientation of the double-helix indicates the arrival time. If the molecule

FIG. 3.6 STReM achieves sub-frame temporal information to resolve interfacial adsorption kinetics not possible by traditional imaging.104 (A) Hardware implementation of STReM using a rotating double helix phase mask. The point spread function orientation rotates based on the arrival time of the molecule relative to the rotation of the phase mask. (B–E) Application of STReM to protein adsorption at a water/fused silica interface. (B) Traditional imaging without a phase mask is compared to (C) STReM where the red cross mark indicates the fitting of the central location of the molecule and highlights the arc-shape of the emission pattern indicating a residence time >5 ms. (D, E) Kinetic analysis of the surface residence times. (D) Traditional imaging resolves a single component, while (E) the improved temporal capabilities of STReM reveal a second faster component below the integration time of single frame. Figure reprinted with permission from Wang, W.; Shen, H.; Shuang, B.; Hoener, B. S.; Tauzin, L. J.; Moringo, N. A.; Kelly, K. F.; Landes, C. F. Super Temporal-Resolved Microscopy (STReM). J. Phys. Chem. Lett. 2016, 7, 4524–4529. Copyright 2016 American Chemical Society.

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remains adsorbed, the signal is spread out into an arc shape as emission of the molecule passes through the rotating phase mask. The arc-length then indicates the residence time of the protein. The final angle of the helix then indicates the desorption time (Fig. 3.6C). STReM achieved improvements in temporal resolution by a factor of 20, from 100 ms to 5 ms, and was applied to the adsorption of individual colloidal beads and single proteins at a solid/liquid interface. With the improved temporal capabilities, the protein desorption kinetics were shown to have a second fast component that was unresolvable with traditional single molecule microscopy, indicating that more complex desorption kinetics are present than previously thought (Fig. 3.6B–E). Additional work determining the twocomponent mechanism of protein adsorption to a polymer-modified surface using STReM suggested that protein conformational changes driven by near-field van der Waals forces leads to an intermediate that is necessary for desorption.105 Future work applying STReM to systematic studies of modified interfacial chemistry can determine the source of the multiple adsorption components for other samples.

3.5 Biophysical interfaces Single molecule spectroscopy is suited to study biophysical interfaces since the dynamic complexity of the constituents within cells are at nanoscale dimensions. Interfaces are present throughout biology: within the cell, organelles are isolated by either lipid membranes or liquid/liquid phase separation where interfaces form without membranes. At the interface between the interior and exterior of the cell, the success of the cellular membrane interface is literally the definition between life and death for individual cells.106 Between multiple cells, two separate membranes must also interface and adhere for barriers to form functional tissue. Fluorescent dyes and labeling chemistries have been developed for biocompatible live-cell microscopy above the diffraction limit, but the organization at cellular interfaces is at length scales on the order of 1–10s of nanometers.107 Therefore, it is natural to progress and use single molecule fluorescence spectroscopy to understand biointerfaces. Here, we highlight single molecule findings from two types of biointerfacial samples: live-cell membranes and intracellular liquid/liquid phase-separated membraneless organelles.

3.5.1 Live cell lipid membranes Phospholipid membranes are the interfacial division between the extracellular matrix and the intracellular space of the cell. Membranes are made up of a bilayer of lipids consisting of a hydrophobic head and lipid tail(s). The hydrophobic headgroups are at the oil-water interface dividing the fatty intrabilayer environment from the aqueous interior or exterior of the cell. This interface forms an

3.5 Biophysical interfaces

important physical and electrical barrier to water, ions, and (macro)molecules so that osmotic, signal-transduction, molecular transport, and molecular recognition responses are possible. The interfacial membrane environment is heterogeneous in composition. Lipids are a major constituent of the membrane. The chemical makeup of lipids is diverse. Upwards of 1000 different lipid species can be present in an individual cell.106 Lipids differ in chemical structure, size, and charge (cationic, anionic, zwitterionic, or neutral) of the hydrophilic head group, and hydrocarbon length, saturation, and number of chains in the hydrophobic tail. Based on the physical properties of the lipids, the membrane can be in different types of liquid-like or gel-like phases. Lateral phase separation can spatially arrange the lipids, driving the signaling, organizational, and barrier formation functions of the membrane.106 Proteins also make up a large portion of the membrane environment, which can be upwards of 50% the mass fraction of membranes.108 Half of the cellular proteome is made up of membrane proteins.107 Proteins in the plasma membrane can vary in which of the interfaces they interact with since the membrane consists of the extracellular/ hydrophilic headgroup interface, the oil/water interface of the hydrophilic headgroup/hydrophobic tail, and the intracellular/hydrophilic headgroup interface. Intrinsic proteins have a portion of the protein embedded in the hydrophobic core and include transmembrane proteins that span the entire membrane. These encounter multiple interfaces. Extrinsic proteins only interact with the hydrophilic head groups and encounter a single interface. Membrane proteins can play roles in the transport of ions, signaling, and connections to the extracellular matrix, intracellular cytoskeleton, or other cells. Finally, lipids and, more prevalently, proteins can be post-translationally modified with sugars. These glycoproteins are present at the extracellular interface of the membrane and play important roles in molecular recognition.109 Overall, the cellular lipid membrane is a complex, heterogeneous environment that is quite different from the commonly-pictured simple barrier consisting solely of a lipid bilayer. The study of single molecules in synthetic phospholipid bilayers was historically an important step in single molecule spectroscopy before studying the complexity of live-cell lipid membranes. As discussed in the methods section, one of the earliest single molecule tracking studies at interfaces was imaging a fluorescently-labeled lipid in a fluid phospholipid bilayer.21 Artificial bilayers can be deposited on a glass coverslip for TIRF imaging by the Langmuir-Blodgett technique or vesicle spreading on a glass coverslip.21,110 Diffusing or tethered vesicles can also be studied by confocal microscopy, where the effect of curvature is present compared to supported bilayers. Doping in a low concentration of fluorescently-labeled lipid (commercially available by suppliers such as Avanti or Molecular Probes) or fluorescently-labeled protein within the mixture of unlabeled lipids allows for the dynamics of isolated molecules to be detected. Single molecule spectroscopy in liposomes and supported lipid bilayers is a practical approach to study models of membranes since the exact concentrations of specific lipids and proteins can be controlled. While there are many historic projects using model synthetic membranes, we will highlight recent work on

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live cell membrane interfaces given the aforementioned heterogeneity and complexity that makes single molecule spectroscopy an exciting approach to study them. The heterogeneous organization of lipid domains and membrane receptor proteins within living cellular membranes can be visualized by single molecule super-resolution imaging. Stone and Veatch, et al.111 imaged B cell receptors (BCRs), proteins that are important in triggering the immune response in B cells. By strategically labeling the receptors and peptide markers that preferentially localized in lipid-ordered and lipid-disordered regions of membranes, super-resolution imaging and correlation analysis showed BCRs are present in the lipid-ordered domains in both fixed and living B cells (Fig. 3.7A and B). The results suggest experimental proof of the “lipid raft” hypothesis, but further experimental evidence by controlling the association of BCRs showed that the lipids do not drive the association of the proteins into domains; instead protein clustering templates the formation of “rafts.” The domain sizes are well below the diffraction limit (Fig. 3.7A, inset), showing the importance of single molecule localization. In other work, Moon and Xu, et al. used spectrally-resolved super-resolution of solvachromatic fluorophores to probe the local polarity and organization of the plasma membrane.113 The fluorophore Nile Red undergoes a
20 nm red shift when going from a less polar lipid environment to more polar environment where significant amounts of cholesterol are present. The emission of single Nile Red dyes was split onto two halves of the detection camera, with one channel having a dispersive prism to detect the spectrum of an individual molecule and the other channel detecting the position of the molecule by traditional localization-based super resolution techniques. The location was then overlaid with the weighted average wavelength of the spectral emission to produce “true color” super-resolution images. When applied to fixed and live cells, the plasma membrane was less polar than organelle membranes. Treatment of the cells with cholesterol could create lower ordered domains, similar to the “lipid rafts,” but these were not observed at the 30 nm resolution of the native, untreated live or fixed cells. Creative combinations of localization and correlative single molecule techniques can offer complementary information on the dynamic organization of the membrane interface. For example, Owen and Wiseman, et al. used localization-based super resolution imaging and spatio-temporal image correlation spectroscopy (STICS) to show that the intracellular cytoskeleton drives the movement of the membrane during the immune response of T-cells.114 STICS is an extension of image (cross) correlation spectroscopy that quantifies not only the diffusion coefficient, but also the velocity vectors of membrane proteins by performing correlation over both space and time.115,116 Upon encountering an antigen-presenting cell, T-cells structurally reorganize and form a cell-cell junction with the target cell called the “immunological synapse.” Super-resolution imaging mapped the dense meshwork of the intracellular cytoskeleton at the interface of the membrane, while STICS showed that the dynamics of the plasma membrane was quantitatively similar to the cytoskeleton within the T-cells undergoing an immune response. These results combined with protein knockouts and two-color cross-correlative imaging showed important insight that the

3.5 Biophysical interfaces

FIG. 3.7 The organization and dynamics of single molecules can be visualized in lipid membranes. (A, B) B cell receptor (BCR) is located in ordered lipid domains.111 (A) Super-resolution images of BCR (fuchsia) and a peptide that marks ordered lipid domains (PM, green) in chemically-fixed CH27 cells. The inset emphasizes the overlap between the intensity of the two. (B) Quantification of the fluorescence overlap between BCR and PM (red circles) and BCR with a marker for disordered lipid domains (blue triangles) by cross-correlation analysis. A value of 1 indicates a random co-distribution, >1 indicates co-clustering, and t)

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FIG. 3.9 Molecular mechanism of competitive interactions between molecules in multicomponent ion-exchange chromatography. (A) Super-resolution imaging of α-lactalbumin binding with 0 mM (left) and 3000 nM insulin (right) shows introducing competitors reduces the number of ligands available to analytes but not the number of analyte binding events at each ligand. (B) Competitor insulin (0–3000 nM) does not change the kinetics of desorption of the analyte α-lactalbumin from ion-exchange ligands. Cumulative distributions of the duration of α-lactalbumin binding events are plotted as the competitive insulin concentration is varied. (C, D) Proposed possible mechanisms of competitive interactions between α-lactalbumin and insulin on spermine ligands. The imaging and kinetic results did not support a (C) temporary blocking model where competitor and analyte have comparable adsorption/desorption kinetics. Instead, (D) a permanent blocking model where the insulin prevents α-lactalbumin binding due to a long competitor desorption lifetime was used to explain the observed experimental results. Reproduced from Kisley, L.; Patil, U.; Dhamane, S.; Kourentzi, K.; Tauzin, L. J.; Willson, R. C.; Landes, C. F. Competitive Multicomponent Anion Exchange Adsorption of Proteins at the Single Molecule Level. Analyst 2017, 142, 3127–3131 with permission from The Royal Society of Chemistry.

3.7 Interfacial catalysis

chemistry concepts don’t always translate to complexity interfacial interactions between biomolecules and heterogeneous materials. Instead, competitors block certain ligands from the analyte while other ligands remain available for analyte binding (Fig. 3.9D). The available ligands surprisingly have no change in the adsorption kinetics and minimal changes in the total number of binding events per ligand over three orders of magnitude of competitor concentration. While single molecule experiments offer a great deal of information on the molecular mechanisms occurring in chromatography, the representation of data can seem distant from actual chromatographic elution columns. The stochastic theory of chromatography relates single molecule spectroscopy results to ensemble column performance. Pasti, Felinger, and Dondi, et al. have shown how to unify the stochastic theory of chromatography158–160 with single molecule data and ensemble chromatography.161–163 Experimental realities can therefore inform, quantify, and predict the performance of chromatography through theory. Likewise, experimental single molecule work can provide valuable insight into related theoretical models. Modeled elution profiles from reverse phase, capillary liquid, and ion-exchange chromatography have been performed showing that adsorption site heterogeneity can lead to peak broadening. Direct comparisons of modeled elution profiles from single molecule kinetics and ensemble chromatography column results have only been reported in one manuscript for reverse phase chromatography.151 Schwartz et al. showed that additional nonspecific adsorption events occurring one order of magnitude faster that the detection limit of the single molecule setup (
1s of ms) were needed to reproduce the elution shape, suggesting additional faster processes in the column occur beyond the 13 Hz image collection rate.

3.7 Interfacial catalysis Heterogeneous catalysis of reactions that take place at the interface between a solid material surface and a liquid phase play an important role in the energy, automotive, agricultural, and pharmaceutical industries. The use of nanoparticles for heterogeneous catalysis also has benefits compared to catalysis with bulk materials due to the increased surface area, easier recoverability, and milder reaction conditions.164 Metallic nanoparticles have catalyzed C-C coupling, hydrosilylation, oxidation, and selective hydrogenation reactions.164 Both micro- and nanoscale solid catalytic materials are spatially heterogeneous on the nanoscale, including heterogeneity within individual particles and between particles. Solid catalytic surfaces can also undergo crystalline rearrangement and lose activity over time. The ability of single molecule spectroscopy to monitor the spatiotemporal heterogeneity of reactions at the solid/liquid interface at nanoscales has hence made it a tool to understand heterogeneous catalysis.14,44,165 By combining single molecule spectroscopy with ex situ techniques,166 the activity differences can be spatially related to the chemical and structural properties of the particles, such as the elemental composition, porosity,

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crystal lattices, and dimensions of particles. Characterizing the dynamics of the interfacial processes taking place between the heterogeneous solid catalytic surfaces and a liquid phase is needed for rational design of more effective catalytic materials that produce reliable, reproducible activities and reactions.167

3.7.1 Sample considerations to achieve single molecule detection at heterogeneous catalytic interfaces Individual reaction events at heterogeneous catalytic interfaces utilize fluorophores that have a significant fluorescence contrast between the reactant and product states. There are several approaches for fluorophores to “turn-on” when undergoing a catalytic reaction. For monitoring redox reactions, one of the most commonly used dyes has been amplex red/resorufin/resazurin (Fig. 3.10). When the dye reacts with holes, electrons, or radicals at the interface of catalytic particles, amplex red “turns-on” to resorufin upon oxidation, while resazurin “turns-on” to resorufin upon reduction. Further synthesis of libraries of dyes that turn-on at a range of potentials can expand the redox events monitored in electrochemical catalysis.168 Additionally, using fluorophores that undergo chromatic shifts and selecting the appropriate filter sets can be used.169 Finally, catalytic cleavage or linkage to non-radiative partners can change the spectra of dyes covalently conjugated to quenching groups5,44 or a FRET partner.170 Overall, a range catalytic processes can be monitored at heterogeneous interfaces by strategically selecting fluorogenic reactions. Surface modification of catalytic nanoparticles is often required to monitor heterogeneous catalysis with single molecule spectroscopy. A challenge with monitoring interfacial reactions with small molecule organic fluorophores is that the molecules can have short residence times at the interface and fast diffusion rates of
10–100s of μm2/s in the bulk liquid phase. There is also possibly quenching of fluorescence when gold nanomaterials are studied.171,172 This makes it difficult to localize individual molecules with wide-field techniques. To overcome this, groups have modified nanoparticles171,173–175 and bulk electrochemical surfaces176 with mesoporous silica to temporarily hinder the fluorophores so that localization

FIG. 3.10 Example of a “turn-on” fluorogenic reaction. Fluorescent resorufin (λem ¼ 583 nm) forms from either non-fluorescent amplex red or resazurin through oxidative or reductive processes, respectively, at heterogeneous catalytic interfaces.

3.7 Interfacial catalysis

analysis is possible. The silica can also stabilize the morphology of the catalytic particles to prevent surface reconstruction and remove any effects of ligands required for colloidal stabilization.173 This modification is usually notated as X@SiO2, where “X” indicates the solid catalytic material. It is important to consider that the porous layers of SiO2 can be strained and contain imperfections at nanoparticle edges and corners compared to flat areas. Strained SiO2 can sterically provide more accessibility of the fluorophores to the nanoparticles, biasing and increasing the apparent activity of edges and corners.177 Therefore, it is important to correlate results with silica coatings to ex situ imaging. Alternative means of varying the solution viscosity, dye chemistry, or using polymeric materials to change the steric accessibility of the solid surface could be modifications to achieve adequate adsorption residence or diffusion times near catalytic interfaces. Further, as single molecule camera technology advances with improved quantum yields and synthetic approaches improve the library of “turn-on” dyes with different spectral ranges, fluorescent lifetimes, and quantum yields, the activity of the unmodified catalytic interfaces could be monitored. Measurements on bare particles have been demonstrated for some materials,171,177 but aspects of structural rearrangement need to be considered in the spatial and kinetic results.

3.7.2 Resolving spatiotemporal heterogeneity at catalytic solid/liquid interfaces Single molecule spectroscopy images the nanoscale heterogeneity of reactivity in acid-base, redox,171,175,177 photo-,178–180 and electro-181 catalysis.14,44,165,182,183 For example, some of the earliest single molecule work on catalysis was localizing the nanoscale heterogeneity within microscale-sized zeolites.184 Catalytic zeolites used in the petroleum industry are solid acidic catalytic materials embedded within nanoporous clay, silica, or alumina particles. Hofkens et al. have pioneered the use of single molecule techniques to monitor the spatial inter- and intra-particle heterogeneity of catalytic active sites and temporal diffusion properties of molecules within these industrial-relevant materials.169,184,185 Ristanovi
c and Hofkens, et al. examined the catalytic activity of commercial zeolite particles with a Bronsted-acid catalyzed fluorogenic reaction of non-fluorescent furfuryl alcohol to fluorescent oligomers (Fig. 3.11A).185 Localization-based super-resolution imaging was difficult due to low signal-to-noise ratios within the industrial catalysts, as commercial materials contain increased amounts of autofluorescent impurities. Alternatively, correlation-based SOFI analysis was used where fluorescent fluctuations were caused by a combination of the constant formation, diffusion, and photobleaching of the fluorescent oligomers at different imaging planes throughout the axial volume of the particle (Fig. 3.11A and B). A thresholding procedure of the SOFI images quantified the area of catalytic sites at the porous interfaces throughout the commercial 3D zeolitic particle, showing catalytic domain sizes were similar throughout the μm-sized particle (Fig. 3.11C). But further analysis of the intensity of the SOFI image showed heterogeneity in the SOFI brightness (Fig. 3.11D). The brightness

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FIG. 3.11 Catalytic activity of zeolites within fluid catalytic cracking (FCC) particles imaged by SOFI.185 (A) Schematic of sample where data were collected at different axial planes within the particle by imaging the “turn-on” of the fluorophore by oligomerization of a molecule at reactive Bronsted sites at the zeolites. (B) Example SOFI images at different axial positions within the particle where bright spots indicate catalytic sites; scale bar 2 μm. Analysis of the size of the catalytic sites by a thresholding technique showed that (C) the reactive domain sizes were uniform throughout the particle. (D) Detailed SOFI image; scale bar 200 nm. The brightness of the pixels in the boxed areas corresponded to the (E) catalytic turnover rates. Colors of boxes and labels in (D, E) correspond. Figure from Ristanovic
, Z.; Kerssens, M. M.; Kubarev, A. V.; Hendriks, F. C.; Dedecker, P.; Hofkens, J.; Roeffaers, M. B. J.; Weckhuysen, B. M. High-Resolution Single-Molecule Fluorescence Imaging of Zeolite Aggregates Within Real-Life Fluid Catalytic Cracking Particles. Angew. Chem. Int. Ed. 2014, 54, 1836–1840. Reprinted with permission from John Wiley and Sons, Inc.

3.7 Interfacial catalysis

in SOFI images scales with the degree of fluctuations,82,83 in addition to the fluorescence intensity. Therefore, the SOFI brightness correlated with the heterogeneous catalytic turnover rates at different domains within the particle (Fig. 3.11E). Future possibilities could exist in determining the effects of the porosity of the fluorophores diffusion if the correlation curves produced by SOFI could be analyzed further within the later-developed fcsSOFI84 technique where the correlation curves are fit to known diffusion models (Section 3.3). Catalytic reaction mechanisms can be determined from single molecule spectroscopy. Sambur and Chen imaged photocatalytic oxidation at a semiconductor/liquid interface by monitoring the “turn-on” oxidation events of nonfluorescent amplex red to fluorescent resorufin at TiO2 nanoparticle surfaces.178,180 Photoexcitation of semiconductors produces holes and electrons that can either react directly with a molecule at the nanoparticle surface or react with other organic molecules and oxygen in solution to produce hydroxyl, hydrogen peroxide, or oxygen radicals which can in turn react with the molecule of interest in an indirect mechanism. Sambur derived kinetic mechanistic models for these direct and indirect pathways where the reaction rate equations have different dependences on light intensity and applied potential. By monitoring the reaction rate on the active areas of individual TiO2 nanoparticles versus potential and intensity, it was found that the reaction rate scaled with the square root of the excitation intensity and quad root of the applied potential (Fig. 3.12). This followed the mechanistic model for indirect photoelectrocatalytic oxidation of amplex red by surface adsorbed hydroxyl radicals, as opposed to the indirect oxidation by hydrogen peroxide or direct oxidation by holes at the surface. Thorough kinetic analysis at the single molecule level can hence determine molecular reaction mechanisms that are challenging to resolve with ensemble techniques. Single molecule spectroscopy can monitor the changes in catalytic surface reactivity at hours-long time scales. Typical single molecule studies of catalytic nanoparticles are performed over time resolutions of 10s of ms to several minutes. Yet, the time scales of reactions in heterogeneous catalysis span ultrafast ps-timescales for intermediate formation to the days-long use of catalytic particles.44 Zhang and Alivisatos, et al. expanded single molecule studies closer to the latter time scales with time-lapsed super resolution imaging. They showed that the reactivity of nanocatalysts was not spatially static over time by monitoring fluorogenic reactions at the same individual nanoparticles over 10–13 h.177 In their super-resolution images, the most reactive sites at defects near the facets or the edges of nanoparticles lapsed over time, so that more stable, flat surfaces actually dominated the activity over hours-long time scales. Oscillations in the local activity, sites that would be deand reactive, were observed and attributed to blocking and desorption of surface adsorbates. These findings are significant, as most single molecule studies of catalytic particles done on 2) samples closer to real column conditions should be pursued. Imaging an analyte in the presence of cellular lysate

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would present a challenging, complex mobile phase relevant to recombinantlyexpressed biologic pharmaceuticals. Using realistic organic mobile phases, such as acetonitrile or methanol that are frequently used in reverse phase chromatography, could be achieved as more dyes compatible with organic solvents are developed.200 Incorporating three-dimensional imaging could also resolve the diffusion and adsorption of analytes through realistic chromatographic columns that are packed with stationary phase particles in three dimensions.6 Finally, more comparisons between modeled elution profiles from single molecule kinetics and ensemble chromatography column results are needed for the diverse types of chromatography. The only study with reverse phase chromatography151 highlighted that faster imaging capabilities are needed. Mass transfer properties of flow, high pressures, and particle packing need to be studied at the molecular level and incorporated into theoretical models. An approach connecting single molecule findings and predicted stochastic theory elution profiles to actual column performance would be an exciting direction to truly understand the predictive nature of single molecule spectroscopic studies of chromatography. In single molecule imaging of heterogeneous catalysis, studies in more complicated, industry-relevant solution conditions could examine how “poisons” that irreversibly bind to the catalytic active sites and prevent reactants from adsorbing are spatially distributed and kinetically effect the catalysts turnover rate.201 Expanding beyond location and temporal information, incorporating spectroscopic single molecule techniques202,203 with acid- or base-chromosensitive fluorophores could relate spatial activity to local pH. While zeolites, metal nanoparticles, carbon nanotubes, metal-organic frameworks, and semiconductor nanoparticles have all had high degrees of inter- and intraparticle heterogeneity that can change over time,5,182 these results should be connected to the ensemble activity. This would require determining the difference in the catalytic activity of particles immobilized on microscope-compatible coverslips compared to colloidal suspensions of particles used in solution-based reactors. Incorporating aspects of mass transport, solvation, and temperature201 would also bridge the nanometer, millisecond active site dynamics to the industrial scale to inform the design of improved catalysts. New capabilities in hardware and analysis of single molecule techniques will also advance the temporal, spatial, and physicochemical identification capabilities of single molecule techniques at interfaces. First, molecular dynamics monitored using single molecule fluorescence imaging are conventionally observed from 10s of ms to minute time scales. Expanding the temporal scale to both shorter and longer scales should be pursued. With recent improvements in camera technology, back illuminated scientific CMOS can detect single molecules at the
80 Hz frame rate capabilities of CMOS detectors but with detection quantum yields better than EMCCD detectors. Further integrating pump-probe techniques with single molecule fluorescence microscopy could access sub-millisecond processes in reactions. As demonstrated with STReM, shorter time scales can determine intermediates of reactions.105 On the other hand, measuring longer time scales presents challenges with

3.9 Outlook

sample drift and data storage, but super resolution measurements with
14 h collection times at 2 Hz frame rates have been previously demonstrated.204 Measurements at hour- or day-long time scales could determine temporal changes and passivation that take place over the lifetime of the use of interfacial materials. Expanding the use of three-dimensional single molecule imaging at interfaces beyond those discussed in Section 3.4 will lead to better understanding of interfacial molecular properties. The current use of engineered phase masks for interfacial single molecule spectroscopy has mainly focused on the double-helix point spread function. Using more recent developments with alternative point spread functions50,51 and analyzing orientation and rotational mobility information in addition to axial information will quantify additional molecular properties. It is also anticipated that three-dimensional and super-temporal resolution techniques will be more accessible with the commercial availability of spatial light modulators and phase mask hardware and open-source analysis software.100 Further experimental tuning of the chemistry of solid surfaces and liquids could determine the effects of non-specific physical interactions at interfaces, such as van der Waals, electrostatic, steric, hydrogen bonding, and hydrophobic interactions on the dynamics of single molecules. Threedimensional single molecule fluorescence approaches with wide-field imaging could complement force techniques that quantify the nanoscale axial distance-dependences of these various forces at interfaces, but that are limited laterally to micron-scale dimensions.205 Finally, expanding the use of engineered point spread function techniques to more diverse interfacial samples beyond glass/water or water/oil interfaces will result in new findings for interfacial science. A unique application imaging the three-dimensional shape of the liquid/air interface of nanobubbles has shown the potential for diversifying interfacial three-dimensional single molecule spectroscopy.39 Integrating additional microscopies with single molecule fluorescence to produce in situ correlative images would provide additional structural and chemical knowledge of interfaces that cannot be achieved by fluorescence alone. Having coupled in situ AFM/single molecule fluorescence could localize topological features at interfaces that correlate with optically observed single molecule results. The improvement of commercial AFM systems to video frame rates of 10 Hz – the same frame rates as single molecule wide field imaging – shows the potential of having simultaneous fluorescence and force imaging.206 Chemical specificity can also be a challenge in single molecule fluorescence due to the limited number of spectrally-isolated channels and cross talk. Utilizing spectral detection of individual fluorophores expands the number of chemical species that can be measured at a time without the purchase of expensive filters for each individual channel. Recent demonstrations of spectroscopic single molecule and single plasmonic nanoparticle imaging shows the potential of detecting spectra as a routine variable.202,207 Additional integration of X-ray, Raman, or electron microscopy techniques could also provide complementary chemical or structural information to provide single molecule fluorescence,44,166 but present challenges in reasonable sources, low signal, and appropriate sample environments, respectively.

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Overall, single molecule fluorescence spectroscopy is a useful tool to understand the spatiotemporal nanoscale heterogeneity that occurs at interfaces. From the detection of single immobilized molecules at solid/air interfaces in the 1990s to the exciting current work on the dynamics of molecules in three dimensions, in living cells, and at commercially-relevant separation and catalytic interfaces, single molecule spectroscopy has determined heterogeneity and complexity inaccessible to other techniques. There are still many interesting interdisciplinary problems single molecule spectroscopy can tackle in future studies of interfaces.

Acknowledgements The Arnold O. and Mabel M. Beckman Foundation is to thank for partial support of this work by the Beckman-Brown Interdisciplinary Postdoctoral Fellowship. Additional thanks to Dr. Sergio Dominguez Medina for critical reading of the manuscript and Professor Christy F. Landes for kindly nominating me as a contributor to this book.

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Quantum dots in single molecule spectroscopy

4 Colin D. Heyes

Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, AR, United States

4.1 Introduction In the early-to-mid 1990s, fluorescence from single organic dye molecules,1–3 single fluorescent proteins (FPs)4 and single direct-bandgap semiconductor nanoparticles (also called quantum dots, QDs) were separately observed.5–7 There are other luminescent nanomaterial species which have also sometimes been observed (and utilized) at the single particle level, such as small metal clusters,8–13 organic polymers/nanomaterials,14–16 and lanthanide/actinide ion-doped upconverting nanocrystals,17 some of which have also been called quantum dots (albeit somewhat inconsistently) in the literature. However, in this book chapter, the primary focus will be on direct-bandgap semiconductor nanoparticles and so we will use the term quantum dots to refer to this specific class of fluorescent nanoparticle. The key criterion for such single molecule/nanoparticle observations (beyond the equipment perspective) is the “brightness” of the fluorophore – the product of extinction coefficient (ε) and the photoluminescence quantum yield (PL QY). It is possible to overcome a low extinction coefficient by increasing the excitation power. However, the background also increases with excitation power so, at some point, the background fluorescent signal may dominate over the signal from the single molecule or particle. Organic dye molecules and fluorescent proteins usually combine a moderate extinction coefficient at their peak absorbance wavelength (λmax) with a moderate-to-high PL QY (with some common dye molecules reaching unity PL QY). QDs exhibit a higher extinction coefficient at or above their band gap energy than organic dyes and FPs do at their λmax (approx. 3–10 fold higher). In the 1990s, PL QYs of QDs were usually below 50%, but nowadays can approach unity,18–21 meaning that QDs are often significantly brighter than organic dyes and FPs under similar experimental conditions. This fact, combined with their much higher photostability, narrower emission spectra and broad excitation bands have led to QDs becoming somewhat of a competitor to organic dyes and FPs for certain applications. Of course, the advantages of QDs come with some disadvantages that still render organic dyes and FPs superior for other applications. In particular, the size of QDs, while they Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.00004-3 # 2019 Elsevier Inc. All rights reserved.

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can be made to a size comparable to FPs, are larger than organic dyes. Moreover, QDs are rarely monovalent/monofunctional, meaning that conjugates of 1:1 label: target are much more difficult to achieve with QDs than with organic dyes or FPs. Finally, the most common QD compositions contain heavy elements (usually Cd, although some may contain Hg and Pb), and much more care must be taken in their handling and disposal. This latter disadvantage was first mitigated by “shelling” the QD with a lower toxicity material (usually ZnS)22,23 and, more recently, by replacing the toxic elements with less toxic ones, such as In, Cu and/or Ag.24–26 A comparison of each of these fluorescent probes in terms of the various properties that one must consider when choosing a particular fluorescent probe, especially when planning to use them at the single molecule level, is summarized in Table 4.1. Table 4.1 Comparison of organic dyes, fluorescent proteins and quantum dots as single-molecule fluorescent probes. Organic dyes

Fluorescent proteins

Quantum dots

1–5 nm (smaller than most proteins)

5–10 nm (same size as most proteins)

Bioconjugation chemistry well developed and easy to use. 1:1 conjugates easy

Bioconjugation chemistry well developed but requires biochemistry expertise. 1:1 conjugates easy. Commercially available but requires biochemistry expertise. Optical properties are consistent.

5–20 nm (same size or bigger than most proteins) Bioconjugation chemistry less well developed. 1:1 conjugates very difficult.

Easy to use–commercially available. Optical properties are consistent

Bright but not very photostable. Photostability can sometimes be improved by adjusting solution conditions Moderate difficulty to use in vivo

Not very bright or photostable

Multicolor requires multiple excitation sources. Spectral overlap can be a problem

Multicolor requires multiple excitation sources. Spectral overlap can be a problem

Extremely compatible for in vivo use

Requires chemistry expertise to synthesize but are commercially available. Optical properties can vary significantly. Very bright and very photostable

Moderate to high difficulty to use in vivo. Most commercial sources use toxic elements Multicolor can be realized with a single excitation source. Can have very little spectral overlap

4.2 Synthesis, shelling and functionalization of colloidal QDs

While QDs have been successfully used for regular ensemble-level applications that dyes and FPs are commonly used for, such as labeling cells, proteins and membranes, and in chemical and biochemical sensors, this chapter will focus primarily on their particular properties and uses at the single molecule/particle level. We will start by briefly introducing the synthetic approaches of colloidal quantum dots, as well as their shelling and functionalization in order to use them in various applications. We will then describe the electronic structure and single QD photophysics, paying particular attention to the significant efforts aimed at understanding and controlling the exciton relaxation dynamics that underlies the fluorescent properties at the single particle level. We will then discuss applications in which QDs have been used as fluorescence probes to understand single molecules of interest and the local environments in which they are placed, as well as their potential as single photon sources.

4.2 Synthesis, shelling and functionalization of colloidal QDs Although the focus of this chapter is the properties and applications of single QDs, it is necessary to briefly discuss the synthesis of QDs, since there is a strong relationship between the QD structure and optical properties that are tuned by the synthetic methods employed. There is a great deal of literature on QD synthesis, which cannot be fully covered here. The purpose of this section is to discuss the general synthesis approaches so that it will be easier to understand the ways that different researchers have attempted to understand and control the single QD optical properties. QDs can be synthesized using both colloidal and non-colloidal approaches. Non-colloidal approaches include Molecular Beam Epitaxy (MBE) and Chemical Vapor Deposition (CVD) in which atoms that comprise the QD are deposited on a substrate either using a carrier gas (CVD) or under ultra-high vacuum (MBE). These methods allow for the QD to be synthesized with high accuracy and reproducibility and without surface-attached organic ligands, but it is slow, expensive and results in substrateimmobilized QDs that limits processability. Colloidal approaches are much cheaper and produce much higher yields of QDs which are dispersed in condensed phases. Colloidal approaches require ways to arrest the growth of the crystal so that the crystals remain in the nanoscale quantum-confinement regime. In the early days (pre 1993), crystal growth was arrested by growing QDs in amorphous solids such as glasses and polymers, but nowadays uses coordinating organic ligands in liquids that form micelles. While this approach significantly improves processability, they usually result in some degree of size and quality distribution. Due to the fact that the majority of current QD applications, especially fluorescence-based ones, use colloidally-synthesized QDs, we will focus our attention on this. The first (and still most widely used) class of colloidal QDs synthesized were CdE (E ¼ S, Se, Te), together with their shelling and functionalization. More recently, Cd-free QDs have been developed to help alleviate the toxicity concerns associated with CdE QDs.

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The optical properties of these new Cd-free materials are generally less well understood than CdE and their application is still in the early stages, so their discussion in this chapter will be somewhat limited, but there is significant potential for their use, particularly in more advanced fluorescence lifetime-based imaging applications.

4.2.1 Colloidal CdE (E 5 S, Se, Te) QD synthesis Two major routes exist to the organic-based synthesis of QDs. The first one was introduced in 1993 by Murray and Bawendi and used dimethylcadmium and trioctylphosphine chalcogenide as the precursors and trioctylphosphine oxide (TOPO) as the coordinating, micelle-forming solvent.27 The high boiling point of TOPO allowed the reaction to proceed at high temperatures and thus to improve crystallinity while its role as the coordinating ligand arrested uncontrolled growth and reduced Ostwald ripening, allowing smaller (blue) QDs to be synthesized by limiting reaction time via rapid lowering of the temperature, and larger (red) QDs to be synthesized by maintaining the high temperature for longer periods. One disadvantage of the use of dimethylcadmium as the precursor was that it is air-sensitive and the use of an inert glovebox was required. In 2001, a second route was introduced by Peng, using CdO or cadmium acetate as air-stable precursors,28 and subsequently modified to include high boiling point non-coordinating solvents in the reaction.29 By heating the airstable precursors to moderate temperatures (170 °C) in the presence of fatty acids such as stearic, oleic or phosphonic acids, metal-coordinated fatty acids intermediates were produced that could decompose when heated to high temperatures (300 °C). This approach still required the removal of oxygen and water vapor from the reaction vessel by degassing the reagents under vacuum and replacing with an inert gas such as argon, but a Schlenk line could now be used instead of a glove box, making the synthesis much more accessible. Other modifications to the recipe, such as including amine-containing fatty acids (hexadecylamine or octadecylamine) as a co-coordinating ligand,30 or by adding inorganic anionic ligands31,32 have also been introduced over the years to improve PL QY of the QD. CdE crystal lattices can adopt one of two structures; wurtzite (hexagonal) and zinc blende (cubic).33 It was found that the synthetic conditions could be tuned so that QDs would adopt one of these two structures and the crystal structure of the QD was found to have an effect on the optical properties, particularly the PL QY.34–36

4.2.2 QD shelling One of the first ways reported to improve the PL QY of the QD was by coating the surface of the QD with an inorganic crystalline shell material (called “shelling”). ZnS was the first shell material used, developed by Hines and Guyot-Sionnest in 199622 and by Dabbousi and Bawendi in 1997.23 Shelling improves the PL QY by reducing non-radiative relaxation pathways at the QD surface that molecular ligands alone

4.2 Synthesis, shelling and functionalization of colloidal QDs

cannot accomplish to the same degree, although as will be discussed below, factors such as lattice strain play a large role. In those early papers, dimethyl zinc and hexamethyldisilathiane were used as zinc and sulfur precursors added to CdSe QDs at elevated temperatures (170–190 °C). It is important to use a temperature that is high enough to allow the crystallization of ZnS on the CdSe QD, but low enough to avoid both ZnS particle formation (nucleation) and Ostwald ripening of the QDs. This then produces CdSe/ZnS core shell QDs. Subsequently other shell materials were developed for shelling CdSe, such as ZnSe and CdS, often using less atmosphere-sensitive ligand precursors that were subsequently introduced.37–39 It had already been established in 2001 that CdO coordinated with fatty acids could be used to make CdSe cores, so extending this approach to the shell by using coordinated Zn (or Cd) salts rather than dimethyl zinc allowed for a much safer synthetic approach. One of the major disadvantages of the single-injection approach to shelling was controlling the shell thickness homogeneity from QD to QD. The Subsequent Ion-Layer Adsorption and Reaction (SILAR) method was developed around the same time in which a precisely calculated amount of shelling precursors to produce single monolayers of shell at a time were injected sequentially rather than concurrently,38 which was then combined with thermal annealing to provide additional control.40 By repeating the sequential injection and thermal cycling a fixed number of times, increasing the amount of precursors in each step to account for the increase in surface area from the previous monolayer addition of shell, precisely-controlled numbers of shell monolayers with significantly improved size homogeneity was made possible. Furthermore, using this approach, it was possible to produce well-defined multi-shells or alloyed shells, since different precursors (Cd and/or Zn with Se and/or S) could be added in different injection cycles to produce pre-determined multi-shell thicknesses.41–45 Although it had been possible to produce multishells via the older, non-SILAR method, it required a 2 step shelling process with a purification step after the first shell was grown.46 SILAR avoids this step while providing better size/shell thickness control. More recently other shelling approaches have been developed, usually accomplished by changing the reactivity of the shelling precursor reagents, so that shell growth can be either slowed down by reducing the reactivity of the precursors,47 or can be performed at lower temperatures by increasing the reactivity of the precursors.48 Often these different synthetic conditions lead to determining whether the shell adopts a wurtzite or a zinc blende crystal lattice, similarly to the way that the synthesis conditions of the core can be used to control the core crystal lattice, as well as affecting the quality of the shell crystallinity. These different shelling approaches have had significant impacts on the single QD photophysics, which will be described later.

4.2.3 QD functionalization As discussed above, the most successful QD synthesis approaches use the organic solvent approach using ligands that form reverse micelles, bound to the QD surface

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with a hydrophilic headgroup and a long hydrocarbon tail protruding from the QD to impart organic solubility and lack of reactivity. These ligands can be used to either disperse the QD in an organic polymer, or to allow for self-assembly of the QD into two-dimensional (2D) or 3D structures, provided that the size distribution of the QD sample is low enough. The former method is used extensively to study the timedependent single QD photophysics, since the QDs are immobilized in an optically-clear polymer at low concentration to allow spatial isolation and study of single QDs. The latter method has been used for the study of ensemble-based properties as they relate to devices such as LEDs, optoelectronics and photovoltaics, and will not be discussed further in this chapter. To extend their scope, such as labeling biomolecules for biological applications or to use them as aqueous metal ion sensors in environmental applications, it is necessary to modify the QD ligands. This is accomplished primarily in three ways: the addition of an amphiphilic polymer, adding a silica shell or ligand exchange. While some routes to synthesize QDs directly in water do exist,49–55 they usually result in lower quality QDs mainly due to their lower crystallinity resulting from lower temperatures used during synthesis. While some of the hurdles to low quality direct aqueous QD synthesis have been overcome recently, the post-synthesis watersolubilization route is still the most often employed. While adding a silica shell has been used successfully,56–59 it is less popular than the other two methods, ligand exchange and amphiphilic polymer addition. Several reviews have been published on the varieties of polymers and ligands that have been used.60,61 In general, for ligand exchange approaches, water-soluble bifunctional or multifunctional ligands that usually contain one or more thiol group(s) (-SH) are used. The thiol group(s) coordinate to the QD surface while a water-soluble functional group on the ligand, such as a carboxylic acid or an amine (or both), protrude out from the QD to impart water-solubility. This method allows compact QDs to be made, but such ligands can dissociate from the QD, especially under oxidative conditions, and lead to QD precipitation.62,63 Furthermore, if the QD shell is not thick enough, the thiol groups of the ligand can cause QD quenching.64 Some of these problems are solved using amphiphilic polymer approaches, which uses a monomer that contains a hydrophobic part and a hydrophilic part. Either the hydrophobic part or, more commonly, the hydrophilic part has a crosslinkable group. First, the hydrophobic section of the polymer intercalates with the organic ligands on the QDs that were already present during QD synthesis and the hydrophilic section of the monomer protrudes into the solution. Then, the monomers are crosslinked when on the QD surface. The most common approach is to use a vinyl alcohol for crosslinking, although several others have also been used. In one example crosslinking in the hydrophobic region was achieved with a diacetylene group that was photocrosslinked.65 The method of photocrosslinking avoids having to add chemical crosslinkers which aids in reducing inter-particle crosslinking, but the diacetylene ligand is not commercially available, whereas many of the amphiphilic vinyl alcohol monomers are. While the amphiphilic polymer-coated QDs are generally more chemically

4.2 Synthesis, shelling and functionalization of colloidal QDs

stable than ligand exchanged QDs, they are usually much larger in diameter, which can limit them for certain applications. All these methods lead to a functional group that can then be further reacted to biomolecules of interest. The most common approach is to form an amide bond between the QD and the biomolecule of interest via crosslinking of –COOH and –NH2 groups after activation of the –COOH group, often using carbodiimides. Care must be taken when using certain carbodiimides, though, as they can cause QD aggregation.66 A very common approach to biolabeling when overall label size is not so critical is to use amide coupling between the QD and avidin or streptavidin, which binds to a biotinylated antibody.67 This then targets a specific biomolecule of interest with high affinity, either directly or via a secondary antibody. Another method uses targeting peptides that recognize the biomolecule of interest, similar to an antibody but with a smaller overall size.68 In all cases, it is important to fully characterize the degree of specific versus non-specific binding of biomolecules to QDs, as well as determining the functionality of the QD-labeled biomolecule(s).69

4.2.4 Cd-free QDs Cadmium chalcogenide (CdE E ¼ S, Se, Te) QDs are the most well-studied and most prevalent QDs used for fluorescence applications. However, the high toxicity of cadmium is a severe limitation in their adoption in several applications, particularly in biological and environmental situations. Thus, cadmium free QDs that maintain the advantageous properties of CdE QDs have long been sought. InP QDs were one of the first alternatives used, but phosphide precursors are somewhat difficult to handle and are not particularly environmentally friendly. Nevertheless, InP QDs have been well developed and their optical properties at the ensemble and single particle level have been studied. ZnE QDs mostly emit in the ultraviolet-blue region of the spectrum, and are useful when light emission in this region is required. Applications utilizing UV-blue emission are not as widespread, however, but their emission has been extended further into the visible region by adding dopant ions, particularly copper and manganese, to produce so-called doped QDs or d-dots.70–72 Manganese doping in particular leads to yellow emission that can be easily detected. A number of applications using Mn- or Cu-doped ZnSe or ZnS have been reported over the years, such as temperature sensors,73 chemical/environmental sensors),74,75 detecting glucose76 and other biomarkers,77–79 as sensitizers in solar cells80,81 and photocatalysis82,83 CuInS2 and AgInS284,85 are more recently-reported QD compositions for emission-based applications that are similarly easy to synthesize as CdE and maintain other advantageous properties in addition to their lower toxicity.86 One example is that they show fluorescence lifetimes on the 100-ns timescale, an order of magnitude higher than the 10–30 ns for CdE QDs, which greatly improves fluorescence lifetime imaging (FLIM) and time-gated imaging (TGI),87 as discussed in more detail below.

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CHAPTER 4 Quantum dots in single molecule spectroscopy

4.3 Electronic structure and photophysics of single QDs As with all single species, certain photophysical observables become more pronounced when ensemble averaging is removed. This is particularly true for incoherent processes that can be completely hidden through ensemble averaging. Two of the more prominent ones, as they pertain to emission, are the emission spectrum and the emission intensity. Single species usually have a narrower emission linewidth than the ensemble spectrum due to removing of the heterogeneous broadening that exists in an ensemble. Heterogeneous broadening results from variations in each emitter’s structure and/or immediate environment which results in a different emission energy for each species that, when added together, leads to a wider ensemble spectrum than each individual emitter shows – so called static heterogeneity. Additionally, if either the immediate environment or the electronic structure of the single emitting species fluctuates with time, this can also lead to spectral variations of a single molecule – so called temporal or dynamic heterogeneity. Often these two types of heterogeneity are conflated and separating them requires both high spatial resolution and high temporal resolution. Until recently, spatial imaging resolution was limited to a few hundred nanometers by the Abb
e diffraction limit, but this has now been overcome via a range of super-resolution techniques. Near field processes such an electron transfer (ET) and F€ orster resonance energy transfer (FRET) have also been used to probe sub-Abb
e limit spatial resolutions. Both near field and super-resolution techniques will be discussed in detail later in the chapter as they relate to QDs – particularly single QDs. Temporal resolution is limited by both the detection equipment (instrument response function) and the number of photons that can be collected in a given time window. The number of photons that can be collected depends on both the instrument parameters such as the objective, optics, and detector quantum efficiency, as well as fluorophore photophysics such as excited state lifetime, PL QY, and fluorophore photostability.

4.3.1 Electronic structure of QDs The electronic structure of QDs differs significantly from dyes and FPs in that rather than consisting of the typical vibronic structure, where the probability of excitation depends on the wavefunction overlap integral between the ground state and the excited state, it consists of a band where the probability of absorption/excitation depends primarily on the density of states (Fig. 4.1). In Fig. 4.1, the thickness of the vertical black/red arrows represent the relative absorbance/emission strength of the energy transition. For QDs, since the density of states increases with energy, the result of this electronic structure difference is that the excitation probability of QDs (the extinction coefficient) increases with increasing excitation energy above the band gap, rather than having a peak energy resulting from vibrational wavefunction overlap, as is the case with molecular fluorophores. Due to the lower density of states close to the band gap, together with symmetry selection rules, there is some structure in

4.3 Electronic structure and photophysics of single QDs

Molecular fluorophores (dyes, FPs) excited electronic state

absorbance

Intensity

ground electronic state

Vibrational wavefunctions

emission

Vibrational wavefunctions

absorbance emission

wavelength

increasing density of states

Conduction band

conduction band edge

absorbance

emission

Band gap valence band edge

valence band

increasing density of states

Intensity

Energy

Semiconductor Quantum Dots

absorbance emission

wavelength

FIG. 4.1 Effect of electronic structure of molecular fluorophores and QDs on the shape of the absorbance and emission spectra.

the QD absorption spectra in this region that can be seen in Fig. 4.2. For emission of molecular fluorophores, the excited molecule will first relax down to the lowest vibrational state of the excited electronic state and emission is the reverse of absorption, red-shifted due to the loss of energy due to vibrational relaxation – called the Stokes’ shift. Thus, the emission and absorption peaks are of approximately the same width for dyes and FPs. For QD emission, vibrational relaxation also occurs to the lowest energy state in the conduction band (conduction band edge) but, due to the spectroscopic selection rules, only band gap emission is seen, which leads to a narrow, symmetric emission spectrum. The band gap can be increased from the bulk band gap of the material by decreasing the QD radius to below its exciton Bohr radius, due to quantum confinement effects, which can be approximated by the particle in a box (sphere) model (Fig. 4.2). This results in the fact that multiple QDs can be excited with a single light source, provided the energy of the light source is above the band gap of the smallest QD (i.e. the largest band gap) used, but they will all emit at their own band gap energy (color), leading to the possibility of multiple color emission using a single excitation source (Fig. 4.2).

171

Resolved energy levels

band gap absorption energy increases with decreasing size 400 450 500 550 600 Wavelength /nm

650

Normalized Intensity (Arb Units)

CHAPTER 4 Quantum dots in single molecule spectroscopy

Absorbance

172

700

Narrow Symmetric Emission (~30 nm) FWHM

500

550 600 650 Wavelength /nm

700

FIG. 4.2 Upper: Absorbance and Emission spectra of CdSe QDs with diameters ranging from 2.5 nm (blue) to 6.5 nm (red). Lower: Composite photograph of QDs of different sizes excited with the same 366 nm ultraviolet lamp.

The textbook by Kuno88 does an outstanding job of deriving the theoretical basis for the complete absorption and emission spectrum of QDs (as well as the onedimensional and two-dimensional analogs, quantum wires and quantum wells). The interested reader is directed to that source for a more complete description of the underlying quantum mechanics. In reality, the complete electronic structure of a QD is more complicated than that shown in Fig. 4.1. We restrict our discussion here to colloidal quantum dots, since they are the type of QD that are used in the vast majority of single molecule fluorescence applications. As discussed in the previous section, colloidal QDs are synthesized in reverse micelles with coordinating ligands that bind to the QD surface to render them soluble in a condensed phase. Ligands are mostly chosen so that they coordinate with the precursor atoms prior to nucleation while having a high boiling point to allow for high synthesis temperatures to be reached for both QD nucleation and growth. Furthermore, the QD optical properties have also been shown to depend on the crystal structure of the QD. As noted in the previous section, the synthetic conditions (generally the identity of the ligands and/or the precursor reactivity) can be varied to produce CdE QDs with either wurtzite (hexagonal) or zinc blende

4.3 Electronic structure and photophysics of single QDs

type I E

(A)

type II

quasitype II

Energy (absolute vacuum scale, eV)

(cubic) crystal structures. Generally, higher PL QYs can be achieved with zinc blende crystal structures than with wurtzite. In addition to the organic ligands that reside on the surface of a colloidal QD, most QDs that are used in fluorescence-based applications include an inorganic shell consisting of a wider bandgap material that provides an energetic barrier between the core and the ligands/external environment, producing a so-called core/shell QD. The energy barrier caused by the shell helps to confine the electron and/or hole wavefunction to the core, which in turn affects the exciton relaxation dynamics, generally increasing PL QY more than the choice of ligand alone does, although the choice of shell material and its thickness is crucial. It is important here to highlight the difference between type I, type II and quasitype II QDs, since the combination of core and shell materials used can be selected to form each of these types of QD. A more complete description of the differences can be found in Ref. 89, but the key difference is the relative band offsets between the valence band and conduction band of the core and the shell. A type I QD confines both the electron and hole wavefunction to the core. A type II QD purposely separates the electron and hole between the core and the shell. A quasi type II QD confines one of the charge carriers to the core and allows the other to delocalize over both the core and the shell (Fig. 4.3A). In Fig. 4.3A, the black lines highlight the band edge offsets between the core and shell materials on the vertical energy axis. The red curves highlight the approximate delocalized wavefunctions of the electron and the yellow curves represent the approximate delocalized wavefunctions of the hole (hole wavefunctions are inverted for presentation clarity). Note that, although not shown, type II QDs can have can have the electron confined in the core and the hole confined in the shell and quasi-type II QDs can have the electron confined to the core and the hole delocalized through both the core and the shell if the correct combination of materials are used. The bulk band gaps of various QDs are given in Fig. 4.3B. Common examples of type I core/shell QDs include CdSe/ZnS and CdSe/ZnSe while type II QDs include CdSe/ZnTe and CdTe/CdSe. Quasi Type II

−3 −4 −5 CdTe

ZnTe

−6

CdSe ZnSe

−7

CuInTe2 CuInSe2 CuInS2

CdS

ZnS

(B)

FIG. 4.3 (A) Comparison of type I, type II and quasi-type II core/shell QDs. (B) The relative band gaps and band edge offsets between different QD materials. The shaded region is the band gap, so that the lower limit of the shaded region represents the valence band edge and the upper limit of the shaded region represents the conduction band edge.

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CHAPTER 4 Quantum dots in single molecule spectroscopy

include CdSe/CdS and ZnSe/ZnS. Due to the size dependence of the band gaps, CdSe/CdS and CdSe/ZnSe has been shown to be tunable between type I and quasi type-II depending on the relative size of the core and shell thickness,90–94 so these assignments cannot be taken as absolute. Furthermore, a description of trap states needs to also be included when discussing QD photophysics. These trap states become particularly important when considering the emission from QDs and are at the heart of much of the recent research into single QD photophysics. Trap states can be internal to the core of the QD (due to polycrystallinity), at the core-shell interface (due to lattice strain), on the surface of the shell (due to dangling surface bonds) or external to the QD (due to the local environment). Furthermore, the trap state can be an electron trap state or a hole trap state. Finally, the trap state can be a deep trap or a shallow trap state, depending on its energy relative to the band edge (Fig. 4.4). Determining the number and location of trap states and the pathways underlying how the electrons and holes occupy them is necessary to fully understand the optical properties of QDs, which, as Fig. 4.4 highlights, can be quite complex.

Energy

shell

core

e-

shell

External trap state

ehν

surface trap state interfacial trap state

h+ h+

ligands

Dangling surface bonds Interfacial Lattice strain

FIG. 4.4 Comparison of electronic and overall atomic/crystal structure of type I core/shell QDs with potential trap states highlighted at the core/shell interface (caused by lattice strain), shell surface (caused by incomplete ligand passivation leading to dangling surface bonds) and external traps (resulting from the local QD environment).

4.3 Electronic structure and photophysics of single QDs

Trap states in the core of the QD are usually the result of polycrystallinity resulting in twinning planes in the crystal. The high-temperature rapid-injection approach to colloidal QD synthesis largely avoids this problem in the hands of an experienced synthetic nanochemist, but it is still important to characterize the synthesized QD core to ensure that they are indeed monocrystalline. Polycrystallinity is especially problematic for QD synthesis in aqueous solutions due to the lower temperatures employed. In many cases, experienced QD synthetic chemists can produce core QDs with up to 50% QYs. Higher QYs than this are difficult to achieve in core QDs since the organic ligands and unpassivated surface atoms still provide nonradiative relaxation pathways even with purely monocrystalline QDs. Post synthetic ligand exchange with small, densely-packed thiol ligands (e.g. propanethiol) can result in up to 80% QYs for some QDs such as CdTe.95 Binding ligands to QDs requires a strong coordinating bond to overcome the decreased entropy of the bound ligand compared to free ligand. Thiols are a common functional group that fulfills this criterion, and thiolated ligands are available in a range of sizes and geometries.64,69,96 However, the alignment of QD band gap energies with ligand electronic energies plays a significant role. For CdTe, this alignment favors radiative over non-radiative pathways, while for CdSe the opposite is true, making it more difficult for ligand passivation to increase the quantum yield of CdSe, although ionic/molecular inorganic ligands have been somewhat successful in achieving this.31,32 More often, higher QYs are achieved by adding an inorganic crystalline shell using a wider bandgap material than the core (shelling) since this also reduces the number of unpassivated core atoms, but also decouples the ligand electronic energies from the emitting core for all types of QD, allowing for thiols to be used for water solubilization without significantly reducing the QY. However, there are other photophysical factors to consider when shelling. The two most important ones are the lattice mismatch and the band gap offset, which usually compete against each other. As a rule of thumb, the larger the band gap offset, which is beneficial for exciton wavefunction confinement (Fig. 4.3, type-I QDs), the larger the lattice mismatch, which can result in interfacial trap states and can thus be detrimental to the emission (Fig. 4.4). Both the shell material and the thickness of the shell are important, since the relative effect of these competing factors changes with both shell material and thickness. The thicker the shell, the more separated the electron and hole wavefunctions are from the shell surface, but the more likely that lattice strain results in interfacial trap states. This is evident from the fact that a ZnS shell on CdSe core (a wide bandgap, high lattice mismatch combination) initially causes a rise in the QY up to 2–5 monolayers of shell, and then reduces the QY as the shell is thicker.41 ZnSe shells have a lower bandgap offset/lattice mismatch with CdSe cores while CdS has a small lattice mismatch with CdSe but produces quasi type II QDs due to the fact that the conduction band has negligible offset with CdSe, with the valence band having a moderate offset. One way to balance these competing factors is by the use of core/multi-shells (e.g. CdSe/CdS/ZnS or CdSe/ZnSe/ZnS) or core/ alloyed shells (e.g. CdSe/ZnxCd1-xS/ZnS or CdSe/ZnSe1-xSx/ZnS).41–44,46 Another way that the shell has been tuned is in controlling the crystal structure of the shell

175

176

CHAPTER 4 Quantum dots in single molecule spectroscopy

(wurtzite vs zinc blende), which also affect both wavefunction confinement as well as lattice mismatch.36 The different combinations of shell material and crystal structure have effects both on the ensemble optical properties (PL QY and fluorescence lifetime) as well as the single QD optical properties, which will be discussed in more detail below.

4.3.2 Single QD photophysics With the observation of fluorescence from single QDs came a surprising result.7 Under continuous illumination, the fluorescence intensity fluctuated between bright on states and dark off states (Fig. 4.5A). Moreover, the switching time between these states was somewhat random in nature and seemed to span multiple timescales. When on or off event durations were histogrammed and plotted on a log-log scale, a negative linear dependence was observed (Fig. 4.5B and C), and was interpreted as inverse power law behavior according to Eq. (4.1) PðOn or Off Þ ¼ Atm

(4.1)

While the blinking mechanism is interesting from an academic perspective, it poses a serious limitation on the utility of QDs in a wide range of applications. Even at the ensemble level, blinking limits the maximum number of photons that can be emitted from a QD sample since the QD will spend some of its time in the off state. However, at the single molecule/particle level, the limitations can be significant, since the QD becomes impossible to measure/track when it turns off. However, blinking can also be taken advantage of under certain conditions. Examples include verifying that a target molecule is indeed a single molecule, using blinking as a probe of the chemical species bound to the QD, and in using QDs in super-resolution microscopy. These applications will be discussed in the next section, but in order for these applications to reach their full potential, it would be ideal to control blinking to eliminate it when continuous emission is required, or to enhance it when required. In order to control blinking, it is first necessary to fully understand the mechanism underlying it. It is not surprising, therefore, that trying to propose a physical mechanism that is consistent with the underlying power law dynamics has been the subject of a significant number of studies, both experimental and theoretical. The first detailed model to provide a physical basis was described by Kuno and Nesbitt in 200397 and included external trap states in the ligand and/or substrate that had a stochastically time-varying energy and distance from the QD, formalizing and expanding upon previous descriptions along the same lines by Shimizu and Bawendi98 and Verberk and Orrit99 (Fig. 4.5D and E). The key idea was that excited charge carriers were trapped into external trap states, either via excitation to a higher energy level followed by over-the-barrier ejection (process 1) or by quantum mechanical tunneling of electrons (process 2) or holes (process 3) through the shell. During the time period that the charge is ejected, the extra charge carrier left inside the QD renders the QD charged, which quenches any subsequent exciton formation via an Auger process in which recombination of the

eV

Counts/10 ms

75 50

hn = 2.54 eV

Ec FS

˜ 5.50

25

CdSe

4.57

ZnS

1

4.06

0

20

80

60

40 Time (s)

-

2.72

104

103

3

0

2

−0.90

10 moff = 1.74 (3)

mon = 1.61 (4)

1

101

0

100

10

10

10

10–3 10–3

˜

10–1 100 Time (s)

101

102 10–3

(C)

10–2

10–1 100 Time (s)

101

102

TOPO & Fused Silica -

Ev FS

|2>

Distributed Rates

γoff ∝ γ23 e−x

γ12

10–3 10–2

Ev QD

3

−5.00

10–2

–2

+

Tr+ (0,+)

10–1

10–1

(B)

10

P[toff] (s−1)

102

-

Eg

(D)

104

2

Ec QD

2.03

Tr- (0,-)

(E)

γ21 γoff ∝ γ32 e−x'

Charged |3>

|1>

FIG. 4.5 (A) Typical blinking trace of CdSe, (B) probability distribution of on-time durations (log-log plot), (C) probability distribution of off-time durations (log-log plot), (D) physical model of hot electron trapping (process 1) and quantum mechanical tunneling of electrons (process 2) or holes (process 3) to external trap states underlying blinking, (E) distributed rates of QD charging used to explain the inverse power-law dynamics of blinking shown in (B) and (C).

177

Figures from Kuno, M.; Fromm, D. P.; Johnson, S. T.; Gallagher, A.; Nesbitt, D. J. Modeling Distributed Kinetics in Isolated Semiconductor Quantum Dots. Phys. Rev. B 2003, 67, 125304 and reprinted with permission from the American Physical Society.

4.3 Electronic structure and photophysics of single QDs

0

(A)

P[ton ] (s−1)

Vaccum

6.62

22 Å radius CdSe QDs. 0.64 kW/cm2

178

CHAPTER 4 Quantum dots in single molecule spectroscopy

exciton would result in non-radiative transfer of the recombination energy to the extra charge carrier, leading to an off state, rather than radiative recombination that would normally occur in the neutral QD. Only when the externally-trapped charge carrier was recaptured by the QD, neutralizing it, would the radiative recombination recover and the QD turn on again. The stochastically-varying trapping rate of external trapping/charging led to a power law behavior in the on-times, and a diffusive random walk of the trapped external charge back to the charged QD led to power law behavior in the off times. The value of the exponent, α, in a 1-D random walk model is 3/2, which agreed with most experimental data at the time. One of the most direct pieces of evidence for the existence of QD charging during blinking was shown by Krauss and Brus using electrostatic force microscopy.100,101 Under illumination, single CdSe/CdS and CdSe/ZnS core/shell QDs were both found to produce positively charged QDs, which increased in number with illumination intensity. Interestingly, up to 50% of the CdSe/CdS QDs were also found to become positively charged even in the dark over several weeks. CdSe/CdS are pseudo-type II QDs, where the electron is delocalized over both the core and the shell, while CdSe/ ZnS QDs are type I QDs where the electron is strongly confined to the core (Fig. 4.3). Thus it appeared as though the electron could become trapped externally when the shell used was CdS. These results were in strong agreement with the model shown in Fig. 4.5. Modifying the external trap states, such as by embedding QDs in different polymer matrices (with different dielectric constants, conducting polymers),102–105 treatment of SiOx substrates that QDs were attached to,106 placing on ITO vs glass substrates107 or varying the ligands attached to the QD surface108,109 all showed dependencies on blinking that could be interpreted in the framework of the external trap model. Some studies were published that were difficult to explain using the model in Fig. 4.5. For example, some of these early reports noted a cutoff in the on times that limited the maximum length of on events, modifying Eq. (4.1) to Eq. (4.2) for on events.98 PðOnÞ ¼ Atm exp ðt=τc Þ

(4.2)

An interesting study that compared the blinking of QDs embedded in a polymer vs freely diffusing in solution, where the external trap states were expected to be different, found no difference in blinking.110 A temperature-dependent study also suggested thermally-accessible trap states internal to the QD were involved in blinking.111 Studies that examined memory effects in QD blinking found no dependence of blinking on the nature of the substrate,112 in contrast to other reports described above that did observe a substrate dependence. Adding a ZnS shell of up to seven monolayers onto CdSe cores did not significantly decrease blinking, as would have been expected from the model in Fig. 4.5.113 ZnS is a wide band gap material that should have acted as a potential energy barrier through which the tunneling probability should have decreased exponentially with shell thickness, reducing accessibility to the external trap states. The experiment was performed under relatively low excitation powers to reduce the formation of hot charge carriers

4.3 Electronic structure and photophysics of single QDs

and reduce the over-the-barrier ejection pathway present in Fig. 4.5. ZnS is an ideal material for capping from the standpoint of band gap energetics, chemical stability and reducing toxic exposure, and had been shown to increase the ensemble quantum yield by passivating non-radiative decay pathways from trap states at the QD surface.22,23 However, there is significant lattice strain between CdSe and ZnS (12%), which is known to reduce QY as ZnS shell thickness increases beyond 3–5 monolayers41 and, at the single particle level, physical interpretations are far more complex and the picture is more like that shown in Fig. 4.4. The key question is how Fig. 4.4 can be quantitatively related to the blinking mechanism. The dependence of the values of the power law exponent in Eqs. (4.1) and (4.2) and of the characteristic cutoff time in the exponential term, τc of Eq. (4.2) under different conditions has been extensively examined over the years. For example, one of the early landmark studies by the Bawendi group showed a truncation in the exponential cutoff time for the on states with increasing QD size, excitation power and temperature or with ZnS capping, although the exact ZnS shell thickness was not given.98 In our work a few years later, a negligible effect of ZnS shell thickness on either power law exponent or exponential cutoff time was observed.113 These inconsistencies suggested that microscopic structural differences in the shells may play a role. Similar inconsistencies with excitation wavelength dependences on blinking have also been observed. Knappenberger et al.114 and Gomez et al.115 observed a dependence on excitation wavelength, while Stopel et al.116 observed no dependence, again suggesting subtle changes in the QD structure and/or experimental conditions play significant roles. We also found that solution pH of streptavidin-coated water-soluble QDs also played a significant role in blinking.117,118 Interestingly, for CdSe cores or CdSe/ZnS core/shell QDs, when water-soluble QDs were measured, both the on-times and the off times were affected by the nature of the ligand109 and pH117,118 while in most organic-soluble QD blinking studies that showed an effect on blinking,98,106,114 the on-times were affected but the off-times were largely unaffected. When core/shell architectures other than CdSe/ZnS were studied by our group,44 the off-times are affected, again showing that the model needed to describe blinking is more complex than originally thought. Two theoretical models were published by the Marcus group at approximately the same time that provided alternative explanations to the power law blinking dynamics from that of Fig. 4.5D. These are shown in Fig. 4.6. The first, proposed by Tang and Marcus, is not dissimilar to the model in Fig. 4.5D, but recasts it as a photoinduced diffusion-controlled electron transfer (DCET) model between bright and dark states in the framework of classical (Nobel prizewinning) Marcus theory.119,120 In this model, the dark states were considered as originating from long-lived charge carrier trap states similar to those shown in Fig. 4.5, but the model does not limit them to external trap states. The second, proposed by Frantsuzov and Marcus, used a model in which a long-lived trap state hypothesis was not needed.121 It used a diffusive resonance model, whereby temporal stochastic diffusion of the 1Se-1Pe transition energy within the conduction band passed through a point (ε* in Fig. 4.6) where the transition energy was either in resonance with

179

CHAPTER 4 Quantum dots in single molecule spectroscopy

DCET model

Diffusive resonance model excited state

on-event

off-event

ε

intermediate state

1Pe 1Se

kt kd

l + DG0

traps 1S3/2

l + DG0

|L*>

|D>

ke

|L*>

|D>

0 –Q1

kI

kr

0

–DG0

–Q1

reaction coordinate Q

–DG0

1Pe 1Se

reaction coordinate Q

kn hole trap state

10 1 P (t) ~ t –0.5 tc = 10–3 s 0.1 0.01 tc = 10–4 s 1E-3 tc = 10–5 s 1E-4 1E-5 P (t) ~ t –1.5 1E-6 1E-7 1E-8 1E-9 1E-10 1E-11 1E-12 1E-13 1E-14 1n 10n 100n 1μ 10μ 100μ 1m 10m 100m 1 10 100 1k

1S3/2 ground state

ε

P (t)

180

ε∗ t

t (s)

FIG. 4.6 DCET and diffusive resonance model as alternative explanations of inverse power-law blinking (see text). DCET model is from Tang, J.; Marcus, R. A. Mechanisms of Fluorescence Blinking in Semiconductor Nanocrystal Quantum Dots. J. Chem. Phys. 2005, 123 (5), 054704 and reprinted with permission from the American Institute of Physics. Diffusive resonance model is from Frantsuzov, P. A.; Marcus, R. A. Explanation of Quantum Dot Blinking Without the Long-Lived Trap Hypothesis. Phys. Rev. B 2005, 72 (15), 155321 and reprinted with permission from the American Physical Society.

(shaded region) or out of resonance with (unshaded region) the energy difference between the 1S3/2 level and the hole trap state energy levels (which could be short-lived trap states rather the long-lived trap states in Fig. 4.5). When the 1Se and the 1Pe transition energy was in resonance with the energy difference between the 1S3/2 level and the hole trap states, the hole would be trapped by transferring its excess energy to the electron to excite it from 1Se to 1Pe via Auger-assisted hole trapping, leading to the off state. When the resonance condition was not met, the transfer could not occur and the QD was on. In this model, the blinking dynamics were determined by the stochastic energy diffusion rate rather than the lifetime of the trap state. While both models incorporate possible explanations for the inverse-power law blinking dynamics, exponential cutoff behavior in the on times and spectral diffusion122–126 (see below), the DCET model also predicted that a change in power law slope from α ¼ 1.5 to α ¼ 0.5 would be observed

4.3 Electronic structure and photophysics of single QDs

at short (sub-ms) timescales (Fig. 4.6). Subsequent experiments did observe a change in power law slope from 1.5 to 0.5 at short timescales,117,127 providing some support for this model. In addition to blinking, it was found that QDs contain a non-fluorescent dark fraction – QDs in an ensemble that have little to no emission and are thus not observed at the single particle level. This was observed via correlated fluorescence/AFM imaging128,129 (Fig. 4.7A and B) as well as by dye-conjugated QDs130

FIG. 4.7 (A) Atomic force microscopy (AFM) and (B) single molecule fluorescence (Fluor) images highlighting that only a fraction of the physically-present QDs are fluorescent (bright fraction). (C) Cross-correlation curves of dye-labeled QDs to determine the fraction of QDs in water that are bright. (D) Comparison of bright fraction and ensemble QY, highlighting the correlation between these two properties. (E) Effect of pH on blinking and formation of dark fraction. (F) Comparison of various single QD properties that contribute to variations in ensemble fluorescence intensity as a function of pH. (A and B) From Owen, R. J.; Heyes, C. D.; Knebel, D.; Rocker, C.; Nienhaus, G. U. An Integrated Instrumental Setup for the Combination of Atomic Force Microscopy With Optical Spectroscopy. Biopolymers 2006, 82 (4), 410–414 and reprinted with permission from Wiley-VCH. (C) From Yao, J.; Larson, D. R.; Vishwasrao, H. D.; Zipfel, W. R.; Webb, W. W. Blinking and Nonradiant Dark Fraction of Water-Soluble Quantum Dots in Aqueous Solution. Proc. Natl. Acad. Sci. 2005, 102, 14284–14289 and reprinted with permission from the National Academy of Sciences of the U.S.A. Copyright (2005) National Academy of Sciences, U.S.A. (D) From Yao, J.; Larson, D. R.; Vishwasrao, H. D.; Zipfel, W. R.; Webb, W. W. Blinking and Nonradiant Dark Fraction of WaterSoluble Quantum Dots in Aqueous Solution. Proc. Natl. Acad. Sci. 2005, 102, 14284–14289 and reprinted with permission from the National Academy of Sciences of the U.S.A. Copyright (2005) National Academy of Sciences, U.S.A. (E) From Durisic, N.; Wiseman, P. W.; Grutter, P.; Heyes, C. D. A Common Mechanism Underlies the Dark Fraction Formation and Fluorescence Blinking of Quantum Dots. ACS Nano 2009, 3 (5), 1167–1175 and reprinted with permission form the American Chemical Society. (F) From Durisic, N.; Godin, A. G.; Walters, D.; Grutter, P.; Wiseman, P. W.; Heyes, C. D. Probing the “Dark” Fraction of Core-Shell Quantum Dots by Ensemble and Single Particle pH-Dependent Spectroscopy. ACS Nano 2011, 5 (11), 9062–9073 and reprinted with permission from the American Chemical Society.

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(Fig. 4.7C and D). It was known that there was an inconsistency of ensemble and single QD properties. For example, a higher QY does not necessarily result in reduced blinking.44,131 It is considered that the dark fraction contributes significantly to this discrepancy. By analyzing the pH dependence of both the blinking and dark fraction formation for water-soluble CdSe/ZnS QDs, Durisic et al.117 showed that a common mechanism underlies both blinking and dark fraction formation (Fig. 4.7E), and was described in the frameworks of both of the models in Fig. 4.5. The inconsistency of pH dependence of ensemble fluorescence (intensity) and single QD properties (Bright fraction, On fraction and On intensity) were quantified to extract the relative contributions of each single QD property to the ensemble118 (Fig. 4.7F). Some of the most significant progress in elucidating the physical mechanisms underlying blinking was made by studying the time-resolved fluorescence lifetime decay curves under different conditions. Fomenko and Nesbitt found that adding propyl gallate reduced QD blinking, primarily by increasing the exciton radiative recombination rate, as measured from the decrease in the measured fluorescence lifetime.132 Continued exposure of the QDs to light caused the blinking to recover, suggesting that adsorption of propyl gallate to the QD surface reduced surface trap states that came back when continued exposure caused the molecule to photochemically desorb from the QD surface. This observation was in agreement with an earlier study that reported that adding β-mercaptoethanol to a QD solution reduced blinking, although the fluorescence lifetime was not measured in that case.133 Subsequently, correlating the blinking dynamics and the fluorescence lifetime under electrochemical control uncovered two different types of blinking134,135 (Fig. 4.8). The first type was called A-type blinking and involved a lower-QY trion state that decayed faster than regular excitonic emission due to fast Auger-assisted nonradiative energy transfer from the excited electron to a second excited electron resulting from the presence of an extra electron at the conduction band edge. Placing the QD under a negative voltage bias increased the probability of an additional electron being placed in the conduction band thereby increasing the probability of a negative trion state. Due to the increase in the probability of the faster Auger-assisted lower QY process from the trion state (X) relative to the slower, higher QY excitonic decay process (X0), a decrease in the fluorescence lifetime was observed in single QDs when the QD was in an off state, in agreement with previous ensemble-level experiments along the same lines.136 The second type, B-type blinking, involved the occupation of trap states from hot electrons in the conduction band. Occupation of these trap states led to the elimination of radiative emission so that that the intensity decreased (off state) without decreasing the fluorescence lifetime. When these trap states were filled from the electrode under a negative voltage bias (e.g. 1 V), they were no longer available to be occupied from the hot electron, and blinking was reduced, verifying that it was electronic trap states that were occupied rather than hole trap states. Furthermore, it was observed that B-type blinking could be described by a pure power law such as shown in Eq. (4.1) for both on and off events while A-type blinking could be described by an exponential-cutoff power law such as

The two types of QD blinking that were found using spectroelectrochemistry (see text). Figures from Galland, C.; Ghosh, Y.; Steinbruck, A.; Sykora, M.; Hollingsworth, J. A.; Klimov, V. I.; Htoon, H. Two Types of Luminescence Blinking Revealed by Spectroelectrochemistry of Single Quantum Dots. Nature 2011, 479 (7372), 203–207 and reprinted from Nature publishing group.

4.3 Electronic structure and photophysics of single QDs

FIG. 4.8

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shown in Eq. (4.2) for both on and off events. In a given ensemble, some QDs showed one type of blinking, some QDs showed the other type and some QDs were able to be switched between the two types via small adjustments in the bias voltage. For example, Fig. 4.8 lower panel shows that at 1 V, B-type blinking was reduced but at 1.2 V, electrons from the electrode were able to occupy the conduction band, forming a trion state and thus A-type blinking. Again, the fact that different QDs show different types of blinking suggests that the microscopic structure of the QD played a significant role in the blinking mechanism. Using this two-mechanism blinking model, it appears that those earlier experiments that showed pure power law behavior in the off times but an exponential-cutoff power law in the on-times resulted from differences in the on-to-off transitions compared to the off-to-on transitions. However, the involvement of holes in affecting the quantum yield and fluorescence lifetime95 as well as blinking137–139 requires including hole trap states in the blinking model(s) as well as electron trap states. One model that was postulated in 2009 involved the idea of multiple recombination centers where holes were trapped in one of several quenching centers in the QD that were switched between active (fast trapping rate) and inactive (slow trapping rate) states.140 A random walk between these multiple two-level configurations also led to a truncated power law behavior in on and off times. The spectroelectrochemical studies described above showed that, under certain voltage biases, a range of intensity levels were observed. In fact, when the same nanocrystal was measured on different days it was found that on one day, blinking was binary (two states) while on the next day, a more continuous distribution of states was observed.134 The existence of multiple intensity levels in a blinking QD had earlier been observed by Alivisatos and Yang in 2006 and proposed to result from a continuum of states, again using time-resolved fluorescence lifetime decay analysis141 although no bias voltage was applied in the earlier experiments and they used the more common CdSe/ZnS core/shell configuration compared to CdSe/CdS used in the later spectroelectrochemical study.134 The QDs used in the earlier Alivisatos and Yang study141 were commercially sourced, so the synthetic details were not given, but were reported to be water-soluble QD-streptavidin-conjugates, which are more complex than organic-soluble core/shells and make structural connections to the multiple intensity levels difficult to assign. Trap states in B-type blinking will likely be different between different QD architectures, and can even vary between synthetic batches of QDs with the same architecture. Although the continuous distribution of states being related to multiple electronic states was initially not widely accepted, a specific gray (or dim) state was first observed in CdSe/CdS core/shell QDs in 2009.115,142 It was not immediately clear why other reports had not identified it, or whether other core/shell architectures showed it. A closer look at some of the previous reports, such as the reduced-blinking CdSe/CdS reported in 2008 by Mahler and Dubertret143 (figure 3 of that study) shows that a gray state was present, although not discussed in that paper. Time-resolved fluorescence lifetime decay analysis has shown the gray state to result from trions; one study postulated negative trions144 while another postulated positive trions.115

4.3 Electronic structure and photophysics of single QDs

Around this time, the question as to whether blinking indeed showed power law behavior was raised. Given the idea that more than two states were often present, it was shown by the von Borczyskowski group that a multi-exponential model, with different exponentials describing different recombination centers, could resemble power law behavior when several exponentials were used145 (Fig. 4.9A and B). Using state-resolved analysis, they showed that both the dwell time (on the ms timescale) as well as the fluorescent lifetime in each of these states (on the ns timescale) were different, strongly indicating a multiexponential model rather than an inverse power law. The multiple recombination centers were proposed to involve both trapped electrons and trapped holes (Fig. 4.9C). Our group also compared multiple exponential fitting to power law fitting using different shell architectures with varying lattice strains.44 The multi-exponential fitting appeared to be a better fit for the on-times, lending support to this model, but it was not possible to distinguish between the two types of fitting for the off times. However, we re-binned the blinking data at 1-ms and 20-ms time resolution (Fig. 4.9D). If the multiexponential model were valid, re-binning would affect the probability distribution functions, since re-binning would miss some blinking events that occurred in the 1–20 ms time period. If the power law model were valid, re-binning to 20-ms resolution would have no effect on the probability distribution function, since a key characteristic of power law behavior is that it is self-repeating on all timescales. For all shell architectures, re-binning does indeed change the probability density functions for the on times, highlighting that a multiexponential model is valid, while it has no effect on the probability density functions for the off times, suggesting that a power law model is more valid for the off states. Even though these models appear to be valid for all types of core/shell architecture, the differences in blinking dynamics and observed intensity states suggest that determining which recombination centers are present and more dominant is a function of the QD structure. To shine further light onto why the gray state is only observed in some reports, our group analyzed the evolution of the gray state as a function of the shell material and thickness using state-resolved, time-resolved fluorescence lifetime decay analysis.146 We found that a low lattice mismatch between the core and shell (CdSe/CdS < CdSe/ ZnSe < CdSe/ZnS) combined with a moderate shell thickness facilitates the probability of the gray state formation (Fig. 4.10A and B). Furthermore, the gray state was found to be an on-pathway intermediate between the on and off states when it is present. Finally, in addition to the normal long-lived on state observed in a blinking trace (Fig. 4.10C), a significant fraction of the QDs were found to show a short-lived bright on state (Fig. 4.10D). Notice the difference in intensity and time scale compared to Fig. 4.10C, and the agreement with the previous observation by the von Borczyskowski group (S states in Fig. 4.9A) as described above.145 In our study, we found that the relative fraction of QDs that showed a bright on state depended on the shell thickness and material, with low lattice mismatch (CdSe/CdS) and moderate shell thickness (5–8 monolayers) increasing this fraction. These observations led us to propose the model described in Fig. 4.10E, which also helps explain why the gray state is observed in only some QD reports and architectures.

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FIG. 4.9 (A) Multiple intensity levels observed in QD blinking together with their dwell times in these states. (B) Probability of on-dwell times in each intensity state can be explained using a multiple exponential fit rather than an inverse power-law fit. (C) Proposed multiple recombination centers model involving exciton, trapped electron and trapped hole states resulting in different intensity levels. (D) Effect of re-binning blinking data on the probability of on-dwell times (circles) and off-dwell times (triangles) to examine the accuracy of multiexponential vs inverse power-law fitting methods for a range of core/shell architectures. The re-binned (20-ms) data are the solid symbols while the original bins (1-ms) are the open symbols. Panels (A–C) are from Schmidt, R.; Krasselt, C.; Gohler, C.; von Borczyskowski, C. The Fluorescence Intermittency for Quantum Dots is Not Power-Law Distributed: A Luminescence Intensity Resolved Approach. ACS Nano 2014, 8 (4), 3506–3521 and reprinted with permission from the American Chemical Society. Panel (D) is from Bajwa, P.; Gao, F.; Nguyen, A.; Omogo, B.; Heyes, C. D. Influence of the Inner-Shell Architecture on Quantum Yield and Blinking Dynamics in Core/Multishell Quantum Dots. ChemPhysChem 2016, 17 (5), 731–740 and reprinted with permission from Wiley-VCH.

From Gao, F.; Bajwa, P.; Nguyen, A.; Heyes, C. Shell-Dependent Photoluminescence Studies Provide Mechanistic Insights Into the Off-Grey-On Transitions of Blinking Quantum Dots. ACS Nano 2017, 11 (3), 2905–2916 and reprinted with permissions from the American Chemical Society.

187

(A) Photon counting histogram from blinking traces of different core/shell QDs. (B) Fraction of off, gray and on states for CdSe/CdS QDs as a function of CdS shell thickness. (C) and (D) Example blinking traces of 2 differently-behaving QDs in the same sample, with one type of QD showing regular long-lived on states, gray states and off states and another type of QD showing bright, short-lived on states in addition to the other states (note the different intensity scales in (C) and (D)). (E) Physical model of different states and pathways used to describe the various intensities and lifetimes.

4.3 Electronic structure and photophysics of single QDs

FIG. 4.10

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In Fig. 4.10E, the solid circles represent electrons and the empty circles represent holes. Approximate delocalized wavefunctions are shown for each charge carrier, with hole wavefunctions (shown below the QD schematic) inverted compared to electron wavefunctions (shown above the QD schematic). In CdSe/CdS core/shells electrons can delocalize over both core and shell (Fig. 4.3) while holes are confined to the core. The off state forms either from a biexciton or a charge carrier trapped either at the QD shell surface or external to the QD (shown in Fig. 4.10E as a trapped electron). The gray state forms from a trion, either positive or negative depending on the type of trap state (electron or hole) in the QD. The normal on state forms via radiative recombination of a delocalized electron and hole. The bright on state was proposed to form when the hole is trapped external to the QD and the electron is trapped at the shell surface. The presence of the surface-trapped electron charge compresses the wavefunction of the delocalized electron to increase the overlap integral between it and the delocalized hole to increase the radiative rate and thus decrease the fluorescence lifetime while maintaining a high QY, similar to the effect that propyl gallate has on QD emission.132 The faster decay allows the QD to cycle faster between emission events thus increasing the number of photons emitted in the 1-ms time period over which the data are binned. When the shell is thin, the gray state can be bypassed since the delocalized charge carrier that exists in the on state can be directly trapped at the QD shell surface to produce the off state. When the shell is thick, this direct trapping cannot occur, and the on-pathway gray state forms between the on and off states. When the lattice mismatch between the core and the shell is high (such as CdSe/ZnSe and CdSe/ZnS), interfacial trap states play a significant role in trapping the charge carriers, which leads to a higher probability for forming the off state and increasing blinking. In fact, our group reported that a balance between wavefunction confinement and induced lattice strain by a multishell structure of CdSe/CdS/ZnS can be used to reduce blinking when the ZnS outer shell is thin, but as the thickness of the outer ZnS shell increases, blinking increases due to the formation of trap states induced by the lattice strain, leading to a Goldilocks effect of finding just the right shell thickness to reduce blinking while keeping the QD relatively compact.45 A further advantage of this multi-shell approach is that the outer shell is composed of the less toxic ZnS while a low overall size is still maintained. This architecture is likely to be more applicable to studies where toxicity is an issue, such as bioimaging and environmental sensing. When toxicity is less of an issue, complete or near-complete suppression of blinking has been reported for CdSe/CdS core/shell QDs. Initially, high blinking suppression required the shell to be grown very thick and epitaxial (12–15 monolayers).42,143 This approach both reduced interfacial trap states and isolated the QD from external trap states. Subsequently, non-blinking (or at least very low blinking) QDs using thinner shells were reported, still with the low lattice mismatched CdSe/CdS core/shell combination, making sure that the shell crystallinity was exceptionally high through changing the shell precursor reactivities and reaction conditions.47,48 Still, most of these reports of non-blinking QDs come from leading QD synthesis labs with many years of experience,42,47,48,143

4.3 Electronic structure and photophysics of single QDs

and most commercial sources do not specifically sell non-blinking QDs as standard, highlighting that reproducibility in the resulting QD structural quality as it pertains to almost complete blinking suppression is still difficult to reproducibly achieve at present. Spectral diffusion was another initially unexpected single QD optical observation,122–126 which was interpreted in the context of a self-induced Stark effect caused by changes in the local electric field upon excitation. At high excitation intensities, a weaker, blue-shifted peak due to biexciton emission was also found.125 It was subsequently found that the spectral diffusion was correlated to blinking126 (Fig. 4.11) which, again was consistent with the charging model of blinking. The ejection of a charge carrier results in an off state and charge rearrangement. Recapture of the charge carrier then leads to the QD emission at a different

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FIG. 4.11 (A–C) Correlation of spectral diffusion to blinking of 3 different QDs. (D) Spectral diffusion and steady blue-shifting of QD emission under oxidative conditions. (E) Spectral diffusion observed for both on and gray/intermediate (INT) states. (F) Distribution of peak energies resulting from spectral diffusion of on states and (G) gray/INT states. (A–C) From Neuhauser, R. G.; Shimizu, K. T.; Woo, W. K.; Empedocles, S. A.; Bawendi, M. G. Correlation Between Fluorescence Intermittency and Spectral Diffusion in Single Semiconductor Quantum Dots. Phys. Rev. Lett. 2000, 85 (15), 3301–3304 and reprinted with permission from the American Physical Society. (D) From van Sark, W.; Frederix, P.; Bol, A. A.; Gerritsen, H. C.; Meijerink, A. Blueing, Bleaching, and Blinking of Single CdSe/ ZnS Quantum Dots. ChemPhysChem 2002, 3 (10), 871–879 and reprinted with permission from Wiley-VCH. Panels (E–G) are from Ibuki, H.; Ihara, T.; Kanemitsu, Y. Spectral Diffusion of Emissions of Excitons and Trions in Single CdSe/ZnS Nanocrystals: Charge Fluctuations in and Around Nanocrystals. J. Phys. Chem. C 2016, 120 (41), 23772–23779 and reprinted with permission from the American Chemical Society.

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wavelength that remains steady until it blinks again, whereby the emission reappears at another different wavelength. Different QDs appeared to behave differently suggesting that the QD structure and/or local environment played a role (Fig. 4.11A–C). A more recent study on commercial QDs that showed a specific gray state found that the gray state also undergoes spectral diffusion, although at a different energy and with a different distribution147 (Fig. 4.11E–G). van Sark et al. found that, in addition to spectral diffusion, an oxygen-induced irreversible blue-shifting of the emission occurred at high powers due to a photooxidation process that eventually resulted in photobleaching148 (Fig. 4.11D). H+ catalyzed photooxidation was also observed for streptavidin-coated commercial QDs in water that affected ensemble PL intensity, QD blinking and the formation of the dark fraction in complex ways.118 Nazzal et al. found a similar blue-shifting, together with photoenhancement rather than photobleaching that was interpreted in the context of photoinduced annealing, although those experiments were not performed on single QDs.149,150 Similar spectral diffusion was reported for Si QDs151 highlighting that the internal Stark effect caused by charge redistribution is a somewhat ubiquitous feature, although the variability in details reported in the different studies again suggest that the exact properties observed depend strongly on the specific single QD structure. Since QDs are spherical in shape and therefore isotropic, the emission is not polarized. However, as QDs become anisotropically shaped, such as when they become rod-shaped, the emission then becomes linearly polarized.152–154 This occurs both from a single CdSe quantum rod (QR)152,153 or from so-called dot-inrod structures, where a rod-shaped CdS shell is anisotropically grown around a spherical CdSe core (Fig. 4.12A and B),154 which, although structurally different from a CdSe QR, is also sometimes called a quantum rod. In both cases, if the emission is separated into parallel and perpendicular polarization channels and separately detected, there is an anticorrelation in the emitted intensities (I/ and I?, respectively) with angle (Fig. 4.12C), which is plotted in Fig. 4.12D. The transition from zero polarization to high polarization depends strongly on the aspect ratio (length/width) of the nanoparticle,152 in agreement with empirical pseudopotential calculations152 based on a dielectric model.155 The effect of adding various shells to rod-shaped CdSe cores has also been studied both in terms of their photophysics and in terms of their applications as fluorescent biological labels and in polarization-based optoelectronics.156–161 A recent study produced graded-shell NRs between a CdSe QR core and a ZnS shell (CdSe/Cd1–xZnxS) that both increased polarization and reduced blinking.159 As expected, surface states and lattice strain play key roles in blinking of QRs as they do for QDs, but they also discovered that gradually increasing the zinc:cadmium ratio radially through the thickness of the shell increased the polarization of the emission. The effect of the shape anisotropy on electronic structure of core/shell NRs has been studied,162 which shows that there is an excitation energy dependence to the measured polarization. The radially-increasing distribution of zinc in the gradedshell structures was thus found to magnify the effect of the shape anisotropy on electronic structure of single QRs.159

4.4 QDs as single-molecule fluorescent probes

FIG. 4.12 (A) Schematic of a CdSe/CdS dot-in-rod structure, which is also sometimes called a quantum rod (QR). (B) TEM image of as-grown dot-in-rod structures showing a difference in contrast between the CdSe core and the CdS shell. (C) Intensity of emission of parallel (I/) and perpendicular (I┴) polarizations. (D) Emission polarization ratio as a function of angle for single dot-in-rod, where polarization ratio is defined as (I/  I?)/(I/ + I?). Figure from Ohmachi, M.; Komori, Y.; Iwane, A. H.; Fujii, F.; Jin, T.; Yanagida, T. Fluorescence Microscopy for Simultaneous Observation of 3D Orientation and Movement and Its Application to Quantum Rod-Tagged Myosin V. Proc. Natl. Acad. Sci. 2012, 109 (14), 5294–5298 and reprinted with permission from the National Academy of Sciences U.S.A.

4.4 QDs as single-molecule fluorescent probes and single photon sources The first experiments that showed that QDs could be used for biological imaging were published in 1998, independently by Bruchez et al.58 and by Chan and Nie.163 While those first experiments did not take full advantage of the unique optical properties of QDs, they were immediately recognized for their importance in opening up a new era in QD-based bioimaging. As Table 4.1 highlights, there are certain applications where QDs are a superior choice to dyes or FPs. The most prevalent properties are those that take advantage of the highly photostable emission from QDs for long-timescale imaging, and the fact that a single excitation source can be used to excite multiple colored QDs due to their band structure (see Figs. 4.1 and 4.2). These applications have manifested a wide range of methodologies but we will focus on those that have made a major impact on using QDs as fluorescent probes at the single molecule level.

4.4.1 Single particle tracking (SPT) One of the first landmark experiments that took advantage of QD photostablity at the single particle level for a biological application was reported by Dahan et al. in 2003, in which single particle tracking (SPT) was used to measure 2-D diffusion of glycine

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receptors in neural cells.164 Since then, SPT has been a key application in which the photostability and multicolor properties of QDs have been exploited.165,166 There is a huge range of literature on this application, so we will focus here on highlighting some key applications, especially where the unique QD optical properties are taken advantage of. 2-D diffusion of QD-labeled membrane proteins has been particularly well-studied, and the fact that they can be followed for minutes to hours rather than the ms-to-s timescales that dye labeling allows has uncovered a wide range of diffusive behaviors ranging from Brownian, confined diffusion and directed transport.167,168 This has been extended into three dimensions,169 for example by following the diffusion of QDs as they are internalized into cells and interact with sorting endosomes170 (Fig. 4.13A). Also, molecular motors such as kinesin have been labeled with QDs and imaged as they “walk” along microtubules,171 as have myosin motors as they walk along actin filaments.172 The multicolor capability of imaging with QDs also allowed the two heads of a single myosin V motor to be separately tracked and directly visualized a hand-over-hand walking mechanism172 (Fig. 4.13B). A similar two-color QD labeling strategy of myosin VI revealed that this motor protein switches between a hand-over-hand (large steps) and an inchworm (small steps) walking mechanism, depending on strain and ATP, highlighting key differences in how different molecular motors function.173 Other SPT examples include using QDs to label and track enzymatic proteins involved in lipid metabolism at lipid-water interfaces167 and of aquaporins in cell membranes,168 both of which revealed multiple diffusion modes, and to directly label lipids and follow their diffusion both within supported phospholipid membranes and within cell membranes.174–177 Combining specific FP labeling of the endoplasmic reticulum (ER) with QD-based SPT showed compartmentalization of diffusion inside cells as well as exclusion of QDs from microsized domains in perinuclear regions of the ER which uncovered specific effects of intracellular crowding on macromolecular diffusion.178 Blinking can still be a major issue for QD-based SPT, which can limit the maximum trajectory lengths and, to a lesser extent, the brightness, but it is still orders of magnitudes improvement over using single dyes. However, unlike dyes, QD aggregates can negatively affect results since it can be difficult to distinguish larger aggregates of QD labels from changes in the actual diffusion constant of the biomolecules of interest.179 For example, one way of measuring diffusion coefficient by SPT is to find the jump distance of single QDs by measuring the distance moved, r, between successive frames of a movie, Δt, and the diffusion coefficient, Dt, is found according to Eq. (4.3)179,180 pðr, ΔtÞ ¼

  X At r2 r  exp  2Dt Δt 4Dt Δt t

(4.3)

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4.4 QDs as single-molecule fluorescent probes

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FIG. 4.13 (A) 3D SPT of QDs at various stages of internalization into cells. (B) QDs were used to label each head of a kinesin molecular motor and each head was tracked as they walked along microtubules in a hand-over-hand mechanism. (A) From Ram, S.; Prabhat, P.; Chao, J.; Sally Ward, E.; Ober, R. J. High Accuracy 3D Quantum Dot Tracking With Multifocal Plane Microscopy for the Study of Fast Intracellular Dynamics in Live Cells. Biophys. J. 2008, 95 (12), 6025–6043 and reprinted with permission from the Biophysical Society. (B) From Warshaw, D. M.; Kennedy, G. G.; Work, S. S.; Krementsova, E. B.; Beck, S.; Trybus, K. M. Differential Labeling of Myosin V Heads With Quantum Dots Allows Direct Visualization of Hand-Over-Hand Processivity. Biophys. J. 2005, 88 (5), L30– L32 and reprinted with permission from the Biophysical Society.

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a slower one (5.5 μm2/s, blue curve) was assigned to QD aggregates and a faster one (17.5 μm2/s, green curve) to QD monomers (Fig. 4.14). In fact, in this example, the aggregate species were more common than the monomers, so it is important to pay close attention to the aggregation state of QDs when analyzing SPT data. Blinking is a key method by which one determines whether a measured fluorescence spot is from a single QD or an aggregate. If the QD is indeed a single QD, the fact that is blinks completely off is a good indicator of this fact. Unfortunately, when it does blink off, spatial information can no longer be obtained until the single QD turns back on again. By using recently developed nanocomposite QDs of different colors in a multicolor SPT experiment, it is possible to use blinking to verify if a single molecule is being measured while overcoming the inability to track it when it does blinks off.181 As stated above, multicolor imaging is a major strength of using QDs due to the fact that multiple-colored QDs can all be excited by the same excitation source. The key to this new approach lies in producing very well-defined aggregates of different QD sizes/colors, called nanocomposites when this control is obtained, so that blinking of any single QD within the aggregate does not cause all the fluorescence to decrease, but the measured color will vary when one (or more)

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4.4 QDs as single-molecule fluorescent probes

of the QDs blink off, thus being able to characterize the fluorescence is from a single nanocomposite. Effectively the ratio of the multiple emission colors is measured at each frame in the movie rather than just the overall fluorescence intensity and this ratio provides the ability to examine whether the detected species is an aggregate or a single nanocomposite (Fig. 4.15A and B) so that aggregates can be easily excluded from further analysis. Furthermore, it is possible to distinguish between the QD label drifting out of focus vs QD blinking (Fig. 4.15C), which is not possible using conventional single-color SPT.

FIG. 4.15 (A) Composite nanoparticles (CNP) of green and red QDs shows color changes as each QD blinks on and off, which can be followed by the red-to-green ratio of emission. (B) Large aggregates do not show color change. (C) Single QDs blinking cannot be distinguished from QD aggregates diffusing in and out of focus while CNPs allow this distinction to be made. From Ruan, G.; Winter, J. O. Alternating-Color Quantum Dot Nanocomposites for Particle Tracking. Nano Lett. 2011, 11 (3), 941–945 and reprinted with permission from the American Chemical Society.

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As described in the previous section, quantum rods (QRs) show polarized emission at the single particle level. This optical property has also been exploited in SPT to produce so-called 4D SPT traces. In this case, the fourth dimension is polarization information, which can give orientation information of the labeled molecule of interest. For example, following the polarization of QRs attached to the membrane protein CD36 during cell internalization182 (Fig. 4.16) and QRs attached to myosin molecular motors as they “walk” along actin filaments154 (Fig. 4.17) have provided orientation information of these proteins during these processes. In Fig. 4.16, QR-based 4D SPT studies show that the orientation of the CD36 receptor varies as a function of the stage of the cellular internalization process it is in. When on the cell membrane, the receptor rotates rapidly and freely while diffusing laterally (Fig. 4.16F). When in the cytoplasm, one directional movement of the receptor was observed with only slight rotation, most likely traveling via microtubules (Fig. 4.16G). Once near the nucleus, the receptor appeared to drift and rotated slowly in a helical motion, likely a result of the structure of the nuclear membrane (Fig. 4.16H). Fig. 4.17 shows that as myosin walks along microtubules with 30 nm steps, changes in the Φ angle (in the X-Y plane) but not in the θ angle (between the Z-axis and the X-Y plane) are observed. There is a distribution in the Φ angle during these steps, centered at 90°. These fascinating studies highlight the power of using fluorescence polarization combined with high photostability offered by QRs to address important biological questions.

4.4.2 Fluorescence/image correlation spectroscopy (FCS/ICS) Correlation spectroscopy has also been used to uncover interesting single molecule behavior both in QD photophysics as well as QD-labeled biomolecules. Correlation analysis at short (ns) timescales was used to study the quantum emitting nature of a single, immobilized QD blinking though photon antibunching observations.183,184 Point-based Fluorescence Correlation Spectroscopy (FCS)185 and Image Correlation Spectroscopy (ICS)186 were also used to study blinking, but have been much less widely used in the QD blinking field than the threshold-and-histogramming approach described above. Once QDs were applied to time-resolved biological studies, such as protein/membrane transport and diffusion, where correlation spectroscopy is commonly used, it was necessary to understand how blinking affected the conclusions drawn about the biomolecule properties observed using FCS/ICS. The power law behavior of blinking (Eqs. 4.1 and 4.2) was combined with the diffusion and/or transport of biological species to fit the FCS curves (autocorrelation functions). Larson first used two-photon FCS for in vivo imaging, primarily as a way to calculate the number of fluorescent particles in a two-photon confocal volume,187 showing that the count rate per molecule, and thus the number of measured fluorescent particles, saturated at high excitation power. The effect of blinking (through excitation power dependent experiments) on the shape of the FCS curve was subsequently discussed by Doose et al.188 and Heuff et al.189 The effect of blinking on the shape of the FCS curve is show in Fig. 4.18A. At low power, the flat shape

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Figure from Watanabe, Tomonobu M.; Fujii, F.; Jin, T.; Umemoto, E.; Miyasaka, M.; Fujita, H.; Yanagida, T. Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods. Biophys. J. 2013, 105 (3), 555–564 and reprinted with permission from the Biophysical Society.

197

(A) Schematic of QR-labeled CD36 in the cell membrane and during internalization. (B) Fluorescence microscopy image showing emission from several single QRs in the p and s polarization direction overlaid with the location of the cell membrane. (C) Zoomed-in view of single QRs highlighted as 1 and 2 in panel B. (D) Time-dependence of p and s polarization intensity of a single moving QR-labeled protein. (E) Plot of 3D spatial coordinates and angle of a single QR-labeled protein as a function of time. (F–H) 4D trace of spatial coordinates and angle (shown in color) of three different QR-labeled proteins; (F) one on the membrane, (G) one in the cytoplasm and (H) one near the nucleus.

4.4 QDs as single-molecule fluorescent probes

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FIG. 4.17 (A) Schematic of QR-labeled myosin on an actin filament. (B) Position and (C) angles (Φ is the angle in the X-Y plane and Θ is the angle between the Z-axis and the X-Y plane, where the coverslip defines the X-Y plane and the optical axis defines the Z-axis) of QR-labeled myosin as a function of time. (D) Histogram of changes in Φ angle during myosin steps. Figure from Ohmachi, M.; Komori, Y.; Iwane, A. H.; Fujii, F.; Jin, T.; Yanagida, T. Fluorescence Microscopy for Simultaneous Observation of 3D Orientation and Movement and Its Application to Quantum Rod-Tagged Myosin V. Proc. Natl. Acad. Sci. 2012, 109 (14), 5294–5298 and reprinted with permission from the National Academy of Sciences U.S.A.

of the FCS curve before the rapid decrease is indicative of pure diffusion. As excitation power increases, the early part of the FCS curve is more sloped due to the power-law blinking. At the lowest excitation power, where blinking does not contribute significantly to the FCS curve, the hydrodynamic diameters of various bioconjugated QDs were extracted (Fig. 4.18B), peptide coated CdSe/ZnS (pcNCs), peptide coated CdSe/CdS/ZnS (pcNcs(+Cd)), phospholipid coated CdSe/ZnS (lcNCs), commercial amphiphilic polymer coated and streptavidin conjugated CdSe/ZnS (QDots) using the equation for a single species diffusing in solution (Eq. 4.4) to extract the diffusion time, τD, from the (second order) autocorrelation function (ACF) for pure diffusion, g2Diff(t). The confocal beam waist width, w0, and height, z0, defined as when the intensity drops to 1/e2 of its maximum value in the equatorial and axial directions, respectively, must be known for the microscope in fitting the ACF to determine τD. From τD, the diffusion constant, D, and hydrodynamic radius, Rh, can be calculated according to Eqs. (4.5) and (4.6) respectively.190

4.4 QDs as single-molecule fluorescent probes

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FIG. 4.18 (A) FCS curves of QDs as a function of excitation power showing the effect of blinking on the measured autocorrelation functions. (B) Using FCS to obtain hydrodynamic diameters of various types of QD functionalizations. (C) Fluorescence intensity as a function of time of single QDs functionalized with photocrosslinked ligands diffusing through a confocal volume. (D) Fluorescence intensity as a function of time of aggregated QDs resulting from incomplete ligand crosslinking diffusing through a confocal volume. (E) FCS curves of single and aggregated QDs as shown in (C) and (D). Here G(τ) and g2(t) from Eqs. (4.4) and (4.7) refer to the same parameter, and are often interchanged in the literature. Panels (A and B) are from Doose, S.; Tsay, J. M.; Pinaud, F.; Weiss, S. Comparison of Photophysical and Colloidal Properties of Biocompatible Semiconductor Nanocrystals Using Fluorescence Correlation Spectroscopy. Anal. Chem. 2005, 77 (7), 2235–2242 and reprinted with permission from the American Chemical Society. Panels (C–E) are from Gotz, M. G.; Takeuchi, H.; Goldfogel, M. J.; Warren, J. M.; Fennell, B. D.; Heyes, C. D. Visible-Light Photocatalyzed Cross-Linking of Diacetylene Ligands by Quantum Dots to Improve Their Aqueous Colloidal Stability. J. Phys. Chem. B 2014, 118 (49), 14103–14109 and reprinted with permission from the American Chemical Society, https://pubs.acs.org/doi/abs/10.1021%2Fjp505340c. Further permissions related to panels (C–E) should be directed to the ACS.

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1 0 1B 0 C C B B 1 1 CBvffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC B C g2Diff ðtÞ ¼ g2 ð0Þ@ A t Bu  2  !C C Bu 1+ w0 t A τD @t1 + ∙ z0 τD w0 2 4τD

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g2(0), the value of the ACF at time 0, is inversely proportional to both the effective confocal volume, Veff, and the average concentration of emitting species, hCi, i.e. g2(0) ¼ 1/(VeffhCi), kB is the Boltzmann constant, T is the temperature and η is the viscosity of the solution at that temperature. Our group has used FCS as a tool to show the increased ability of visible-light photocrosslinked ligands to maintain colloidal stability of water-soluble QDs compared to when ligand crosslinking with ultraviolet light, which was found to cause ligand desorption and subsequent QD aggregation65 (Fig. 4.18C–E). By fitting the ACF to Eq. (4.7), which adds the blinking parameters to Eq. (4.4), it is possible to extract both the hydrodynamic radii as well as the blinking parameters for the single blinking QDs.189   FðA∙τm2 Þ g2 ðtÞ ¼ g2Diff ðtÞ 1 + 1F

(4.7)

Where g2Diff(t) is the ACF from pure diffusion, Eq. (4.4), F describes the fraction of particles that blink during the transit time in the beam and A and m describe the power-law blinking dynamics, as described in Eq. (4.1). When the QDs are immobilized, FCS and ICS often provide similar information regarding single QD photophysics. The advantage of point-based FCS over ICS is that faster timescales can be measured with FCS, since the fastest timescale is determined only by the response time of the point detector (down to ps timescales). Imaging speeds (and thus ICS data timescales) are limited by frame transfer rates of the camera, which can now reach sub-ms, but rarely reaches sub-100 μs. Both of these are theoretical limits and practical timescale limits are usually determined by the number of photons collected by the microscope. However, when the QDs are not immobilized (i.e. they are undergoing diffusion and/or transport), ICS, like SPT, allows one to follow the same QD in a series of movie frames by cropping regions of interest (ROI) to isolate single QDs one at a time before performing image correlation analysis to extract out diffusion/transport parameters, while FCS will only provide the average diffusion/transport parameters of an ensemble of single QDs passing through a point. However, unlike SPT, ICS can also be used at higher fluorophore densities, which can mean that it is easier for ICS to approach the theoretical

4.4 QDs as single-molecule fluorescent probes

timescale limit of the camera compared to SPT, since there is a higher photon flux when the fluorophore densities are higher.191 By increasing fluorophore concentration, however, the ICS technique becomes more analogous to FCS, losing the single molecule heterogeneity information. Still, spatial heterogeneity is easier to study with ICS than with FCS, since FCS would require many single points to be sequentially measured to build up an image. This is possible, as our group has shown in a recent study imaging flow in a microfluidic device,192 but ICS is much faster in this regard, since spatial data points are collected in parallel. Although multiple analysis methods can sometimes be applied to the same data set (e.g. SPT and ICS at low fluorophore densities), one usually decides on whether SPT, FCS or ICS is the best technique to apply on a case by case basis depending on the goal of the study. One problem with using QDs for ICS is that overestimation of diffusion constants due to QD blinking can be significant, reaching up to 50%, as was observed when using ICS even at only moderate excitation powers.193 An interesting approach to overcome this systematic error is to use k-space ICS (kICS), as developed by the Wiseman group.193,194 The key to this approach is that the time correlation is performed only after taking the spatial Fourier transform of each image frame in the movie. Fig. 4.19 shows an example of kICS when applied to QD-labeled CD73 cell membrane protein diffusing within the basal cell membrane of a fibroblast.193 When temporal ICS was used to analyze the diffusion coefficient, there was an overestimation that occurred due to QD blinking, which became worse at higher excitation laser powers due to faster QD blinking. Using kICS avoids this overestimation, since taking the spatial Fourier transform (F.T) before calculating the image correlation function separates the time-dependent contributions of intensity fluctuations due to fluorophore photophysics from the space/time-dependent fluctuations due to movement, according to Eq. (4.8)194: 

ln

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where the rk(k,τ) is the k-space time correlation function, found by taking the F.T. of each image frame in the movie, then multiplying the F.T. of frame i with the complex conjugate of the F.T. of frame i + τ, and averaging over all i and τ. rk(k,0) is the same function for τ ¼ 0, which is to say the F.T. of frame i multiplied by the complex conjugate of the F.T. of the same frame. j k j2 is the circular average of the spatial F.T. of the image frame. The fluorophore photophysics (such as blinking) are contained in the correlation functionh hθ(t)θ(t i + τ)i, and thus only affects the intercept of plotting rk ðk, τÞ the linear graph of ln rk ðk, 0Þ vs j k j2, while the slope provides the pure diffusion coefficient at each discrete value of τ, Dτ. Finally the diffusion coefficient D is recovered from plotting the linear graph Dτ vs τ. Furthermore, traditional correlation methods (FCS and ICS) requires knowing the point spread function (PSF) of the microscope to extract accurate diffusion, flow and fluorophore concentration parameters. Although the PSF is relatively easy to calculate from knowing the beam waist width, w0, and height, z0, as defined in Eq. (4.4) and approximating the PSF as a

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Gaussian function, it requires a separate experiment using a fluorescent standard (usually a non-blinking dye or a fluorescent dye-loaded polymer microsphere that is smaller in size than the PSF) to determine w0, and z0. This step can be avoided using kICS since taking the Fourier transform of the image before correlating in time does not require knowledge of the PSF.

4.4 QDs as single-molecule fluorescent probes

4.4.3 Single molecule FRET Single Molecule FRET has revolutionized biophysics by uncovering static and dynamic heterogeneity in protein structures, dynamics and interactions. However, although FRET theory has been successfully extended to QDs at the ensemblelevel,195 it took a while for QDs to be extensively used in single molecule FRET assays due to some hurdles that needed to be overcome. Unlike dye molecules, QDs are usually large compared to the protein of interest (see Table 4.1), which can interfere with the protein structure and/or affect its interaction. Also, as Table 4.1 highlights, making 1:1 conjugates of QD:protein is more difficult than 1:1 dye:protein or FP:protein conjugates. Finally, it is very difficult to use QDs as FRET acceptors, since any excitation beam used to excite the donor will necessarily also excite the acceptor. This is because the acceptor must have a bandgap energy lower than the donor, and any light with enough energy to excite the donor will excite the acceptor QD with a higher efficiency due to its higher absorption cross section at any given wavelength. Single molecule QD-based FRET, particularly using QDs as the FRET donors, have been reported in a number of studies. The first example was published by the Ha group using commercial QDs bound to a DNA Holliday junction (that was also labeled with a dye FRET acceptor) and immobilized on a biocompatible coverslip. In that study, relatively large commercial QDs were used with a streptavidin coating that was used to bind the DNA Holliday junction to the QD, and therefore the FRET efficiency was low. Nevertheless, it highlighted the potential for QDs to be used in single molecule FRET and sparked further development of single molecule QD-based FRET assays for a range of biological applications. One subsequent study used a diffusion-based single molecule FRET experiment with a QD donor and dye acceptor to detect specific DNA sequences.196 A recent report used a surface-immobilized FRET assay to detect enzymatic glycosylation of a dye-labeled peptide197 (Fig. 4.20A). When the peptide was glycosylated using O-linked N-acetylglucosamine transferase (OGT), it was able to bind to the QD and FRET was observed, while the non-glycosylated peptide (no OGT) was not able to bind and therefore no FRET was observed. A similar experimental setup was used to measure ATP hydrolysis by myosin Va by labeling the myosin Va with a QD donor and ATP with a dye acceptor.198 Both the immobilization process and the use of QDs were particularly suited here due to the long timescale needed to measure multiple hydrolysis events (Fig. 4.20B, note the several hundred second timescale). The upper trace of Fig. 4.20B shows the time-resolved FRET using Mg-ATPase and the lower trace of Fig. 4.20B uses Ca-ATPase. From these traces, histograms of the off-rates were plotted showing a single Gaussian distribution of the off-rates. Single molecule QD-based FRET has also been applied for studies in live cells (Fig. 4.20C). In Fig. 4.20C, reversible dimerization of epidermal growth factor receptor (EGFR) was studied in live A431 cells by labeling EGF with a QD FRET donor and an antibody for EGF with a dye acceptor.199 Both homodimers of QD-QD and heterodimers of QD-dye were evident from the intensity trace (marked by green arrows and red arrows respectively), which was expected due to the statistical tagging

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4.4 QDs as single-molecule fluorescent probes

of EGFR with either QD-EGF or dye-antibody (see schematic of Fig. 4.20C). Single QD fluorescent microscopy images of donor and acceptor fluorescence and fluorescence lifetime decays curves verified the FRET process. The hurdles associated with using QDs as FRET acceptors have been reviewed recently200 and some progress has been made using fluorescence lifetime approaches. Ensemble-level FRET experiments from QD-to-QD using Ca2+ ions,201 K+ ions202 or trinitrotoluene (TNT)200 to electrostatically bind QD donors to QD acceptors has been reported, as has using biochemical interactions such as antibody-antigen binding to couple QD donors to QD acceptors203–205 but so far, no examples of single molecule FRET using a QD acceptor in a biological application have been reported. Nevertheless, the fact that ensemble level experiments exist provides some confidence that single molecule versions could be forthcoming.

4.4.4 Super-resolution microscopy More recently, QD blinking, which is a major disadvantage from the point of view of single molecule imaging (SPT, FCS, ICS, smFRET), has been exploited in a range of super-resolution imaging techniques. In 2014, Profs. Eric Betzig, W.E. Moerner and Stefan Hell shared the Nobel Prize in Chemistry “for the development of superresolved fluorescence microscopy”. All three fluorescent probes shown in Table 4.1 have been used for super-resolution microscopy,206 but we will focus here FIG. 4.20, CONT’D (A) Single-molecule fluorescence images of donor (green) and acceptor (red) together with the overlay show the presence of FRET when O-linked N-acetylglucosamine transferase (OGT) was used but was absent when it was not used, highlighting that the peptide was glycosylated by OGT. (B) Time resolved fluorescence intensity traces of QD donor-labeled myosin Va (green) and dye acceptor-labeled ATP (red). Binding of ATP resulted in FRET followed by hydrolysis, which resulted in FRET being lost. The upper trace uses Mg-ATPase and the lower trace uses Ca-ATPase. The dynamics of the off-rates are measured from the FRET traces and plotted as a histogram. (C) EGFR dimerization is studied by formation of homodimers (green arrows leading to an increase in QD signal) and heterodimers (red arrows leading to a decrease in QD signal). The traces are measured from the fluorescence microscopy images below and FRET is verified by the fluorescence lifetimes of QD donor in the absence of acceptor (black curve), QD donor in the presence of acceptor (blue curve) and the dye acceptor following FRET (red curve). The green curve is the instrument response function. (A) From Hu, J.; Li, Y.; Li, Y.; Tang, B.; Zhang, C.-y. Single Quantum Dot-Based Nanosensor for Sensitive Detection of O-GlcNAc Transferase Activity. Anal. Chem. 2017, 89 (23), 12992–12999 and reprinted with permission from the American Chemical Society. (B) From Sugawa, M.; Nishikawa, S.; Iwane, A. H.; Biju, V.; Yanagida, T. Single-Molecule FRET Imaging for Enzymatic Reactions at High Ligand Concentrations. Small 2010, 6 (3), 346–350 and reprinted with permission from Wiley-VCH. (C) From Kawashima, N.; Nakayama, K.; Itoh, K.; Itoh, T.; Ishikawa, M.; Biju, V. Reversible Dimerization of EGFR Revealed by Single-Molecule Fluorescence Imaging Using Quantum Dots. Chem. A Eur. J. 2010, 16 (4), 1186–1192 and reprinted with permission from Wiley-VCH.

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on QD-based work. In fact, the bright emission of single QDs had already allowed the localization accuracy of single biomolecules to be measured to the nanometer level using FIONA (Fluorescence Imaging with One Nanometer Accuracy) as part of the SPT technique described above, where individual QD-tagged molecular motors were imaged ‘walking’ along actin or microtubules in a hand-over-hand mechanism, an example of which was shown above in Fig. 4.13B.172 The PSF of a single QD was fit to a mathematical function (usually a 2D Gaussian) which allows the peak position to be determined to an accuracy much narrower than width of the PSF (about half the wavelength of light emitted, also called the Abb
e diffraction limit).207 The photostability and brightness of QDs were taken advantage of for this process, but QD blinking remained an issue, since FIONA is basically an extension to SPT. Blinking is actually an advantage for most super-resolution methodologies. The most simple to use is stochastic optical reconstruction microscopy (STORM).208 STORM is one of a four related techniques that were all developed independently at about the same time (2005–2006) and all use traditional widefield microscopy techniques. In addition to STORM, the techniques include photoactivated localization microscopy (PALM),209 fluorescence photoactivation localization microscopy (fPALM)210 and point accumulation for imaging in nanoscale topography (PAINT).211 While they all rely on the fact that the fluorophores only emit for a fraction of time that they are illuminated, the process by which they switch (or are switched) from non-fluorescent to fluorescent varies. Through this switching, only one fluorophore at a time is active (emitting) within the PSF. By fitting the PSF, similar to FIONA, the localization accuracy of the fluorophore is found to the level of a few nm. As this fluorophore switches off and another switches on in a subsequent image frame, the new fluorophore location is recorded to the same accuracy. This is repeated for many switching events and a super-resolution image is built up (reconstructed) from these individual frames. STORM, as the name implies, relies on the switching occurring stochastically, which is the case for QD blinking, as described in detail in the previous section. STORM can be used to obtain both 2D and 3D images, the latter using astigmatism through a deformable mirror.148 An additional advantage of using QDs for super-resolution imaging is that the blueshifting described in the previous section148 can be used in addition to blinking to further improve spatial resolution.212,213 One disadvantage of STORM is that the target structure to be imaged needs to be static during the movie so that the fluorophores do not move as they are switched on and off. These movies can take from tens of seconds up to several minutes to acquire, although efforts are underway to increase switching speed. Another super-resolution technique called stimulated emission depletion (STED), which was actually the firstreported super-resolution wide-field imaging technique back in 1999,214 uses a second laser which illuminates the sample a short time after the initial excitation laser has excited the fluorophore. The second laser depletes the excited state via stimulated emission before it has a chance to fluoresce. The second laser beam is donut shaped so that the probability of stimulated emission at the center of the donut is zero, but is high in the ring of the donut. The donut hole of the laser beam is controlled by

4.4 QDs as single-molecule fluorescent probes

engineered optics to be 50–100 nm in diameter, so this allows the localization accuracy of the fluorophore to be given in this range. STED can be used to acquire both 2D and 3D images. It is usually lower in accuracy than STORM, but it can be acquired with a much higher time resolution (approaching real-time imaging speeds of tens of frames per second, fps), thus avoiding the necessity of the target structure to be static. However, fast pulsed lasers and advanced optics are needed for STED, which limits its utility to more specialized labs. The stochastic nature of QD blinking allowed another super-resolution technique to be developed, called stochastic optical fluorescence imaging (SOFI).215 SOFI relies on performing a statistical analysis of temporal fluctuations, similar to ICS but since the stochastic nature of blinking is known, it is possible to use higher order (nth) cumulant correlation functions in the analysis to improve resolution by √ n in each dimension. However, the computational time for the analysis increases as n2. Furthermore, the intensity dynamic range increases with n, which also decreases the information content. When all these factors are taken into account, SOFI achieves similar spatial resolution to STED, but with an easier experimental setup. It does not achieve the level of STORM but it can be used at higher fluorophore density than STORM, since it is not necessary to only have a single QD turned on within the PSF at a time, which can greatly simplify the labeling process. One hurdle is that the number of frames necessary to do the statistical analysis by SOFI is high, especially when the fluorophore density is high. A subsequent report used fast-blinking QDs and analyzed the variance rather than the higher order cumulant (a process the authors called VISion). This process can be much faster, increasing imaging speeds so that they approach those of STED (over 10 fps) without losing imaging resolution.216 As can be seen in these examples, super-resolution imaging is able to make positive use of QD blinking (and sometimes blue-shifting) to improve imaging capabilities. Fig. 4.21 shows example super-resolution images acquired with each of these techniques using blinking QDs. All images were selected to be approximately the same magnification for comparison, and each is compared to the traditional fluorescence microscopy images (wide-field or confocal, which both have the same resolution limitation) of the same structures.

4.4.5 Blinking dynamics as a probe of local environment and chemical reactions A number of ensemble-level studies have been developed using QD emission for environmental sensing such as pH217–219 and in metal ion220–222 and pathogen sensing.205,222 Although not as widely studied, it is possible that optical properties such as blinking of single QDs can also be used to probe the QD environment, as well as chemical changes and reactions within its vicinity. For example, it is known that QDs immobilized on different substrates show different particle intensity and blinking dynamics due to changes in the local dielectric fields.106,107,223 While this environment has mostly been under researchers’ control in order to study the details of the blinking mechanisms, it is possible for the converse to be used, where the blinking

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FIG. 4.21 (A) Comparison of STORM image to conventional wide field image. Scale bar is 500 nm. Although not given in the image, the lateral spatial resolution of STORM using QDs was reported to be 24 nm.212 (B) Comparison of STED image to conventional confocal image. Scale bar is 1 μm. The spatial resolution of the confocal image is 287 nm and of the STED image is 106 nm. (C) Comparison of Variance (VISion) image, SOFI image and conventional wide field image. Scale bar is 500 nm. The spatial resolution of the wide-field image is 267 nm, of the variance image is 90 nm and of the SOFI image is 154 nm. (A) From Xu, J.; Tehrani, K. F.; Kner, P. Multicolor 3D Super-Resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy. ACS Nano 2015, 9 (3), 2917–2925 and reprinted with permission from the € American Chemical Society. (B) From Hanne, J.; Falk, H. J.; Gorlitz, F.; Hoyer, P.; Engelhardt, J.; Sahl, S. J.; Hell, S. W. STED Nanoscopy With Fluorescent Quantum Dots. Nat. Commun. 2015, 6, 7127 and reprinted with permission from Nature publishing group. (C) From Watanabe, T. M.; Fukui, S.; Jin, T.; Fujii, F.; Yanagida, T. Real-Time Nanoscopy by Using Blinking Enhanced Quantum Dots. Biophys. J. 2010, 99 (7), L50–L52 and reprinted with permission from the Biophysical Society.

4.4 QDs as single-molecule fluorescent probes

dynamics can be used as a probe for the environment. For example, it was shown that blinking could be used to determine bioconjugation of QDs to bioactive species such as dopamine, where the probability distributions of on and off times showed that there was a decrease in on time duration and an increase in off-time duration when conjugated to dopamine109 (Fig. 4.21A). The pH dependence of QD blinking described by Durisic et al.117 (Figs. 4.7E and 4.21B) could also potentially be used to determine solution pH. In an elegant study, Routzahn and Jain used blinking as a probe of cation exchange kinetics when Cd in CdSe was exchanged for Ag ions224 (Fig. 4.21C). Fig. 4.22A shows the effect of conjugating dopamine (DA) to carboxylic acid ligand-functionalized water-soluble QDs on the on times and off times probability distribution functions (Pon and Poff, respectively).109 Fig. 4.22B shows the variation in blinking parameters with pH where both the distribution of on times and off times were fit to Eq. (4.2) but adding the fact that there was a change in the power law slope from aon to mon at tcon (or from aoff to moff at tcoff ), as described in Fig. 4.6. Not all parameters depended on pH, but there was a clear dependence of mon and τoff with pH. Fig. 4.22C compares the change in ensemble (widefield) intensity (top panel) to the change in blinking of several single QDs as they undergo cation exchange from fluorescent (but blinking) CdSe to non-fluorescent Ag2Se. The ensemble intensity dropped steadily but the single QDs showed an abrupt change to a permanent offstate at specific times, although the times of the abrupt change varied from QD to QD. The reverse of this experiment was subsequently published. The recovery of fluorescence during cation exchange from Ag2Se to CdSe showed a similar result in the abruptness and distribution of switching times from QD-to-QD.225 Another recent study used changes in QD blinking when QD-labeled DNA strands were hybridized causing QD lattices to form.226 Although it was only a binary assay (unhybridized vs hybridized strands), it provided a proof-of-concept of using QD blinking as an output signal for single molecule reference-free detection of biomolecules. Although these results highlight that blinking can be a powerful probe for chemical reactivity and local environment, it must be noted that, at present, a major hurdle with using QD blinking for such experiments is that there are still unknown details of the blinking mechanism, as well as the fact that the exact blinking dynamics of a single QD is sensitive to the exact QD structure (see previous section). Therefore, each new batch of QDs needs to be characterized and calibrated prior to using them for such applications, especially if quantitative conclusions are to be drawn.

4.4.6 Fluorescence lifetime imaging and time-gated imaging (FLIM/TGI) The fact that QDs usually have longer fluorescence lifetimes than molecular fluorophores can be exploited in time-based imaging approaches, fluorescence lifetime imaging (FLIM) and time-gated imaging (TGI).87,221,227–230 Both approaches

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FIG. 4.22 (A) Effect of conjugating dopamine (DA) to water-soluble QDs on the blinking dynamics, expressed as probability of on and off times distributions. (B) Effect of pH on the blinking dynamics, expressed as changes in the various fitted parameters to the probability density curves (see text). (C) Comparison of the ensemble intensity of a collection of QDs in a widefield image as a function of time after adding Ag ions to CdSe with the fluorescence intensity of several single QDs. (A) From Khatchadourian, R.; Bachir, A.; Clarke, S. J.; Heyes, C. D.; Wiseman, P. W.; Nadeau, J. L. Fluorescence Intensity and Intermittency as Tools for Following Dopamine Bioconjugate Processing in Living Cells. J. Biomed. Biotechnol. 2007, 2007, 70145 and reprinted with permission from. (B) From Durisic, N.; Wiseman, P. W.; Grutter, P.; Heyes, C. D. A Common Mechanism Underlies the Dark Fraction Formation and Fluorescence Blinking of Quantum Dots. ACS Nano 2009, 3 (5), 1167–1175 and reprinted with permission from the American Chemical Society. (C) From Routzahn, A. L.; Jain, P. K. Single-Nanocrystal Reaction Trajectories Reveal Sharp Cooperative Transitions. Nano Lett. 2014, 14 (2), 987–992 and reprinted with permission from the American Chemical Society.

4.4 QDs as single-molecule fluorescent probes

use a pulsed laser and a detector that can measure the intensity as a function of time after the laser pulse. Both the laser pulse and the detector response time must be faster than the fluorescence lifetime, but picosecond (ps) pulsed diode-pumped solid state (DPSS) lasers and ps-response time avalanche photodiodes (APDs) that can be attached to a single-molecule confocal microscope are now available at a much cheaper cost compared to just 5–10 years ago so that this time-resolved approach is now widely available. Cellular autofluorescence can be a hurdle to fluorescence imaging, especially when the concentration of the target molecules is low. The first example of using TGI to detect a QDs in a cell was reported by Dahan et al. in 2001, where it was demonstrated that the high autofluorescence of a HeLa cell was reduced to allow the internalized QD to be clearly seen.227 A comparison of using CdSe/ZnS QDs, Cd-free CuInS2/ZnS QDs and fluorescent dyes for FLIM and TGI to image receptors that are expressed in highly autofluorescent human breast cancer cells was performed by our group in 2013, and both types of QD were found to be equally superior to molecular dyes and were able to improve imaging sensitivity by more than an order of magnitude.87 A recent example combined TGI with SPT to follow a QD-labeled FcεRI receptor on a stimulated rat mast cell line (RBL-2H3) in which the clathrin was labeled with yellow fluorescent protein (YFP).231 Normal confocal imaging allowed the clathrin to be imaged in the cell together with the receptor (Fig. 4.23A) while TGI allowed the YFP fluorescence in the cytoplasm to be suppressed so that single QD-labeled receptors could be imaged (Fig. 4.23B) and easily tracked as a function of time (Fig. 4.23C).

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FIG. 4.23 (A) Conventional confocal microscopy image and (B) time-gated image of QD-labeled FcεRI receptor on a stimulated rat mast cell line (RBL-2H3) with clathrin labeled with YFP. (C) Diffusion of QD-labeled FcεRI as a function of time (indicated by the changing color of the trajectory). From DeVore, M. S.; Stich, D. G.; Keller, A. M.; Cleyrat, C.; Phipps, M. E.; Hollingsworth, J. A.; Lidke, D. S.; Wilson, B. S.; Goodwin, P. M.; Werner, J. H. Note: Time-Gated 3D Single Quantum Dot Tracking With Simultaneous Spinning Disk Imaging. Rev. Sci. Instrum. 2015, 86 (12), 126102 and reprinted with permission from American Institute of Physics.

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4.4.7 Single photon sources Single photons on demand, a term used extensively in the literature meaning to produce exactly one photon deterministically rather than probabilistically, can be obtained from single molecules,232 single QDs,233–236 as well as other types of solid state materials.237 Single photon sources offer possibilities in wide ranging applications in quantum photonics, such as communications, cryptography/security and quantum computing. While there are several ways of producing single photons on demand from self-assembled structures using down conversion, photons often requires careful control of splitting after generation to achieve deterministic rather than stochastic photons.237 An attractive approach is to use a single emitter, such as a CdSe QD, to directly produce single photons deterministically. This has been shown to be possible even at temperatures up to 200 K234 (Fig. 4.24A). Furthermore, a single polarization entangled photon pair, which is important for applications such as quantum computing, can be accomplished by subsequent/cascade emission from a biexciton followed by emission from a single exciton within the same QD235 (Fig. 4.24B).

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FIG. 4.24 (A) Deterministic production of single photons on demand using a pulsed laser as a function of temperature. The coincidences of photons correlate with the pulse repetition rate of the laser. (B) Cross-correlation function of biexciton emission followed by single exciton emission in a cascade process. The delay, t is due to the (fast, ps) relaxation time of the biexciton, showing that the single exciton emission photon can be predicted from the biexciton emission photon. (A) From Sebald, K.; Michler, P.; Passow, T.; Hommel, D.; Bacher, G.; Forchel, A. Single-Photon Emission of CdSe Quantum Dots at Temperatures up to 200 K. Appl. Phys. Lett. 2002, 81 (16), 2920–2922 and reprinted with permission from the American Institute of Physics. (B) From Couteau, C.; Moehl, S.; Tinjod, F.; Ge
rard, J. M.; Kheng, K.; Mariette, H.; Gaj, J. A.; Romestain, R.; Poizat, J. P. Correlated Photon Emission From a Single II–VI Quantum Dot. Appl. Phys. Lett. 2004, 85 (25), 6251–6253 and reprinted with permission from the American Institute of Physics.

References

Usually the emission energy of a biexciton is slightly different than that of a single exciton due to Columbic interactions, meaning that the photons are distinguishable, which is not ideal. Several methods to improve photon indistinguishability have been proposed, including shape control of the QD236,238 or using electric fields239 or magnetic fields.240 A newer, interesting approach is similar to that used to affect blinking – lattice strain.241 Obtaining single photons on demand, especially using single QDs, has passed the proof of concept stage and methods exist to improve quantum entanglement of photon pairs. However, using them in an error-free device, which is paramount, still requires a great deal of work, but the studies described above highlight the significant promise of single QDs for this purpose.

Acknowledgments Generous financial support by the NSF (CHE-1255440), the NIH (COBRE P30 GM103450), and the Arkansas Biosciences Institute is gratefully acknowledged. C.D.H. would like to thank his former mentors, Mostafa El-Sayed (Georgia Tech, U.S.A.), G. Ulrich Nienhaus (Karlsruhe Institute of Technology, Germany) and Paul Wiseman (McGill University, Canada) for their support during his academic development. He has also been privileged to have worked with a number of talented postdocs and students that contributed to some of the work referenced in this book chapter. These include Dr. Feng Gao, Dr. Jose Aldana, Dr. Gopa Mandal, Dr. Nela Durisic, Dr. Benard Omogo, Dr. Ashley Howard, Dr. Pooja Bajwa, Hiroko Takeuchi, Randee McBride, Mizuho Kaneko, Dustin Baucom, Colette Robinson, Anh Nguyen, Mamello Mohale, Anthony Emerson and Jean Morales-Orocu. Finally, he would like to express his love and gratitude for his late friend and former colleague, Mona Bakr Mohamed, an excellent synthetic nanochemist that taught him how to synthesize quantum dots while they were in graduate school together. She passed away way too young.

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39.

40.

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Further reading 242. Hanne, J.; Falk, H. J.; G€orlitz, F.; Hoyer, P.; Engelhardt, J.; Sahl, S. J.; Hell, S. W. STED Nanoscopy With Fluorescent Quantum Dots. Nat. Commun. 2015, 6, 7127.

CHAPTER

Three-dimensional single-molecule tracking in living cells

5

Daniel M. Kalb, Duncan P. Ryan, Demosthenes P. Morales, Peter M. Goodwin, James H. Werner Center for Integrated Nanotechnologies, Materials Physics and Applications, Los Alamos National Laboratory, Los Alamos, NM, United States

5.1 Historical background There is a long and rich history behind tracking the movement of small particles in a fluid medium. The origins of this field can be traced to the botanist Robert Brown, who in 1828 reported the motion of fine particles found within pollen when suspended in aqueous media.1 This random movement (in the absence of any currents in the media, with this motion even observed for water trapped in quartz that must have been preserved for millions of years2) later became known as Brownian motion. A theoretical understanding of Brownian motion followed approximately 77 years later, with one of four of Albert Einstein’s seminal 1905 papers directly addressing the origins of this small particle movement.3 Perrin’s experimental verification of the Stokes-Einstein relation (which affirmed the molecular/atomic view of matter, with Brownian motion described quantitatively by the collision of individual water molecules with the microscopic particles) gained Perrin a Nobel Prize in 1927. Clearly particle tracking technology has advanced substantially since the early days of Robert Brown, which relied on tracking the motion in a microscope by eye and recording these observations in a lab notebook. The human eye was replaced by film-based cameras, which in turn were replaced by CCD cameras, which are currently being replaced by CMOS sensors, which at some point will be replaced by a newer camera technology. Additionally, there have been substantial advances in illumination methods (e.g. arc lamps to LEDs to lasers) not to mention substantial computational advances, which enable vastly greater capacities for data storage and analysis than what was achievable even a decade ago. We note that describing any one of these advances in detail could be a whole book in its own right. To narrow our scope (and remain consistent with the title of this chapter), we will primarily focus our efforts on the advances made to go from 2D tracking methods of single fluorescent molecules/particles to three-dimensional (3D) tracking methods, and Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.00005-5 # 2019 Elsevier Inc. All rights reserved.

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the extension and use of these methods to follow individual biomolecular motion in live cells. As far as the historical basis and progress toward 3D tracking of molecules in live cells is concerned, the work of Howard Berg was seminal in this field.4, 5 Berg developed a 3D tracking microscope in the early 1970s to follow the 3D motion of individual bacteria. He then used this tracking microscope to understand how bacteria sense chemical gradients and swim toward sources of nutrients by switching between highly directed swimming (runs) followed by random re-orientations (tumbles).5 As shown in Fig. 5.1, Berg’s tracking microscope design consisted of 3 different image planes, with a total of 6 fiber optics acting as spatial filters spread among the 3 image planes. Three feed-back loops (each using differences in detector signals for active feedback in XYZ) were used for 3D bacterial tracking. We note several pioneering concepts put forth by Berg that are still employed by various 3D molecular tracking methods: 1. The use of multiple image planes for 3D tracking, which was adopted by groups such as Ober’s,6–8 Bewersdorf’s,9 Selvin’s10 as well as our own.11–17 And 2. The use of spatial filtering/confocal detection to enable 3D sectioning for 3D feedback using a small array of single element detectors (which was employed by Yang and coworkers18–20 and us11–17 for single-molecule tracking). We note our own efforts on tracking were ignorant of Berg’s seminal work till our first experimental demonstration of 3D tracking12 went out for review, showing how a couple of years of research can save you an hour in the library. Another very commonly employed method for 3D tracking is to encode the particle Z position in the point spread function (the optical image of a point source) of a fluorescent molecule above or below the image plane, such that the image above and

Z1 + Z2 2

Z1 PhotoZ2 multipliers & X , X 1 2 Amplifiers Y1, Y2 Difference Amplifiers

Comparator

Gates

Light-level Reference

RC Amplifiers

Search Readout

Coil Drive and Damping Circuits

Front - surface Mirror Half - silvered Mirrors

Eyepieces (20X) Fiber-optics Fibers Error Signals X1 – X2, Y1 – Y2, Z1 – Z2

Probe volume

Eyes or Camera Eyepieces

y1 x1

x2

Trinocular Beam Splitter Objective (20X) Box With Bacteria

z1, z2 y2

0.25 mm

Condenser Drive Coils Light source

FIG. 5.1 Left: Schematic of Berg’s 3D tracking microscope. Right: Projection of fiber optics back into the probe volume. Reprinted from Berg, H.C. How to Track Bacteria. Rev. Sci. Instrum. 1971, 42 (6), 868–871 with the permission of AIP Publishing.

5.2 Uses of 3D single-molecule tracking

below the plane are distinct shapes, with the shape reporting the Z position of the emitter. This is most easily achieved by placing a cylindrical lens in the image path, such that the image of a molecule/particle in the focal plane (Z ¼ 0) is symmetric, with the molecule appearing as an ellipse in orthogonal orientations above and below the image plane. We note the astigmatic method of Z tracking/feedback was first reported (to our knowledge) in a 1977 patent for tracking the distance between a compact disc and an excitation light source.21 Its use for tracking and recording 3D motion in a more biological context was introduced in 1994 by Kao and Verkman.22 Thomas Schmidt extended this to tracking single quantum dot labeled proteins in live cells in 2007,23 with the method later adapted for 3D molecular localization for super-resolution imaging.24,25

5.2 Uses of 3D single-molecule tracking We note the complexity of biological systems makes them an ideal target and primary driver for the development of 3D single-molecule tracking methods. Biological systems are heterogenous assemblies constructed of large numbers of molecular machines, complex structural networks, and an overwhelming orchestration of biochemical reactions. By nature, molecules in living cells operate stochastically to drive cellular reactions based on thermal fluctuations and random collisions.26 Understanding how these molecules and molecular systems perform cellular functions is a constant endeavor for biologists. Advances in fluorescence microscopy have greatly impacted this study over the decades providing insight into the structural organization of the molecules within the cell and affording the ability to track single-molecules in 3D over time. With three-dimensional single-molecule imaging and tracking (SMI/SMT) it is now possible to capture location, stoichiometry, kinetics, and dynamics of individual molecules with high spatial and temporal resolution. Thus, quantitative measurements can now be acquired to provide context to the randomness of specific molecules and their interactions within living cells,26 as will be discussed later in the Applications section of this chapter.

5.2.1 Alternatives to 3D molecular tracking In relation to ensemble measurements, single-molecule tracking confers many advantages toward understanding complex biological behavior. Ensemble measurements average over an entire molecular population, obscuring how one molecule behaves over time. Single-molecule analysis embraces and exploits the heterogeneity of molecules within the cell and can capture system level responses without the need for synchronization.27 We note most ensemble methods for measuring kinetics use some type of synchronization (e.g. rapid-mixing or temperature-jump) to rapidly change the system. In contrast, in single-molecule studies, the fluctuations of a molecule around an equilibrium point can be used to extract kinetic information about the process.

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Electron microscopy (EM) is both a competing and complementary method with single-molecule tracking and imaging. EM readily probes fine cellular structures at scales smaller than the diffraction limit, achieving nanometer and subnanometer resolution using a focused electron beam.28 Recent advances in cryogenic-EM techniques have bypassed many harsh sample preparation steps such as dehydration, enabling EM studies of biological samples in context making EM more attractive. However, it still remains difficult to measure live or wet samples due to the highvacuum operating conditions.29 Furthermore, the limited number of electron dense labels (e.g. colloidal gold of different sizes) makes multiplexed imaging substantially more difficult than fluorescence-based approaches.30 Atomic force microscopy (AFM) is another powerful technique that can resolve structures beyond the diffraction limit of optical systems. Most importantly, AFM is a label free technique, requiring only a cantilever spring with a sharp tip that scans across sample surfaces.31 AFM is capable of determining topography of a surface and directly probing mechanical properties through local force and elasticity measurements. Again, the resolution achieved by AFM is better than that of conventional optical microscopy but is restricted to surface measurements and therefore lacks the ability to track molecules in a 3D volume. While these alternative techniques cannot independently be used to study live biological samples, they can be combined to reinforce the results acquired from single-molecule analyses. Techniques such as EM, AFM and spectroscopy can all be integrated with optical microscopy techniques producing results that build on the strengths of each technique and offset their weaknesses. Figs. 5.2 and 5.3 provide two examples of how correlative microscopy can be used for biological studies and provide additional detail based on the combination of data from multiple instruments.

FIG. 5.2 Correlative PALM–TEM as an initial validation of PALM. Correlative (A) PALM, (B) TEM, and (C) Superimposed PALM and TEM images of mitochondria in a cryoprepared thin section from a COS-7 cell expressing a fluorescent dEosFP-tagged cytochrome c oxidase import sequence. Scale bars: 1.0 μm (A–C). From Betzig, E.; Patterson, G.H.; Sougrat, R.; Lindwasser, O.W.; Olenych, S.; Bonifacino, J.S.; Davidson, M.W.; Lippincott-Schwartz, J.; Hess, H.F. Imaging Intracellular Fluorescent Proteins at Nanometer Resolution. Science 2006, 313 (5793), 1642. Reprinted with permission from AAAS.

Correlative SRM–AFM of cells. (A) Correlative STED, confocal, AFM height, and AFM elasticity mapping of a fixed COS-7 cell labeled with Atto 647N against tubulin. (B) Overlaid AFM and STORM images of Alexa Fluor 647-labeled tubulin of a fixed HeLa cell. (C–E) Correlative (C) STORM, (D) AFM height, and (E) AFM elasticity images of the boxed area in panel B. (F, G) AFM surface topology of a live CHO-K1 cell at two time points. (H, I) Correlative PALM results of the same live cell taken after AFM, corresponding to the white box in panel G, at two time points. Reprinted with permission from Odermatt, P.D.; Shivanandan, A.; Deschout, H.; Jankele, R.; Nievergelt, A.P.; Feletti, L.; Davidson, M.W.; Radenovic, A.; Fantner, G.E. HighResolution Correlative Microscopy: Bridging the Gap Between Single Molecule Localization Microscopy and Atomic Force Microscopy. Nano Lett. 2015, 15 (8), 4896–4904. Copyright 2015 American Chemical Society.

5.2 Uses of 3D single-molecule tracking

FIG. 5.3

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5.3 Theoretical background Microscopes that are used for particle tracking in cells contain the same basic components: a sample holder, an illumination source (a laser or a lamp), a lens or objective to form an image, and a detector (such as a camera). In a fluorescence microscope used for particle tracking, the sample will contain particles that are detectable because they emit light when excited by the illumination source. The emission from the excited sample is collected by the objective (or other collection optics) and then focused onto the detector to create the image. Tracking microscopes fall under the category of single-particle microscopy because individual molecules are detected as separate objects so that they can be distinguished from other particles in the same field of view. Single-molecule microscopy is a set of techniques and methods that tease out information from a limited amount of signal. One molecule may only emit a few thousand photons before it goes dark or the emission rate of a single fluorophore may be so small that the photon signal is barely perceptible above background noise. As such, single-molecule instrumentation focuses on maximizing collection efficiency, with single-molecule analysis methods developed to extract as much information as possible from the sparse data. We note one substantial strength of single-molecule imaging and tracking is that molecules can be located with a precision that exceeds the diffraction limit of light,32–34 with sub 2-nm localization precision possible from single fluorescent molecules under favorable conditions.34 Objects of interest for 3D tracking in cells may be either individual fluorescent molecules or larger objects that are labeled with fluorophores. Therefore, the object that is actually tracked by the microscope is the fluorescent particle, which may not necessarily be the object of interest. Because of their size, typically in the a˚ngstr€ om to nanometer range, fluorescent particles are considered point-like emitters: the signal originates from essentially an infinitesimally small region of space. However, the light propagates and, when imaged onto a detector forms a spot of significant size. This spot is diffraction-limited and cannot be made any smaller by optical means. The resolution of a conventional microscope is its ability to distinguish two point-like emitters that produce finite sized spots, which is given by the Abbe criteria as: Δx,y 

0:61  λ N:A:obj

(5.1)

where λ is the wavelength of the emission and N. A.obj is the numerical aperture of the collection objective. Typical resolutions lie within the range of 200—500 nm, which can be a substantial fraction of the overall size of a cell. Therefore, analysis methods that can take the raw data—the diffraction-limited spot—and localize the particle to a region smaller than the size of the spot are often employed to explore cellular structure and traffic on smaller length-scales.

5.3 Theoretical background

5.3.1 Single-particle localization Imaging-based 3D tracking experiments determine the motion of particles by postprocessing sequences of camera images. This involves first identifying the subregions in each image that contain particles, typically done by intensity thresholding, followed by fitting a model point spread function (PSF) to each sub-region. Images are 2D datasets; therefore, localization in the third dimension may come from additional parameters to the model function being fit, as in the case of engineered PSF microscope configurations, or from knowledge of where in the sample the image was measured, as is the case of light-sheet microscopes. Further processing may be required after the three-component positions of the particles are determined, such as identifying individual particles across sequences of frames to establish their position trajectories. For sufficiently sparse particle densities with no trajectory crossing, manually curating the localization results may be simpler than utilizing one of the many tracking algorithms available to do this. Model fitting is an iterative process whereby estimates of the parameters are used to generate a prediction of what the data should look like which is then compared against the true data. Therefore, a fitting routine requires three pieces of information: the data, a model function q({θ}) that describes how a particle will appear in the image (the PSF), and a metric for determining if the parameter estimation is better or worse than the previous estimation. In this notation {θ} is the set of all model parameters. The parameters θx, y are the localization coordinates that we seek for 3D tracking. There are many choices of PSFs for localization microscopy. Some model functions are used because they have convenient analytical expressions, although varying degrees of computational complexity. The Airy function, for example, describes the solution to the diffraction of a wave by a circular aperture  0  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 12 J 1 θ σ ð x  θ x Þ2 + y  θ y C B C qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qðx, y, fθgÞ ¼ B @ 2 A 2  θ σ ðx  θ x Þ + y  θ y

(5.2)

where J1 is the Bessel function of the first kind of order one and the parameter θσ has physical meaning, but is typically left as a free parameter to be fit. This model has the advantage that the diffraction rings, though of small amplitude, are part of the model PSF. Another model PSF popular for localization is the Gaussian approximation "  2 # y  θy 1 ðx  θ x Þ2 qðx, y, fθgÞ ¼ exp   2πθσx θσ y 2θ2σ x 2θ2σ y

(5.3)

where θσ x,yare the width of the PSF. The 2D Gaussian is not an optics-based solution to image formation but is a substitute that captures the shape of real PSFs well. It is computationally fast, with similarly simple derivatives, and contains adjustable parameters to correct for shape.35 Independent width parameters, θσ x,y, are useful

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for astigmatic imaging methods where the eccentricity encodes the third dimension (alternative forms of Eq. 5.3 can include a rotation angle). Attaining the limits of parameter estimation precision requires optimizing experimental conditions and selecting the most descriptive model PSF. The latter can be computationally expensive and non-trivial. For example, a dipole emitter will produce a PSF that is dependent on the orientation of the emitter.36–39 Enderlein derived an expression for the dipole PSF through a high-numerical aperture objective, based on the vector wave equations from Richards and Wolf, that can be used as a more ideal PSF.40,41 Fig. 5.4 compares the images of a Gaussian model PSF, an Airy disc PSF, and a 1D dipole emitter. Engineered PSFs can also necessitate more sophisticated model functions to achieve the best localization precision. When an analytical expression is not possible, or the aberrations of the optical system render no reasonably descriptive PSF, an experimentally characterized PSF is often used. There are a variety of strategies for measuring and characterizing PSFs including hybrid analytical/residual approaches that combine parameter-based analytical PSFs with correction terms.38,42,43 In addition to the model PSF, the details about how an image is recorded are often incorporated into the analysis. Because cameras have pixels with finite size and the data captured is the number of photons striking the entire area of each pixel, the expected number of photons recorded by pixel k is the integration over its area ð

 qðx, y, fθgÞdx dy + θbg :

μk ðfθgqÞ ¼ θI

(5.4)

Ak

When a PSF changes rapidly over the area of a pixel, this correction can be important. Otherwise, the integration is often approximated as the value of the PSF at the center of a pixel and integration is not necessary. Fig. 5.4 shows how various PSFs change when pixelated as they would appear on a camera. Analytical expressions for the pixel-integrated 2D Gaussian have been derived; however, many model PSFs do not have simple pixel-integrated expressions. The fit parameters θI and θbg in Eq. (5.4) are the emitter intensity and photon background rates times the integration period. In this notation, the background photon rate is different from the image offset introduced by the camera electronics. This distinction is important because photon background rates have Poisson noise while a digitization offset is a constant value. In all fitting methods, baseline subtraction should be based on a measurement of the camera digitization and not taken as simply the minimum value of the data. Once an appropriate PSF is chosen, the model it generates must be compared against the data. Generally, a fitting routine works by testing changes to each parameter in the model, calculates a metric value that compares the test to the data, and then compares the metric to the previous parameter guesses to see if the metric improved. Two metrics are primarily used for localization: least-squares fitting (LS) and maximum likelihood estimation (MLE). The former seeks to minimize a difference metric while the latter seeks to maximize a probability metric. More often, however, the likelihood maximization is posed as a minimization of the negative logarithm of the likelihood.

5.3 Theoretical background

FIG. 5.4

237

Example PSFs for a Gaussian (left), Airy disc (center), and 1D dipole emitter (right). The bottom row shows pixelated versions of the highresolution PSFs of the top row. (Contrast for high-resolution Airy disc saturated to make ring features visible.)

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CHAPTER 5 Three-dimensional single-molecule tracking in living cells

Least-squares fitting is conceptually straightforward: calculate the difference between the values of the test model (sk) and the data (μk) χ 2LS ¼

X

ðsk  μk Þ2

(5.5)

k

Here, the sum runs over all the pixels in the sub-region being fit. While the LS metric is intuitive, pixels with larger values contribute more significantly to the sum while pixels with small values contribute less significantly. Recall the benefit of using an Airy PSF is that it represents the diffraction rings farther away from the center. However, these detailed features are largely ignored with a least-squares metric because they are such low intensity. An improvement is the weighted least-squares (WLS) metric χ 2WLS ¼

X ðsk  μk Þ2 k

sk + boffset

(5.6)

where the difference between the model and the data is scaled relative to the magnitude of the measured pixel value. This ensures smaller values are given more significant weight. In Eq. (5.6), an offset term is included because, after the camera offset is subtracted from the data, the data can take on negative values which would introduce negative terms to the sum that artificially lower the value of the metric. The value of boffset should be chosen judiciously to maximize the accuracy of the WLS metric.37 An improved method that does not involve user-specified tweaks to the metric is MLE. Given the computational resources now available, MLE has quickly become the metric of choice for localization problems. MLE is based on calculating the probability that a pixel will have a certain value given the expected value of the pixel as specified by the model PSF. The likelihood function—the probability of a set of parameters, {θ}, and the model PSF, q({θ}), given the data—for the entire sub-region is the product of the probabilities from each pixel Lðfθg, qj sÞ ¼

Y

psk ðfθg, μk Þ

(5.7)

k

The probabilities psk embed statistical distributions based on physical descriptions of the measurement system. Walking through the details for one imaging system (an EM-CCD camera) illustrates the level of detail needed for an accurate model of the photon count probability distribution. For example, the number of photons detected from a single fluorophore within a finite time window (e.g. exposure time) is a Poisson distribution, with a mean value determined by the PSF of the emitter and the intensity of the emitter. However, an EMCCD further amplifies the photoelectrons generated by single photons. This amplification process does not simply multiply the signal but is exponentially distributed where the average of the distribution is the specified multiplication factor. Therefore, the number of photoelectrons delivered to the readout electronics is the convolution of the Poisson distribution and the exponential distribution. The readout process further introduces noise to the system

5.3 Theoretical background

in the form of a Gaussian distribution with a relatively small variance.44 Hence, the total distribution for the entire series of events that lead to the digital counts is given by the convolution h i psk ðfθg, μk Þ ¼ pðGaussianÞ ⨂ pðexponentialÞ ⨂pðPoissonÞ ðsk , μk Þ

(5.8)

Because the Gaussian convolution can generate negative values, the signal is offset by a value set by the manufacturer of the EMCCD to ensure positive readout values and this must be correctly removed from the data. Again, walking through the stages of the signal generation like this emphasizes the level of detail necessary to specify a proper probability distribution to be used in Eq. (5.7). Furthermore, different detectors, such as an sCMOS camera, may have additional considerations. In the case of an sCMOS camera, each pixel will have a different gain factor and readout noise variance that must be individually characterized and applied to the corresponding terms in the likelihood calculation.45 Once a fitting algorithm produces an estimate of the model PSF parameters, one must ask, “how precise are these estimates?” This question essentially asks how sensitive is the model PSF to the final parameter selection. Consider the LS method for a pixel-integrated Gaussian PSF. The variance of the position parameters θx, y is σ 2LS

"  # θ2σ + A=12 16 8πθbg θ2σ + A=12 ¼ + θI A θI 9

(5.9)

where A is the area of an individual pixel, θI is the number of signal photons detected, θbg is the number of background photons detected, and θ2σ is the variance of the microscope point spread function. Eq. (5.9) explicitly illustrates that increasing the signalto-noise ratio (SNR) will improve the localization precision.33,37 It also demonstrates the role optical magnification plays in optimizing localization precision through the dependence on A. While higher magnification spreads the PSF distribution across multiple pixels and provides more information, it also reduces the signal at each pixel. There is an ideal balance that minimizes the variance across multiple instrument design parameters, fluorophore intensity, and background conditions. MLE provides a means of calculating the precision using elements of the covariance matrix   σ 2MLE  J 1 ðfθgÞ θx, y , θx, y

(5.10)

where the Fisher information matrix is defined as

*   + ∂ lnLðfθg, qj sÞ T ∂ lnLðfθg, qj sÞ J ðfθgÞ ¼ ∂θ ∂θ

(5.11)

In this notation, the brackets denote the expectation value of the inner product over all possible values of s. Because the likelihood function can include noise models, the precision calculated through the covariance matrix will reflect the uncertainty due to those stochastic processes that the LS method has no mechanism to incorporate.

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5.4 Experimental design How the third dimension is encoded into the recorded data depends upon the microscope configuration and optical system used. There are primarily three imaging approaches that encode a third dimension: PSF engineering that imparts an image pattern unique to the axial position of a particle, multi-plane imaging that compares the images from different focal planes, and light-sheet microscopy that decouples the excitation and emission to selectively image different planes in the sample very rapidly. Once the 3D information is encoded into the data, localization methods that consider how the images were formed and related to one another are then used to determine the positions of the particles.

5.4.1 PSF engineering While a microscope intrinsically encodes the axial position of particles by virtue of the depth of focus—particles outside of the depth of focus are too dim to measure and those nearest the ideal focus produce smaller spots—the resolution is limited and the axial position has a large uncertainty, particularly near the focus where the PSF changes shape weakly with axial position. To enhance this effect and improve the localization resolution, researchers have modified the optical systems in a class of microscopes for 3D imaging that utilize engineered PSFs. The excitation scheme may be any variety of wide-field illumination, including bright-field illumination, epifluorescence, or total internal reflection fluorescence (TIRF). The simplest PSF modification approach introduces an astigmatism to the imaging system,22 illustrated in Fig. 5.5A. Inserting a cylindrical lens between the microscope’s tube lens and the camera forms a compound lens system for one of the in-plane axes with a different effective focal length. If oriented appropriately with the camera, the resulting image will have a horizontal focus at a given z-position and a vertical focus at a different z-position. The center of the PSF identifies the in-plane location of a particle and the ellipticity of the rendered spot encodes the third dimension, which is typically obtained through a calibration table. At magnifications appropriate for single-cell biological experiments, astigmatic imaging can generate quality localizations in the Z-dimension of approximately 50 nm over an 1 μm Z range, limited primarily by the depth of focus, the imaging sensor pixel size, and the signal-to-noise ratio.24 A major drawback of astigmatic imaging is that the size of the PSF changes across the focal range. Therefore, the same number of photons is spread out across a broader spot at the extremes of the useable focal range, reducing localization precision as the background count rate becomes comparable to the signal. However, in other PSF modification approaches, the image is manipulated by a phase plate, deformable mirror, or spatial light modulator placed at a plane conjugate to the back focal plane of the objective, as shown in Fig. 5.5B. These configurations alter the phase of the propagating wave, producing images with unique patterns that encode

5.4 Experimental design

4f-imaging system

f4f

focusing lens

focusing lens dichroic mirror

excitation

dichroic mirror

excitation emission

emission

tube lens

tube lens

cylindrical lens camera

f4f

f4f

–Z

0

+Z

phase plate at Fourier plane

f4f

camera

to 4f-imaging system

(A)

intermediate imaging plane

(B)

–Z

0

+Z

FIG. 5.5 Microscope designs that encode the third dimension into the imaging system. Astigmatic imaging, (A) places a cylindrical lens before the camera in a traditional imaging design. Particles at different z-planes will produce spots with different shapes that can be referenced to a calibration curve to extract axial positions. More complex PSF engineering, such as the double-helix PSF shown in panel (B) can improve localization accuracy. The intermediate imaging plane is relay imaged onto a phase plate or spatial light modulator and, finally, onto the camera in a 4f-imaging system. The rotation angle between the pair of spots representing a single particle indicate the axial location.

the axial information and have superior localization precision over a larger range as the PSF is not typically broadened across the usable focal range. Many PSF engineering methods utilizing phase modulation have been developed for 3D imaging: rotating PSFs,46–51 tetrapod PSFs,52,53 phase-ramps,54 and selfbending beams.55 These PSFs have greater ranges of usability, 3 μm, compared to astigmatic imaging. The tetrapod PSFs extend the usable range out to 20 μm, enabling tracking in large cells. To obtain the full 3D localization from a doublehelix PSF, for example, a pair of spots are individually localized. The center of the pair corresponds to the in-plane localization and the angle of rotation about that center indicates the axial position, as determined by a calibration curve.

5.4.2 Multi-plane imaging Another set of 3D microscopy approaches seek to expand the information contained in the data rather than encoding sharply varying PSFs as functions of axial location. Utilizing the intrinsic depth-dependency of an unmodified PSF in a conventional microscope configuration is limited because the Fisher information matrix near the focus is relatively flat and the resulting uncertainty is large. However, farther

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away from the focus the slope is steeper, meaning a fitted PSF will be more sensitive to small axial displacements. Therefore, simultaneously imaging multiple planes of the same particles can guarantee at least one plane will overlap with an axial position where the Fisher information matrix has a large slope. The combination of multiple image planes expands the available information for fitting. Bi-plane8 and multi-plane microscopy7 can achieve 30 nm axial precision across 3 μm range. Experimentally, these methods are implemented by splitting the optical path of the emission and sending each path to individual cameras focused at different positions within the sample, as illustrated in Fig. 5.6A.

FIG. 5.6 Microscope designs that determine the third (axial) position of an emitter by simultaneously imaging at multiple focal planes. In a bi-plane, (A), the emission is split between two cameras positioned to image different focal planes. Correlating the spots between the two cameras and comparing the relative intensities yield the axial positions of the particles. A variation of this concept in a confocal arrangement, (B), splits the signal from a single particle in the focal volume onto two fiber arrays oriented perpendicular to one another. Comparing the signal intensity within each fiber pair yields the in-plane position of the particle and comparing the combined intensities of each pair yields the axial position because the fiber arrays are positioned to image different focal planes.

5.4 Experimental design

5.4.3 Confocal tracking All of the methods previously described are wide-field measurements that image multiple particles for tracking at once and rely heavily on post-processing of the data to generate the 3D position traces. In addition to the fitting and localization computational demands, each particle must be registered in sequences of frames to obtain the full 3D tracking trace. However, confocal tracking records this during an experiment and does not require significant post-processing steps nor massive amounts of data storage in the form of raw images. Because tracking experiments required low particle densities, a substantial amount of information on a camera is wasted to empty space and background. Rather than image a large field of view, confocal microscopes examine only one diffraction-limited volume at a time. A confocal 3D tracking microscope, illustrated in Fig. 5.6B, captures the trajectory of a particle by moving the sample to keep the particle inside a small volume fixed relative to the objective.12–17,56,57 A collimated beam entering the microscope produces a diffraction-limited excitation volume—typically about 250  250  750 nm. The movements required to maintain a particle in this volume represent the path the particle traveled during the measurement. Feedback to reposition the particle back into center of the excitation volume as it moves through the sample is based on the intensity distribution across an array of single-photon detectors. Two dual-core fiber bundles are oriented perpendicular to one another and offset to image different focal planes that overlap the top and bottom of the excitation volume. In this configuration the confocal 3D tracking microscope resembles the detection arm of a bi-plane imaging microscope. In-plane position feedback is based on comparing the count rates within a single bundle pair and the axial position feedback is based on comparing the combined count rates between the two bundles. The position of the sample is moved until the count rates are evenly balanced among all four detectors. While the confocal method is limited to tracking a single particle at a time, the configuration overcomes many limitations of camera-based methods. Confocal tracking can achieve 50 nm in-plane resolution and 80 nm axial resolution. This is comparable to the best imaging setups. However, the depth range over which a particle can be track extends to the working distance of the objective—up to 200 μm for water immersion objectives—whereas camera-based tracking microscopes are limited to the depth of focus of the objectives used. Photodamage to a biological sample due to exposure to intense excitation light is confined to the diffraction-limited region whereas the entire sample is illuminated in any wide-field imaging method. Using single-photon detectors means the particles can be tracked at faster time-scales than imaging-based microscopes, which have camera-limited frame-rates. Moreover, since the arrival of individual photons can be recorded by single element detectors in confocal tracking techniques, a number of analysis methods are possible on the raw photon data, including: 1. Fluorescence lifetime measurements of the tracked particle during the trajectory, enabling the measurement of environmental conditions that may affect the tracked particle. 2. Photon pair correlations (anti-bunching) which definitively proves the trajectory came from a

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single molecule or 3. Fluorescence correlation of the raw photon stream to observe fast photon fluctuation dynamics. Notably, all of these methods can be performed in live cells. We point out that the use of single element detectors (for 3D sectioning) accompanied by dithering of the excitation around the molecule of interest represent other classes of 3D tracking technologies. These methods (which started as circular sweeps about the molecule/particle of interest and are generally referred to as orbital tracking methods) were proposed for 2D single-molecule tracking by Enderlein58 and demonstrated experimentally for 3D tracking first by Enrico Gratton and coworkers (for fluorescent beads)59 and later by Hideo Mabuchi and coworkers (for individual quantum dots diffusing in aqueous solution).60 Gratton and coworkers also extended these methods into the important arena of 3D tracking of particles in live cells.61

5.4.4 Light-sheet microscopy A new technology to the field, light-sheet microscopy, promises an alternative imaging modality for 3D tracking. Stacks of unaltered (no PSF engineering) 2D images taken throughout the entire depth of a sample are captured by separating the excitation and imaging optical paths. 2D localization of particles in every image of the stack, combined with the knowledge of the location of the focal plane when the image was taken, produces full 3D reconstructions of the particles within the sample. Rapid repeated imaging of the volume captures the dynamics of all particles in motion. There are many light-sheet microscope configurations, from the exotic to the simple to implement: Bessel beam light-sheet microscopes improve localization resolution by structuring the light-sheet,62,63 dual-view arrangements lower photodamage and improve scanning time,64 swept confocally-aligned planar excitation (SCAPE) microscopy delivers a the light-sheet and images through a single objective,65 and high-speed volumetric scanning using remote focusing.66 Fig. 5.7 illustrates the simplest configuration of a light-sheet microscope whereby a plane of excitation is generated within the sample by a dedicated excitation objective oriented perpendicular to an imaging objective. The plane of excitation is formed by either rapidly scanning a focusing beam along the one axis shared with the imaging plane or by using a cylindrical lens to create one collimated axis exiting the objective while the other axis produces a focused beam. The focus of the imaging objective and the light-sheet are coplanar; therefore, only the particles within the light-sheet are excited. This reduces background emission and scattering from the sample as well as the light-exposure to the sample. A stack of images is obtained by scanning the sample through the coplanar excitation light-sheet and imaging focal plane. Post-processing the image stacks is a major computational task—and significant hurdle—for light-sheet microscopy. In addition to the large amounts of data generated, particles must be localized in each image of a stack, as opposed to the single image of an engineered PSF approach. Identifying the same particles in 3D between time slices is a more demanding computational task than in 2D.

5.4 Experimental design

FIG. 5.7 A light-sheet microscope design consists of a thin excitation region that is imaged perpendicular to the generated sheet. By scanning the sample through the sheet, images at dozens of different planes can be acquired and the particles in each plane can be localized with typical fitting methods. With a fast acquisition sCMOS camera, the entire volume of interest can be repeatedly scanned to obtain a time-series of volumetric images.

5.4.5 Interference methods Interference methods are another path to 3D positional sensing.67,68 Phase-based interferometry uses the interference from two coherent light waves (a reference and a sample path) to create a signal modulated on a length scale on the order of the wavelength of light used for observation. While interferometry only works with a coherent light source and seems ill-suited for fluorescence microscopy, we note that single fluorescent molecules are intrinsic quantum emitters, enabling 3D interferometric localization methods via single-photon self-interference.67,68

5.4.6 Labeling strategies There are a variety of probes available for fluorescent labeling of target proteins or nucleic acids inside live cells. These range from organic fluorophores to fluorescent protein variants69 to quantum dots70 and Raman probes.71 Each probe has advantages and disadvantages in terms of optimal fluorescent properties. Ideally, the probe would be substantially smaller than the target to which it is attached, possess a high

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FIG. 5.8 Schematic of the binding of a benzylguanine (BG) substrate to a SNAP-tag fusion protein. The SNAP-tag is fused to a protein of interest. Upon binding, the benzyl group reacts with a cysteine in the active site of SNAP-tag, releasing the guanine group. Here, BG is shown conjugated to a fluorescent dye, but BG can in principle be coupled to any molecule of choice. Reprinted from Bosch, Peter J.; Corre^a, Ivan R.; Sonntag, Michael H.; Ibach, J.; Brunsveld, L.; Kanger, Johannes S.; Subramaniam, V. Evaluation of Fluorophores to Label SNAP-Tag Fused Proteins for Multicolor Single-Molecule Tracking Microscopy in Live Cells. Biophys. J. 2014, 107 (4), 803–814. Figure reprinted with permission from Elsevier.

quantum yield, large extinction coefficient, and be very photostable. Several strategies have been developed to label a biomolecule of interest that induce little interference with the molecules native state. For example, fusion proteins with fluorescent proteins is highly specific for labeling the desired protein. Similarly, genetically encoded self-labeling enzymes such as HaloTag and SNAP-tags are also attractive as the Tag is fused to the protein of interest. Fluorescently labeled cell permeable substrates can be introduced that are then covalently attached to the fusion protein (Fig. 5.8).72 Additionally, bioconjugate techniques to label antibodies, nucleic acid complements with desired fluorophores, are also available depending on the desired biomolecule to be resolved.73 We note that since the size of typical antibodies used for directed labeling can be on the order of 10 nm or so in linear dimension (which can, in some cases, be greater than the single-molecule localization uncertainty), there is also substantial research into creating smaller antibody fragments (such as minibodies)74 that retain targeted binding with a smaller protein form factor. Additionally, we note reports from members of his lab that Stefan Hell maintains a herd of llamas in order to generate single domain camelid antibodies suitable for super resolution imaging or high-precision molecular tracking. Furthermore, quantum dots experience fluorescence intermittency that will cause the emitter to temporarily go dark, leading to gaps while tracking.

5.5 Precautions A 3D tracking experiment seeks to determine the position of particles within a sample as a function of time. As such, an experimentalist must be aware of the factors that can lead to incorrect measurements of single-particle trajectories. Most considerations revolve around being able to accurately determine the positions of particles at each instance of time. The instrument design, the measurement, and the analysis all play roles in the final localization efficacy.

5.5 Precautions

Being composed primarily of water, cells are generally considered transparent to visible light. However, biological systems are complex environments that are far from a spatially homogeneous environment. Cells contain light scattering organelles and structures with different indices of refraction. As a result, excitation light entering a sample can have penetration issues and emission from fluorescent markers can be distorted before being collected by the objective. Uniform illumination of a sample across the field of view ensures all probes are imaged and treated with equal weight but, in practice, this can be difficult to achieve. Top-hat diffusers or over-filling the back aperture of the objective can be used to create semi-uniform profiles in wide-field illumination. Counter-propagating dual excitation planes have been used to improve uniformity in light-sheet microscopes where the light-sheet can scatter and lose intensity as it propagates through the sample.75 Scattering of excitation light that passes through the bulk of a sample also creates unwanted and inhomogeneous background signals. This can be compensated for, with Lim et al. developing a method of recording two images, one with uniform illumination and one with speckle, and deconvolving the images to remove the background contribution.76 Scattering has also been compensated for by using structured illumination in the light sheet pathway for a similar effect.77,78 Emission from single particles in scattering biological systems or simply through non-optimized optical systems is susceptible to distortion of the PSF in imaging-based and confocal tracking instruments. Distortions will affect the localization accuracy by either decreasing precision or creating bias if not properly corrected or accounted for. While adaptive optics can compensate for distortions during acquisition,79 distortions due to deviations from the ideal optical system are generally first characterized and then corrected for during analysis.9,14,38,42,43 Characterization of the PSF is often done using a sample of beads in a similar index of refraction environment as the sample of interest in order to mimic the imaging conditions but to also ensure fewer aberrations due to a heterogeneous environment. Fixing beads, for example in agar solutions, also minimizes Brownian motion during characterization. In camera-based imaging, z-stacks of the calibration bead sample are acquired for analysis. Confocal tracking experiments require the characterization of the collection efficiency function (CEF) which is measured by raster scanning a fixed single-particle through the confocal region and repeating at multiple depths.14 Characterized PSFs or CEFs are also used for fine alignment of the detection optics. Acquisition and measurement conditions can greatly affect localization results. Maintaining a high signal to noise ratio—through the use of background suppressing methods such as total internal reflection (TIF) excitation and appropriately selected filters, or signal enhancement such as higher excitation power selection and setting the optimal camera gain—will improve localization precision.33 Optimizing localization accuracy is nuanced and requires attention to detail. Particles of interest in tracking experiments are interesting because they are moving. However, their movement may be rapid compared to either the exposure time of the camera or the binning time of detectors in confocal microscopes. Wong et al. and Deschout et al. have studied the limitations of localization due to movement during the acquisition interval,

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indicating lower limits to the precision of such measurements.80,81 While faster integration times and shorter binning times can reduce the distance a particle will move during an acquisition, it comes at the expense of a smaller signal to noise ratio and a less precise localization. Hence, the acquisition time and the signal intensity must be balanced to achieve the optimal precision and accuracy. Furthermore, for confocal tracking, properly selecting the feedback parameters is coupled to the binning time. Decisions that a researcher has control over at the time of measurement (or before) that have implications on the localization results include how the sample is labeled with fluorescent probes. The choice of probe is important: some probes can bleach quickly and limit the length of time the particle is tracked before it goes dark. This is a greater concern for single-molecule probes compared to beads, containing hundreds to millions of fluorescent molecules, that do not photo-bleach as rapidly. Quantum dots are more photo-stable and can be used to long duration tracking,15,57 but their relatively large size (tens of nm) and need to be introduced exogenously can preclude their use for many live cell systems. The density with which a sample is labeled plays a significant role in the quality of the localization. Higher probe densities in camera-based tracking experiments can mean larger numbers of tracked particles. However, the density must be kept sufficiently low that the likelihood of overlapping emission spots from multiple emitters is small. Such overlapping can be difficult for algorithms to localize and track. While multi-emitter localization algorithms are available, they have difficulties tracking particles in 3D and can only isolate the individual signals when the emitters are still separated by a significant distance (50 nm in some cases).82 The final steps where a researcher can make either good or poor decisions that impact the final results are during the post-processing and analysis phases. Applying an inaccurate PSF to a localization algorithm will result in incorrect results. Beads are generally considered isotropic emitters, meaning there is no orientation dependence, and using a Gaussian or Airy disc PSF will be valid. However, if the sample is labeled with single-molecule probes, such as dyes or quantum dots, dipole effects may be present and there is some orientation dependence to the emission pattern. Anisotropic emitters create the situation most susceptible to inaccurate localizations, leading to displaced localizations that vary with the orientation of the emitter.83–85 In such cases, dipole PSFs can be used to reduce such localization errors.37,38 We note that anisotropic emitters can be accurately treated with simple PSFs if the molecule freely rotates during the image acquisition. However, single-molecule fluorophores attached to larger molecules or structures may not have complete rotational freedom. Finally, movement of the entire sample, either because of stage drift or biological motion, must be corrected in the final results of tracking experiments. Confocal tracking does not provide a means of identifying such motion unless wide-field images are simultaneously recorded. Multiple strategies can be employed to determine the drift over the course of a measurement such as adding fiducial markers to a sample86,87 or cross-correlating multiple independent fluorophores.87–89 The trace of the drift is then subtracted from the tracks of individual particles.

5.6 Data analysis

5.6 Data analysis

Mean Square Displacement

After the acquisition of the raw tracking data and subsequent analysis (with either point spread function for image data or XYZ stage/photodiode data for modified confocal data) a researcher is left with a history of 3D positions over time for each single molecule analyzed. This spatial-temporal information can yield valuable information about the fundamental nano-scale processes of the system under test, most commonly either a biological or materials science system. The underlying physics driving the motion of these 3D tracks can vary widely, ranging from various modes of diffusion, e.g. free diffusion or locally constrained diffusion, all the way to the directed motion of molecular motors that transport particles along specific pathways within a cell. Here we will examine the tools necessary to quantify these various types of nanoscale motions such that the particle motion can be rigorously analyzed and contextualized to the systems under test. Following the initial analysis that extracts the particle positions across time, further understanding of these tracks generally involves applying an appropriate model to characterize the motion. One of the simplest and most widely adopted method of analyzing 3D tacking data is to characterize the position over time in terms of a Mean Square Displacement (MSD) (Fig. 5.9).90,91 For the case of a freely diffusive particle, the MSD scales linearly with time lag and can be expressed as MSD(Δt) ¼ 6DΔt where D is the diffusion coefficient and Δt is the sampling time (the time between

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FIG. 5.9 Theoretical models of various particle trajectories (Left) and the corresponding MSD-Δt plots (right). (A) Simple Brownian diffusion, (B) Directed diffusion mode, (C) Restricted diffusion mode, and (D) Stationary mode (not shown on right).90 Reprinted from Kusumi, A.; Sako, Y.; Yamamoto, M. Confined Lateral Diffusion of Membrane-Receptors as Studied by Single-Particle Tracking (NANOVID Microscopy)—Effects of Calcium-Induced Differentiation in Cultured Epithelial-Cells. Biophys. J. 1993, 65 (5), 2021–2040, reprinted with permission from Elsevier.

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each frame or position observation). We note that for a freely diffusing particle that the MSD scales as twofold the number of degrees of freedom, e.g. MSD(Δt) ¼ 4DΔt for 2D diffusion, but MSD(Δt) ¼ 6DΔt for 3D diffusion. The linear relation between mean squared displacement and time for freely diffusing particles can be used to experimentally measure the diffusion coefficient of single-molecules, including individual organic dyes and fluorescent proteins.14 Deviations from a linear relationship between MSD and time can be generalized into several categories, with Saxton grouping these into four groups of motion beyond the zero-order immobile particle (no motion).90 These groups include: normal diffusion where the particles are free to move uninhibited, anomalous diffusion a type of diffusion that is ‘damped’ from free motion (most likely due to obstacles and/or binding energies and particle traps), directed motion with diffusion or transport mode in cells (characterized by directed motion toward a target), and corralled or confined motion (where small diffusive motion is observed, but travel over time is limited to a locally defined region).91 Each of these diffusive modes can be modeled and applied to tracking data to understand a variety of dynamic process and probe the physical structures within cells. Combinations of multiple travel modes can even be applied to understand discreet stages of cellular process over time. Fig. 5.10 shows such an example of a multi-stage process of a quantum dot labeled IgE-FcεRI receptors on a rat tumor mast cell (RBl-2H3). The receptor first travels diffusively along a ruffled cell membrane before it is eventually taken up by an endocytic vesicle and rapidly transported across the cells.13 There are many methods developed to analyze molecular trajectories that extend beyond the MSD approach, including more rigorous approaches to fit and analyze the MSD curve over time.92 Additionally, Yang developed a Maximum Likelihood Estimation (MLE)-based approach,93 for fast and robust estimation of diffusion coefficients and a change point analysis to determine and parse when changes in the a observed diffusion coefficient may appear in a trajectory.74 In contrast to MLE based approaches, Elf and coworkers developed a variational Bayesian analysis94 that assumes no a-priori knowledge of the trajectory to estimate the number of discrete diffusion states and their distributions from a collection of complex molecular trajectories. We note the approaches of Michalet,92 Yang,93 and Elf94 all offer a robust method of characterizing the diffusive, constrained, and directional motion seen within typical particle tracks. As a reminder, it is worth noting that any of these methods is only as good as the tracking data itself, and rigorous experimental controls are necessary to ensure true tracking of single-molecules. Further instrumentation developments, including the use of time-resolved anti-bunching data13,15,16,57 can help improve these experimental controls. Finally, rigorous quantification of the system errors due to both static (photon statistics) and dynamic errors (blurring or images/data during exposure time) can further improve the modeling and understanding of tracking data.95

5.6 Data analysis

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FIG. 5.10 Tracking data for quantum dot labeled IgE-FcεRI receptors on a rat tumor mast cell (RBl-2H3). (A) The 3D track of the quantum dots over time. The probes move along a ruffled cell membrane. After 250 s (purple color in plots) the quantum dots are rapidly transported across 7 μm of the cell by an endocytic vesicle. (B–D) The X,Y and Z position of the quantum dots over time. (E) Bright-field image of the cell overlaid with initial position of the quantum dots. (F) Photon Counts over time. (G) MSD of the quantum dots during the rapid uptake and transportation of the quantum dots across the cell (time 246–253 s). The parabolic shape of the MSD is indicative of directed motion at a constant velocity. Reprinted with permission from Wells, N.P.; Lessard, G.A.; Goodwin, P.M.; Phipps, M.E.; Cutler, P.J.; Lidke, D.S.; Wilson, B.S.; Werner, J.H. Time-Resolved Three-Dimensional Molecular Tracking in Live Cells. Nano Lett. 2010, 10 (11), 4732–4737 Copyright 2010 American Chemical Society.

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5.7 Applications Three-dimensional tracking of particles has a wide range of application to both biological and materials science systems. This insight into kinetic process at the nanoscale can shed light on the structure and mechanisms of systems at the single- molecule level. Unlike bulk measurements, which inherently tend to measure averages, single-molecule measurements allow for statistical characterizations of processes that may exhibit a wide range of temporal or spatial distributions across a large number of particles. Such variation in the motion, signaling, and transportation of particles can yield key information about the kinetics and mechanism of the underlying processes. Locating regions of molecule sequestration, determining the stoichiometry of units in molecular assemblies, observing the dynamics and kinetics of molecular processes in the cell at real-time are just a few uses for tracking single-molecules in living cells.

5.7.1 Location Since the spatio-temporal organization of cell structure controls their function, molecular tracking to discern protein localization and trafficking between locations can yield valuable insight into cellular processes. For example, in order to manufacture protein rapidly where it is needed most, many cell types use local translation of mRNA into protein. Additionally, translocation of mRNA provides a mechanism of compartmentalization as seen in dendrites of neurons which permit local responses and processing to extrinsic signals.96,97 Thus, understanding localization of molecules is necessary to understand the inner workings of the cell. In one example of using 3D tracking to understand molecular localization, diffusion and transport in cellular compartments, Smith et al. sought to measure the diffusion of mRNA in entire volumes of the nucleus. Using single-molecule tracking they investigated the access of β-actin mRNA to heterochromatin regions. They observed that β-actin mRNA was not excluded from or enriched in heterochromatin and did not exhibit specific translocation tracks as it traveled to the nuclear envelope.98 Instead, their findings suggest that β-actin mRNA traveled freely through the nuclear landscape and with a substantial fraction (60%) ultimately located within approximately 0.5 μm of the central channel of nuclear pore complexes.98 In Fig. 5.11, using a fluorescent protein fusion of β-actin mRNA (green) the authors observed overlapping fluorescence with a nuclear pore complex (red) over a wide range of viewing angles. Furthermore, β-actin mRNA was observed to interact with the complex repeatedly over time, revealing details of nuclear pore complex and its activity in translocation.

5.7 Applications

FIG. 5.11 Tracking location of biomolecules in live cells by single-molecule analysis. Smith et al. monitored the location of β-actin mRNA relative to nuclear pore complexes. (A) Rotational view of β-actin mRNA (24  MS2 stem-loop cassette labeled with eYFP MS2 coat protein, green) and nuclear pore complexes (POM121-td, tomato red). They observed that β-actin mRNA partially overlaps with an NPC at all angles of rotation (bottom arrow). (B) β-actin mRNA association with the nuclear pore complexes over time. Final three panels are time points further along in time of acquisition at 0° rotational perspective. Bars under images indicate identical time groups.98 Republished with permission from Smith, C.S.; Preibisch, S.; Joseph, A.; Abrahamsson, S.; Rieger, B.; Myers, E.; Singer, R.H.; Grunwald, D.; Nuclear Accessibility of β-Actin mRNA Is Measured by 3D Single-Molecule RealTime Tracking. J. Cell Biol. 2015, 209 (4), 609; permission conveyed through Copyright Clearance Center Inc.

5.7.2 Stoichiometry 3D molecular tracking methods also can be used to measure the assembly and ratio of protein types in macromolecular complexes. In particular, assemblies of proteins can lead to quick activity regulation to enhance, repress, and couple responses to stimuli within the cell. For example, clusters of receptors, such as G-protein coupled receptors (GPCRs), have long been observed to function as homodimers, heterodimers, or higher order oligomers. With single-molecule tracking it is now possible to determine the oligomeric state of molecules within cells. For example, Hern et al. observed the formation and disruption of a dimer for the muscarinic acetylcholine receptor M1 in real time.99 As shown in Fig. 5.12, two color imaging of M1 receptors was performed in live Chinese hamster ovary cells by labeling the receptors with a 1:1 ratio of Cy3B-telenzepine and Alexa488-telenzepine, which bind tightly to M1 receptors. By tracking thousands of fluorescent spots (green and red) separately they showed when the tracks merged to form dimers and when they dissociated back to monomers, finding a steady-state mixture of M1 receptor monomers and dimers associate and dissociate on the seconds timescale.99 We note protein association can also be observed by changes in the measured diffusion coefficient in addition to two-color imaging methods. As shown in Fig. 5.13, Han and coworkers demonstrated the ability to quantify motion in a well-defined protein oligomerization series (a monomer, dimer, and tetramer of the fluorescent protein Azami Green). A change point algorithm (such as that developed by Yang and coworkers) could be used (even in a one-color 3D trajectory) to estimate when and whether a diffusing molecule has associated with a target.93

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5.8 Kinetics and dynamics

FIG. 5.13 Single-particle tracking data for Azami Green oligomers. Each particle configuration (monomer, dimer, and tetramer) has a distribution of measured diffusion constants. Additionally, the time-resolved photon pair information can be utilized to confirm single particle dynamics such as anti-bunching.14 Reprinted with permission from Han, J.J.; Kiss, C.; Bradbury, A.R.M.; Werner, J.H. Time-Resolved, Confocal Single-Molecule Tracking of Individual Organic Dyes and Fluorescent Proteins in Three Dimensions. ACS Nano 2012, 6, 8922–8932. Copyright 2012 American Chemical Society.

5.8 Kinetics and dynamics 3D molecular tracking can be used to examine the kinetics and dynamics of cellular processes at the single-molecule level. For example, Schmidt and coworkers used 3D single-particle tracking of quantum dots to explore their diffusive interaction with cellular membranes, followed by a rapid uptake and directed motion by endocytosis.23 This work shed light into both the speed and location of the transport along the endocytic vesicles. Quantum dots have also been attached to IgE-FcεRI receptors and tracked over time upon interaction with a rat tumor mast cell (RBl-2H3).13,15 As the quantum dots probe along the cell membrane surface, they show a complex ruffled topology, while their rapid uptake by an endocytic vesicle (Fig. 5.10) can be used to extract the rate of endocytic transport. Further work has added the capability to simultaneously acquire spinning disk images16 or two-photon imaging20 with the tracking data. When overlaid onto the tracking data, these images help contextualize the cellular structure around the path of the tracked particle. For example, Welsher and Yang used aggregates of nanoscale particles as a model for the processes of viral infection and targeted delivery of therapeutics.20 In both of these processes, the general progression of particle uptake is a multistep process where free diffusing particles in the extracellular

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solution will eventually find and attach to a cell membrane. Once on the membrane, the probes will often migrate on the surface of the cell membrane for an extended period of time before they are eventually taken up into the cell. After passing through the membrane, the probe can finally be trafficked or directed by molecular motors to specific targets within the cell. Welsher and Yang examined this process by tracking cellular uptake of peptide (HIV1-Tat)-modified nanoparticles using a two-photon laser scanning microscopy system.20 The results, highlighted in Fig. 5.14, sheds light into dynamic uptake interactions: including a long-range deceleration (possible due to binding with cellular receptors) and nanoscale interactions with local membrane structures. In a different study exploiting molecular tracking, Knight et al. followed individual Cas9 proteins as they searched for its target site within a living cell.100 Using a HaloTag labeled Cas9, this work investigated live-cell dynamics of Cas9 to determine the diffusion and chromatin binding properties within the nucleus of mouse cells. To visualize the binding dynamics they introduced guide RNA for short interspersed nuclear elements (SINEs) of the B2 type and measured that against nonsense guide RNA and mismatched RNA distal to the protospacer adjacent motif (PAM) sequence (B2_0M & B2_13M), See Fig. 5.15. They observed biphasic kinetic behavior of Cas9 reflecting fast- and slow-moving populations in the nuclei, while nonsense and mismatched guide RNA Cas9 protein were highly mobile. These results concluded that Cas9 with B2 SINE guide RNA were necessary for chromatin binding, as confirmed by decreased diffusion across the nucleus.100 The study also reinforces the observations acquired from prior studies that the Cas9-guide RNA complex uses diffusion-dominated targeting as it searches the cell nucleus. Along with molecular dynamics, tracking of particles intracellularly may also provide insight to kinetic activity of proteins. For example, Liao et al. measured the diffusion coefficients of a DNA polymerase in Bacillus subtilis, PolC, and modeled its binding to other replisomal subunits (Fig. 5.16).101 Many of the PolC exhibited dynamic diffusion rates from fast to slow, at times diffusing slower than 0.1 μm2/s, suggesting that slower PolC proteins were actively engaged in DNA replication. Interestingly, the recruitment of PolC to the replisome was not inhibited by the arrest of DNA replication by HPUra. HPUra blocks DNA synthesis without deconstructing replisome complexes but prevents new ones from being formed. Upon treatment, the PolC diffusion coefficients remained similar to the untreated controls, suggesting that the diffusion transitions from fast to slow are a result of protein-protein interactions taking place at the replication fork and that PolC is recruited later in replisome formation. Additionally, they measured dwell-time of PolC at the replication fork by time—lapse imaging determining that the dwell-time of PolC corresponded to active engagement in leading and lagging strand synthesis. These results complemented by their stoichiometry and dwell-time analyses indicate that the high concentration of PolC is required to accommodate the rapid exchange of PolC to ensure recruitment at the replisome at the lagging strand for Okazaki fragment synthesis.

5.8 Kinetics and dynamics

FIG. 5.14 (See figure legend on next page)

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5.8.1 Future prospects At present feedback-based molecular tracking methods using single or multiple discrete detectors (e.g., Avalanche photodiode, APDs or photomultiplier tubes, PMTs) provide the highest temporal resolution at the expense of low throughput (i.e. one track at a time). These will continue to be useful when molecular tracking at the highest temporal resolution is required or when tracking analytes in highly scattering media using nonlinear (multiphoton) excitation. Camera-based, wide-field methods coupled with engineered PSFs, multiple image planes or interferometric methods that provide unambiguous readout of lateral (x,y) and axial (z) positions of multiple tracked particles hold the promise of high-throughput 3D tracking, but at a temporal resolution limited by the frame readout rate of the camera. With the increasing availability of high quantum efficiency, low readout noise sCMOS cameras with high frame readout rates this limitation is becoming less severe. Additionally, recent CMOS developments to reduce pixel capacitance have enabled new quanta image sensors that enable photon counting and discrimination at high count rates,102 technology that will definitely impact the fields of molecular tracking and superresolution imaging. Moreover, the development of large CMOS-based APD arrays will provide affordable photon-counting imaging detectors with sub-nanosecond timing resolution comparable to that of the fastest discrete detectors. Ultimately these will provide pixel- and time-stamped photon streams useful for imaging in photon-starved applications. Another important recent advancement is the development of lattice light-sheet microscopy capable of generating 3D image stacks of cell-sized objects at hundreds of image planes per second with high sensitivity and minimal photodamage due to the thinness of the light-sheet used to excite fluorescence in the sample.63 This technique has already been used, for example, for 3D tracking of microtubule plus ends during mitosis and will likely be improved to track faster moving analytes.63 The ultimate spatial and temporal resolution limits of all of the above molecular tracking methods are imposed by the brightness of the optical reporter used to label the analyte. Developments leading to smaller, brighter reporters with increased photostability will lead to concomitant improvements in tracking applications. FIG. 5.14, CONT’D Tracking of peptide-modified nanoparticles throughout the process of cellar uptake. These tracks illustrate the complex nanoscale 3D terrain features of the live cell. (A) A particle randomly diffusing in the extracellular environment finds and docks to a cell. (B) Fluorescence image overlaid with tracking data of nanoparticle docking onto cell. (C) Localized track of nanoparticle as it moves along a membrane protrusion of the cell. (D) For the same particle seen in C, the local diffusion constant of the particle is calculated over time. (E) A particle moving along the cell membrane shows multiple small protrusions. (F) For same data seen in E, the diffusion constant over time. (G) High-resolution track of a nanoparticle traveling along the cylindrical surface of a filopodium. (H) 2D plane of cylindrical particle motion alone the filopodium.20 Reprinted by permission from Welsher, K.; Yang, H. Multi-Resolution 3D Visualization of the Early Stages of Cellular Uptake of Peptide-Coated Nanoparticles. Nat. Nanotechnol. 2014, 9 (3), 198.

5.8 Kinetics and dynamics

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FIG. 5.15 Single-molecule tracking of Cas9 in mouse cells. (A) Diffusion coefficients of Cas9 proteins loaded with either guide RNA for B2 SINE, nonsense guide RNA, mismatched guide RNA distal to PAM sequence, B2_0M & B2_13M. Bimodal population observed in B2 SINE loaded Cas9 indicating a highly mobile, unbound fraction and a less mobile fraction bound to chromatin. Nonsense and mismatched samples indicate Cas9 is predominantly mobile as it searches for a target within the nucleus. (B) 2D projections of single-particle trajectories obtained from 3D imaging showing highly diffusive Cas9 when loaded with nonsense guide RNA and immobile Cas9 when targeted to the B2 SINE.100 From Knight, S.C.; Xie, L.; Deng, W.; Guglielmi, B.; Witkowsky, L.B.; Bosanac, L.; Zhang, E.T.; El Beheiry, M.; Masson, J.-B.; Dahan, M.; Liu, Z.; Doudna, J.A.; Tjian, R. Dynamics of CRISPR-Cas9 Genome Interrogation in Living Cells. Science 2015, 350 (6262), 823. Reprinted with permission from AAAS.

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(A) 3D superresolution reconstruction image of PolC-PAmCherry in untreated B. subtilis, overlaid on a phase contrast image of the cells. The position of each localization is indicated by a single dot with width corresponding to the average localization precision in the lateral plane (25 nm). The axial (z) position is color-coded according to the color bar above. (Red arrows) Regions of PolC enrichment in the cell. (Inset) A representative, color-coded 3D single-molecule trajectory illustrates a PolC-PAmCherry molecule making a transition from diffusing (bottom) to dwelling (top). (B) Distribution of PolC-PAmCherry diffusion coefficients, D, in untreated cells. (Inset) Zoom-in on the 0–0.1 μm2/s region of the original histogram. (Red dashed line) Average apparent diffusion coefficient (0.003 μm2/s) for stationary PolC-PAmCherry molecules measured in fixed cells. (C) Localization probabilities of dwelling events along the longitudinal cellular axis in untreated cells. L: cell length, N: total number of dwelling events analyzed. (D) 3D superresolution reconstruction image of PolC-PAmCherry in HPUra-treated cells. (E) Distribution of PolC-PAmCherry diffusion coefficients, D, in HPUra-treated cells. (F) Localization probabilities of dwelling events in HPUra-treated cells. Scale bars 1 μm.101 Reprinted from Liao, Y.; Li, Y.; Schroeder, J.W.; Simmons, L.A.; Biteen, J.S. Single-Molecule DNA Polymerase Dynamics at a Bacterial Replisome in Live Cells. Biophys. J. 2016, 111 (12), 2562–2569. Reprinted with permission from Elsevier.

CHAPTER 5 Three-dimensional single-molecule tracking in living cells

FIG. 5.16

References

Acknowledgments This work was performed at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility at Los Alamos National Laboratory (Contract DE-AC52-06NA25396) supported, in part, through Los Alamos National Laboratory Directed Research and Development (LDRD) funds.

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Further reading

101. Liao, Y.; Li, Y.; Schroeder, J. W.; Simmons, L. A.; Biteen, J. S. Single-Molecule DNA Polymerase Dynamics at a Bacterial Replisome in Live Cells. Biophys. J. 2016, 111(12), 2562–2569. 102. Ma, J.; Masoodian, S.; Starkey, D. A.; Fossum, E. R. Photon-Number-Resolving Megapixel Image Sensor at Room Temperature Without Avalanche Gain. Optica 2017, 4(12), 1474–1481.

Further reading 103. Betzig, E.; Patterson, G. H.; Sougrat, R.; Lindwasser, O. W.; Olenych, S.; Bonifacino, J. S.; Davidson, M. W.; Lippincott-Schwartz, J.; Hess, H. F. Imaging Intracellular Fluorescent Proteins at Nanometer Resolution. Science 2006, 313(5793), 1642. 104. Odermatt, P. D.; Shivanandan, A.; Deschout, H.; Jankele, R.; Nievergelt, A. P.; Feletti, L.; Davidson, M. W.; Radenovic, A.; Fantner, G. E. High-Resolution Correlative Microscopy: Bridging the Gap Between Single Molecule Localization Microscopy and Atomic Force Microscopy. Nano Lett. 2015, 15(8), 4896–4904.

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Multiparameter fluorescence spectroscopy of single molecules

6

George Hamilton, Hugo Sanabria Department of Physics, Clemson University, Clemson, SC, United States

6.1 Outline The attractiveness of Multiparameter Fluorescence Spectroscopy (MFS, or multiparameter fluorescence detection, MFD, used interchangeably here) for single molecule experiments is derived from its simultaneous use of eight parameters of fluorescence information (Fig. 6.1), achieved using Pulsed-interleaved Excitation (PIE) or Alternating-Laser Excitation (ALEX) with Time-correlated Single Photon Counting (TCSPC) and Fluorescence Correlation Spectroscopy (FCS).1–6 MFS combines a holistic approach to fluorescence experiments and compatibility with a broad range of fluorescence analysis methods. This approach maximizes the use of fluorescence information and allows resolution of both structural and dynamic characteristics of target molecules. The timescales resolvable using MFS span decades in time from picoseconds to hours (Fig. 6.2), while spatial information can be obtained for distances as small as nanometers but with Angstrom precision in combination with F€ orster resonance energy transfer (FRET).7 Further, MFS provides solutions to problems associated with compatible techniques through the simultaneous measurement of all fluorescence information in the time domain, making it ripe for integrative and hybrid approaches which are more powerful together than each methodology by itself. For instance, in single molecule FRET (smFRET) studies, MFS allows the identification and correction of artifacts which arise in smFRET experiments (i.e. dynamic and static quenching, problems with the orientation factor, dye mobility, blinking, triplet and dark state kinetics, photobleaching, cross talk, and other correction factors), removing ambiguity in the interpretation of data.7 In fact, the most common application of MFS is to multichromophoric systems such as those in FRET studies; thus, this will be a focus of this chapter. Moreover, combination of MFS with Fluorescence Correlation Spectroscopy (FCS) (and even FRET and FCS together) provides a powerful means of resolving fast dynamics in heterogeneous systems through filtered FCS (fFCS), utilizing differences in the fluorescence parameters of fluorescent species to perform correlations of fluorescence signal from the different species.8 Additionally, MFS is compatible with imaging techniques like Fluorescence Spectroscopy and Dynamics of Single Molecules. https://doi.org/10.1016/B978-0-12-816463-1.00006-7 # 2019 Elsevier Inc. All rights reserved.

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Excitation spectrum (i)

Emission spectrum (ii) Fluorescence lifetime (iv)

Anisotropy (iii)

FRET (viii) Quantum yield (vi) Time (v) Stoichiometry (vii)

FIG. 6.1 Eight dimensions of fluorescence accessible through Multiparameter Fluorescence Spectroscopy (MFS). (i) MFS uses differences in the excitation spectrum to selectively excite dyes, while (ii) dichroic mirrors and bandpass emission filters allow detection in specific spectral windows. (iii) Polarization splitters provide fluorescence anisotropy information. (iv) Pulse excitation and Time-correlated Single Photon Counting electronics are used to determine the fluorescence lifetime. (v) Continuous data acquisition monitors the time evolution of fluorescence observables and is used in fluctuation analysis. (vi) The intrinsic fluorescence quantum yield of fluorophores helps to differentiate species in a heterogeneous solution. (vii) Brightness and stoichiometry analysis permit the study of various phenomena such as oligomerization. Both are also used as characterization parameters of the fluorophores. (viii) Combination of single molecule and FRET allows for determination of distances between sets of fluorophores.

Lifetime Imaging Microscopy (FLIM),9 where individual pixels become analogous to single-molecule bursts as in Burst Integrated Fluorescence Lifetime (BIFL) experiments and much of the analysis carries through the analogy.10,11 In this chapter, we will describe the principles of MFS, including the theoretical basis, basic experimental setup and design, data registration/acquisition, and data treatment and analysis. Further, we will discuss the capabilities of MFS with respect to single-molecule experiments, including comments on the probed timescales and length-scales and the types of obtainable fluorescence information. Finally, we

6.2 Multiparameter fluorescence spectroscopy

Biologically Relevant Motions Biochemical Interactions Local Flexibility Methyl Rot.

Collective Motions

Side-Chain Totamers

ps

ns

Fluorescence Decay

Confocal

Cargo Transport

Loop Motion

Larger Domain Motions

µs

ms t diff

Receptor Trafficking

s

min

Time

Time-Resolved Fluorescence Burst-Integrated Fluorescence Lifetime Fluorescence Fluctuation Spectroscopy

FIG. 6.2 Biologically relevant motions and timescales probed by fluorescence. Fluorescence detection of single, freely diffusing or immobilized, biomolecules span over ten decades in time. The same scales of biological relevant motions. The schematic shows characteristic times for these motions. In this chapter we focus on confocal detection and burst-integrated fluorescence analysis and fluorescence fluctuation spectroscopy. Figure adapted from Felekyan, S.; et al. Analyzing Forster Resonance Energy Transfer With Fluctuation Algorithms. Methods Enzymol. 2013, 519, 39–85.

discuss examples of MFS uses, including of previous studies which have utilized MFS with FRET for studies of biomolecular structures and dynamics.

6.2 Multiparameter fluorescence spectroscopy One of the greatest challenges of biology is to simultaneous probe the spatial and time domain information at high accuracy and resolution in order to inform the biomolecular function. Because fluorescence and dynamics, for most common organic dyes, occur on the nanosecond timescale,13,14 fluorescence is ideal for probing biomolecular dynamics, which largely happen on slower timescales (Fig. 6.2). The use of multiple fluorophores for methods such as FRET allows probing distances at the molecular level. In reality, with respect to multichromophoric experiments, fluorescence is at least 8-dimensional (Fig. 6.1). These eight fluorescence parameters are the excitation spectrum, the fluorescence spectrum, the fluorescence anisotropy, the fluorescence lifetime, the fluorescence quantum yield, the time evolution of the fluorescence signal and the fluorescence intensities of the fluorescence markers as influenced by the stoichiometry and distance between fluorophores (FRET).1,2,15 Some fluorescence characteristics are intrinsic to the fluorophore, while several are sensitive to changes in the fluorophore’s environment, be it the presence of other fluorophores, proximity to other fluorophores, or flexibility of the dye linker on the biomolecular surface. Thus, each of these parameters provides information which is invaluable

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in identifying and characterizing molecules of interest. MFS aims to utilize the information from all parameters simultaneously to maximize its usefulness. When combined with single molecule detection, MFS provides an unprecedented selectivity in identifying components of highly heterogeneous samples, such as in the case of labeled biomolecules. A typical MFS setup is diagrammed in Fig. 6.3. The idea Clock (pico sec.) TCSPC

2 3 1

Filter 4

DB

485nm

Polarizer Beamsplitter Pinhole Tube lens Dichroic Beamsplitter

Objective 640nm Pulsed, lin. pol. lasers

Confocal Volume

FIG. 6.3 Example confocal MFS setup. A typical MFS setup consists of four detectors covering two different spectral windows and two polarizations. Detectors are connected to the time-correlated single-photon counting (TCSPC) electronics and detect the emission fluorescence freely diffusing molecules from a confocal volume within the sample. The sample is illuminated by two pulsed and interleaved, linearly-polarized lasers used as excitation sources. Separation of the fluorescence emission by wavelength and polarization in this setup is accomplished through the introduction of optical elements. Namely, a polarizer beam splitter is used to send light perpendicularly polarized with respect to the excitation beam to detectors 1 and 2 and light which is parallel to the excitation to 3 and 4; dichroic beam splitters further separate each polarization into green and red spectral windows. Thus, each detector corresponds to one pairwise combination of parallel or perpendicular and red or green emission. Finally, before each detector is a cleanup filter to “clamp” the detected signal’s wavelength range to a smaller range about the wavelength of interest. The pinhole element can be used to control the amount of emission which reaches the detectors based on the pinhole size. While laser excitation sources at 485 nm and 640 nm are pictured, the chosen excitation sources and detection optics will depend on the excitation and emission spectra of the fluorophores used in the experiment (or vice versa).

6.2 Multiparameter fluorescence spectroscopy

was pioneered by the group of Prof. Claus A.M. Seidel in Refs. 1, 16. Since, numerous groups have contributed further in the development of MFS, MFS software, and related techniques; as this is not the focus of this chapter, the reader is referred to the literature (many not included here).2,7,10,17–30 As the crux of MFS is the simultaneous measurement of all fluorescence parameters, this is the main consideration in the design of an MFS experiment and the analysis of the photon stream data. An understanding of the independence or interplay between each of the fluorescence parameters, whether it be intrinsic or a result of the measurement methodology, is key. Quantum yield determination aids in the accurate determination of FRET distances; emission spectra alongside intensity information allows identification of different dyes and determination of sample stoichiometry; anisotropy aids in positive identification of labeled biomolecules and rotational motions; and measurement in real-time allows dynamics, as opposed to static structural information, to be probed. While this description of the usefulness of each parameter is incomplete, it serves to show the power of the MFS approach in removing ambiguity of results and obtaining maximum information about a given system. Further, through the use of multiparameter histograms in two or three dimensions, it is possible to accurately select subpopulations of some heterogeneous sample, based on their characteristics as determined by MFS, for further analysis. That is to say, MFS allows the specification of a molecule of interest, in an inhomogeneous sample, in a way not possible through other methodologies. To better understand the power of MFS and the insight it provides in single-molecule studies, it is helpful to more clearly define the use of the eight parameters presented in this chapter. Further, it is worth giving special consideration to the theory behind some of these parameters and the methodologies involved in MFS experiments; namely, FRET (steady-state and time-resolved), fluorescence correlation spectroscopy (FCS), time-correlated single photon counting (TCSPC), and burst-integrated fluorescence lifetime (BIFL).

6.2.1 Data acquisition with time-correlated single-photon counting MFS uses pulsed excitation (PIE, ALEX) and TCSPC to monitor the time evolution of fluorescence. TCSPC was first conceived by Bollinger and Thomas in 1961 and further developed later by others.29–33 At the single molecule level, TCSPC allows the selection of events that share similar properties through burst selection for further analysis. This is in contrast with ensemble TCSPC (eTCSPC) measurements. As the name suggests, eTCSPC finds fluorescence parameters as averaged over the whole ensemble of molecules, typically measured at higher concentrations than singlemolecule studies. While this method is good for acquiring the time evolution of fluorescence, information about short-lived or low-population fluorescence states of individual molecules is more difficult to extract from the ensemble averaging. Trace analysis and, further, burst analysis allow the resolution of the finer details by tracking the fluorescence properties of subensembles of molecules or individual molecules. This concept is detailed in Fig. 6.4.

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τ2 Time

Free Energy Time Freq. Free Energy

Fluorescence parameter

Energy Landscape Freq.

Time Freq. Free Energy

τ1

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Signal

τf

Signal

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Time

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Fluorescence parameter

Signal

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Time

(C)

Ensemble Sub-Ensemble Single Burst

Tier 1 Tier 2

Selection by time or structure parameter

Free Energy

(A) Levels of study

274

Tier 3

(B)

FIG. 6.4 Time-correlated single photon counting. (A) TCSPC is able to resolve fluorescence information in several complementary regimes. Ensemble studies allow high data throughput but only obtain information averaged over many molecules, obscuring the finer details. Trace analysis of more dilute samples allows identification of sub-populations of the sample, identified by differences in their fluorescence parameters as present in the data stream. Analysis of data within single bursts of fluorescence corresponding to single molecules allows determination fluorescence parameters with minimal averaging, giving an accurate picture of the states of molecules. The poor statistics arising from low photon counts are typically handled through use of noise reduction methods or by maximum information algorithms like maximum likelihood estimator34 and histogramming of many bursts’ data in multiparameter histograms. In conjunction with other techniques and knowledge of the experimental design, TCSPC can provide physical insights into the system of interest, such as the energy landscape. (B) Here, the free energy landscape of a hypothetical molecule as determined by ensemble and subensemble measurements of fluorescence lifetimes in a FRET experiments are used to illustrate the usefulness of the different approaches in resolving different levels of detail as shown in panel (C).

6.2 Multiparameter fluorescence spectroscopy

The basic principles and typical implementation of TCSPC and BIFL for single molecule measurements are covered in this section. In MFS, the TCSPC setup is typically a pair of pulsed lasers that are coupled to a confocal microscope and which alternately excite molecules diffusing through the confocal volume. Such a system is the focus of this section; for a more complete description of TCSPC, readers are referred elsewhere.5,13,35 A typical setup for TCSPC is pictured in Fig. 6.3. TCSPC relies on a two-fold timing of single-photon detections events following rapid, periodic excitation light pulses, with only one photon detection per cycle and photon counting over many cycles. Histograms of photon counts sorted by their detection times are constructed to retrieve the fluorescence lifetimes. For an idea of the required sampling rates for building such histograms, it is useful to recall that the fluorescence lifetimes for most commonly used fluorophores are in the nanosecond scale.13,14 Thus, to properly reconstruct decay curves, we should use sampling rates much faster than this in the picosecond range. Each detected photon is identified by three parameters: the macro-time, the micro-time, and the channel number if multiple detectors are used. First, a hardware clock such as a crystal oscillator sets the repetition rate for excitation pulse cycles, typically in the nanosecond range. The total number of cycles is recorded corresponding to the multiplication of the duration between pulses by the number of pulses. This time interval is known as the macro-time. Hence, the macrotime is a measure of the experiment duration, from the start of the experiment to the corresponding cycle when a photon is detected. A second, faster clock records the time difference between the excitation pulse at the beginning of each cycle and the single-photon detection. This delay time is referred to as the micro-time. For construction of the decay histogram, photon events are binned with at most the resolution of the micro-time over many cycles. For single molecules, it is the duration of the single molecule event. Because of the rate of de-population of the excited state is proportional to the excited molecules, the micro-time bins, just after the excitation pulse, will represent the initial excited population and will register photon events more frequently. Similarly, later time bins will register fewer photon detections, and the constructed histogram should recreate the fluorescence decay curve. Mathematically this will be presented later in this chapter. Typically, the bin width of the decay histogram is set to the maximum resolution of the micro-time clock. However, the width of the bins can be adjusted to multiples of this resolution to avoid overbinning of data with low count rates. Often, as in a typical MFS setup, the fast micro-time clock is actually a time-to-amplitude converter (TAC) which ramps a signal starting at the same time as the excitation pulse and stops upon photon detection. This amplitude is used to determine the time difference between excitation and emission, with micro-time bins referred to as the TAC channel for each photon (this is not the aforementioned detection channel number). The last photon-identifying parameter is the detection channel number. TCSPC measurements can be performed with detection for multiple spectral windows and with separate detectors for different polarizations. In the scenario of a FRET measurement, pulsed-interleaved excitation is used to alternatively directly excite the

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donor and the acceptor fluorophores and thus monitor their fluorescence by direct excitation.3,36 Then, photons from each source fluorophore can be detected in corresponding detector channels after signal separation with dichroic mirrors and bandpass emission filters. This separate detection allows decay histograms for each emission color and polarization to be constructed separately for the same sample.37 A diagram of the TCSPC photon tagging scheme (by micro-time, macro-time, and channel number) is shown in Fig. 6.5. These histograms allow the determination of sample fluorophore lifetime decays, FRET rates, and anisotropy, as discussed in later sections. Additionally, signals from the different detection channels are used to calculate auto and cross-correlation of fluorescence fluctuations. It is important to note that, due to hardware limitations, the accurate construction of the time resolved fluorescence decay histograms relies on there being, on average, fewer than one photon detection event per excitation pulse (in practice, about a rate Pulsed Interleaved Excitation (PIE)

Start of Experiment

Detected photon

Micro-time

excitation pulse

i-th photon

ti

Macro-time

excitation pulses

i-th photon

Ni

Time[ns]

End of Experiment

start of the experiment

number of pulses before detection

1

2

3

4

n

Micro-time

t1

t2

t3

t4

tn

Macro-time

N1

N1

N2

N2

Nn

Photons Channel number

FIG. 6.5 TCSPC data registration. In TCSPC, each photon (circles) is identified by three parameters: (i) micro-time, or time after the excitation pulse; (ii) macro-time, or the number of excitation pulses (dark and light gray bars representing the two excitation colors) from the start of the experiment; and (iii) channel number. These three parameters are required for off-line analysis. Top: Schematic of pulse-interleaved excitation. Middle: Schematic of micro- and macro-time. Bottom: Each detected photon is recorded with these parameters. Single molecules diffuse freely through the confocal volume and are excited by laser pulse, after which photons are emitted, creating a burst of photons as a function of time.

6.2 Multiparameter fluorescence spectroscopy

of 1% of the laser repetition rate). This is because most photon detectors will have a characteristic dead time after a photon detection during which additional photons will not be detected. If the photon count rate is too high, then, this will introduce a bias toward shorter micro-times within each cycle, distorting the decay histogram. Because fluorescence emission is a random process, some small number of multiphoton events is unavoidable with reasonable experimental count rates; the key is minimization of these events. There are several simple methods to reduce the number of photons, including adjustment of excitation pulse power (excite fewer fluorophores), dilution of the experimental sample, and introduction of an adjustable pinhole or optical density filters before the detectors to cut out photons, although must of the time in single molecule experiments the opposite is true. Another important factor to consider in the construction of decay histograms via TCSPC is the instrument response function (IRF). The IRF for each detection channel describes the experimental setup’s response to the excitation pulse and its width sets the timing uncertainty for photon detection following the pulse. Thus, the perfect TCSPC apparatus would have an IRF, which appears as a delta function (width 0), while in reality the IRF shape and width are dependent on the excitation source (laser), the detectors, and other TCSPC electronics. Specific instrumentation choices utilized to minimize contributions from IRF and other artifacts are discussed elsewhere.32,38–40 Measurement of the IRF is necessary for proper fitting of TCSPC data as the directly-measured signal is actually the convoluted sample signal and the IRF. Typically, IRF is measured by performing a TCSPC measurement with pure water or some other non-fluorescent, light-scattering medium such as silica particles in solution. IRF can also be measured in other conditions, such as with solutions of the fluorophore to be used in experiments, but quenched by quenching agents like potassium iodide, to get a good representation of IRF in the presence of sample (as the spectrum will be the same, but emission will be quenched).41 The TCSPC histogram from this sample is then taken as the IRF and used to process the time-resolve fluorescence decays.

Burst-integrated fluorescence lifetime One major advantage of TCSPC is that it allows the identification of individual molecules as they diffuse through the confocal volume.11,33 This is accomplished through selection of bursts of tens to hundreds of photons corresponding to single-molecule events. Burst integrated fluorescence lifetime (BIFL) was first introduced by Tellinghuisen et al.,11 utilizing TCSPC to determine the fluorescence lifetime of Rhodamine 110 by analyzing 5–300 photon-long “bursts” corresponding to single-molecule detection events. Consider a solution of freely diffusing fluorophores. For a sufficiently low concentration of fluorophores, the confocal volume will contain, on average, less than one fluorophore at any given time. This means that usually the measured photon intensity will be low, as only background signal will contribute to it. However, when a fluorescent molecule enters the confocal volume and is excited and fluoresces over several pulse cycles, the intensity will spike. Plotting the intensity vs. time trace of the signal by a typical multichannel scaler

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(or, equivalently, the delay time between photon detections) makes this phenomenon clear and allows selection of photons corresponding to high-intensity events (singlemolecule events, or bursts of photons) either through setting of intensity thresholds or manual selection of bursts. Too high of a concentration makes such selection impossible, as the baseline of and fluctuations in intensity become too high to distinguish events due to transit of single molecules while many photons in any identifiable bursts likely come from aggregated or multiple molecules. Selection of bursts is aided through the use of noise reduction filters (e.g. running average, Lee filter) or more complex statistical analysis.42,43 The photons in selected bursts can be used for the calculation of all MFS parameters corresponding to single molecules. Fig. 6.6 illustrates burst selection of a typical single molecule experiment for subsequent MFS analysis. This selection means that the parameters calculated from such a measurement are not ensemble averages and thus better reflect the true states of the measured molecules. This is the basis of burst-wise analysis in MFS and it allows the analysis of defined sub-ensembles that share common fluorescence parameters in comparison to ensemble-based measurements. Burst selection as discussed here is analogous to individual pixels or clusters of pixels in FLIM experiments. Due to the low number of photons per burst (a few hundred, at the high-end), care must be taken in calculating the fluorescence parameters. For instance, a maximum likelihood estimator (MLE)34 is used to estimate the burst fluorescence lifetime even for low photon numbers. Additional selection of bursts based on other parameters is also possible. For example, bursts can be selected based on detector specific count rates, based on color and polarization. Further, time-window analysis utilizes the definition of small and equal time-windows into which photons in selected bursts will be grouped; thus, a new set of “bursts” is defined, each having the same duration. This is useful in both acquiring information for short-lived molecular states and in getting a better handle on the distribution of photon counts per burst. This first benefit is simply because the parameters of interest can be averaged over shorter timescales, better reflecting heterogeneity in molecular states during the burst duration or TG and TR for green and red, respectively. The second benefit is because burst durations are not uniform due to the random nature of diffusion in confocal detection, so even if molecular brightnesses are similar, the bursts will contain different numbers of photons.44 Reducing burst duration to smaller, uniform time-windows makes it so that molecules of similar brightness will have bursts containing similar numbers of photons, thus maintaining similar photon statistics over individual bursts.44 Alternatively, bursts can be defined directly by number of photons. This, however, may obfuscate heterogeneities in molecular brightness. Regardless, in both scenarios, bursts are subdivided into smaller bursts, with the last of these smaller bursts being entirely disregarded to avoid inconsistent sorting due to the burst ending (for instance, binning a 53-ms burst into 10-ms windows leaves a much shorter 3-ms window at the end, which will be disregarded). Many other parameters can be calculated on a burst-by-burst basis (or over many bursts) for later use. This feature is what allows analysis of specific sub-ensembles

6.2 Multiparameter fluorescence spectroscopy

Total Intensity

Burst Integrated Fluorescence Lifetime (BIFL)

Time [ms] D|D

D|A

Number of Photons

1

0

5

3

10 0

5

1

10

0

5

A|D

5

4

10 0

10 0

5

10

A|A

2

0

3

5

2

10

0

5

4

10 0

5

10

Time [ns] FIG. 6.6 Burst integrated fluorescence lifetime. Individual spikes in the intensity traces correspond to the passage of single molecules through the confocal volume, with burst duration depending on the molecule’s diffusion time (tdiff). Selection of a single-molecule burst allows calculation of MFS parameters such as the fluorescence lifetime (thus, burst-integrated fluorescence lifetime). Often, the used plots are not raw photon-by-photon data, but instead are processed by filters to aid in burst selection. For instance, filtering by using background subtraction along with a running average of inter-photon delays over several events smooths the intensity curve, increasing contrast between bursts and background signal (Lee filter).42 Using each photon as a data-point can lead to rapid variation in intensity and difficulty in positively identifying bursts. Smaller averages are useful, however, in identifying bursts for low-brightness molecules as well as separating different bursts which occur in rapid succession. Time resolved decay histograms are built based on each detection channel at either donor (j D) or acceptor excitation (j A) and emission of either Donor (D) or acceptor (A). Thus, four combinations are possible (D j D, D j A, A j D, and A j A).

with MFS. Histograms of calculated parameters for each burst can be used to select for specific ranges that define sub-ensembles. Further, these histograms can be expanded to two or even three dimensions to select for subpopulations based on multiple parameters simultaneously or even for analysis as-is. To name just a few useful

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parameter combinations: the mean macro-time of bursts versus count rates and other parameters allows one to monitor the stability of the sample over long measurements; average time between green and red photon detection events within a burst helps to reduce events with significant photobleaching; the stoichiometry in PIE measurements allows for the selection of donor-only or FRET populations within the sample; and calculated FRET efficiency or anisotropy vs. fluorescence lifetime for local and global dynamics. Mathematical details on these parameters are provided later in this chapter. It is worth noting that, while all fluorescence parameters can be determined from single-molecule experiments with burst-integration, it is sometimes the case that it is more practical to perform ensemble measurements for some samples. This is due to hardware and sample limitations, which make the large amount of data that is desirable for fluorescence lifetime and anisotropy determination difficult to obtain. Some examples of these problems are instability of protein samples or low molecular brightnesses resulting in low data counts. In these cases (barring rapid sample degradation), it is still often viable to obtain this type of data in single-molecule conditions, but much longer experiments must be performed. As photon detection technologies improve or as brighter, more stable fluorophores are engineered, ensemble measurements will be less necessary, as collection of enough photons through single-molecule experiments will become more feasible, overcoming current limitations. Additionally, ensemble conditions set boundaries to make sure that single molecule experiments could reproduce ensemble observables.

6.2.2 Spectral information The absorption, or excitation, spectra for fluorophores provide convenient means of exciting target dyes and molecules to induce fluorescence because they select and reflect the energy levels of the fluorophores in use. While detailed spectral analysis is lost, the fluorescence over selected spectral windows can be achieved. Given a sufficient separation in excitation or emission spectra, this allows selectivity of excitation and emission even in samples with more than one fluorescent probe (as is the case in FRET experiments). Additionally, the use of fluorophores with distinct emission spectra allows similar selectivity in identification and measurement of fluorescent parameters for each fluorophore; dichroic mirrors and bandpass filters allow splitting of emission signal into separate spectral windows sent to different detection channels. This selectivity at both “ends” of the experiment allows accurate determination of other fluorescence parameters in complete experimental conditions both for each fluorophore independently and for relative parameters like stoichiometry and inter-fluorophore distance.

6.2.3 Quantum yield The quantum yield of a de-excitation process refers to the efficiency ratio of events corresponding to that process with respect to the total number of excitation events, or, equivalently, the probability of each type of de-excitation event. Thus, the

6.2 Multiparameter fluorescence spectroscopy

quantum yield for fluorescence is the rate of photon emission events over the summed rate constants of all de-excitation events. The full space of de-excitation pathways for a fluorophore will usually be more complex than just paths involving fluorescence emission, with each pathway having an associated quantum yield between 0 and 1 and the sum of all paths’ quantum yields being 1. These other de-excitation pathways may be distinguishable through measurement of the heat emitted, differences in emitted photon energy, etc. However, when using the term “quantum yield,” we will henceforth be referring specifically to the fluorescence quantum yield (Φf) as that is most relevant to the topics discussed in this chapter. Quantum yield serves as an important correction factor for determination of other MFS parameters, such as FRET efficiency and fluorescence quenching, thus, it is an important consideration when choosing fluorophores and experimental conditions.45,46

6.2.4 Stoichiometry and brightness Molecular brightness refers to the fluorescence emission rate of excited fluorophores. In other words, the brightness is a measure of the fluorescence intensity of a single fluorophore. Note, however, that this is not exactly the measured signal; what we measure in experiments includes background signal, the instrument response function, etc. Determination of molecular brightnesses allows determination of FRET efficiency and fluorescence anisotropy (detailed later), and to otherwise resolve heterogeneity in a system or select subpopulations for analysis, such as in studies of oligomerization.47,48 Fluorophore stoichiometry (S) refers to the number fluorophores per target molecule and thus a function of molecular brightnesses. In the case of multichromophoric experiments, the stoichiometry reflects the number of photons from one fluorophore amongst the detected photons from all fluorophores during their respective direct-excitation windows. For a FRET sample (detailed later), the stoichiometry can serve as an indicator of the ratio of donor fluorophores to the number of donors plus acceptors, allowing identification of donor-only, acceptor-only, and donoracceptor molecules, only when both fluorophores are alternatively excited. For a donor-acceptor labeled sample with one of each fluorophore, the expected stoichiometry is close to 0.5, while for a donor-only sample the stoichiometry is 1 and for an acceptor-only sample it is 0. By utilizing stoichiometric information, labeling schemes can be tested for efficacy, subpopulations of differently labeled samples in a mixture can be selected for analysis (such as when both acceptor-only and donoracceptor molecules are present), and calculated FRET efficiency can be corrected to account for fluorophore stoichiometry. To treat stoichiometry as a measure of the number of each type of fluorophore, the relative brightnesses of the fluorophores under direct excitation, as well as other factors such as detection efficiencies for the corresponding signals, must be accounted for. One example of the use of fluorophore stoichiometry can be found at the end of this chapter, including the expression for the stoichiometry as defined for the PIE experiment, SPIE.49

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6.2.5 Fluorescence lifetime The fluorescence lifetime describes the characteristic time it takes for an excited fluorophore to de-excite.50 Specifically, the fluorescence lifetime, τ, is the time after which a fraction 1/e of a population of excited fluorophores has yet to de-excite. This is equivalent to the timescale on which the fluorescence intensity for a fluorescing population has decayed to 1/e times the initial intensity, since the intensity is proportional to population size. Analogously, for a single fluorophore, τ is inversely related to the rate of de-excitation by fluorescence. Fluorescence lifetime can be determined using either frequency- or time-domain measurements. In the frequency domain, this involves the determination of amplitude demodulation and phase shift in detected signal compared to a high-frequency oscillating excitation signal, from which the lifetime can be calculated.13 One example is in fluorescence lifetime imaging (FLIM) experiments, which produce images where contrast between areas of the image represents differences in fluorescence lifetimes (rather than spectral differences), though the frequency-domain approach is less common.51–54 However, the tools presented in this chapter utilize timedomain measurements. In MFS, TCSPC allows us to directly measure the intensity as it decays in time after an excitation pulse. The fluorescence lifetime can then be directly determined from the decay curve. A brief treatment of the math involved is relatively simple: Following an excitation event which puts some population of fluorophores in the excited state, the rate of de-excitation events (or the rate of depopulation of the excited state) is proportional to the number of excited fluorophores. Thus, for an excited population size, N, the rate of change in population is given by dN ðtÞ ¼ kN ðtÞ + f ðtÞ, dt

(6.1)

with t as time and k as a proportionality constant. f(t) describes the excitation event, and in the ideal case can be taken as a delta function. If we integrate this equation from the time that the excitation is terminated, denoting this t ¼ 0, we obtain lnðN ðtÞÞ + a ¼ kt + b:

Rearranging, and grouping the constants a and b, N ðtÞ ¼ exp ðkt + b  aÞ ¼ N ð0Þ exp ðktÞ ¼ N ð0Þ exp

(6.2)
t τ

,

(6.3)

where N(0) is the initial number of excited fluorophores, τ is still the fluorescence lifetime and the reciprocal of k, the rate constant for de-excitation events which gives the number of events per unit time per molecule. It is worth noting that k is actually the sum of the rate constants for each possible de-excitation process, and not just for fluorescence. Such processes include non-radiative decays, internal energy conversion to vibrational energy, and others. The specifics here depend only on the internal

6.2 Multiparameter fluorescence spectroscopy

structure of the fluorophore, making the fluorescence lifetime a fluorophore-intrinsic property.55 In fact, the fluorescence quantum yield (for fluorescence involving one photon emission), Φf, is actually the ratio of the fluorescence rate constant, kf, to the total rate constant: Φf ¼

kf : k

(6.4)

In the simplifying case where fluorescence is the dominant de-excitation process, k  kf and τ ¼ 1/kf. Regardless, the measured intensity, F(t), for a fluorescent sample is proportional to the excited population and it is given by FðtÞ ¼ kf N ðtÞ ¼ kf N ð0Þexp


t τ

¼ Fð0Þ exp


t τ

:

(6.5)

Because the fluorescence lifetime is independent of external factors, including the total fluorescence intensity, this equation is usually normalized for simplicity. This also allows direct visual comparison between decays for different samples. Further, for heterogeneous samples, since the intensity contributions from different fluorescent species are additive, the total intensity decay can be treated by a linear combination of each component: FTotal ðtÞ ¼

X

xðlÞ exp l



 t , τðlÞ

(6.6)

where x(l ) are the l-th component fractions for each species that contribute to the normalized intensity. Therefore, heterogeneity in a fluorescent sample can be resolved through analysis of the shape of the fluorescence decay, as each additional decay mechanism will contribute a distinct lifetime and amplitude which affect the shape of the decay. For most commonly used fluorophores, the fluorescence lifetime is on the order of nanoseconds.13 Some examples of fluorescence decay curves can be seen later in this chapter.

6.2.6 Inter-fluorophore distance and F€ orster resonance energy transfer F€ orster resonance energy transfer (FRET, or fluorescence resonance energy transfer) is utilized as a valuable tool in several disciplines, including physics, chemistry, and biology. Despite the well-understood and characterizable dependencies of FRET information, intensity-based FRET approaches are often only used as a binary indicator for answering “yes” or “no” questions.56 Nonetheless, accounting for the known limitations of FRET measurement with MFS allows accurate and quantitative information to be obtained and, thus, the use of FRET as a precise, molecular-scale ruler. In this section, we will discuss the basic principles of FRET, steady-state and time-resolved FRET, and the dependency between FRET and fluorescence anisotropy. Important equations will be presented here, but in-depth derivations are left out, with interested readers referred elsewhere.57–60

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Energy transfer between fluorophores can occur via either radiative or nonradiative processes with various underlying mechanisms.7 FRET is a non-radiative mechanism of energy transfer between two fluorescent molecules caused by Coulombic effects.57 In FRET, an excited donor fluorophore transfers its energy to a second nearby fluorophore, or acceptor, through long-range electric dipole-dipole coupling. This coupling is weak enough and does not disturb the energy levels of either donor or acceptor. The “resonance” in the name comes from the conceptual similarity to energy transfer between classical coupled oscillators in resonance with one another. Fluorescence emission from the excited acceptor molecule following FRET can be detected and used in conjunction with donor fluorescence to quantify the efficiency of energy transfer, or FRET efficiency. Alternatively, changes in the donor fluorescence intensity decay can be used to the same end, as FRET introduces an additional fluorescence decay term which can be quantified. As it turns out, FRET is sensitive to both the distance between the fluorophores and their relative orientation. Therefore, detection of FRET serves as a useful probe for inter-fluorophore distance and inter-molecule interactions while being sensitive to fluorescence anisotropy. Consider a pair of dyes, one donor (D) and one acceptor (A), as point sources which are coupled to a biomolecule, as in Fig. 6.7A. The rate constant for decay via FRET from D to A is given by kFRET ¼

1 ðD, 0Þ

τD



R0 RDA

6 :

(6.7)

Here, τ(D,0) is the D fluorescence lifetime in the absence of A, RDA is the inter-dye D distance, and R0 is the F€ orster radius, specific for each dye pair. R0 is sensitive to the overlap of the D emission spectrum and the A excitation spectrum as in Fig. 6.7B and C. Additionally, R0 is sensitive to relative fluorophore orientations through a multiplicative factor κ2. κ 2 accounts for the average angle of orientation between D and A dipoles (Fig. 6.7D). Typically, κ2 is taken as 2/3, corresponding to the isotropic limit in which both fluorophores freely reorienting at timescales that are fast compared to the fluorescence lifetime and hκ2i ¼ 2/3. However, deviations from this value can have a significant impact on measured FRET efficiency.61 Thus, FRET is sensitive to dye anisotropy and so calibrations must be performed for each selection of FRET pairs and labeling locations. The specifics of donor-acceptor pair selection and properties are not covered here but are reviewed in the literature and in Chapter 2 of this text.45,62,63 At this stage, we introduce the superscript notation to specify the fluorescence species. (D,0) refers to the donor-only sample in the absence of acceptor. (D,A), then, is the donor-acceptor sample. The subscript notation refers to the detection channel for each parameter, with D the donor and A the acceptor. The FRET efficiency for a dye pair is defined as the number of quanta of energy transferred from D to A divided by the total number of quanta absorbed by D. Thus, FRET efficiency is the probability that an excitation of D will result in FRET to A.

(A)

k FRET

S1(D)

S1(A)

k01D k0D

k0A

S0(A)

S0(D)

Donor (B)

Acceptor Abs. A488 Fl. A488

Abs. A594 Fl. A594

norm. values

400

(C)

500 600 wavelength [nm]

700

symmetry axis θ disk δ

β1

β2

θ D=θ disk

(D)

Donor

E

1

0

(E)

RDA

Acceptor

0

R0,1 R

0,2

100

interdye distance [Å]

FIG. 6.7 Principles of FRET: (A) Schematic of a donor and acceptor labeled molecule in two different configurations. (B) Simplified Perrin-Jablonski diagrams of D and A. D is excited at a rate k01(D) to the first singlet state S1D. In the absence of A, it is depopulated with rate constant k0(D). Due to the coupling of the possible de-excitation of D and excitation of A, energy transfer can occur at a rate kFRET resulting in the excitation of A from S0(A) to S1(A) which is depopulated with a rate constant k0(A). (C) The emission (fluorescence) spectra of Alexa488 (A488) (Green dye) and the excitation (absorption) of Alexa594 (A594) (Red dye). A488–A594 dyes constitute a commonly used D–A pair in FRET studies. The amount of the overlap between the emission of D and excitation of A (shaded region) influences the value of the F€orster radius R0. (D) R0 strongly depends on the mutual orientation of the dipoles given by κ 2. However, dynamic averaging ensures hκ 2i  2/3 for unbiased, random reorientation of fluorophores, so this is the typically used value. The wobble in a cone model is commonly used to represent the mobility of the fluorophores as attached to the biomolecules.64 (E) FRET efficiency (EFRET) versus the normalized interdye distance (RDA/R0). The value of the F€orster radius, R0, defines the useful dynamic range of distances (0.5  RDA/R0  1.5; 0.98  E  0.08) that can be measured with a specific dye pair. The F€orster radius is specific to the chosen dye pair and the local environments of the dyes; to illustrate this, curves for two different F€orster radii are indicated.

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CHAPTER 6 Multiparameter fluorescence spectroscopy of single

Several equivalent expressions for the FRET efficiency, E, result from this definition: E¼

ðD, AÞ ð D , AÞ ðD, AÞ FA =ΦF, A nA kFRET F τ ¼ ¼ ¼ 1  DðD,0Þ ¼ 1  DðD,0Þ : ð D , 0 Þ ð D , A Þ nD + nA k0 + kFRET FD =Φ + FA =Φ F τ F, D

F, A

D

(6.8)

D

Here, nA and nD are the number of photons emitted by A and D, respectively; is the de-excitation rate constant of the excited D in the absence of A; k0 ¼ 1/τ(D,0) D and τ(D,A) are the fluorescence lifetimes of D in the absence and in the τ(D,0) D D and FD ¼ F(D,A) are the corrected fluorescence presence of A, respectively; F(D,0) D D intensities of D in absence and presence of A; FA represents the corrected fluorescence (D,A) intensity of A; and Φ(D,0) are the fluorescence quantum yields of F, D and ΦF, A the unperturbed D and A, respectively. The (D,0) parameters are usually determined by using a donor-only sample as a reference. Through combination of Eqs. (6.7) and (6.8), the dependence of FRET efficiency on inter-dye distance can be derived: E¼



1

RDA 1+ R0

6 :

(6.9)

The R6DA dependence means that the FRET efficiency is extremely sensitive to distances near the F€ orster radius, with a rapid drop-off in FRET events beyond R0 and a plateauing behavior below R0 as FRET becomes the primary decay pathway, as seen in Fig. 6.7E. It is worth noting now that RDA is conveniently defined such that for RDA ¼ R0 the FRET efficiency is 0.5 (and there is maximum sensitivity to changes in distance). The definitions of FRET efficiency in Eqs. (6.8) and (6.9) clearly lend themselves to at least two methods for determining experimental FRET efficiencies. The first is by photon-counting intensity measurements for steady-state FRET. The second method is time-resolved FRET by timing individual photon events to determine the relevant fluorescence lifetimes. These two methods can provide different insights in non-ideal conditions; thus, both are covered in this section. Additionally, an important facet of FRET is that, often, measurements for several FRET pairs at different positions on the same protein are used for gathering insights into structural information which can be used for modeling purposes. While design of these FRET networks is not a trivial or optimized task, it is worth touching on the usefulness of such an approach. Optimization of FRET network design is an active area of research.

Steady-state FRET Ensemble steady-state FRET can be determined via measurement with a fluorometer or microscope.65 FRET microscopy has the advantage of good spatial resolution and applicability to in situ measurements but suffers from high signal-to-noise ratios due to low photon numbers and non-trivial selection of the donor-only reference. The most intuitive and easy approach to measuring FRET is via an intensity-based approach. Because the donor fluorophore will de-excite via both fluorescence and

6.2 Multiparameter fluorescence spectroscopy

FRET and the acceptor will de-excite via fluorescence after excitation via FRET, the raw intensity count rates can be measured separately in green and red channels, given as SG and SR, respectively. These signals can be used as an indicator of FRET, given by the proximity ratio, PR: PR ¼

SR : SG + SR

(6.10)

It is important to note that the proximity ratio is not equivalent to FRET efficiency, except in ideal conditions, and is often dubbed incorrectly as FRET (as it does not contain the proper correction factors). It does serve as qualitative validation that FRET is occurring and that the dyes are in close proximity to each other. The principle of spectral intensity information as an indicator for FRET is visualized in Fig. 6.8. Acceptor

Intensity

Intensity

Donor

400

600

(B)

700

400

Wavelength [nm]

500

600

700

Wavelength [nm]

Intensity

Intensity

(A)

500

Time [ns]

Time [ns]

FIG. 6.8 Principles of FRET measurement methods: (A) The ratiometric approach can be employed by measuring the fluorescence intensity of the donor and acceptor over their entire fluorescence spectra or in specific spectral windows. The intensity plot on the left is the result of a high-FRET sample measurement, with the one on the right corresponding to low-FRET. Note the inter-dye distances in the corresponding cartoons. (B) FRET efficiency can be extracted by time resolved fluorescence decay (F(t)) measurements of DA and D(0) samples. In DA samples, presence of acceptor near the donor partially quenches the donor, resulting ) relative to the lifetime of the donor in a lower characteristic fluorescence lifetime (τ(D,A) D ). Quenching becomes more severe for higher FRET rates. Shown in the D(only) sample (τ(D,0) D as the leftmost curve in each plot, fluorescence decays of the donor correspond to high-FRET on the left and low-FRET on the right. FRET-sensitized acceptor decays, shown in red, intrinsically contain information on donor decay.

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CHAPTER 6 Multiparameter fluorescence spectroscopy of single

Quantitative determination of the true FRET efficiency, even in simple cases of homogeneous FRET species, requires determination of specific experimental parameters that depend on the experimental setup. The corrected FRET efficiency is given by 0

E¼ 1+γ  Φ

ðD, AÞ

FD

!1

ðD, AÞ

FA

    FD 1 FG 1 ¼ 1 + γ0  ¼ 1+γ , FA FR

(6.11)

Φ

where γ 0 ¼ ΦFF,,DA , γ ¼ ΦFF,,DA ggGR is a standard correction factor for the quantum yields and and FA ¼ F(D,A) are the corrected fluorescence detection efficiencies, FD ¼ F(D,A) D A signals of D and A, respectively. FD and FA depend on the detection efficiencies of the green (gG) and red (gR) channels such that: FG SG  hBG i ¼ , gG gG

(6.12)

FR SR  α FG  hBR i ¼ : gR gR

(6.13)

FD ¼

FA ¼

hBGi and hBRi are the background signals in green and red channels, while α is the spectral cross-talk from the donor fluorescence to the acceptor channel. The detection efficiencies are difficult to measure,17,66 but the ratio of detection efficiencies can be calibrated with a well-characterized sample.67,68 While Eq. (6.11) is called the corrected FRET Efficiency, it does not account for artifacts due to the direct excitation of the acceptor by the donor excitation pulse. Therefore, care must be taken in choosing a donor fluorophore with an excitation spectrum which is sufficiently distinct from the acceptor’s. An alternative intensity-based approach developed by Clegg does account for these factors.69 Here, the acceptor intensity ratio from signal after direct and FRET mediated excitation is calculated, yielding transfer efficiencies which are less prone to experimental artifacts. As with all FRET experiments, proper determination of the degree of labeling and dye stoichiometries is necessary for quantitative analysis. The approach described here is valid for both ensemble-based and single molecule experiments (in the latter the efficiency is calculated for each burst, or the equivalent analog depending on the experiment). Moreover, the same definitions apply for immobilized or freely diffusing samples. The differences between these conditions rely on the instrumentation used, the selection of the signal in space (the confocal volume in confocal setups or pixels on a camera in imaging studies), and time (binning of photons from freely diffusing molecules or series of images). In the case of ensemble conditions, care must be taken in the case of heterogeneous populations.

Time-resolved FRET Time-resolved measurements provide a deep insight of the energetics of a system through the use of fluorescence intensity decays. As opposed to the intensity-based approach, here the information of interest is encoded into the shape of the fluorescence intensity decay, allowing resolution of heterogeneity within a sample and

6.2 Multiparameter fluorescence spectroscopy

quantification of species component contributions to the decay. Intensity decays can be taken from ensemble experiments as well as from the photons selected as part of bursts in single molecule experiments. In contrast, BIFL or burstwise average fluorescence lifetimes reflect the mean photon arrival time of photons emitted from single molecules.34 Here, it is worth re-stating Eq. (6.6) in a more specific notation since there is more to keep track of: X

ðsÞ

FEm|Ex ðtÞ ¼

i


 xðiÞ  exp t  kðiÞ ,

(6.14)

where F(S) Em|Em(t) is the time-resolved fluorescence decay of the labeled molecules, x(i ) are the ith fractions or pre-exponential factors of each lifetime species, k(i ) are the de-excitation rate components for the i-th species, Ex and Em are the excitation and emission channels (either donor or acceptor), and s is the sample type (either donor-only (D,0) or donor and acceptor labeled (D,A)). Then, the FRET-rate decay is given by70 EðtÞ ¼

X l


 ðlÞ xðlÞ  exp t  kFRET ,

(6.15)

) with k(lFRET the FRET species-specific rate constants.71 When the distribution of FRET states is continuous, Eq. (6.15) becomes

Z

EðtÞ ¼

pðkFRET Þ  exp ðt  kFRET ÞdkFRET ,

(6.16)

where p(kFRET) is the probability distribution of FRET states. The FRET-rate decay is related back to the donor lifetime and the donor fluorescence in the presence and absence of acceptor by ð D , AÞ

FD

ðD, AÞ ðD,0Þ ¼ FD|D ðtÞ ¼ EðtÞ  FD|D ðtÞ:

(6.17)

Substituting this into Eq. (6.12), we obtain for the steady-state FRET efficiency, E: Z

ðD, AÞ

E¼1

FD

ðD,0Þ

FD

¼1

ðD,0Þ EðtÞ  FD|D ðtÞdt Z : ðD,0Þ FD|D ðtÞdt

(6.18)

Thus, the steady-state FRET efficiency can be determined from the integrated FRET decay, but with the added advantage over intensity-based approaches that heterogeneity is considered through component analysis of the decay with maximal temporal resolution. An alternative approach to using donor fluorescence is to monitor acceptor emission via FRET-sensitized fluorescence. In this case, the FRET-sensitized emission of the acceptor for the i-th FRET state, with lifetime τ(0,A) A|A ¼ 1/kA, a single donor life(l ) time τ(D,0) ¼ 1/k , and a FRET rate constant k , D D FRET is given by
 ðD,0Þ ðD, AÞ ð Þ ð Þ ð Þ  E t  F t  F t D|D A|A ðlÞ kA  kD
 kFRET  ðD,0Þ ðD, AÞ ðl, m, nÞ EðtÞ  FD|D ðtÞ  FA|A ðtÞ , ¼g

ðD, AÞ FA|D ðtÞ ¼

ðlÞ

kFRET

(6.19)

289

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CHAPTER 6 Multiparameter fluorescence spectroscopy of single

with the FRET decay for the l-th species given by


 ðlÞ EðlÞ ðtÞ ¼ exp t  kFRET ,

(6.20)

and gðl, m, nÞ ¼

ðlÞ

kFRET

ðlÞ

kA  kD  kFRET

:

(6.21)

To calculate this distance from measurable fluorescence decay patterns, we use the F€ orster-equation, Eqs. (6.9), and (6.18). The calculated inter-dye distances provide useful distance constraints for the conformational changes within a labeled biomolecule or interactions between biomolecules when dye mobility and linker effects are properly accounted for. Experimentally, the analysis of the donor fluorescence in presence of the acceptor, F(D,A) D|D , requires knowledge of the donor fluorescence in (D,0) absence of the acceptor, FD|D , to yield FRET-rates. Meanwhile, the time-resolved FRET-sensitized acceptor emission, F(D,A) A|D , additionally requires the response of the directly-excited acceptor, F(D,A) A|A . These experimentally measured decays are usually fitted globally, without directly calculating the ratiometric quantities, through an iterative re-convolution approach with an assumed form of the model function describing the rate distribution. Compared to the ratiometric approach, this approach avoids the necessity of specially designed ratiometric fluorophores, thus allowing greater freedom in fluorescent marker selection, and reducing the instrumental calibrations necessary for quantitative FRET.54 Fluorescence polarization can also be used as a FRET indicator, though this is detailed in the section on fluorescence anisotropy.

FRET network design One of the goals in smFRET is to derive inter-dye distances in labeled biomolecules.72–75 Inherent in this is the need to find suitable sites to fluorescently tag the biomolecule of interest. The goal of FRET-guided structural modeling is to reach a near atomistic depiction of biomolecules.76–82 However, even if the ultimate goal is not to provide a full structural characterization of the biomolecule, careful selection of the labeling sites is needed to reduce potential artifacts due to dye behavior or potential disruption of molecule functionality by the dyes. Further, often one FRET pair provides fairly limited information. Therefore, several samples with complementary FRET pairs are designed and prepared to fully resolve the molecular structural dynamics of even simple molecules. Here, we present a brief list of considerations that need to be taken to properly design a FRET network for probing the structural dynamics of a biomolecule. I) Solvent-exposed residues are generally targeted for proper labeling reaction chemistry. II) If known, active sites or residues which are required for proper folding of the biomolecule should be avoided. If this information is not known, bioinformatics

6.2 Multiparameter fluorescence spectroscopy

approaches can be used to identify conserved residues in similar structures which are most likely an evolutionary advantage and, thus, important to the structure or function. III) If possible, residues near the middle of alpha helices or other relatively rigid secondary structural elements should be targeted for labeling. These provide the required rigidity to assure the motions that are captured by fluorescence detection correspond to the whole molecule or larger domain motions (and not motions due to local flexibility). If the motions of interest are the local motions, similar considerations should to be taken to account for larger-scale motions. IV) The size, shape, and motions of molecules should be considered in deciding the number and locations of FRET pairs. The number of required FRET distances should be different for different numbers of moving domains, different kinds of motions, and differences in available labeling sites. For example, the toy model of two rigid bodies has at least 6 degrees of freedom (3 spatial and 3 rotational) which can be probed by FRET. Using too few FRET pairs to properly resolve changes in these six can result in ambiguity in interpretation of data or even incorrect conclusions. If more motions are expected, additional structural information can be used to reduce and complement the measured distances. This can include a priori knowledge about the secondary structural elements, the structural orientation of domains, or an approximated structural model derived from a given sequence. In most cases, this prior knowledge can be provided by crystallographic or NMR structures. If any structural information is unavailable, ab initio modeling algorithms (e.g. ROSETTA83 or homology modeling techniques like ModeRNA,84 MODELLER,85 and SWISS-MODEL86 (for review see87) can be used to generate initial structural models. V) To ensure maximal contrast between conformations of the molecular backbone, we must account for the motions of the labels, themselves, in the context of the chosen labeling sites. One method for evaluating suitability of label locations for FRET studies before an experiment is through accessible volume (AV) simulations.70,88 These coarse-grained Monte Carlo simulations place the dyes in the correct environment on the protein of interest, connected by a linker, and allow the dye to freely diffuse through the allowed space, providing similar results to molecular dynamics simulations. From these simulations, the volume through which the dye can diffuse and reorient, as determined by the protein surface and the linker, can be obtained, and the distribution and mean of κ can be calculated. This approach assures that the dye sites do not restrict dye motions too much for them to be suitable for experiment. Further, AV simulations allow predictions for observed FRET distributions and variance. The working assumption for these considerations is that local dye motions are decoupled from the larger motions of the biomolecule. In summary, it is necessary that all FRET distances capture the desired motions of the molecule of interest and that each FRET distance contributes maximally to the differentiation of conformational states or the motions of interest while minimally

291

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CHAPTER 6 Multiparameter fluorescence spectroscopy of single

disrupting the native molecule’s structure and function. Applications of the considerations discussed in the section are discussed later.

6.2.7 Time-resolved anisotropy Fluorescence, in general, leads to signal depolarization. A polarized excitation signal will preferentially excite fluorophores which have their absorption transition dipole moment aligned with the excitation photon’s polarization. The emitted fluorescence photons, after some delay (on average, the fluorescence decay lifetime), will then be emitted with polarization aligned to the emission transition dipole moment. This preferential polarization of fluorescence emission is equivalently called the fluorescence anisotropy. However, reorientation of the dipoles due to Brownian rotational diffusion, along with differences in orientation of each fluorophore’s excitation and emission dipoles, will cause the fluorescence signal to depolarize. Thus, in general, there is a characteristic anisotropy decay for a given sample. Determination of fluorescence anisotropy is accomplished through the separate measurement of fluorescence intensity decays for the emission of the parallel to and perpendicular to excitation polarization. For isotropic emission with z-axis symmetry (that is, symmetry about the axis defined by the polarization of the excitation light such that the perpendicular x and y emission components are equal), the total fluorescence intensity is given by the sums of the intensities for the orthogonal components: FT ¼ Fx + Fy + Fz ¼ 2F? + Fk :

(6.22)

It is worth noting that in order to avoid artifacts resulting from differing detection efficiencies, which depend on polarization and can affect the shape of the fluorescence intensity decays, measurements of total fluorescence intensity are done at magic angle conditions with an emission polarizer placed at 54.7° compared to the excitation polarizer. This serves as a reference measurement to recover the proper ratio between parallel and perpendicularly polarized photons in an isotropic sample for the setup, as intensity decay terms (as in Eq. 6.6) due to sample anisotropy go to zero for this angle. This ensures that any measured deviations from this ratio or additional decay terms in other conditions are a result of anisotropic effects.13 The parallel and perpendicular components of the intensity, in terms of time-dependent anisotropy, are given by Fk ðtÞ ¼

FðtÞ ½1 + 2r ðtÞ 3

(6.23)

F? ðtÞ ¼

FðtÞ ½1  r ðtÞ, 3

(6.24)

and

where r(t) is the time-dependent anisotropy of the emission. Note that, for the case where r(t) ¼ 0, the expected ratios of intensities are recovered. For r(t) ¼ 1, all emission is polarized in the excitation direction. However, it is not actually possible to obtain r(t) ¼ 1 for fluorophores in solution with single-photon excitation since it

6.2 Multiparameter fluorescence spectroscopy

is impossible to obtain a perfectly-oriented excited state population.13 In reality, fluorescence signal is collected after it passes through complex optical elements, leading to polarization mixing. Correcting for this mixing, Eqs. (6.8) and (6.9) can be rewritten as Fk ðtÞ ¼

FðtÞ ½1 + ð2  3l1 Þ  r ðtÞ 3

(6.25)

F? ðtÞ ¼

FðtÞ ½1  ð1  3l2 Þ  r ðtÞ, 3

(6.26)

and

where l1 and l2 are constants which correct for polarization mixing and which depend on the specifics of the experimental setup.89,90 From Eqs. (6.23) and (6.24) (or Eqs. (6.25) and (6.26)), r(t) is given by r ðt Þ ¼

Fk ðtÞ  F? ðtÞ : Fk ðtÞ + 2F? ðtÞ

(6.27)

It is usually necessary to account for differences in detection efficiencies between the parallel and perpendicular polarizations. Thus, F? is multiplied by the ratio of parallel to perpendicular detection efficiencies, G.13 Typically, r(t) is modeled using a multi-exponential decay, given by r ðt Þ ¼

X

ðk Þ

r exp k 0



 Z   t t ¼ p ð ρ Þ exp dρ, ρ ρðkÞ

(6.28)

where ρ(k) are the rotational correlation times for the system and r(k) 0 assign weights to the different depolarization processes. ρ(k) correspond to the average time over which the k depolarization process occurs, analogous to the fluorescence decay lifetime. Typical timescales for some depolarization processes are included in Table 6.1. P (k) , r ¼ r , gives the fundamental anisotropy of the The sum of the weights r(k) 0 0 k 0 molecule, or the anisotropy at t ¼ 0, whereas r(k) 0 are products of contributions to the fundamental anisotropy and weight factors. The maximum fundamental anisotropy for single-photon excitation is 0.4 and for two-photon excitation is Table 6.1 Typical timescales of various types of motion measured by time-resolved anisotropy. Timescales of k depolarization process include re-orientations of a fluorophore due to global motions of a fluorophorelabeled biomolecule, dynamics associated with the linker connecting a fluorophore to a larger molecule, and smallscale dye reorientations. Type of motion

Timescale of motion

ρ(global)

>10 ns

ρ

1–5 ns

(linker)

ρ(dye)

0.3–0.5 ns

293

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CHAPTER 6 Multiparameter fluorescence spectroscopy of single

0.57 (when one element of the two-photon absorption tensor dominates), in the case where the fluorophore’s absorption and emission transition moments are parallel. In the case that these two moments are perpendicular, the anisotropy can reach 0.2 for single-photon excitation and 0.29 for two-photon excitation. It is the fundamental anisotropy, the component amplitudes, and the correlation times that give us physical insight into the fluorophore and the labeled molecule. Eq. (6.28) allows us to quantify dye mobility and identify potential problems arising from restricted mobility of dyes. This is especially important for FRET experiments as FRET-determined distances are sensitive to relative dye orientation.91,92 The insight provided by Eq. (6.28) in determining the local flexibility of dye labels is useful for troubleshooting FRET, since FRET is sensitive to the relative orientation of the D and A dyes through the mutual orientation factor κ2. Additionally, the Perrin equation provides a useful relationship between the fluorescence lifetime and anisotropy.93 In the simple case of mono-exponential decays for both fluorescence intensity and anisotropy, the Perrin equation is given by r¼

r0 , 1 + τ=ρ

(6.29)

where r0 can, in practice, be determined through photon-weighted integration of Eq. (6.28). Thus, it is clear that, being dependent on the fluorescence lifetime, the anisotropy can also be used as an indicator for FRET and for quantitative FRET measurements.94 Aside from rotational motions and lifetime changes, fluorescence depolarization can also be caused by energy transfer between chemically identical fluorophores. Such homotransfer is also described by F€orster’s theory, i.e. transfer efficiency depends on the inter-fluorophore distance, but does not change the observed fluorescence lifetime, making anisotropy the only changing observable for this process. HomoFRET is commonly used to study protein interactions in situ with polarization microscopy,95–97 having the advantages of relatively simple labeling schemes (one type of dye) and instrumentation (only polarization or polarization and frequency-domain information are needed, as in FLIM). HeteroFRET has the advantage of measuring more observables, i.e. FD/FA and fluorescence lifetime, providing better distance resolution and options for controlling experimental conditions. The definitions for the steady-state and time-resolved anisotropy are analogous to the steady-state FRET efficiency and the FRET decay and are calculated similarly. One caveat, though, is that, in anisotropy, a fast-rotational time (high rate constant) results in a low anisotropy, whereas a high FRET rate (low decay time) results in a high FRET efficiency. Table 6.2 summarizes the analogous equations of FRET and anisotropy decays.

6.2.8 Fluorescence correlation spectroscopy Fluorescence correlation spectroscopy (FCS) was first introduced by Elson and Magde in 19726,98,99 and is used as a denoising algorithm to extract changes in measured signal over time. In combination with FRET (FRET-FCS), it becomes a powerful tool to study dynamics over a wide range of time-scales100–104 from

6.2 Multiparameter fluorescence spectroscopy

Table 6.2 Description of FRET-rate decay E(t) and time-resolved anisotropy r(t). FRET

Anisotropy Ð

Model

E(t) ¼

Signal

(D,0) (D,A) FD|D ¼ E(t)  FD|D (t)

Reference

(0,A) F (D,0) (t), FA|A (t), D|D

p(kFRET)  exp ( t  kFRET)dkFRET

R

Steady-state E ¼1

ðD,0Þ E ðtÞ  FD|D ðtÞdt R ðD,0Þ FD|D ðtÞdt


 R r ðtÞ ¼ pðρÞ  exp  ρt dρ   F? ðtÞ ¼ FM ðtÞ  13  13 r ðtÞ 1 2 a Fk ðtÞ ¼ FM ðtÞ  3 + 3 r ðtÞ FM(t) R r ðtÞ  FM ðtÞdt r¼ R FM ðtÞdt

a M stands for measurement at magic angle conditions, by setting the excitation polarizer and the emission polarizer at 54.7° difference.

nanoseconds to seconds. Further, employing filters based on the fluorescence and anisotropy decay signatures for a sample allows the resolution of heterogeneity in a sample and interchange between different fluorescent states. Hence, FCS is an ideal method to study conformational dynamics of biomolecules, the formation of macromolecular complexes, and folding and kinetic process that otherwise are difficult to identify.57,78,100–102,104–108 In a typical FCS experiment, fluorescently labeled molecules diffuse freely in solution. Typically, in a confocal configuration as previously described, although other geometries have been implemented.109–112 The signal over this volume is recorded and processed in real-time using hardware correlators,113 or post-acquisition using off-line correlation algorithms.114 When FRET is combined with FCS, fluctuations in FRET reflect changes in the structure of the biomolecule. These are then recorded by monitoring the emissions of the donor and acceptor, which in turn provide useful information on the kinetics of the system. As previously, we present the final equations that describe some of the simplest cases for FRET-FCS and discuss various experimental scenarios. Detailed reviews are available in the literature.12,115–117 The auto and cross-correlations of two time-dependent signals (SA(t) and SB(t)) are given by: G A, B ð t c Þ ¼

hSA ðtÞ  SB ðt + tc Þi hδSA ðtÞ  δSB ðt + tc Þi ¼1+ : hSA ihSB i hSA ihSB i

(6.30)

If SA equals SB the correlation function is called an autocorrelation function, otherwise it is called the cross-correlation function. In this notation, δSA(t) is used to reflect the deviation in SA from its mean value, hSAi, such that in the absence of fluctuations or when correlation time tends to infinity (tc ! ∞) then GA, B(∞) ! 1. Therefore, the correlation functions (auto and cross) are a measure of the time evolution for changes in the system. Nonetheless, thermodynamic equilibrium is always assumed; otherwise, the autocorrelation function will change over time as the system evolves.

295

296

CHAPTER 6 Multiparameter fluorescence spectroscopy of single

If we consider that the correlated signal is generated from fluorescence emission of labeled biomolecules, and if all species have the same brightness, the amplitude of the autocorrelation function at time zero, GA,A(0), reflects the average number of emitting molecules (NFCS) which are in the detection volume, VFCS. In other words, it is possible to determine the equilibrium concentration of molecules, c, if the volume is properly calibrated. This detection volume is defined by the geometry of the focus volume for the laser passing through the sample. For a homogenous solution of labeled samples, and assuming a three dimensional Gaussian profile wFCS(x, y, z) ¼ exp (2(x2 + y2)/ω20)  exp (2z2/z20), with ω0 and z0 as characteristic widths of the 3D Gaussian, that describes the shape of VFCS, it is possible to derive a formal expression for the autocorrelation function: G A, A ð t c Þ ¼ 1 +

1 Gdiff ðtc Þ, NFCS

(6.31)

where the factor that is given by the molecules diffusing through the confocal volume Gdiff(tc) is  Gdiff ðtc Þ ¼ 1 +

tc

1

tdiff

!1=2  2 ω0 tc  1+ z0 tdiff

(6.32)

Here, tdiff is the diffusion time, or the average time a molecule spends in the confocal volume. For one-photon excitation the characteristic diffusion is time related to the difω2

ω2

0 0 (for two-photon excitation, this becomes 8Ddiff ).27 fusion coefficient (Ddiff) as tdiff ¼ 4Ddiff

Therefore, FCS is commonly used to determine the diffusion coefficient. In a heterogeneous mixture of n species with corresponding brightness, Q(i ), and where each species has a diffusion constant, D(idiff) and population fractions given by x(i ) with i ¼ 1, …, n, the autocorrelation function is defined as118 X

GA, A ðtc Þ ¼ 1 +

1 NFCS



 2 ðiÞ xðiÞ QðiÞ  Gdiff ðtc Þ :
X  2 2 xðiÞ ðQðiÞ Þ i i

(6.33)

Even if the brightness, Q(i ), is known for the i-th species, the diffusion coefficient for each species, D(idiff) , must be significantly different in order to derive the concentration of each species, c(i ). For this reason, FCS is very powerful as equilibrium constants that depend on the concentration of the reagents can be derived, even in live cells.118 For an experimental set-up with two detection channels, one for the emission of the donor, G or “green,” and one for the acceptor emission, R or “red,” with corresponding signals SG(t) and SR(t), respectively, two auto correlation functions (GG,G(tc), (GR,R(tc)) and two cross correlation functions (GG,R(tc), GR,G(tc)) can be derived from Eq. (6.30). An informative, simple example case for the study of conformational dynamics with FRET-FCS is to consider the isomerization reaction between two states k12 Sð1Þ Ð Sð2Þ k21

(6.34)

6.2 Multiparameter fluorescence spectroscopy

(2) where both have the same diffusion coefficients D(1) diff ¼ Ddiff. In this case, the ratio of molecules per species is given by the equilibrium constant K

K¼

k21 N ð1Þ ¼ , k12 N ð2Þ

(6.35)

with N ð1Þ ¼ NT 

k21 k12 , N ð2Þ ¼ NT  and NT ¼ N ð1Þ + N ð2Þ : k12 + k21 k12 + k21

(6.36)

Assuming that the characteristic time of the triplet state is much smaller than the relaxation time given by the exchange rate constants (tT ≪ tR ¼ k12 +1 k21 ), the autoand cross-correlations are given by GG, G ðtc Þ ¼ 1 +

1  Gdiff ðtc Þ  ð1 + ACG, G exp ðtc =tR Þ Þ NT

(6.37)

GR, R ðtc Þ ¼ 1 +

1  Gdiff ðtc Þ  ð1 + ACR, R exp ðtc =tR Þ Þ NT

(6.38)

GG, R ðtc Þ ¼ GR, G ðtc Þ ¼ 1 +


 1  Gdiff ðtc Þ  1  ðACG, G  ACR, R Þ1=2 exp ðtc =tR Þ : NT

(6.39)

Here, Gdiff(tc) is given by Eq. (6.32), and ACG,G and ACR,R are the amplitudes of the kinetic reaction terms, which depend on the molecular brightnesses, Q(i ), of the FRET states. The molecular brightness corresponds to the observed photon count FðiÞ rate per molecule, QðiÞ ¼ ðiÞ , where F(i ) is the total number of fluorescence photons N from N(i ) molecules of the i-th species. The molecular brightness is an intrinsic molecular property of the dyes. It is proportional to the product of the focal excitation irradiance, I0, the extinction coefficient, ε(i ), fluorescence quantum yield, Φ(iF ), and spectral dependent detection efficiencies gG or gR for green and red detectors, respectively, as Q(iG,) R ∝ I0ε(i )Φ(iF )gG,R.17,119 The FRET efficiency E(i ) of species i is related to the molecular brightness by the relationship: EðiÞ ¼ Φ

ðiÞ ðiÞ QR  αQG ðiÞ ðiÞ ðiÞ QR  αQG +  γQG

(6.40)

where γ ¼ ΦFF,,DA  ggGR ¼ γ 0  ggGR and α is the spectral cross-talk into the red channel. Examples of FRET-FCS used to study multi-state systems can be found in the literature.103,106,120,121 In case of small contrast between the species in the correlation channels, each species contributes to the signal in both channels. Therefore, the brightnesses of the species in the correlation channels must be considered to calculate the pre) , the preexponentials factors for Eqs. (6.37)–(6.39). Given the brightnesses Q(iG,R exponential factors are summarized in Table 6.3. In the case where each species (1) (2) contributes to only one of the correlation channels (Q(1) G ¼ 1, QR ¼ 0, QG ¼ 0, (2) and QR ¼ 1), maximal contrast is achieved and the pre-exponential factors simplify as in Table 6.3.

297

298

CHAPTER 6 Multiparameter fluorescence spectroscopy of single

Table 6.3 Correlation coefficients. Small contrast

Maximal contrast ACG, G ¼ K1

ð1 Þ ð2Þ 2 QG QG ð1Þ ð2Þ 2 KQG + QG

ACG, G ¼

ð ð

Þ K Þ

ACR, R ¼

ðQðR2Þ QðR1Þ Þ 2 K ðQðR2Þ + KQðR1Þ Þ

CCG, R ¼

ðQðG1Þ QðG2Þ Þ ðQðR2Þ QðR1Þ Þ 2 2 K ðKQðG1Þ + QðG2Þ Þ ðQðR2Þ + KQðR1Þ Þ

ACR,R ¼ K

2

2

CCG,R ¼  1

2

To increase contrast between correlation channels B€ohmer et al.122 used differences in fluorescence lifetimes to separate molecular species. More recently, filtered FCS (fFCS) was introduced,8,73 expanding this idea through use of MFS to optimally separate molecular species by their specific fluorescence lifetime-, polarization-, and spectrally-resolved fluorescence decays. In principle, fFCS can be used to separate even more than two species based on species-specific MFS patterns; however, separating four or more species is still a major technical challenge. fFCS relies on the generation of filters (fj(i )) which correspond to the i different fluorescence species components in a heterogenous sample. These filters can then be used to perform correlations of components of the total fluorescence signal from the sample (Sj(t)) using12 *  Gði, mÞ ðtc Þ ¼

2L X

ðiÞ

fj Sj ðtÞ 

FðiÞ ðtÞ  FðmÞ ðt + tc Þ j¼1 ¼ * 2L X hFðiÞ ðtÞihFðmÞ ðtÞi

2L X

+ ðmÞ

fj

Sj ðt + tc Þ

j¼1

+* ðiÞ fj Sj ðtÞ

j¼1

2L X

+:

(6.41)

ðmÞ fj Sj ðtÞ

j¼1

Eq. (6.41) corresponds to the species Auto- or Cross-Correlation function (sAC or sCC) when i and m are the same or different, respectively. In the simple scenario of two polarization channels in a single spectral window, the filters for each of the i-th species are generated from a bimodal decay histogram, Hj (one for each polarization, jj and ?), where j is the TAC channel index (covered later). Thus, the bimodal decay histogram has a maximum length of 2L, where L is the number of TAC channels. For two spectral windows each with two polarizations as the set-up presented in Fig. 6.3, this becomes 4L, and so on such that the maximum length is twice the number of TAC channels. The conditional probabilities, pj, represent the weights of species-specific histogram decays (w(i )) with length equal to that of Hj, satisfying Hj ¼

m¼2 X i¼1

ðiÞ

wðiÞ  pj ,with

dL X j¼1

ðiÞ

pj ¼ 1:

(6.42)

6.2 Multiparameter fluorescence spectroscopy

Filters are thus generated through simultaneous minimization of the weighted species-specific histograms and the weighted Hj, *

m¼2 X

!2 +

f

ðiÞ

ðiÞ

 Hj  w

! min :

(6.43)

i¼1

This results in the optimal generation of filters for all species simultaneously.73 Using these filters, species-specific auto-correlation and cross-correlation functions (sAC and sCC) can be computed, elucidating the dynamic timescales for interspecies conversions of interactions in heterogeneous mixtures. Compared to TAC gating filters,119,123 fFCS does not subjectively define the TAC channels, and fFCS can properly separate heterogeneous mixtures due to their fluorescence properties. Thus, the fast timescales of dynamics for individual subpopulations of a sample as well as interchange between them can be probed via fFCS. An important note is that it may be difficult to obtain fluorescence information for an individual species for use in fFCS. As species may not be well-defined, they may actually correspond to multiple conformational states in a molecule’s conformational space, or the number of states may be too large to fully resolve. In this case, fFCS can still reveal the timescales for dynamics, but care must be taken in the interpretation of data. Examples of fFCS curves from specific studies can be seen later in this chapter. There are several methods currently in use which provide information similar to that derived from FCS through related methods. Imaging correlation spectroscopy (ICS) utilizes either spatial and/or temporal correlations of series of high-resolution images to extract parameters characterizing the system, such as concentration and diffusion times. Numerous variations on ICS exist with different advantages.124 Fluorescence intensity distribution analysis (FIDA) resolves heterogeneity in fluorescent samples through correlation of molecule brightnesses.125 Fluorescence recovery after photobleaching (FRAP) tracks the recovery of fluorescence following the complete bleaching of all fluorophores in a detection volume, allowing probing of diffusion and binding dynamics.126 Additionally, compatibility of FRAP with imaging means movies can be produced for qualitative analysis.

6.2.9 Accuracy of MFS with FRET The main attraction of MFS is its ability to simultaneously resolve all available fluorescence information, thus providing insight into both the spatial and temporal domains for fluorescently-labeled molecules. The precision of MFS is limited only by the time resolution and detection efficiencies of the instruments. However, it is worth discussing the accuracy of MFS in probing the distances and timescales relevant to molecular structures and dynamics through FRET.

Spatial accuracy While FRET is often treated as a ruler for distances between biomolecules or parts of biomolecules, in reality we are measuring and calculating only related quantities, as the dyes used as probes are attached to the molecules of interest via linkers and have an associated accessible volume through which they can move (Fig. 6.9A). Dye

299

300

(B)

Inter-dye distance definitions (Rmp, ⟨RDA⟩ and ⟨RDA⟩E) are related to different fluorescence-observables. (A) dsDNA model system where the results of AV simulations for donor (G) and acceptor (R) are overlaid. (B) All inter-dye distances can be interrelated through empirical polynomials of 3rd order, shown as a 3D plot. Accurate and precise determination of Rmp is important for later use in structural modeling.

CHAPTER 6 Multiparameter fluorescence spectroscopy of single

(A) FIG. 6.9

6.2 Multiparameter fluorescence spectroscopy

linkers are responsible for two major effects: (i) a considerable displacement of the mean dye position with respect to the attachment point, and (ii) measured FRET efficiencies actually being averages over a distribution of donor-acceptor (D,A) distances p(RDA). The second effect renders the well-known Eq. (6.9) inaccurate. In general, there are three different averaging methods and, before interpreting results, it is important to identify which of these distances are provided by experiments (Fig. 6.9B). Although commonly used, the distance between mean dye positions Rmp is not accessible in FRET experiments. Rmp provides a graphical description of interdye distances and it is defined as





D* E D* E 1 X n m *ðiÞ *ð jÞ

1X

ðiÞ ð jÞ

Rmp ¼ R D  R A ¼

RD  R A ,

n i m j

*ðiÞ

(6.44)

*ð jÞ

where R D and R A are all the possible positions that the donor and the acceptor fluorophores can take modeled by stochastic Accessible Volume (AV) or Molecular Dynamic (MD) simulations. In contrast to Rmp, two FRET observables are experimentally accessible. In time-resolved fluorescence experiments the distribution of the donor-acceptor distances p(RDA) ¼ p(kFRET) is accessible. However, in real experiments often only the mean and the width of the distribution p(RDA) can be determined. Given an arrangement of fluorophores in space, the mean donor-acceptor distance hRDAi is defined as



* n m

ðiÞ *ð jÞ 1 X X *ðiÞ *ð jÞ

hRDA i ¼ R D  R A ¼

R D  R A : nm i j

(6.45)

In contrast to time-resolved methods with sub-ns-time resolution, intensity-based measurements have a limited time-resolution. Therefore, information on the distribution function p(RDA) of the fluorophores cause by dye linker motion is completely lost. Still, a quantity with a unit of distance can be determined:
1=6 , hRDA iE ¼ R0 hEi1  1

where the average efficiency is defined as

1

0

n X m 1 X B hEi ¼ @ nm i j

(6.46)

C

*

A

ðiÞ *ð jÞ 6 R0 + R D  R A

R0

(6.47)

instead of Eq. (6.9). Assuming a certain spatial arrangement of fluorophores, all distance measures can be interconverted as depicted in Fig. 6.9. The Rmp, hRDAi, and hRDAiE average distances exhibit marked differences depending on the size, shape and the mutual orientation of the dye distributions. The difference is particularly pronounced for distances below R0 and can be as much ˚ (or 30%). If not considered properly, this error contributes to large as 10 A

301

CHAPTER 6 Multiparameter fluorescence spectroscopy of single

uncertainties in determined distances. Rmp can be approximated from experimentally obtained hRDAi or hRDAiE using a conversion function based on the set of calculated dye distributions on known structures73,88 or empirically.72 The relation is described graphically in Fig. 6.9. The distributions of single-molecule FRET distances for both static and dynamic systems can be analyzed using photon distribution analysis (PDA). PDA considers fluctuations in FRET efficiency along with background and shot noise to accurately reconstruct the FRET distribution. Global analysis is performed using differently-sized time bins, obtaining the limiting FRET states for interconversion of states taking place on the timescale of the diffusion time. For the technical details of PDA, the reader is referred elsewhere.127

Temporal accuracy

# of bursts

To demonstrate the ability of MFD in probing the temporal domain, let’s consider the isomerization reaction presented in Eq. (6.34), with each state having different FRET efficiencies (or FD/FA ratios). Assume the forward and backward rate constants are equal. An application of the static- and dynamic-FRET lines is illustrated in Fig. 6.10. There is also a 2-state system with varying state-interconversion rate constants presented. The FRET-levels of the states, the exchange rate constants, and the burst durations determine the shape of the histograms. The diffusion time (here tdiff ¼ 0.5 ms) sets the upper time-scale of the experiment and the FRET-levels deter(1) (2) mine the donor lifetimes (τD(A) and τD(A) ). Depending on the exchange rate constant, different shapes in the FD/FA vs. hτD(A)if histograms are observed. Static states, with

102 101

FD/FA

302

100

10-1 0

k 12 = 1 ms-1

k 12 = 0.01 ms-1 1

2

3 [ns]

4

1

2

3 [ns]

k 12 = 10 ms-1 4

1

2

3 [ns]

k 12 = 100 ms-1 4

1

2

3 [ns]

4

FIG. 6.10 MFD histograms of an isomerization process occurring at different timescales. Burst-wise analysis of interconverting simulated FRET-states presented in 2D histograms of FD /FAvs. hτD(A)if. The shape of the histograms is determined by interconversion that occurs between states. From left to right the interconversion rate constants, assumed to be symmetric (k12 ¼ k21), increased from 0.01 ms1 to 100 ms1. In all cases, the diffusion time tdiff ¼ 0.5 ms was considered to be the same. The static-FRET line (extending from the bottom to the top of each plot) or dynamic-FRET line (branching from the static FRET line and connecting the limiting states) are guidelines to identify whether a state appears to be “static” during the duration of the observation of the molecule or if dynamic averaging occurs.

6.2 Multiparameter fluorescence spectroscopy

respect to the diffusion time, are described by the static-FRET line, which gives the expected average FRET efficiency of a static FRET state given the fluorescencelifetime-weighted average donor lifetime, hτD(A)if. In fast exchanging systems, mixed populations shift toward higher lifetimes with respect to the static-FRET line appear. This shift is called dynamic shift and occurs because intensity-based parameters such as FD/FA are weighted by the species fraction (as the total intensity will be the summed intensities of components) while hτD(A)if is weighted by the fluorescence lifetime. The maximum density of the histograms follows the dynamic-FRET line. With an increasing number of interconverting FRET-states the dynamic shift becomes smaller and may not follow the simple dynamic FRET line as given by FD =FA ¼

1 ðD,0Þ  ΦF, D τDð0Þ   1 , ðA,0Þ τDðAÞ ΦF, A 1

E¼ 1+

ðA,0Þ Φ F, A  FD =FA ðD,0Þ ΦF, D

¼ 1

τDðAÞ : τDð0Þ

(6.48)

(6.49)

To study complex kinetic networks, a combination of methods must be applied, i.e., TCSPC to determine the limiting states and correlation methods for the kinetic rate constants. Resulting models of the kinetic network require testing by simulating the fluorescence observables of a given model and comparing with experimental outcome. Examples of different comprehensive treatments of multidimensional FRET-efficiency histograms are presented in.23

Temporal accuracy of FCS The power of fluorescence correlation spectroscopy lies in its ability to resolve molecular concentrations and the timescales associated with various kinetic processes. For example, the diffusion time for a freely diffusing species of molecule can be determined from Eqs. (6.37)–(6.38). For individual biomolecules, this is typically on the order of milliseconds. Further, FCS can resolve even fast triplet-singlet kinetics (99% of the events recorded arise from single molecules. Thus, a molecular occupancy of 0.01 is usually selected as the criteria when performing single molecule detection experiments. From Eq. (7.1), there are two methods to assure that single molecule experiments are carried out under conditions where K < 0.01; reduce the analyte concentration or reduce the probe volume size, P. For the probe volume size, optical monitoring for the detection of single molecule events, P, is defined by the excitation laser beam size (1/e2 intensity), ω0, and is given by
 P ¼ πω20 ð2zÞ

where the symbols are defined in Fig. 7.2.

(7.3)

7.1 Introduction

0.4

K=1 0.35

Probability, P(m)

0.3

0.25

K=3

0.2

K=5

0.15

K=0.1

0.1

0.05

0

K=0.01 0

2

4

6

8

10

12

m

FIG. 7.1 Poisson distribution probability of finding m molecules in a probing volume for different values of the average molecular occupancy, K.

2z

2 ω0

FIG. 7.2 Left – Schematic of a focused laser beam serving as the excitation source with the probe volume, P, defined by the laser beam waist size, ω0. Right – Drawing of the probe volume assuming a cylindrical geometry, and the terms defining its volume, P (see Eq. 7.3).

337

CHAPTER 7 Single molecule analysis in nanofluidic devices

The beam waist and thus the probe volume size is typically determined by the diffraction-limited focusing of the excitation beam, which can be approximated from the wavelength of the excitation light (λ), and the properties of the focusing optic (NA – numerical objective or focal length, f ): ω0 ¼

λ 2NA

(7.4)

To determine z (see Eq. 7.3) to calculate the probe volume size, we can assume z is determined by the relay optic’s depth of focus (DOF) (see Eq. 7.5; assumes that the detector spatial resolution is small). DOF ¼ λ n

. (7.5)

NA2

Assuming an air-immersion objective (n ¼ 1.00), 532 nm excitation, and a 100  objective with a NA ¼ 1.1, inserting these values into Eq. (7.5) produces a DOF of 0.4 μm. Using the DOF of 0.4 μm and a beam waist of 10.6 μm would produce a probe volume of 35 μm3 (35 fL). In Fig. 7.3 is plotted the average single molecule occupancy for different beam waist sizes assuming a DOF as noted above. As can be seen, to keep the double occupancy probability below 1% at all probe volume sizes will require a molecular concentration less than 1 pM (beam waist < 70 μm).

100

Average Molecule Occupancy

338

10 1 0.1 0.01 1E-3

100 fM 1 pM 100 pM 1 nM

1E-4 1E-5 1E-6 0

20

40

60

80

100

Beam Waist (um)

FIG. 7.3 Plots of the average molecule occupancy (Pm) as a function of the excitation beam waist (ω0). The calculations used equations (7.5) (DOF 0.4 μm), (7.4), (7.3) and (7.1). The y-axis is plotted on a log scale, while the x-axis is on a linear scale. The dashed line represents the average molecular occupancy of 0.1 so that the probability of double occupancy is 1%.

7.1 Introduction

The challenge with diffraction limited probe volumes required when using optical monitoring of single molecule events is that the concentrations required are relatively small and as such, challenges can result when biological systems must be studied. For example, in the case of biological enzymes studied at the single molecule level to obviate issues with ensemble averaging, the low concentration requirements to assure the monitoring of single molecules in the probing volume can generate issues with mechanistic pathways due to the relatively high MichaelisMenten constants (mM–μM) requiring high ligand concentrations. Therefore, it is advantageous to consider alternative methods to restrict the probe volume besides diffraction-limited probe volumes. Nanofluidics is a field of research in which synthetic boundaries are imposed on the probing volume, with the dimensions typically being below the diffraction limit. These sub-diffraction boundaries can be produced by nanostructures that can range in size from