[1st Edition] 9780128050804, 9780128047156

Table of contents :
Content:
Series PagePage ii
CopyrightPage iv
ContributorsPage ix
PrefacePages xi-xiiAleš Iglič, Chandrashekhar V. Kulkarni, Michael Rappolt
Chapter One - The Importance of Planarity for Lipid Bilayers as BiomembranesPages 1-23K. Sakamoto
Chapter Two - Interaction of Cells and Platelets with Biomaterial Surfaces Treated with Gaseous PlasmaPages 25-59I. Junkar
Chapter Three - Competition Between Electrostatic and Thermodynamic Casimir Potentials in Near-Critical Mixtures with IonsPages 61-100A. Ciach
Chapter Four - Effect of Dendrimers and Dendriplexes on Model Lipid MembranesPages 101-116M. Ionov, T. Hianik, M. Bryszewska
Chapter Five - The Membrane Bending Modulus in Experiments and Simulations: A Puzzling PicturePages 117-143D. Bochicchio, L. Monticelli
Chapter Six - Bicontinuous Phases of Lyotropic Liquid CrystalsPages 145-168W. Góźdź
Chapter Seven - Peculiarities in the Study of Preformed DSPC Lipid Vesicles by Coarse Grain Molecular DynamicsPages 169-185H. Chamati, R. Trobec, J.I. Pavlič
Chapter Eight - Extracellular Vesicles in CancerPages 187-204N. Yamada, Y. Akao
IndexPages 205-210

Citation preview

EDITORIAL BOARD Dr. Mibel Aguilar (Monash University, Australia) Dr. Angelina Angelova (Universite´ de Paris-Sud, France) Dr. Paul A. Beales (University of Leeds, United Kingdom) Dr. Habil. Rumiana Dimova (Max Planck Institute of Colloids and Interfaces, Germany) Dr. Yuru Deng (Changzhou University, China) Prof. Dr. Nir Gov (The Weizmann Institute of Science, Israel) Prof. Dr. Wojciech Góźdź (Institute of Physical Chemistry Polish Academy of Sciences, Poland) Prof. Dr. Thomas Heimburg (Niels Bohr Institute, University of Copenhagen, Denmark) Prof. Dr. Tibor Hianik (Comenius University, Slovakia) Prof. Dr. Wolfgang Knoll (Max-Planck-Institut fu¨r Polymerforschung, Mainz, Germany) Prof. Dr. Angelica Leitmannova Liu (Michigan State University, USA) Dr. Ilya Levental (University of Texas, USA) Prof. Dr. Reinhard Lipowsky (MPI of Colloids and Interfaces, Potsdam, Germany) Prof. Dr. Sylvio May (North Dakota State University, USA) Prof. Dr. Philippe Meleard (Ecole Nationale Superieure de Chimie de Rennes, France) Prof. Dr. Yoshinori Muto (Gifu, Japan) Prof. Dr. V. A. Raghunathan (Raman Research Institute, India) Dr. Amin Sadeghpour (University of Leeds, United Kingdom) Prof. Kazutami Sakamoto (Tokyo University of Science, Japan) Prof. Dr. Bernhard Schuster (University of Natural Resources and Life Sciences, Vienna) Prof. Dr. P.B. Sunil Kumar (Indian Institute of Technology Madras, India) Prof. Dr. Mathias Winterhalter (Jacobs University Bremen, Germany)

Academic Press is an imprint of Elsevier 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, USA 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK 125 London Wall, London, EC2Y 5AS, UK First edition 2016 Copyright © 2016 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. ISBN: 978-0-12-804715-6 ISSN: 2451-9634 For information on all Academic Press publications visit our website at http://store.elsevier.com/

CONTRIBUTORS Y. Akao United Graduate School of Drug Discovery and Medical Information Sciences, Gifu University, Gifu, Japan D. Bochicchio Physics Department, University of Genoa, Genoa, Italy M. Bryszewska Department of General Biophysics, Faculty of Biology and Environmental Protection, University of Lodz, Poland H. Chamati Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria A. Ciach Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland W. Go´z´dz´ Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland T. Hianik Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia M. Ionov Department of General Biophysics, Faculty of Biology and Environmental Protection, University of Lodz, Poland I. Junkar Jozˇef Stefan Institute, Ljubljana, Slovenia L. Monticelli Molecular Microbiology and Structural Biochemistry (MMSB), University of Lyon, CNRS UMR 5086, Lyon, France J.I. Pavlicˇ Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria; Institut Jozˇef Stefan, Ljubljana, Slovenia K. Sakamoto Department of Pure and Applied Chemistry, Tokyo University of Science, Noda, Chiba, Japan R. Trobec Institut Jozˇef Stefan, Ljubljana, Slovenia N. Yamada United Graduate School of Drug Discovery and Medical Information Sciences, Gifu University, Gifu, Japan

ix

PREFACE Today’s scientists are still greatly challenged by countless aspects of biomembranes and by developing novel artificial systems based on lipid self-assembly, mainly because they resemble structurally and dynamically highly complex multicomponent systems. Nevertheless, over the last decade, a new trend is becoming more and more evident: complex systems are increasingly tackled. From novel asymmetric cell membrane models to the engineering of hybrid nanoparticles, complexity seems no longer deterrent. At the same time, the arising multifaceted scientific questions demand increasingly an interdisciplinary approach. Thus in the field of biomembranes and related lipid self-assembly research, mathematicians, physicists, chemists, biologists, engineers, and medics are starting to work closer together than ever. The newly titled Elsevier book series Advances in Biomembranes and Lipid Self-Assembly (ABLSA) will try to embrace this vivid scientific spirit and therefore will cover a broad range of topics from theoretical membrane models, over novel biomimetic membrane systems to various two- and three-dimensional lipid self-assemblies. Planar lipid bilayers are widely investigated due to their ubiquity in nature and find their application in the design of liposomal dispersions. Increasingly evident though, also nonlamellar membrane phases play an important role in nature, especially in dynamic processes such as vesicle fusion and cell communication. Selfassembled lipid structures have an enormous potential ranging from model systems to cell membranes and from biosensing to controlled drug delivery. Likewise, the contributions of Volume 23 are spanning a wide range of new and exciting topics including coarse grain molecular dynamics on preformed vesicles (Hassan Chamati), simulation studies on the membrane bending modulus (Luca Monticelli), investigations on the importance of planarity in biomembranes (Kazutami Sakamoto), membranes interaction with dendrimers and dendricomplexes (Tibor Hianik), interactions of cells and platelets with biomaterial surfaces (Ita Junkar), Casimir potentials in near-critical mixtures (Alina Ciach), bicontinuous cubic phases in the light of latest developments (Wojciech Gozdz), and extracellular vesicles in cancer are discussed (Yukihiro Akao). We wish to express our gratitude to all authors who contributed their chapters to the Volume 23 of ABLSA, to Ms. Shellie Bryant and Ms. Poppy xi

xii

Preface

Garraway from Elsevier Office in London, Mr. Magesh Kumar Mahalingam from Elsevier division in Chennai, and to all members of the Editorial Board who helped to prepare this volume of ABLSA. ALESˇ IGLICˇ CHANDRASHEKHAR V. KULKARNI MICHAEL RAPPOLT

CHAPTER ONE

The Importance of Planarity for Lipid Bilayers as Biomembranes K. Sakamoto1 Department of Pure and Applied Chemistry, Tokyo University of Science, Noda, Chiba, Japan 1 Corresponding author: e-mail address: [email protected]

Contents 1. 2. 3. 4.

Introduction How CPP Translocates into the Cytosol Pore Formation How Does Curvature Modulation by Changing Vesicle Size Effect the CPP Translocation? 5. Conclusion Acknowledgments References

2 4 14 18 20 21 21

Abstract Questions like “What is the cell or vesicle size that frees lipid molecules in bilayers from membrane curvature strains?” and “Why is the size of self-reproducible eukaryotic cell over 10 μm?” are topics regarding membrane shape deformation caused by cationic peptide interacted with anionic head group of membrane lipids. The mechanism of direct translocation (cytolysis) of cell-penetrating peptides (CPPs) and antimicrobial peptides (AMPs) through biomembranes is discussed in relation to membrane curvature and lipid mobility. It is confirmed that cytolysis happens when cationic CPP or AMP molecules interact with anionic lipid head groups to generate local and transient catenoid pores with negative Gaussian curvature. The translocation of CPP and AMP, or more generally, the vesicle shape change caused by physical or chemical modifiers is possible only under the condition that the lipid is under a lamellar liquid crystal (Ld) phase to be mobile. This condition could be given primarily for the planar membrane with negligible curvature strain to make local or even whole topological modification. There must be a threshold level in the vesicle size that forces lipids to become immobile to maintain vesicle structures, which exceeds the bending energy provided by CPP or AMP to release curvature strain. As such, planarity is important for biomembranes to be flexible enough to accommodate necessary local topology changes, which is the key of controlling the stimuli responsive barrier function of cell membrane.

Advances in Biomembranes and Lipid Self-Assembly, Volume 23 ISSN 2451-9634 http://dx.doi.org/10.1016/bs.abl.2016.01.001

#

2016 Elsevier Inc. All rights reserved.

1

2

K. Sakamoto

1. INTRODUCTION In this chapter, the question “What is the cell or vesicle size that frees lipid molecules in bilayers from membrane curvature strains” is the topic for discussion. This question also relates to the question “Why is the size of a self-reproducible eukaryotic cell over 10 μm?” (Fig. 1) [1,2]. Taking analogical comparison, the ratio of bilayer thickness (ca. 5 nm) to the diameter of erythrocyte (ca. 10 μm) is 1/2000, while those of large unilamellar vesicles (LUVs) with 200 nm diameter is 1/40. As smaller particles have larger curvatures, the stability of bilayers would be dependent on the cell size. Kodama et al. reported that vesicles made of dimyristoyl phosphocholine are thermodynamically stabilized by the enthalpy effect, resulting from a closely packed aggregation of the lipid molecules [2]. They revealed that the relative thermodynamic stability of vesicles at the liquid crystal (LC) phase and gel phase are both at the order of SUV (
40 nm), LUV (
200 nm), and large multilamellar vesicle (>1 μm), respectively. Regarding the topological effect of the vesicle, the surface energy depends on the curvature as expressed by Laplace equation; Pin ¼ Pout + 2 γ/r, where Pin is the inside pressure, Pout is the outside pressure, γ is the flat surface tension, and r is the radius of the curvature. As shown in Fig. 2, Pin for LUV (400 nm) and SUV (40 nm) are 25 and 250 times larger than giant unilamellar vesicle (GUV; 10 μm), respectively; in other words, the bending energy of the membrane is larger for the smaller vesicles. In order to keep an enclosed spherical shape to overcome curvature stress, lipids are less mobile and more ordered for

d = x nm h = 5 nm

Self-reproducible cells

ca. 5 nm 25 nm 30 nm d ~ 40 nm 150–250 nm 200–500 nm ~ 200 nm (1–10 µm) 2 µm 9 µm (10–30 µm) 10 µm 100 µm

Thickness of cell membranes (h) Microtubule [1] Small virus (picornaviruses) [1] SUV [2] Small bacteria such as mycoplasma [1] Lysosomes [1] LUV [2] The general sizes for prokaryotes [1] E. coli — a bacterium [1] Human red blood cell [1] Most eukaryotic animal cells [1] GUV [2] Human egg [1]

Fig. 1 Size of cell and vesicle [1,2]. Relative size of cells and vesicles to find the importance of total planarity and local curvature modulation for the function of biomembrane.

3

The Importance of Planarity for Lipid Bilayers

Laplace equation Pin = Pout + 2 γ/r

GUV LUV SUV

r (nm) 10,000 400 200 40

Pin r

Pout

Relative 2 γ/r 1 25 50 250

Fig. 2 Relative pressure difference by Laplace equation.

smaller vesicles [2]. All these data suggest that the bilayer curvature has a significant effect for the mobility and function of biomembranes. There could be a threshold diameter which curvature over rules against the mobility of lipid molecules in the membrane, which is the key of controlling the stimuli responsive barrier function of cell membrane. When I was invited to join the Editorial Board of Advances in Planar Lipid Bilayers and Liposomes (APLBL), I was asked about my opinion on changing the name of the journal to Advances in Biomembranes and Lipid Self-Assemblies (ABLSA), with the explanation that APLBL was originally chosen by the founding editor who started the book series in 2004. He selected this name based on the nature of the research at the time, but the situation has seen a significant change since. The current editors were concerned that it is no longer as relevant due to the changing nature of this research area and decided to change the name of the book series to ABLSA. I had no objection for this decision but chose the title of this chapter as “The Importance of Planarity for Lipid Bilayers as Biomembranes.” The title explains itself, but I would like to emphasize the importance of planarity in regards to the functionality of lipid bilayers for material trafficking through biomembranes. The reason this title came to me is that we have recently faced contradictory results for the effect of curvature of unilamellar vesicles by changing their sizes against the transmembrane trafficking of cellpenetrating peptides (CPPs). This is the reason I started this chapter to wonder “What is the cell or vesicle size that frees lipid molecules in bilayers from membrane curvature strains?” which would be closely related to the question “Why is the size of self-reproducible eukaryotic cells over 10 μm?.” I will first review the mechanism of CPP’s translocation through biomembranes in terms of topology and functions in relation to the curvature, then continue further to the topic we have faced during the CPP translocation study that relates to the question above.

4

K. Sakamoto

2. HOW CPP TRANSLOCATES INTO THE CYTOSOL Discreetness of cell is the key of life with cell membranes that separate their interior cytosol (or cytoplasm) from their surrounding environment. In this regard, cytosol is never connected to outside media, even during the course of cell fission or fusion. However, a water-soluble peptide called CPP can spontaneously translocate through cell membranes without any particular transporters or receptors [3]. There are two pathways of CPP translocation through biomembranes as shown in Fig. 3, which are (i) endocytosis followed by endosomal release into cytosol and (ii) direct translocation through the membrane (cytolysis) [3]. Although well-established mechanisms are reported for the endocytosis, no conclusive mechanism has been found for the cytolysis, which is a more direct and efficient internalization of water-soluble CPP through hydrophobic biomembranes. In general, CPP is considered to be safe against membrane integrity and cell viability, so CPP could be a potential DDS vector with varieties of the bioactive cargos attached to it. There is another type of peptide called antimicrobial peptide (AMP) that also spontaneously translocate into cytosol by pore formation [4]. Typical AMP called cationic amphipathic polypeptide has structural resemblance to CPP with cationic amino acid residues, which cause AMP to absorb onto the anionic head group of membrane lipids. AMP also has substantive hydrophobic moieties, which is different from CPP. Although there are no clear distinctions between CPP and AMP, we take a position to define each other as CPP is a type of peptide that spontaneously translocate through a biomembrane without damaging the membrane integrity and cell viability. On the other hand, AMP kills microorganisms, as its Direct internalization (cytolysis)

Endocytosis CPP

Outer media

Inner media (cytosol)

Direct internalization

Inner media (cytosol)

Formation of endosome

Fig. 3 Translocation of CPP through biomembrane.

5

The Importance of Planarity for Lipid Bilayers

name tells, primarily by causing an efflux of cytoplasmic constituents through the transient or permanent pore. As the translocation processes, both CPP and AMP first absorb onto the biomembrane, then cause membrane curvature deformation from flat bilayer to the local negative Gaussian curvature, and lead to pore formation. More details of this topology change will be discussed later. Despite of plentiful reports on the CPP’s translocation through biomembranes, a conclusive mechanism is yet to be established as Brock explained in his recent review [3]. We have taken CPP’s cytolysis as local and temporal phase transitions of amphiphilic self-assembly at its liquid crystal state (LC) by modulating the molecular geometry of lipid with CPP [5,6] as shown in Fig. 4. In general, LC as highly ordered self-organization of amphiphiles has series of structures such as hexagonal, cubic, or lamellar. The topology of each LC determined by the molecular geometry parameter of the amphiphile is called surfactant parameter (SP) defined by Eq. (1), and SP corresponds to the proportion of the hydrophilic part and hydrophobic part in the amphiphile as shown in Fig. 5 [7,8] SP ¼ v=ða  lÞ

(1)

where a is the cross-sectional area per molecule at the hydrophilic– hydrophobic interface, l is the length of hydrophobic chains, and v is the volume of hydrophobic parts. SP correlates to the surface curvature of molecular assembly as a LC and can be changed by modulating the value of a, l, or v through changing the level of ionization, hydration, solute, temperature, or many other chemical and physical mediators. SP is also related to the curvature of self-assembly by Eq. (2) for surfactant monolayer SP ¼ v=ða  lÞ ¼ 1 + Hl + Kl2 =3

(2)

Local positive curvature change CPP

Cytosol

Fig. 4 Hypothesized mechanism for the cytosolic translocation of CPP through biomembrane. A local and temporal phase transition of membrane lipids at liquid crystal state (LC) by modulating the molecular geometry of lipid by CPP absorption.

6

K. Sakamoto

a n

Cone

Truncated cone

Cylinder

Inverted cone

l

SP = n/al

1/3 ~1/2

1/2 ~1

>1

~1

Structure of amphiphile and surfactant parameter (SP) SP Curvature

Micelle

H1

Mesh phase has catenoid Gaussian pores in bilayers

V1

Lα

Mesh1

V2

Mesh2

Fig. 5 Surfactant parameter (SP) defines curvature of liquid crystal as self-assembly at equilibrium [7,8].

where H is the mean curvature, and K is the Gaussian curvature [8]. This equation suggests that the shape of surfactant (membrane lipid) expressed as SP can be related to the global geometries of self-assembly, assuming homogeneous interfaces. This assumption implies a relatively small bending energy constraint on the overall shape of self-assembly [9]. Also, it is apparent that H and K can be varied even under a given SP, i.e., Eq. (2) can be satisfied by a number of surface shapes which can be distinguished by their topology [10]. The resulting local/global “phase diagram” is shown in Fig. 6 [8]. The Lα type lamellar LC has zero mean curvature (SP ¼ 1), and a slight modification of curvature toward positive (convexity toward aqueous phase) leads to bicontinuous cubic LC (V1: 1/2 < SP < 2/3). On the other hand, modifying the curvature toward negative (convexity toward lipid phase) leads to bicontinuous cubic LC (V2: SP > 1). Bicontinuous cubic phases (V1 or V2) are hyperbolic surfaces as Infinite Periodic Minimal Surfaces with three or more genus. There are other hyperbolic surfaces called Mesh1 or Mesh2 as intermediate phases between Lα and bicontinuous cubic phases with genus 2 as shown in Figs. 5–7. They form an array of holes with a catenoid structure as shown in Fig. 5. To make a curvature from planner surface (Lα) with SP ¼ 1 to any hyperbolic curved surface, it would cost some energy which can be expressed as bending energy (Fb) by Eq. (3) [11] Fb ¼ ðkb =2Þ  ðHb Þ2 + Kb  Kb

(3)

7

The Importance of Planarity for Lipid Bilayers

Fig. 6 Average molecular shape (SP) as a function of the concentration of the surfactant and the geometry of the interface (according to Hyde et al. [8] with permission of Elsevier). a

A

Water v

C

l SP = v/al

Positive curvature V1 H1 1/2 < SP < 2/3 SP = 1/2

B Mesh1 1/2 < SP < 2/3 D La SP = 1

Negative curvature Oil V2 SP > 1

H2 SP > 1

Mesh2 SP > 1

Fig. 7 General aspects of geometrical changes from Lα to H via Mesh and V [6].

where kb is the bending elastic constant, Hb is the mean curvature, and Kb is the bending Gaussian curvature as Kb ¼ 1=Cb 2 . Kb is the Gaussian curvature elastic modulus [11,12]. As the Mesh phase appears between Lα

8

K. Sakamoto

and V phases, the energy cost to attain this modification would be quite small. Figure 7 [6] shows general aspects of this geometrical change from Lα as multi-bilayers by changing SP or mean curvature H. In the case of Mesh1, pores in the membrane connect aqueous layers. On the contrary, at Mesh2, pores in the membrane connect reversed bilayers consequently leading them to connect hydrophobic lipid chains. Figure 8 [6] shows the same geometrical change from Lα to Mesh for vesicles as an enclosed unilamellar bilayer. For a normal vesicle with hydrophilic groups that make the surfaces of bilayer toward water, positive curvature change can induce porous intermediate phase like Mesh1, and in this occasion, outer water and inner cytosol are interconnected through pores. If this pore formation was a local and temporal event, CPP, as a counter ion to the anionic lipid, would translocate into cytosol without any distraction to the membrane integrity. On the other hand, negative curvature change to form Mesh2 is only possible for the reversed vesicle as shown in Fig. 8, but not for normal vesicle or living cells. As a brief summary of the above, the determining factor for CPP to translocate by cytolysis would be the direction of SP change of vesicle which considered to be planar membrane (SP ¼ 1). In case where SP changes to 0), cytolysis occurs through Mesh1. Meanwhile, the SP change to >1, which corresponds to the negative mean curvature change (H < 0), leads vesicle fusion or fission (including the endocytosis) through Mesh2 phase by

Water

Normal vesicle or cell membrane A

B

Water

Water

Positive Water

(cytosol)

Water (cytosol) Mesh1 Oil

Reversed vesicle C

Oil

D

Oil Negative Oil Inner medium

Oil

Inner medium Mesh2

Fig. 8 Mesh phase for vesicle as unilamellar membrane [6]. Only positive curvature change is possible for cell membrane, toward Mesh phase which has pores.

9

The Importance of Planarity for Lipid Bilayers

well-known Stalk process. It is quite useful to determine phase conversion of lipid bilayer upon addition of CPP. We have confirmed this by adding octaarginine peptide (R8) as a CPP to the model lipid membrane composed of 1-oleyl-2-hydroxy-sn-glycero-3-phosphocholine (OPC) and water at OPC/water ¼ 15/85 (wt% at 25 °C). Here, R8 as CPP promoted a positive membrane curvature change as shown in Fig. 9 [6]. Increasing the amount of R8 in the lipid solution converted the Lα phase to V1 and even further to a H1 phase [6]. This intrinsic nature of CPP that induces phase transition toward positive curvature (or smaller SP) would promote local and temporal phase fluctuation of lipid membrane to the Mesh1 which has pores with a catenoid structure as shown in Fig. 5, enabling the CPP translocate across the membrane. Despite this curvature change, no phase transition across the system occurs as long as the amount of CPP is less than the threshold level that causes an equilibrium phase transition to the entire system (Fig. 9). As a result, the translocation of CPP can be enabled at the point, where a Mesh1 phase is formed locally, while the structure of the lipid bilayer membrane as a whole is maintained to be at the Lα phase so that no pores remain after CPP passes through. Based on the reversibility of the process, CPP moved inside would under equilibrium to desorb into cytosol, but there is less probability to leak out to the outer media since there is a negative mean curvature to suppress translocations from the inside to the outside. This CPP translocation could be controlled if positive curvature change caused by CPP is stimulated or suppressed by means of physical or chemical modulation. To prove this, we have utilized erythrocyte (red blood cell), Curvature R8AcOH (CPP) 0

Positive curvature 0.2

A

0.8

Intensity (a.u.)

1

B

0.4

0.6

E

C

F

0.6

0.4 D

0.8 0.2

x

W m

x x

x x x

0

x

x

x x

x

H 1

G

x

x

x

x x

x x

V

x

La

1

H1

V1 La

1

1

0.8

0.6

0.4

0.2

0

2 3 4 5 OPC (phospholipid) q (nm-1) OPC: 1-oleyl-2-hydroxy-sn-glycero-3-phosphocoline Water

H1

V1

La

6

7

Fig. 9 The effect of CPP on phase transition of lipid membrane [6]. Arginine octamer (R8) as CPP changed the membrane curvature toward positive (Lα ! V1 ! H1) according to the addition of R8 in the OPC/water system [6].

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K. Sakamoto

which has a slightly negative mean curvature. As expected, we have found that erythrocyte membrane is resistant to the translocation of CPP in comparison to normal cells [5,6]. Furthermore, we were able to promote or suppress the translocation of CPP into erythrocyte under a hypotonic or hypertonic condition by changing the osmotic pressure of the medium to make the membrane surface curvature either positive or negative (Fig. 10). Throughout these experiments, no hemolysis was observed within the range of osmotic pressure tested, which suggests that the membrane barrier for hemoglobin in the erythrocyte was kept intact. As a result, we have succeeded to control the level of permeation of CPP by changing the surface curvature through physical modulation. To the best of our knowledge, this is the first example to control the direct (cytosolic) internalization of CPP with membrane curvature modulation. Utilization of GUV instead of erythrocyte further confirmed these hypotheses. As shown in Figs. 10 and 11, cytosolic internalization of R8 with FITC as a fluorescent cargo proportionally increased by reducing osmotic pressure, which is in good concordance with the results obtained for erythrocyte. Under the tested condition, FITC alone could not pass through the membrane regardless of osmotic pressure change. Additionally, the barrier function of the GUV membrane was kept constant, as the leakage level of rhodamine encapsulated in GUV was

GUV

Erythrocyte p < 0.01

p < 0.01

0.53

0.60 0.50

0.35 p < 0.01

0.32

0.40

0.26

0.30 0.20 0.10

Penetrated FITC-R8 (mg)

Penetrated FITC-R8 (mg)

0.70

0.30

0.29

0.25

p < 0.01

0.20 0.12

0.15

0.08

0.10 0.05 0.00

0.00 Hypotonic

Isotonic

Hypertonic

Hypotonic

Isotonic

(37 °C , L/P = 1000, n = 5)

(Curvature) (Translocation)

Fig. 10 Effect of osmotic pressure on the translocation of Arg8 (CPP) [6].

Hypertonic

11

0.40

0.40 : Integrated FITC-R8

CPP

0.35

: Integrated FITC : Rh leakage without R8

0.30

: Rh leakage with R8

0.25

0.35 0.30 0.25

Rh

0.20

0.20

0.15

0.15

0.10

0.10

0.05

0.05

0.00 0

20

40

60

80

100

0.00 120

The amount of leakage from GUV (mg)

The amount of penetration into GUV (mg)

The Importance of Planarity for Lipid Bilayers

Osmotic pressure (mOsm)

Fig. 11 The correlation between osmotic pressure and CPP translocation [6]. FITC-R8 or FITC translocation into GUV (circle) and Rhodamine (Rh) leakage from GUV (square) (10 min, at 37 °C, L/P ¼ 1000, n ¼ 5). Only FITC-CPP translocation is osmotic pressure dependent.

negligible and did not change under different osmotic pressures in the presence or absence of R8 in the outer medium (Fig. 11). When FITC-R8 as CPP was applied to the GUV composed of 1-stearoyl-2-oleoyl-phosphocholine (SOPC: Tc ¼ 6 °C) at 2 °C, CPP translocation was suppressed regardless of the osmotic pressure change. This is a proof of the cytosolic mechanism, as local- and temporal-positive curvature changed under LC condition (disordered lamellar phase: Ld) where membrane lipids are mobile to adjust bending energy of gloss curvature of GUV to be minimum. In addition to the physical modulation, we have succeeded to control CPP internalization by chemical modulation [5]. We have chosen 1,3butanediol (1,3-BG) and sodium thiocyanate (NaSCN) as chaotropic solutes, a water structure breaker in the Hoffmeister effect, to make membrane curvature positive [13,14]. As expected, both solutes dose dependently enhanced R8 translocation into dermal fibroblast cell similar to the hypotonic osmotic pressure for erythrocyte (Figs. 12 and 13). On the other hand, sucrose, which is a kosmotropic solute, a water structure maker to make membrane curvature negative [13,14], suppressed the R8 translocation dose dependently same as hypertonic osmotic pressure did (Fig. 14). Thus, it is confirmed that local- and temporal-positive curvature change seems to be a crucial mechanism to promote translocation of CPP directly into the cytosol. By knowing this, controlling the translocation of CPP by physical or

12

K. Sakamoto

Fluorescence intensity (AU)

Protein (µl/ml)

Cell viability 300

45,000 250

40,000 35,000

200

30,000 25,000

150

20,000 100

15,000 10,000

Protein (ml/ml)

Fluorescence intensity (AU)

Arg8 penetration 50,000

50

5000 0

0 ctrl

2.5 mM

5 mM

10 mM

1,3-Butanediol (1,3-BG)

Fig. 12 Effect of chaotropic solute (water structure breaker) on the Arg8 penetration to dermal fibroblast cell [5]. 1,3-Butanediol (1,3-BG) makes lipid layer curvature more positive and enhances Arg8 penetration.

Fluorescence intensity (AU)

Protein (µl/ml)

Arg8 penetration

Cell viability

300

40,000

250 30,000

200 150

20,000

100

Protein (ml/ml)

Fluorescence intensity (AU)

350

10,000 50 0

0 ctrl

2.5 mM

5 mM

10 mM

Na thiocyanate (NaSCN)

Fig. 13 Effect of chaotropic solute (water structure breaker) on the Arg8 penetration to dermal fibroblast cell [5]. Sodium thiocyanate (NaSCN) makes lipid layer curvature more positive and enhances Arg8 penetration.

chemical modulation of membrane curvature would be a promising way both for the development of advanced DDS and prevention of CPP’s invasion. The mechanism explained above seems like rather general phenomena for vesicles or cells that are enclosed lipid bilayer. Imai et al. discussed in their recent review that simple binary phospholipid vesicles as a protocell have the potential to reproduce relevant functions of adhesion, pore formation, and

13

The Importance of Planarity for Lipid Bilayers

Fluorescence intensity (AU)

Arg8 penetration

Protein (µl/ml)

Cell viability 200

20,000

150

15,000 100 10,000

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25,000

50

5000 0

0 ctrl

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Fig. 14 Effect of kosmotropic solute (water structure makers) on the Arg8 penetration to dermal fibroblast cell [5]. Sucrose makes lipid layer curvature less positive and suppresses Arg8 penetration. Stomatocyte

Vesicle in the vesicle (endocytosis)

Discocyte

Sphere Starfish

Prolate

Tube

Strings Bispheres

Pear

Fig. 15 Shape modification of binary phospholipids [15]. By osmotic pressure control, vesicle shape can be modified reversibly. All these forms maintain closed bilayer structure. There are natural cells such as erythrocyte and dendritic cells that can transform their shapes purposely.

self-reproduction of vesicles, by coupling the lipid geometries (spontaneous curvatures) and the phase separation [15]. For example, by various external conditions, vesicle shapes can be modified reversibly from sphere to prolate, tube, strings, pear to bispheres or to discocyte, stomatocyte to vesicle in the vesicle (endocytosis) or starfishes (Fig. 15). All these forms maintain closed bilayer structures, and there are natural cells such as erythrocyte and dendritic cells that can transform their shapes purposely. The observed shape deformations are well described by the area difference elasticity (ADE) theory [16–18]. In the ADE theory, the vesicle shape is determined from the minimization of the total elastic energy Ft,

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Ft ¼ Fb + FADE

(4)

where the first term Fb (Eq. 3) is the bending energy of the membrane given by mean (H) and Gaussian (C) curvature, membrane area (A), bending elastic constant (κ), and Gaussian elastic modulus (Kb ). FADE, the area difference elasticity term, is associated with the relative stretching of the monolayers in the bilayer, defined by nonlocal bending modulus (κ r), the distance between the monolayer’s neutral planes (d), and the bilayer’s intrinsic area difference before and after external stimuli application. Minimization of the total energy for a given area A and volume V gives the vesicle shape. Baumgart et al. [19] showed domain segregation for GUV with mixed components, DOPC, spingomyelin, cholesterol, with mixing/demixing transition temperature (Tm) between disordered (Ld) and ordered (Lo) phases. Ld and Lo phases can be visualized by two-photon fluorescence microscopy with two dyes preferentially labeling specific phases to either Ld or Lo. By changing the temperature below Tm, the global shape could be changed from sphere to starfish, string pearls, prolates, and pears, correlated between domain composition and local membrane curvature in accordance to Imai’s experiment. They concluded that global shapes result from line tension and constraints on domain areas and internal volume, and also noticed that mobile Lo phase domains prefer regions with high curvature.

3. PORE FORMATION Imai et al. showed the utilization of SP of membrane lipids to control vesicle shape deformation [15]. They demonstrated stable pore formation using binary GUVs composed of cone- and cylinder-shaped lipids [20]. 1,2-Dihexanoyl-sn-glycero-3-phosphocoline (DHPC, Tm ¼  46 °C) is a cone-shaped lipid (SP < 1), and 1,2-dipalmitoyl-sn-glycero-3-phosphocoline (DPPC, Tm ¼ 41 °C) is a cylinder-shaped lipid (SP ¼ 1). The binary GUV with DHPC and DPPC shows a phase separation below Tm of DPPC ( 1) increased the line tension (T ) to destabilize pore.

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s

e

/r

r

Fig. 17 Transverse view of a pore, with radius r, the membrane thickness e, drawn schematically. Pore opening is driven by the membrane tension, σ, and is opposed by the line tension term, T /r (according to Karatekin et al. [22] with permission of Elsevier).

Yamazaki et al. also showed tension-induced pore formation [23]. They investigated the effects of tension (σ) induced by micropipet aspiration on GUVs composed of DOPG–DOPC, by analyzing the time course of the fraction of intact GUVs under constant tension σ. They obtained the rate constants of pore formation kp (σ) and determined the line tension (Γ) of a prepore. When the radius of a prepore reaches a critical value, it transforms into a pore. The value of Γ of a DOPG/DOPC bilayer was smaller than that of a DOPC bilayer because DOPG/DOPC with negatively charged lipid (DOPG) has more positive curvature (SP < 1) thereby the edge of the prepore is stabilized by the positive curvature of the monolayer. Yamazaki et al. suggested that this tension-induced pore formation and its control by the intrinsic membrane curvature can be adapted to the AMP’s pore formation by binding to the GUV membrane resulting in pore formation. Those pore formations are in good accordance with the mechanism we have proposed for the CPP’s cytolysis by generating local- and temporalpositive curvature (SP < 1) and control of translocation by modulating the curvature with physical or chemical stimulus. In the case of AMP, similar pore formation has been reported to cause efflux of cytoplasmic materials to cease cell viability. Hotani et al. showed that talin, a cytoskeletal submembranous protein, opened stable holes [24]. By increasing talin concentration, the holes turned to cup-shaped vesicle then eventually to a bilayer sheet. These morphologies reversed by talin dilution back to a sphere. This phenomenon corresponds to Imai’s experiment for binary vesicle by temperature-dependent domain formation without protein as mentioned earlier [20]. As a first direct observation of cytosolic translocation of CPP, Thoren et al. reported that antennapedia peptide penetratin translocated into the vesicle without pore formation [25]. CF-penetratin as CPP with carboxyfluorescein (CF) group as fluorescent prove penetrated into both multilamellar and unilamellar giant vesicles, which were monitored by a fluorescence microscope. To investigate pore formation during the cytolysis, the leakage of GUV-entrapped CF was measured for penetratin and melitin as a control peptide. Melitin, a typical AMP as a pore-forming

The Importance of Planarity for Lipid Bilayers

17

peptide, induced CF leakage with the threshold peptide/lipid ratio (P/L) as ca. 0.02 mol/mol and over. This result is well correlated with similar reported studies [26]. On the other hand, penetratin showed minute efflux, an almost negligible amount versus leakage by melitin regardless of P/L even at 1/10. Thus, penetratin as CPP is assumed to translocate into the cytosol through the catenoid structured pore as Mesh1 without damaging membrane integrity as a whole. This is exactly the same induction of negative Gaussian curvature we have proposed to R8 cytolysis as a local and temporal phase transition to Mesh1 as shown in Fig. 8. This local transition to Mesh1 is to release curvature strain by negative Gaussian curvature (G) formation with saddle- and splay-shaped pore caused by ionic interaction of R8 to membrane lipid toward positive mean curvature (H) change. Wong et al. reported similar results for the translocation of HIV TAT into the GUV composed of DOPS/DOPE/DOPC mixture by inducing pore with saddle–splay topology as a negative Gaussian curvature [27]. They proposed that multidentate coordination of arginine’s guanidinium side chain induces positive curvature strain along the peptide. In the following report, they noticed structural similarities of CPP and AMP, but the latter is more hydrophobic as a molecule. Furthermore, their hypothesis suggests that the difference between peptides that kill and those do not may be caused by a time scale of the induced membrane deformation [28]. CPPs only induce transient pore-like translocation structures in the membrane, presumably reminiscent of those observed in recent simulations [29], rather than the stable pores of AMPs. This is also in agreement with our proposal of CPP’s cytolysis by local and temporal phase transition to Mesh1 [5,6]. They also proposed the indirect internalization by endocytosis including micropinocytosis when cargo with CPP is large. Futaki et al. reported that R8 localizes to the Ld phase then translocates through the cell membrane or GUV, which is in good agreement for the previously mentioned pore formation by localization of cone-shaped lipid (SP < 1) with positive mean curvature to create a catenoid-negative Gaussian curvature under the mobile lipid phase (Ld). Furthermore, the combination of pyrenebutyrate (PyB) promoted accumulation of CPP (R8) to negatively charged GUV membranes to accelerate translocation. PyB also increased the membrane fluidity by decreasing Lo domain. They speculated that PyB as a hydrophobic anion would concertedly enhance pore formation with R8 [30,31]. Futaki et al. also observed accompanied efflux of dye by the influx of R8-Alexa, which resembles the AMP’s transient pore formation. Positive membrane curvature induction by epsin

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N-terminal peptide also boosted internalization of R8 [32]. These are good indications that cytosolic translocation of CPP and AMP is regulated by the same mechanism. They further investigated the effect of hydrophobicity in the R8 molecule by acylation of N-terminal with fatty acids [33] or introduction of hydrophobic moiety in the peptide [34,35]. Hexanoyl octaarginine (C6R8-Alexa) showed the highest efficiency of cellular uptake, 10 times higher than R8-Alexa, among butanoyl (C4), hexanoyl (C6), and decanoyl (C10). Thus, the introduction of a hydrophobic moiety to CPPs increased their interaction with membranes and facilitates their translocation into cells [33]. Besides these experimental evidences for the cytosolic translocation of CPPs and AMPs by transient pore formation, several molecular dynamic simulations are reported to support the interaction of cationic peptide with anionic phospholipids [29,36,37].

4. HOW DOES CURVATURE MODULATION BY CHANGING VESICLE SIZE EFFECT THE CPP TRANSLOCATION? To avoid any unknown additional effect rather than the curvature with physical or chemical modulation, we have tried the size effect of vesicle, which only changes the membrane curvature while maintaining all the other experimental conditions for the CPP translocation [38]. Our expectation was that CPP translocation would be enhanced for the smaller vesicle due to the increased membrane curvature. On the contrary, translocation of CPP (FITC-R8) into egg yolk GUV was suppressed by reducing vesicle size, and for the LUV less than 400 nm, translocation was almost stopped as shown in Fig. 18. This result indicates that the strong bending modulus caused by small vesicles inhibited the topological change to release bending energy. As the effect of osmotic pressure was observed even under suppression by reduced vesicle size, physical modulation toward positive curvature concertedly stimulates CPP’s interaction with anionic phospholipids to create transient catenoid pore formation. Confocal laser scanning microscope observation for the GUV (ca. 10 μm) composed of SOPC with LC to gel transition temperature (Tc) at 6 °C confirmed such contradictory effects as shown in Fig. 19, namely, there are uniform green (gray in the print version) colors of FITC-R8 observed inside the vesicle at 30 °C with smaller vesicles less green (gray in the print version), which well correspond to the effect of vesicle size in Fig. 19A. While no translocation was observed for FITC-R8 at 0 °C which is under Tc of SOPC (Fig. 19B), this corresponds

19

The amount of penetration into GUV (mg)

The Importance of Planarity for Lipid Bilayers

GUV (14 mm) 5 mm 3 mm

0.4

1 mm

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0.1 mm FITC-R8

0.2 0.15 0.1

FITC

0.05 0 0

20

40

60

80

100

120

Osmotic pressure (mOsm)

Fig. 18 Effect of vesicle size for the CPP direct translocation (cytolysis) [38]. EPC, lipid/ CPP ¼ 1000/1 (mol), CPP ¼ FITC-R8, 10 min, 37 °C, n ¼ 5. Results: The amount of penetrated CPP into vesicle was decreased by reducing the size.

FITC + Nile red

A

10 µm

FITC (CPP)

10 µm

B

Nile red (Lipid)

10 µm

Fig. 19 Effect of the size of vesicle for the CPP translocation [38]. (A) Translocation of CPP (FITC-R8) into egg yolk GUV was suppressed by reducing vesicle size (yellow (white in the print version) arrow). (B) Translocation was suppressed under gel phase.

to the inhibition of translocation for the vesicle less than 400 nm. To confirm the mobility of lipids, a determinant factor of CPP translocation, anisotropy of fluorescent dye (1,6-diphenyl-1,3,5-hexatrien, DPH) incorporated with the vesicle membrane during the translocation experiment was studied. As shown in Fig. 20, the mobility of SOPC was significantly suppressed under Tc as a gel phase (Fig. 20A). Clear inverse relationship between lipid mobility and translocation of FITC-R8 was observed at 30 °C (Fig. 20B).

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Tc: 6 °C

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LC phase

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Fluorescent anisotropy of DPH

A

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Temp (°C)

Particle size (nm)

Fluorescent anisotropy of DPH at gel and LC phase (SOPC, n = 3)

Relationship between fluidity and translocation at LC phase (SOPC, 30 °C, n = 3)

Fig. 20 Effect of the size of vesicle for the CPP translocation and lipid fluidity at Ld phase (30 °C) [38].

These results well explain the contradictory effect of positive curvature modulation by reducing osmotic pressure against vesicle size reduction that increase vending modulus to suppress pore formation. As such, smaller vesicles require more energy to deform membrane structures from the lamellar to Mesh1 phase. To my best knowledge, there are no articles found discussing such size-dependent pore formation or shape deformation for vesicles in relation to CPP, AMP, or physical modulators. However, there are several data found that likely relating to this topic. Almeida et al. observed translocation of AMP and influx of fluorescent dye for double GUV (multiple small GUVs with 10–20 μm are entrapped in the large GUV with 50–100 μm). They have noticed a relatively quick peptide translocation even to the inner vesicle but slow and stepwise influx to the inner vesicle [39]. Although they have not discussed the influx difference between inner vesicles, it seems that smaller vesicles took a longer time to show the influx color. This could be another example of size effect that we have observed for R8 translocation mentioned above.

5. CONCLUSION As I have put “What is the cell or vesicle size that frees lipid molecules in bilayers from membrane curvature strains” at the beginning of this chapter, translocation of CPP and AMP, or more generally, the vesicle shape change caused by physical or chemical modifiers is only possible under the condition that the lipid is under the Ld phase to be mobile, and this could be given primarily for the planar membrane with negligible curvature strain

The Importance of Planarity for Lipid Bilayers

21

to make local or even whole topological modification. There must be a threshold level of vesicle size to force lipids to be immobilized in order to maintain a vesicle structure that exceeds the bending energy provided by CPP or AMP to release curvature strain. This threshold vesicle size would be dependent on the type or composition of lipid composing the vesicle and kind of modulator, i.e., peptides such as CPP, AMP, or other chemical and physical stimulant. In the case of FITC-R8 and SOPC vesicle, the threshold diameter is 400 nm, which is a 1/40 ratio of bilayer thickness (5 nm) versus vesicle diameter. In the case of 10 μm GUV, the ratio is 1/2000. The relative Laplace pressure difference from 400 nm to 10 μm diameter is 25/1. As such, planarity is a key factor for biomembranes to be flexible enough to accommodate the required local topology changes, and this could be an answer to the question “Why is the size of selfreproducible eukaryotic cells over 10 μm?.”

ACKNOWLEDGMENTS I am grateful to Professor Masahiro Abe and Professor Hideki Sakai providing opportunity to conduct this research at Tokyo University of Science. Mr. Taku Morishita and Ms. Haruka Kuwahara contributed most of experiments in Figs. 10, 11, and 18–20.

REFERENCES [1] Cell Biology/Introduction/Cell size; http://en.wikibooks.org/wiki/Cell_Biology/. [2] Y. Takaichi, S. Kittaka, M. Kodama, Calorimetric investigation of phase transitions of dimyristoylphosphatidylcholine sonicated vesicles of and their stabilities, Netsu Sokutei 19 (1992) 103–112. [3] R. Brock, The uptake of arginine-rich cell-penetrating peptides: putting the puzzle together, Bioconjug. Chem. 25 (2014) 863–868. [4] A. Adem Bahar, D. Ren, Antimicrobial peptides, Pharmaceuticals 6 (2013) 1543–1575. [5] K. Ogasahara, Y. Takino, K. Sakamoto, Method for controlling membrane permeability of membrane substance and screening method for a membrane permeable substance, US Patent Appl. 2005/0118204, Jun 2, 2005; JP Appl/2003-3 774224. [6] K. Sakamoto, K. Abrai, T. Morishita, K. Sakai, H. Sakai, M. Abe, I. Nakase, S. Futaki, Bioinspired mechanism for the translocation of peptide through the cell membrane, Chem. Lett. 41 (2012) 1078–1080. [7] J.N. Israelachvili, D.J. Mitchell, B.W. Ninham, Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers, J. Chem. Soc., Faraday Trans. 2 72 (1976) 1525–1568. [8] S. Hyde, S. Andersson, K. Larsson, Z. Blum, T. Landh, S. Lidin, B.W. Ninham, The Language of Shape, Elsevier, Amsterdam, 1997, pp. 143–146. [9] R.W. Corkery, Biocontinous liquid crystals, Surfactant Sci. Series 127 (2005) 114–115. [10] M.C. Holes, M.S. Leaver, Biocontinuous liquid crystals, Surfactant Sci. Series 127 (2005) 31–33. [11] W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. 28c (1973) 693–703. [12] Dp Siegel, Biocontinous liquid crystals, Surfactant Sci. Series 127 (2005) 84–85.

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[13] K.D. Collins, M.W. Washabaugh, The Hofmeister effect and the behavior of water at interfaces, Q. Rev. Biophys. 18 (1985) 323–422. [14] T. Iwanaga, M. Suzuki, H. Kunieda, Effect of added salts or polyols on the liquid crystalline structures of polyoxyethylene-type nonionic surfactants, Langmuir 14 (1998) 5775. [15] Y. Sakuma, M. Imai, From vesicles to protocells: the roles of amphiphilic molecules, Life 5 (2015) 651–675. [16] V. Heinrich, S. Svetins, B. Zeks, Nonaxisymmetric vesicle shapes, Phys. Rev. E 48 (1993) 3112–3123. [17] L. Miao, U. Seifert, M. Wortis, H.G. Dobereinner, Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity, Phys. Rev. E 49 (1994) 5389–5407. [18] U. Seifert, Configurations of fluid membranes and vesicles, Adv. Phys. 46 (1997) 13–137. [19] T. Baumgart, G. Hunt, E.R. Farkas, Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension, Nature 425 (2003) 821–824. [20] Y. Sakuma, T. Taniguchi, M. Imai, Pore formation in a binary giant vesicle induced by cone-shaped lipids, Biophys. J. 99 (2010) 472–479. [21] F. Nomura, M. Nagata, T. Inaba, H. Hiramatsu, H. Hotani, K. Takiguchi, Capabilities of liposomes for topological transformation, Proc. Natl. Acad. Sci. U.S.A. 98 (5) (2001) 2340–2345. [22] E. Karatekin, O. Sandre, H. Guitouni, N. Borghi, P.H. Puech, F. Brochard-Wyart, Cascades of transient pores in giant vesicles: line tension and transport, Biophys. J. 84 (3) (2003) 1734–1749. [23] V. Levadny, T. Tsuboi, M. Belaya, M. Yamazaki, Rate constant of tension-induced pore formation in lipid membranes, Langmuir 29 (2013) 3848–3852. [24] A. Satoh, K. Takiguchi, Y. Tanaka, H. Hotani, Opening-up of liposomal membrane by talin, Proc. Natl. Acad. Sci. U.S.A. 95 (1998) 1026–1031. [25] E.G. Peter Thoren, D. Persson, M. Karlsson, B. Noerden, The Anntennapedia peptide penetratin translocates across lipid bilayers—the first direct observation, FEBS Lett. 482 (2000) 265–268. [26] S. Ohki, E. Marcus, D.K. Sukumaran, K. Arnold, Interaction of melittin with lipid membranes, Biochim. Biophys. Acta Biomembr. 1194 (1994) 223–232. [27] A. Mishra, V.D. Gorgon, L. Yang, R. Coridan, G.C.L. Wong, HIV TAT forms pores in membrane by inducing saddle-splay curvature: potential role of bidentate hydrogen bonding, Angew. Chem. Int. Ed. 47 (2008) 2986–2989. [28] A. Mishra, G. Hwee Lai, N.W. Schmidt, V.Z. Sun, A.R. Rodriguez, R. Tong, L. Tang, J. Cheng, T.J. Deming, D.T. Kamei, G.C.L. Wong, Translocation of HIV TAT peptide and analogues induced by multiplexed membrane and cytoskeletal interactions, PNAS 108 (2011) 16883–16888. [29] H.D. Herce, A.E. Garcia, Molecular dynamics simulations suggest a mechanism for translocation of the HIV-1 TAT peptide across lipid membrane, Proc. Natl. Acad. Sci. U.S.A. 104 (2007) 20805–20810. [30] S. Katayama, I. Nakase, Y. Yano, T. Murayama, Y. Nakata, K. Matsuzaki, S. Futaki, Effects of pyrenebutyrate on the tranlocation of arginine-rich cell-penetrating peptides through artificial membrane: recruiting peptide to the membranes, dissipating lipidordered phased, and inducing curvature, Biochim. Biophys. Acta 828 (2013) 2134–2142. [31] K. Takayama, I. Nakase, H. Michiue, T. Takeuchi, K. Tomizawa, H. Matsui, S. Futaki, Enhanced intracellular delivery using arginine-rich peptides by the addition of penetration accelerating sequences (Pas), J. Control. Release 138 (2) (2009) 128–133. [32] S. Pujals, H. Miyamae, S. Afonin, T. Murayama, H. Hirose, I. Nakase, K. Taniuchi, M. Umeda, K. Sakamoto, A.S. Ulrich, S. Futaki, Curvature engineering: positive membrane curvature induced by epsin N-terminal peptide boosts internalization of octaarginine, ACS Chem. Biol. 8 (2013) 1894–1899.

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[33] S. Katayama, H. Hirose, K. Takayama, I. Nakase, S. Futaki, Acylation of octaarginine: implication to the use of intracellular delivery vectors, J. Control. Release 149 (2011) 29–35. [34] K. Takayama, H. Hirose, G. Tanaka, S. Pujals, S. Katayama, I. Nakase, S. Futaki, Effect of the attachment of a penetration accelerating sequence and the influence of hydrophobicity on octaarginine-mediated intracellular delivery, Mol. Pharm. 9 (5) (2012) 1222–1230. [35] H. Hirose, T. Takeuchi, H. Osakada, S. Pujals, S. Katayama, I. Nakase, S. Kobayashi, T. Haraguchi, S. Futaki, Transient focal membrane deformation induced by arginine-rich peptides leads to their direct penetration into cells, Mol. Ther. 20 (5) (2012) 984–989. [36] H. Leontiadou, A.E. Mark, S.J. Marrink, Antimicrobial peptides in action, J. Am. Chem. Soc. 128 (2006) 12156–12161. [37] B.S. Perrin Jr., A.J. Sodt, M.I. Cotton, R.W. Pastor, The curvature induction of surface-bound antimicrobial peptides Piscidin 1 and Piscidin 3 varies with lipid chain length, J. Membr. Biol. 248 (2015) 455–467. [38] K. Sakamoto, Y. Yamashita, H. Ohtaka, H. Kuwahara, K. Aburai, Can LUV with Submicron Size be a Good Model for Bio-Membrane? (COLL575), in: Spring 2013 New Orleans ACS National Meeting (April 7–11, 2013), 2013. http://presentations.acs.org/ common/media-player.aspx/Spring2013/COLL/COLL05a/23461. [39] S.A. Wheaten, F.D.O. Ablan, B.L. Spaller, J.M. Trieu, P.F. Almeida, Translocation of cationic amphipathic peptides across the membranes of pure phospholipid giant vesicles, J. Am. Chem. Soc. 135 (44) (2013) 16517–16525.

CHAPTER TWO

Interaction of Cells and Platelets with Biomaterial Surfaces Treated with Gaseous Plasma I. Junkar1 Jozˇef Stefan Institute, Ljubljana, Slovenia 1 Corresponding author: e-mail address: [email protected]

Contents 1. Introduction 1.1 Biomaterials 1.2 Interaction of Biomaterials with Biological Environment 1.3 Plasma: The Fourth State of Matter 1.4 Functional Groups on the Surface 1.5 Surface Morphology and Roughness 1.6 Wettability 2. Experimental 2.1 Plasma Treatment 2.2 Surface Topography by AFM 2.3 Water Contact Angle Measurements 2.4 X-ray Photoelectron Spectroscopy 2.5 Adhesion of Human Umbilical Vein Endothelial Cells by MTS Assay 2.6 Platelet Adhesion on Surfaces 3. Results 3.1 Surface Morphology 3.2 Wettability 3.3 Chemical Composition 3.4 Interaction of Endothelial Cells (HUVEC) 3.5 Interaction of Platelets 4. Discussion 5. Conclusions References

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Abstract Interaction of cells and platelets with biomaterials is very complex and still not fully understood. Yet, we already know that the surface of a biomaterial is responsible for initiating the primary response to body fluids, so it is of vital importance to ensure that it is suitably conditioned to provide a desired biological response

Advances in Biomembranes and Lipid Self-Assembly, Volume 23 ISSN 2451-9634 http://dx.doi.org/10.1016/bs.abl.2016.01.002

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2016 Elsevier Inc. All rights reserved.

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(biocompatibility/hemocompatibility). Modern blood-connecting devices still lack the desired hemocompatibility primarily due to insufficient knowledge of the influence of surface parameters on the biological response. In this chapter, we investigate interaction of important surface features with biological system, mainly interactions with endothelial cells and platelets in contact with blood-connecting device. State of the art in the field of blood-connecting devices will be presented and a novel approach to alter surface properties by highly reactive gaseous plasma, an environmental friendly technique, will be investigated and discussed. Gaseous plasma treatment techniques became increasingly useful in the medical field for surface modification of biomaterials, sterilization, and treatment of living tissue. The focus of this chapter will be on surface modification of vascular implants and on fine-tuning of plasma and discharge parameters in order to achieve the desired biological response, without influencing the bulk attributes of the material.

1. INTRODUCTION Interaction of cells with biomaterial surface is very complex and is still not fully understood, especially in cases where biomaterials are used in contact with blood. As the surface of the biomaterial is responsible for initiating the primary interaction with the biological environment, it is of vital importance to ensure that the surface is suitably conditioned to ensure an appropriate biological response [1]. It was thought for many years that the surface of the biomaterial should be inert. However, it has been recently found out that the contact of biomaterials with biological environment should enable integration with the body, prevent infections, inflammatory reactions, blood coagulation, and other correlated reactions. Therefore, it is of primary importance to appropriately condition the surface for desired biological response. The surface properties of biomaterials are mainly described by chemistry, surface charge, texture (roughness), wettability, and in case of polymers also by crystallinity. All these factors influence the sequence of protein adsorption and subsequent platelet adhesion/thrombus formation and attachment of cells. The main goal in designing biomaterials is to ensure appropriate surface properties and desired physical and mechanical characteristics so as to function properly in the biological environment. Yet, it is hard to satisfy all these characteristics. Many surface treatment techniques are available to improve surface properties of materials. However, designing appropriate surface properties for blood-connecting devices is still extremely challenging, as

Interaction of Cells and Platelets

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there are no general findings as to what kind of surfaces are compatible with blood. This chapter deals with surface modification of blood-connecting devices used for vascular grafts in which: • biomaterial surfaces with key surface parameters are presented and discussed in the light of its influence on in vitro biological response; • introduction to surface modification with gaseous plasma and its influence on surface properties is given; • experimental example of surface modification of biomaterial surface with gaseous plasma is presented, as one of the promising ways to alter surface characteristics to achieve improved biological response of bloodconnecting devices made of polymers; • the influence of surface modification on interaction of endothelial cells and platelets is presented and discussed.

1.1 Biomaterials The biomedical field, as it is known today, does not have a long history; it was first introduced in the 1960s by a successful Clemson University symposium, which in 1975 led to the formation of the Society for Biomaterials [2]. However, the so-called biomaterials have been in use through history as gold was used in dentistry, while glass eyes and wooden teeth have also been in use throughout history. When plastic materials become available, they were quickly adopted in the medical field due to their appropriate characteristics. In dentistry, for example, polymeric material polymethyl methacrylate was introduced in 1937, and in relation to cardiovascular prosthesis a cloth made of polyvinyl chloride (Vinyon-N) was discovered and used [2]. Overall it could be said that biomaterials are used in contact with living tissue and biological fluids for prosthetic, therapeutic, and storage applications [3]. The widely accepted definition of biomaterial is “any natural or synthetic material, foreign to the body, which can be employed to substitute, totally or in part, any tissue, organ, or body function” [4]. While biocompatibility is usually defined as “the ability of a material to perform with an appropriate host response in a specific application” [5]. The compatibility of surfaces with blood (hemocompatibility) is, however, even harder to define, as to date there is still no clear definition of compatibility of surfaces with blood, and no standard tests exist which could be performed in order to assess compatibility with blood [6]. Ratner defines blood compatibility as “the property of a material or device that permits it to function in contact

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with blood without inducing undesirable reactions” [6]. Unfortunately, this definition gives little insight on what actually blood-compatible materials are. Usually, it is easier to look from the opposite perspective by observing which materials are not blood compatible. Usually, testing the material in contact with blood is done exactly in this manner, and studies are mainly focused on detecting an adverse response. Mainly, studies are directed at observing platelet adhesion and activation, coagulation, clot or thrombus formation, etc. Moreover, no material has been found to be truly biocompatible/hemocompatible, but many cardiovascular devices function with low or acceptable risks of complications. Atherosclerotic cardiovascular disease is still the largest cause of mortality in Western society [7]. Arterial damage produces localized reductions in the caliber of arteries (stenosis) which ultimately stops the flow of blood through the affected vessels [8]. The disease is treated surgically by bypassing the segment of affected vessels to restore blood flow [9]. Usually, if possible, an autograft is the best choice for a replacement vessel; in this procedure, sections of the patient’s healthy blood vessels (usually veins) are harvested and implanted into the required location. However, many patients, especially those with preexisting vascular diseases and patients who have already undertaken autograft procedures, do not have blood vessels healthy enough to adequately serve as replacements. In such cases, the most common form of treatment is by using synthetic polymeric materials, such as Dacron (PET— polyethylene terephthalate) or ePTFE (extended polytetrafluoroethylene). Such materials exhibit a unique through-pore microporous wall structure and have highly flexible mechanical properties [10]. An example of Dacron vascular graft is presented in Fig. 1. These synthetic vascular grafts have been used successfully to replace large-diameter blood vessels; however, the long-term patency for smalldiameter vascular grafts is still unsatisfactory; this is primarily due to thrombus formations [11]. Postsurgical complications are observed in 10% of patients most of such complications are due to inflammatory reactions, infections, and aneurysm. In such cases, the artificial blood vessel has to be removed, and the new material for vascular graft must be implanted. Such procedures more than double the costs of treatment [12]. The most common problems associated with artificial blood vessels are the insufficient proliferation of endothelial cells on the inner surface of vascular implant and high possibility of undesired thrombotic reactions on the surface, which are connected with high adhesion and activation of platelets on the surface. Improvements of surface properties have been mainly directed in coating

Interaction of Cells and Platelets

29

Fig. 1 Example of artificial vascular graft made from PET polymer (Dacron).

the inner surface of vascular grafts. Currently, knitted Dacron is impregnated with gelatine [13,14], albumin [15,16], or collagen [14,17,18] to reduce its permeability and to obviate the need for preclotting [18,19]. The coated vascular graft surface of Dacron or ePTFE was improved by chemical crosslinking with glutaraldehyde, formaldehyde, or diepoxided poly(ethylene glycol) and heparin impregnation of these protein immobilized systems [20]. However, successful results have not yet been reported for small-caliber vascular grafts. ePTFE and Dacron vascular grafts possess many of the properties of ideal vascular prostheses, but they are highly hydrophobic surfaces and thus limit endothelial surface adhesion [21]. Modifications of the surfaces to stimulate endothelialization could reduce thrombosis, eliminate platelet deposition, resist bacterial infection, and extend graft patency [21,22]. Although various modification techniques have already been employed, these methods have limited success and need to be improved.

1.2 Interaction of Biomaterials with Biological Environment To achieve the desired biological response, the attachment of cells to the surface of biomaterials is of primary importance. When a biomaterial is exposed to biological environment, many extremely complex reactions may occur at the cell–biomaterial surface. These reactions include coagulation, healing, inflammation, mutagenicity, and carcinogenity and play an

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important role in the successful implementation of the implemented material or device [6,23]. Immediately after contact of a biomaterial with body fluids (nanoseconds to milliseconds), the layer of proteins is adsorbed onto its surface, which further dictates interaction of material with biological system [24]. In case of blood-connecting devices, the layer of plasma components is formed (primarily proteins); therefore, interactions of platelets and other blood cells with the artificial surface are actually the interactions with the formed layer of adsorbed plasma proteins. After the protein layer on the surface is formed adhesion of cells follows; thus, the composition and concentration of the protein layer will determine subsequent cellular response [16]. Under normal conditions, blood contacts an endothelium, which is believed to be an ideal anthithrombogenic material with anticoagulant and antithrombotic properties. When blood interacts with a biomaterial, which is not covered with endothelial cells, this represents a foreign surface. As normal blood is a metastable state stabilized between two opposing driving forces coagulation and anticoagulation, blood–material interactions trigger a complex series of events, including protein adsorption, platelet and leukocyte activation/ adhesion, fibrin formation, and coagulation, i.e., blood clotting may occur [6,25,26]. Cells will adhere strongly to some surfaces, while they will not adhere to others, mainly due to the special structure of individual cell membranes and surface properties of materials (e.g., adsorbed proteins). Different parts of a cell membrane correspond to different functions, such as adsorption, secretion, fluid transport, mechanical attachment, and communication with other cells [27]. The protein adsorption is an interfacial phenomenon and is strongly influenced by the physicochemical properties of the biomaterial (polymer) surface. The type, the amount, and the conformational state of the adsorbed proteins determine whether platelets will adhere and become activated or not. For example, adsorption of fibrinogen (Fg) has been shown to be correlated with ability of the surface to promote platelet adhesion and activation [28]. Thus, Fg adsorption was extensively studied, especially their mechanisms of adsorption. However, recent findings showed that certain concentration of Fg adsorbed on the artificial surface will cause rapid accumulation of platelets. An even higher Fg adsorption would actually reduce platelet and leukocyte adhesion, mainly due to surface-induced Fg unfolding and formation of a nanoscale (10 nm) multilayer matrix [29]. While adsorption of albumin, one of the predominant protein in blood plasma is correlated with lower platelet adhesion and activation; thus, coating of vascular implants with albumin has been of the

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approaches to reduce thrombus reactions [15,16,30]. One possibility to determine platelet activation degree is to study adherent platelets shape and number. According to Goodman [31,32], their shape can be categorized on a scale from lower to higher level of activation as: round or discoidic (R), dendritic or early pseudopodial (D), spread-dendritic or intermediate pseudopodial (SD), spreading or late pseudopodial (S), and fully spread (FS). Figure 2 presents different degrees of platelet activation measured by atomic force microscopy (AFM). As thrombus formation begins with protein adsorption, the main efforts to improve hemocompatibility of materials have been directed towards controlling (mainly preventing) protein adsorption. In Fig. 3, a schematic illustration of the interaction of vascular graft surface made of polymer with biological environment is presented. Surface parameters, such as surface chemistry, surface topography, roughness, wettability, and the degree of crystalline fraction, influence protein adsorption, which further dictates subsequent cellular reactions. Thus, by carefully tailoring surface properties, one could engineer the surface for a specific protein adsorption which could be used to control subsequent cell response. An intriguing way to alter all of the above-mentioned surface properties is by highly reactive gaseous plasma, as with such treatment it is possible to alter all the mentioned surface properties.

1.3 Plasma: The Fourth State of Matter In this section, the term plasma will refer to ionized gas or so-called the fourth state of matter. Plasma treatment technique will be presented as one of the intriguing ways to alter biomaterial surfaces. Although the name plasma in this part does not have much to do with blood plasma, which was mentioned in the previous section, it is interesting to note that some connections between the two terms actually exist. The term plasma, which was first introduced by Irvin Langmuir in 1982, is actually believed to get its name from blood plasma, as multicomponent ionized gas reminded Irvin of blood plasma. Ionized gas is usually called plasma when it is electrically neutral (i.e., electron density is balanced by that of positive ions) and contains a significant number of electrically charged particles, which is sufficient to affect its electrical properties and behavior [33]. Therefore, plasma is composed of highly excited atomic, molecular, ionic, and other native radical species. It is typically obtained when gasses are excited into energetic states by radio frequency (RF), microwave (MW), or electrons from a hot filament discharge [34]. To produce plasma, electron separation from atoms or

A nm 500 400 300 200 100 0 0

µm 3.5 0.5

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2.0

2.0

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2.5

1.0

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0 µm

B

nm 400 µm0

µm 4.0 3.5

3.5 3.0

3.0 2.5

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0

C

nm 600 300 µm

0

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0 µm

Fig. 2 Different morphology of platelets interacting with the artificial surface as observed by AFM, from the least activated to the most activated: (A) round or discoidic, (B) dendritic or early pseudopodial, (C) spread-dendritic or intermediate pseudopodial,

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Interaction of Cells and Platelets

D

nm 250 200 150 100 50 0 µm

µm 2.5 2.5

2.0

2.0 1.5

1.5 1.0

1.0 0.5

0.5 0 E

nm 250

µm 5

0 0

4

1 2

3 3

2

4 1

5 6 µm

0

Fig. 2—cont’d (D) spreading or late pseudopodial, and (E) fully spread.

molecules in gas state, or ionization is required. When an atom or a molecule gains enough energy from an outside excitation source or via interaction (collisions) with one another, ionization occurs [35]. Plasmas generated in gas discharge can be obtained in a wide range of pressures, electron temperatures, and electron densities and can be used in many industrial applications [36–39] as well as in medicine [40–44]. For the purpose of surface modification of sensitive polymeric biomaterials, it is important to know that plasma states can be divided into two main categories: thermal near-equilibrium plasmas and thermodynamically nonequilibrium plasmas or cold plasmas. Thermal near-equilibrium plasmas are characterized by very high temperatures of

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Fig. 3 Schematic illustration of interactions between biological system and polymer surface. In first few nanoseconds, the water molecules and proteins reach the surface, followed by the cells. The interaction of proteins and cells with the surface is driven by the specific surface features: surface chemistry, topography, roughness, wettability, and crystallinity.

heavy particles (often about 10,000 K) and are not of particular interest in medicine. While the nonequilibrium plasmas are composed of low temperature heavy particles (charged and neutral molecular and atomic species) and very high temperature electrons (often about 50,000 K) and can be used in many technological applications. Nonequilibrium cold plasmas are further divided into high- and low-pressure plasma. Low-pressure nonequilibrium discharges are initiated and sustained by direct current and RF or MW discharge. These plasma sources operate at low pressure because the breakdown electric field is smaller and the current is more controllable and it is possible to generate large area uniform plasma with a well-controlled electron density [35]. Application of low-pressure plasma is highly intriguing for surface finishing of medical implants, sterilization, production of antibacterial or bacteriostatic surfaces, etc. Moreover, low-pressure plasma enables uniform

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treatment of complex geometries in short treatment time and is environmental friendly process, which could replace many wet chemical processes that are currently in use in the medical field. While in the recent years, the nonequilibrium atmospheric pressure discharges [45,46] that are often recognized as partial discharges showed considerable promise for future translation in medicine for blood coagulation, treatment of wounds, as well as cancer treatment [44,47,48]. Although many studies show exciting results on interaction of atmospheric plasma with the living organisms, the mechanisms behind are not fully understood and its influence on cytotoxicity and gene expression are not well known [49–51] and extensive work in this direction will have to be done. Overall plasma treatment techniques are gaining significant importance in the medical field as there are numerous possibilities for their use; from treatment of biomaterial surfaces with improved properties to treatment of living tissues. The focus of this chapter is to employ RF plasma technique for surface modification of biomaterials used for blood-connecting devices. Therefore, surface modification possibilities by RF plasma are presented in the light of its influence on interaction with cells and platelets. Biomaterials used in vascular grafts are made from polymers; therefore, the interaction of plasma species with polymeric surfaces is addressed. The interaction of polymer surface with highly reactive gaseous plasma results in surface functionalization (introduction of novel functional groups on the surface), altered morphology and roughness (on the nanoscale), increase or decrease in hydrophilicity (depending on the type of gas used for plasma generation), altered degree of surface crystallinity, and removal of weakly bound impurities. Functionalization of polymeric surfaces by plasma is an attractive approach, as polymeric materials are relatively inert and lack surface functionality necessary for specific medical application. Functionalization of biomaterial is especially intriguing for further adhesion of bioactive coatings. In nonthermal plasma, functionalization of polymeric surfaces is created by plasma components, especially by electrons, ions, excited particles, atoms, radicals, and UV radiation. In this case, reactions between gas-phase species and surface species and reactions between surface species produce functional groups and cross-linking at the surface. The functionalization is achieved on the top surface layer; thus, the changes in surface chemistry can be detected by the use of surface sensitive analyzing techniques, like X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectrometry. The changes in surface morphology and roughness of polymers treated by gaseous plasma are of interest not only to improve adhesion of various coatings due to

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surface roughening but also to produce desired nanotopography which would influence on biological response. Morphological changes on polymers by gaseous plasma are obtained by physical sputtering of the surface with ions as well as with chemical etching. Both processes are involved during plasma treatment and could not be separated, but could to some extent be balanced by altering discharge and plasma parameters. Altered morphology of polymers obtained after plasma treatment is, however, highly connected with the type of polymer used for modification (degree of crystallinity, fillers, copolymers, etc.). Changes in hydrophilic or hydrophobic character of polymers treated by plasma are the result of plasma functionalization as well as etching, as even surface morphology on the nanoscale could to some extent influence on the wettability. Usually, changes in wettability are employed as the first and simple method to determine success of surface modification. Degree of crystalline fraction on the polymer surface after plasma treatment usually increases, as the amorphous parts of polymers are known to be easier etched in plasma then the crystalline counterparts [52,53]. Moreover, chemical reactions on the surface can also influence on crystallinity, as radicals created on the surface can cross-link. Overall plasma treatment is a powerful tool to modify relevant surface properties that dictate its interaction with biological system. Effects of functional groups, morphology, and wettability on interaction with biological system are discussed in more detail below.

1.4 Functional Groups on the Surface The chemical nature of the surface in contact with blood is closely linked to its biological response. One of the strategies to improve hemocompatibility of the surface is to introduce new functional groups, such as hydroxyl (dOH), amine (dNHx), methyl (dCH3) sulfate (dSO4), or carboxylic (dCOOH) [54–56]. This is either employed to tailor the biological response (improve cell proliferation, reduce platelet adhesion, etc.) or to enable immobilization of biomolecules (enzymes, proteins, etc.). The effects of functional groups on hemocompatibility have been extensively studied, but again results are not always consistent. It has been generally observed that increased surface hydroxyl concentration causes increased complement activation [57], whereas increased methylation results in reduced complement activation [58]. Yet, increased oxygen concentration has been shown to reduce coagulation activation [59,60], while increasing the negative charge of the surface has generally increased surface activation [61]. Interestingly, the study by Wilson et al. has shown that treatment of polymer

Interaction of Cells and Platelets

37

(polyethyetherurethane) surface with RF ammonia and nitrogen plasma (incorporation of nitrogen groups) significantly reduces contact activation [62]. However, no changes in thrombogenicity, as compared to the untreated surface, were observed after oxygen and argon plasma (incorporation of oxygen groups). Moreover, oxygen or nitrogen gas plasma treatment is one of the strategies to alter surface properties by enriching the surface with new functional groups known to enhance cell proliferation [52,63].

1.5 Surface Morphology and Roughness Numerous studies have dealt with cell behavior on different nanosurfaces; this is because nanomorphology of material may significantly influence protein and cell adhesion. Cells can sense the chemistry and topography of the surface to which they adhere. Focal adhesions interacting with the surface are established by cell filopodia (which are 0.25–0.5 μm wide and 2–10 μm long) [64]. Filopodia can interact with the surface due to surface features which are either arranged randomly or in some geometrical order and have dimensions from the micro to the nanometer range [65]. Beyond micrometers, it has been shown that nanometric (1–500 nm) features can elicit specific cell response [65,66]. In addition, it is known that the recognition of morphology by cells also depends on cell type and origin [67]. Surface morphology is also important in protein adsorption and subsequent cell response. Thus, Riedel and colleagues showed that adsorption of albumin dramatically increased due to presence of nanoislands [68]. While Vertegel et al. showed that the adsorption of lysozyme to silica nanoparticles decreased with decreasing nanoparticle size [69]. They proposed that the increase in the radius of curvature of small nanoparticles (which are thus almost the same size as proteins) results in less protein denaturation on these surfaces, preserving native protein conformation. While Kulkarni et al. showed effectively higher binding of various plasma proteins to nanotubes with 100 nm in diameter in comparison to 50 and 15 nm in diameter [70]. According to the literature, proteins adhere to nanostructures, but it is difficult to develop broad generalizations regarding the strength of adhesion and whether the proteins would be denaturized on these surfaces. Surface topography plays an important role in providing threedimensionality of cells [65]. For instance, the topography of the collagen fibers, with repeated 66 nm binding, has shown to affect cell shape [66]. Techniques based on micropatterning of biologically important proteins

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Fig. 4 Size distribution of cells and plasma proteins, together with the size distribution of features on PET (Dacron) vascular grafts.

(e.g., laminin and fibronectin) are of a particular interest because these proteins could provide cell guidance [71]. The formation of large clusters of immobilized peptides on glass surfaces has been shown to affect the cell– substratum adhesiveness of endothelia cells [72]. Thus, by properly adjusting surface topography on a micrometer and nanometer scale, it might be possible to obtain a specific biological response from cells. This would be a very attractive way to design biomaterial surfaces for specific applications. Figure 4 presents the size distribution of cells and plasma proteins together with the size distribution of features on PET (Dacron) vascular grafts. Modification of the surface on the nanometer scale is achieved with plasma treatment which is in the range of plasma proteins and could specifically interact with these nanostructures.

1.6 Wettability Surface wettability is believed to be one of the most important parameters which influences on biological response with biomaterials. It is established that protein adsorption is the first event that takes place on the surface of a biomaterial after its contact with biological fluids [73], and that the biological response is controlled by the nature and confirmation of the proteins adsorbed to the surface. The first molecules to reach the surface in nanosecond scale are water molecules. Water is known to interact and bind differently depending on surface properties; thus, surface water “shel” influences on attachment of proteins and other molecules, which arrive a little later. In cases, where different proteins are presented in a biological fluid, such as in blood plasma, the competition between these proteins to the surface takes place in the so-called race for the surface. The strength of protein interactions, which first reach the surface, further influence the exchange reactions between different proteins and some exchanges may not even take place [74]. Thus, wettability is believed to play an important role in the amount

Interaction of Cells and Platelets

39

and conformational changes of adsorbed proteins [75] platelet adhesion/ activation, blood coagulation [76], and adhesion of cells [77]. Mainly, when the cells arrive to the surface, they respond to a protein-covered surface; therefore, cell–surface interactions are ultimately interactions between cells and surface bound proteins (or other biomolecules) as already mentioned before. Generally, hydrophobic surfaces are considered to be more protein– adsorbent than hydrophilic surfaces, due to strong hydrophobic interactions occurring at these surfaces [78]. It has been shown by the study of Xu et al. that a stark transition between protein adherent and protein nonadherent materials was in the range of water contact angles (WCAs) 60–65 degrees. Statistical analysis of the adhesion force measurements done on differently wettable surface of low density polyethylene (LDPE) and protein coated AFM tips demonstrated that proteins were more strongly adherent onto poorly wettable (hydrophobic) surfaces than to wettable surfaces. The adhesion of proteins to the surface is a time-dependent process, which involves relatively high energy scales together with conformational and reorientational changes following contact with the surface [79]. Therefore, wettability and surface chemistry greatly influence time-dependent conformational changes in adsorbed proteins and mediate adsorption kinetics, the strength of binding, and subsequent protein activity [80]. Many theories have been proposed regarding platelet adhesion and surface wettability. According to the Lampert rule, blood coagulation is proportional to the capacity of the surface to repel water (hydrophobic surface). Donovan and Zimmerman [87] attributed longer clotting time (lower thrombogenicity) of polyethylene to low surface wettability. Vogler et al. [88] showed that coagulation is the step function of surface wettability, with very low activation for poorly wettable surfaces and high activation for fully wettable surfaces. Contrary to this, it was shown by Sperling et al. [55] that surfaces with more hydrophobic characteristics (contact angle 72–112°) greatly enhance platelet adhesion. Similar observations were also reported in the study by Rodrigues et al., where the most hydrophobic surfaces showed the highest number of adherent platelets in a highly activated state. In contrast to more hydrophilic surfaces (dOH-terminated self-assembled monolayers), where only a small amount of adherent and activated platelets was observed [31]. Although surface wettability probably plays an important role in hemocompatibility of materials no straight correlation between surface wettability and blood compatibility has so far been acknowledged, as the results of different studies are still controversial. This is probably due to the high degree

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of complexity of the reaction paths in the blood and considering also the interplay of other important surface parameters (such as surface chemistry, surface morphology, and surface charge).

2. EXPERIMENTAL 2.1 Plasma Treatment Plasma treatment of PET foils (Maylar A, Du Pont) was conducted by RF oxygen or nitrogen plasma. The samples were treated in the experimental system shown in Fig. 5. The plasma was created with an inductively coupled RF generator, operating at a frequency of 27.12 MHz and an output power of about 200 W. The plasma parameters were measured with a double Langmuir probe and a catalytic probe [81]. The treatment was done by commercially available nitrogen or oxygen gas which was leaked into the discharge chamber and the pressure was fixed at 75 Pa. At this pressure, the highest degree of dissociation of molecules, as measured by the catalytic probes, was obtained. The samples of PET foil as well as PET vascular graft were placed into the discharge chamber as shown in Fig. 5 and were treated by nitrogen or oxygen gas from 3 to 90 s.

2.2 Surface Topography by AFM Topographic changes of the PET foil after plasma treatment were monitored with an AFM (Solver PRO, NT-MDT, Russia) in the tapping mode in air. RF coil Sample Discharge Chamber

Plasma glow

Air cooling

Working gas

Fig. 5 The RF plasma reactor chamber with the sample.

RF

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The samples were scanned with a standard Si cantilever with a force constant of 22 N/m and at a resonance frequency of 325 kHz. The surface roughness has been measured on 1 1 μm AFM images. The surface roughness was expressed in the terms of average roughness (Ra) and it corresponded to the average height of the features on the surface.

2.3 Water Contact Angle Measurements The surface wettability was measured immediately after plasma treatment by determination of the WCA with a demineralised water droplet of a volume of 3 μl. A homemade apparatus equipped with a CCD camera and a PC computer was used for taking high-resolution pictures of a water drop on the sample surface. For each sample, 10 measurements were performed in order to minimize the statistical error. The relative humidity was kept at 45% and the temperature at 25 °C. The contact angles were determined by our own software which enables fitting of the water drop on the surface in order to allow for a relatively precise determination of the contact angle.

2.4 X-ray Photoelectron Spectroscopy The surface of the sample was analyzed with an XPS instrument TFA XPS Physical Electronics. The base pressure in the XPS analysis chamber was about 6  10 8 Pa. The samples were excited with X-rays over a 400-μm spot area with a monochromatic Al Kα1,2 radiation at 1486.6 eV. The photoelectrons were detected with a hemispherical analyzer positioned at an angle of 45° with respect to the normal of the sample surface. The energy resolution was about 0.5 eV. Survey-scan spectra were obtained at a pass energy of 187.85 eV, while the C1s, O1s, and N1s individual highresolution spectra were taken at a pass energy of 23.5 and a 0.1 eV energy step. Since the samples are insulators, an additional electron gun for surface neutralization during the measurements was used. All spectra were referenced to the main C1s peak of the carbon atoms which was assigned a value of 284.8 eV. The XPS spectra were measured for an untreated sample and samples treated by nitrogen or oxygen plasma after different treatment times ranging from 3 to 90 s. The concentration of the different chemical states of carbon in the C1s peak was determined by fitting the curves with symmetrical Gauss–Lorentz functions. The spectra were fitted using MultiPak v7.3.1 software from Physical Electronics, which was supplied with the spectrometer. A Shirley-type background subtraction was used.

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2.5 Adhesion of Human Umbilical Vein Endothelial Cells by MTS Assay Human umbilical vein endothelial cells (HUVEC-c, PromoCell GmbH, Heidelberg, Germany) were cultured in endothelial cell growth medium containing endothelial cell growth supplements (PromoCell, Heidelberg, Germany). All HUVEC used in this study were no more than passage four. Incubation of PET foils (10 mm in diameter) with HUVEC (104 cells per sample in each well) and 0.5 ml of culture media in 24 wells polystyrene plate was preformed 2 h after plasma treatment. Unattached or poorly attached cells were gently removed by rinsing with phosphate-buffered saline (PBS) and the attached cells with culture media were left to proliferate for 3 days at 37 °C in a humidified CO2 incubator. After the incubation time, the proliferation and viability of HUVEC was quantified by an MTS assay (Sigma-Aldrich Chemie) and the absorbance was measured at 490 nm using a microtiter plate reader. All the experiments were run in triplicates and were repeated twice.

2.6 Platelet Adhesion on Surfaces The PET foils (Maylar A, DuPont) were incubated for 1 h with whole blood. Whole blood was drawn from healthy volunteers via vein puncture. The blood was drawn into 9 ml tubes with tri sodium citrate anticoagulant (Sigma), and the number of platelets in whole blood was counted (CellDYN 3200, Abbott). Afterward, the fresh blood was incubated with PET surfaces in 24-well plates for 1 h at room temperature and at gentle shaking at 300 RPM. Each sample (measuring 13 mm in diameter) was incubated with 1 ml of whole blood. After 1 h of incubation, 1 ml of PBS was added to the whole blood. The blood with PBS was then removed and the PET surface was rinsed five times with 2 ml PBS in order to remove weakly adherent platelets. Preparation of PET foils for SEM analysis was done in the following manner. After incubation of whole blood weakly adherent cells were removed from the surface by rising with PBS. Adherent cells were subsequently fixed with 400 μl of 1% paraformaldehyde solution for 15 min at room temperature. Afterward, the surfaces were rinsed with PBS and then dehydrated using a graded ethanol series (50, 70, 80, 90, 100, and again 100 vol.% ethanol) for 5 min and in the last stage in the series (100 vol.% ethanol) for 15 min. Afterward, the samples were placed in a Critical Point Dryer and dried samples were subsequently coated with gold and examined by means of SEM (Carl Zeiss Supra 35 VP) at accelerating voltage of 1 keV.

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3. RESULTS 3.1 Surface Morphology The experimental results show that both oxygen and nitrogen plasma treatment influence on morphology and surface roughness of PET polymer. Short exposure to oxygen or nitrogen plasma caused an increase in surface roughness and formation of small nano-hills after 3 s of treatment. With longer treatment time, the nano-hill structure became even more pronounced and surface roughness increased from 0.6 nm for untreated sample to about 9.9 and 4 nm after 90 s of treatment by oxygen and nitrogen plasma, respectively. From Fig. 6, we can observe changes in morphology between the untreated surface (Fig. 6A), which has no special topography, and 90 s nitrogen (Fig. 6B) and oxygen (Fig. 6C) plasma-treated surface, which exhibits nano-hill structure. Comparison between oxygen and nitrogen plasmatreated surfaces shows different morphology as the nano-hills formed on oxygen plasma-treated samples are bigger and more apart than on nitrogen plasma-treated samples. The average height of nano-hills after 90 s oxygen plasma treatment is about 30 nm and the width is about 100 nm, while in case of nitrogen plasma treatment the average height of the nano-hills is about 12 nm and its width is about 50 nm. Results of measured surface roughness on PET polymers treated from 3 to 90 s with oxygen and nitrogen plasma are presented in Table 1 and the roughness is increased by plasma treatment time.

3.2 Wettability WCA measurements confirmed that plasma modification rendered surface hydrophobic character to hydrophilic one, which was increasing with plasma treatment time and is presented in Table 1. The high drop in contact angle was noticed already after 3 s of treatment for both oxygen and nitrogen plasma treatment; however, lower contact angles were measured on oxygen plasma-treated surfaces. In fact, after 90 s of oxygen plasma treatment, the surface become superhydrophilic (the WCA was not possible to measure). The superhydrophilic character of oxygen plasma-treated surface could be connected with increased surface roughness. Results obtained from AFM after longer plasma exposure show that the surface features are more than 10 nm in height and, according to Wenzel equation, this could influence on the measured contact angle [82,83]. According this equation, surfaces

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A

1.0 3.337.5

0.9 0.8

3.0 0.7

µm

2.0

0.5 0.4

nm

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1.5

0.3 1.0 0.2 0.5 0.077

0.1 0 0

0.1

0.2

0.3

0.4

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0.6 µm

0.7

0.8

0.9

1.0

B 30 900 24.28

800 700

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15

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nm

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5.67

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0 0

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600

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900

Fig. 6 Surface morphology on (A) untreated, (B) 90 s oxygen plasma-treated, and

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C

1.0 0.9

80

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70

0.7

58.1

60

0.6

40

nm

µm

50 0.5 0.4 30 0.3 20 10.2

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1.0

Fig. 6—cont’d (C) 90 s nitrogen plasma-treated PET surface.

Table 1 Atomic Composition, Average Surface Roughness, and Water Contact Angle of Untreated Polymer Surface and Polymer Surface Treated by Oxygen or Nitrogen Plasma Atomic Composition Working Gas

Treatment Time (s)

O/C

N/C

Ra (nm)

WCA (degree)

Untreated

0

0.26

–

0.6

72

Oxygen

3

0.65

–

1

19.1

10

0.67

–

1.4

15.3

30

0.72

–

3.9

8.6

60

0.74

–

4.9

6.1

90

0.79

–

10

–

3

0.38

0.19

1.3

24.1

10

0.40

0.20

1.5

22.4

30

0.43

0.23

2.5

17.3

60

0.38

0.24

3.8

10

90

0.44

0.24

4.1

10

Nitrogen

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having a contact angle, lower than 90°; like in present case, the increase in surface roughness would decrease the contact angle. However, according to Busscher et al. [84], roughness bellow 100 nm should not have any influence on the contact angle measurement. Therefore, it can be presumed that, at least for short plasma treatment times, the influence of roughening is negligible.

3.3 Chemical Composition Effects of chemical modification on plasma-treated surfaces were determined by XPS analysis. Marked differences in oxygen functional groups on the surface of PET were observed immediately after treatment in oxygen plasma (3 s). As can be seen from Table 1, the concentration of oxygen functional groups increased and it seems that the surface became saturated with oxygen already after 30 s of treatment. While for the case of nitrogen plasma treatment, the incorporation of nitrogen as well as oxygen functional groups was observed. However, for this case, surface saturation with newly formed functional groups was achieved already after 3 s of treatment. Type of functional groups on oxygen plasma-treated surface from high-resolution C1s spectra was studied in more detail, as oxygen plasma-treated surfaces highly influenced platelet adhesion. It was shown that CdC and CdH functional groups decrease with plasma treatment, as the number of CdC and CdH groups drops from initial 75% to 34% due to chain scission and incorporation of oxygen. Already after short plasma treatment new component C]O appeared on the surface, which correspond to carboxyl and aldehyde functional groups. Interestingly, the concentration of C]O component remains practically the same up to 30 s of treatment and it more than doubles after 60 s of treatment. It actually raises from 4% (after 3 s of treatment) to about 10.6% (after 60 s of treatment). Concentration of CdO bonds, which correspond to hydroxyl and ether functional groups, is increased from about 13% to about 30% for untreated and 3 s treated surface, respectively. With longer treatment time, the number of these functional groups is slowly decreasing and it drops to about 25%, which is still much higher in comparison to untreated sample. Incorporation of O]CdO groups on the surface corresponds to ester and carboxyl functional groups, and it seems to be the least affected by the time of treatment. Concentration of these groups increases from initial 11% to about 30% and stays practically unchanged even with longer treatment time. Changes in type of functional groups formed during oxygen plasma are relevant for further adhesion of platelets and are in this light discussed later (Fig. 7).

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1.6

Optical density / MTS 492 nm

1.4 1.2 1 0.8 0.6 0.4 0.2 0 PS

PET

PET 3s

PET 30 s

PET 60 s

PET 90 s

PET 3s

PET 30 s

PET 60 s

PET 90 s

Fig. 7 Viability of endothelia cells (HUVEC) cultured on surfaces treated by oxygen and nitrogen plasma for different treatment times.

3.4 Interaction of Endothelial Cells (HUVEC) Interactions of endothelial cells with differently treated PET surfaces were evaluated from MTS assay. Figure 5 shows the measured absorbance, which is directly proportional to viability of endothelia cells, cultured on different samples. Viability and proliferation of HUVEC on polystyrene surfaces was used as a positive control. From Fig. 5, differences in cell viability and proliferation between the untreated surface and plasma-treated surfaces can be clearly seen, as all plasma-treated surfaces exhibited higher viability. However, slightly higher viability of HUVEC was observed on oxygen plasma-treated surfaces, especially on those treated for longer treatment time (60 and 90 s). However, it should be noted that the differences between plasma-treated surfaces are not significant and are in the range of experimental error. Therefore, it could be concluded that endothelial cell growth is promoted on all plasma-treated surfaces, regardless of the increase in oxygen and nitrogen functional groups nor differences in nanotopography.

3.5 Interaction of Platelets The adhesion of platelets on PET surfaces was determined by counting the number of adherent platelets from images taken by SEM. Interestingly, plasma modification highly influences on platelet adhesion and their

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activation. Observable differences in the number of adherent platelets and their shape can be seen in Fig. 8. There are many platelets adhering on untreated PET surface (Fig. 8A), similar goes for nitrogen plasma-treated surface (Fig. 8B and D), while significant difference is observed for oxygen plasma-treated surface (Fig. 8C and E). On oxygen-treated surface, indeed much lower number of adherent platelets is observed already after 3 s of treatment, while practically no platelets were after 90 s of treatment. Moreover, images taken by SEM further reveal the state of platelets and their aggregation. After 90 s of treatment in oxygen (Fig. 8E), virtually no platelets were observed, while those that did adhere seemed to be in a more round form, which is thought to be attributed to low platelet activity. On the contrary, there were many aggregated platelets on untreated (Fig. 3A) and nitrogen plasma-treated surfaces (Fig. 3B and D) and they were mostly in well spread form. Fibrin formation was also observed on these surfaces, especially on the untreated surface and the surface treated for 90 s in nitrogen plasma. As interaction of platelets with oxygen plasma-treated surfaces seemed to provide more blood-compatible PET surfaces, thus the interaction of platelets after exposure to oxygen plasma from 3 to 90 s was studied in more detail. In Fig. 9, the number of adhered platelets on differently treated surfaces obtained from SEM analysis is presented with the respect to the concentration of functional groups determined by fitting the C1s high-resolution peaks obtained from XPS analysis. Analysis of SEM images showed that the number of platelets and their activation is the highest on the untreated surface, as most of platelets were in activated form (spreading or FS) and some were aggregating. A significant reduction in the number of adherent platelets was observed already after a short oxygen plasma treatment time (3 s), as shown before in Fig. 8. After 10 s of treatment, slight increase in platelet number on the surface was observed, and they were mainly in the spread and FS form. After 30 s of treatment, there only a few platelets were observed on the surface, similarly goes also for surfaces treated for 60 and 90 s (Fig. 9). Moreover, the shape of platelets in this case was predominantly round and dendritic. Moreover, it should be noted that the platelet–platelet interactions (aggregation) on oxygen plasma-treated surfaces were not observed, probably due to the low number of adherent platelets in general. This could mean that although platelets are in spread form, the activation of coagulation would not be initiated. Interestingly, Hunt et al. [85] found that a majority of hydrophobic surfaces cause most activation of platelets yet least activation of coagulation. In the present case, activated platelets were also found on hydrophilic surfaces, but according to Hunt et al., it is not necessary that platelet activation would also lead to coagulation.

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Fig. 8 SEM images of platelets interacting with: (A) untreated, (B) 3 s nitrogen plasmatreated,

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Fig. 8—cont’d (C) 3 s oxygen plasma-treated, (D) 90 s nitrogen plasma-treated, and

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Fig. 8—cont’d (E) 90 s oxygen plasma-treated PET surface.

80.00 CJC and CJH

CKO 60.00

OKCJO

80.00

Platelets 50.00 60.00 40.00

30.00

40.00

20.00

Number of platelets per 1000 mm2

Functional groups from C1s spectra %

100.00

CJO

70.00

20.00 10.00

0.00

PET

PET 3 s

PET 10 s

PET 30 s

PET 60 s

PET 90 s

0.00

Fig. 9 Number of adhered platelets on PET surfaces with different concentration of functional groups obtained from C1s spectra.

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4. DISCUSSION Modification of polymer material used for vascular implant was obtained by RF oxygen and nitrogen plasma. The modification itself altered the surface chemistry, wettability, and topography. Although these surface properties could not be viewed separately, it should nevertheless be taken into account that these surface changes all together influence on biological response. As only poor adhesion of endothelia cells was achieved on PET and PTFE vascular grafts, the results of the present study show improvement in interaction of endothelial cells with plasma-treated surfaces with evidently higher proliferation and viability of cells. Moreover, no significant differences in interaction of endothelial cells with differently treated surfaces were observed, which is in accordance with the results published in the literature [86]. Improved proliferation of cells can be attributed to newly formed functional groups (oxygen and nitrogen) even after short plasma treatment time (3 s), as well as to higher hydrophilicity of the surface. It seems that longer treatment time (longer than 30 s) by oxygen plasma is even more affective in promoting endothelia cell attachment than nitrogen plasma. However, these differences are not significant and could as well be attributed to an experimental error. However, much more pronounced differences in interaction of plasma-treated surfaces with platelets were observed. Significantly lower amount of platelets adhered on oxygen plasma-treated surfaces, while there were no significant changes in the number of platelets on the nitrogen plasma-treated surfaces. This could be attributed to higher wettability of oxygen plasma-treated surfaces as well as to the incorporation of oxygen functional groups. The former might be more important, as the change in wettability between oxygen and nitrogen plasma-treated surfaces is not so significant. However, increased oxygen concentration has been reported to reduce coagulation activation [59,60]. Moreover, reduction in platelet adhesion was observed also on dOH-terminated SAM surfaces [55,57]. Thus, incorporation of oxygen functional groups during oxygen plasma treatment can be considered an important parameter influencing platelet adhesion on PET polymer surfaces. Other surface parameters probably have an important role in platelet adhesion as well, as many attempts in considerable changes of surface chemistry only, did not yield any significant differences in platelet adhesion [57]. Our results indicate that even a short exposure of PET polymer to oxygen plasma would reduce platelet adhesion. Again, this could be attributed

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Number of platelets per 1000 mm2

Interaction of Cells and Platelets

100.00

80.00

60.00

40.00

20.00

0.00 0.00

0.20

0.60 0.40 O/C ratio

0.80

1.00

Fig. 10 The number of adherent platelets with respect to O/C ratio.

to the incorporation of oxygen functional groups, which is fairly achieved already after 3 s of treatment. If we look in Fig. 10, a good correlation between oxygen concentration and the number of adherent platelets can be seen. It seems that a higher O/C ratio leads to lower platelet adhesion. The lowest platelet adhesion was observed on surfaces treated for longer than 30 s, where also a more pronounced increase in O/C ratio was observed. For 3 and 10 s of treatment time, the O/C ratio was 0.65 and 0.67, respectively, while after 30 s the O/C ratio increased to 0.72. Although, this still does not explain the high number of adherent platelets on surfaces treated in plasma for 10 s. Interestingly, it has been shown by Sperling et al. [55] that different oxygen functionalities have different effects on platelet adhesion. Thus, it has been shown that dOH-terminated SAM exhibit lower platelet adhesion, while platelet adhesion onto dCOOHterminated SAM is not reduced. From the XPS analysis, it is possible to determine the concentration of CdO and OdC]O groups, but unfortunately, the concentration of CdO can be attributed to CdOH as well as CdOdC groups, while the concentration of OdC]O groups can be attributed to dCOOH as well as OdC]OdC. Thus, it is not possible to propose a correlation between these functional groups and the adhesion of platelets. The adhesion of platelets could also be linked to surface topography, as noticeable changes in surface morphology were observed after 30 s of oxygen plasma treatment. By this time, the average surface roughness increased

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from 1.4 to about 3.9 nm for 10 and 30 s treated surfaces, respectively. It is also interesting to observe the formation of nano-hills; as at this point, their height increased from approximately 3 to 13 nm and after 90 s of treatment the hills height was about 30 nm. Increased height could be important for protein adsorption and conformation, which would further influence cell response. Moreover, nano-hill formation could also results in increased surface crystallinity, as it has been established that surface morphology is altered by plasma treatment due to preferential etching of amorphous parts of the polymer. Thus, more pronounced changes in surface topography would result in higher surface crystallinity, which is thought to have an influence on biological response.

5. CONCLUSIONS Interaction of important surface features with biological system, mainly interactions with endothelial cells and platelets in contact with blood-connecting device after implementation, was presented and discussed together with the current state of the art in this field. An environmentally friendly and relatively simple approach to use highly reactive gaseous plasma for modification of biomaterial surfaces made of polymers proved at the experimental level to effectively alter surface properties of polymers used for vascular implants. By fine-tuning of the discharge and plasma parameters, it was possible to modify the surface of PET polymer to improve proliferation of endothelial cells and simultaneously reduce platelet adhesion. It is evident that plasma can alter chemical composition, topography, and wettability of PET surface, subsequently influencing on interaction with biological system. Oxygen plasma treatment seems to be of particular interest for improving biological response of vascular graft surface made of PET polymer. The mechanisms behind lower adhesion and activation of platelets to the surface are not fully understood; however, it seem that platelet adhesion on PET polymer surface is highly correlated with increased oxygen content on PET surface. We believe that plasma treatment technique is a promising tool for modification of medical implant surfaces made of PET polymer. Extensive research work should still be carried out, though, to fully understand the material–cell and even plasma–cell interactions in the use of atmospheric pressure plasma systems. Plasma applications for medicine will most probably gain a wide range of uses, including treatment of biomaterial surfaces for improved cell interaction, prevention of bacteria, for sterilization purposes, for treatment of living tissue, and even for cancer therapy.

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[78] A. Kongdee, T. Bechtold, L. Teufel, Modification of cellulose fiber with silk sericin, J. Appl. Polym. Sci. 96 (2005) 1421–1428. [79] J.S. Tan, P.A. Martic, Protein adsorption and conformational changes on small polymer particles, J. Colloid Interface Sci. 136 (1990) 415–431. [80] F. Fang, J. Satulovsky, I. Szleifer, Kinetics of protein adsorption and desorption on surfaces with grafted polymers, Biophys. J. 89 (2005) 1516–1533. [81] I. Poberaj, M. Mozetic, D. Babic, Comparison of fiber optics and standard nickel catalytic probes for determination of neutral oxygen atoms concentration, J. Vac. Sci. Technol. A 20 (2002) 189–193. [82] N. Sprang, D. Theirich, J. Engemann, Plasma and ion beam surface treatment of polyethylene, Surf. Coat. Technol. 74–75 (1995) 689–695. [83] S. Brandon, N. Haimovich, E. Yeger, A. Marmur, Partial wetting of chemically patterned surfaces: the effect of drop size, J. Colloid Interface Sci. 263 (2003) 237–243. [84] H.J. Busscher, A.W.J. Vanpelt, P. Deboer, H.P. Dejong, J. Arends, The effect of surface roughening of polymers on measured contact angle of liquids, Colloids Surf. 9 (1984) 319–331. [85] B.J. Hunt, R. Parratt, M. Cable, D. Finch, M. Yacoub, Activation of coagulation and platelets is affected by the hydrophobicity of artificial surfaces, Blood Coagul. Fibrinolysis 8 (1997) 223–231. [86] M. Chen, P.O. Zamora, P. Som, L.A. Pena, S. Osaki, Cell attachment and biocompatibility of polytetrafluoroethylene (PTFE) treated with glow-discharge plasma of mixed ammonia and oxygen, J. Biomater. Sci. Polym. Ed. 14 (2003) 917–935. [87] T.J. Donovan, B. Zimmerman, The effect of artificial surfaces on blood coagulability, with special reference to polyethylene, Blood 4 (1949) 1310–1316. [88] E.A. Vogler, J.C. Graper, G.R. Harper, H.W. Sugg, L.M. Lander, W.J. Brittain, Contact activation of the plasma coagulation cascade. I. Procoagulant surface chemistry and energy, J. Biomed. Mater. Res. 29 (1995) 1005–1016.

CHAPTER THREE

Competition Between Electrostatic and Thermodynamic Casimir Potentials in Near-Critical Mixtures with Ions A. Ciach*,1 *Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland 1 Corresponding author: e-mail address: [email protected]

Contents 1. Introduction 2. Experiments 2.1 Hydrophilic Ions in the Case of ξ > λD 2.2 Hydrophilic Salt in the Case of ξ < λD 2.3 Antagonistic Salt 3. From Microscopic to Mesoscopic Description 3.1 The Model 3.2 The Coarse-Graining Procedure 3.3 The Linearized Euler–Lagrange Equations 4. Critical Mixture with Inorganic Ions 4.1 Effect of the Critical Adsorption on the Charge-Density Profile 4.2 Effect of the Charge-Density Profile on the Near-Surface Concentration 5. Critical Mixture with Antagonistic Salt 5.1 Bulk Properties 5.2 Effects of Confinement 6. Summary Acknowledgments References

62 68 68 70 72 75 75 77 79 81 83 86 88 89 92 94 97 97

Abstract The review focuses on effective interactions between charged and selective surfaces confining a critical mixture with ions. Recent experiments are briefly reviewed. From the experiments, it follows that the interactions differ from a sum of the potential predicted by the Debye–Hückel theory and the thermodynamic Casimir potential, and in the presence of antagonistic salt stable inhomogeneities on the length scale
10 nm appear. A mesoscopic theory developed from a microscopic description by a coarse-graining procedure is described and compared with experiments. The origin of the unexpected behavior, in particular an attraction when both the Casimir and DH Advances in Biomembranes and Lipid Self-Assembly, Volume 23 ISSN 2451-9634 http://dx.doi.org/10.1016/bs.abl.2015.12.004

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2016 Elsevier Inc. All rights reserved.

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potentials are repulsive, is explained. The membrane inclusions in lipid membranes of living cells can interact with the thermodynamic Casimir potential, and the presented results may be an inspiration for further investigations.

1. INTRODUCTION Recently, it was discovered that multicomponent lipid bilayers in living cells are about to phase separate into phases with different concentrations of the components [1, 2]. The discovery that as a rule thermodynamic conditions in living cells are close to the critical point of the demixing transition suggests that the critical fluctuations of the concentration may play an important role in life processes. The spatial extent of the regions with excess concentration of one type of components is of order of the correlation length ξ. When the temperature T approaches the critical value Tc, the correlation length increases according to the law ξ ¼ ξ0jτjν, where τ ¼ (T  Tc)/Tc, ξ0 is a system-dependent amplitude of the order of a few angstroms, and ν is the universal critical exponent; in the case of fluid, it depends only on the dimensionality of the system [3–5]. The thermodynamic states corresponding to the critical behavior are shown in the schematic phase diagram in Fig. 1. T 1-Phase region Critical fluctuations Tc 2-Phase region

hc

h

Fig. 1 Schematic representation of the phase diagram of a binary mixture with an upper critical point. T is the temperature and η denotes the concentration of the component represented by the red color (dark gray in the print version). Thick arrow shows the relevant thermodynamic states, i.e., concentration fixed at the critical value ηc and temperature approaching the critical temperature Tc.

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One of the consequences of the critical fluctuations is the phenomenon of critical adsorption [6–8]. Near a surface preferentially adsorbing one type of the components, a layer of a thickness
ξ with excess concentration of the preferred components is formed. In the case of the lipid bilayer, such a layer with excess concentration can surround large membrane inclusions which preferentially adsorb one type of lipids. When two objects embedded in a near-critical mixture are separated by a distance L
ξ, then the adsorbed layers overlap and influence each other. The L-dependent modification of the concentration profile leads in turn to the L-dependent excess grand potential, i.e., the excess pressure. The effective interactions between the objects with selective surfaces mimic the interactions between the components which tend to be phase-separated. The adsorbed layers surrounding two objects with different adsorption preferences lead to an effective repulsion, while the layers surrounding two objects with similar adsorption preferences lead to an effective attraction between these objects. The above effective interactions are called thermodynamic Casimir potential because of the crucial role of the fluctuations that are subject to the boundary conditions. In this respect, these interactions are similar to the original Casimir potential between conductive plates that results from the constraints imposed by the boundary conditions on the spectrum of the fluctuations of the electromagnetic field [9]. In fact, fluctuations of an order parameter (OP) associated with a critical point of any phase transition (for example, gas–liquid) lead to similar effective interactions. The thermodynamic Casimir potential has been predicted by Fisher and de Gennes [10] and has been extensively studied theoretically and via Monte Carlo simulations [11–18]. For L/ξ > 1, the Casimir potential per unit area between parallel surfaces decays as expðL=ξÞ. Important feature of the Casimir potential is its universality. The potential is independent of the strength of the surface–fluid interaction h1 that measures the selectivity of the surface. It matters only if the adsorption preferences of the two surfaces are similar or opposite. Apart from that, the magnitude of the potential depends only on the dimensionality of the system. However, the temperature range jτj corresponding to the above universal behavior shrinks with decreasing h1 [17, 19]. In the case of very weakly adsorbing surfaces, the Casimir potential can deviate from the universal form for experimentally accessible range of τ [14, 17–19]. In the lipid bilayers, various types of inclusions such as membrane proteins are embedded (Fig. 2). The Casimir potential between like-type inclusions is attractive, and inclusions preferentially adsorbing different types of

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Fig. 2 Cartoon showing a portion of a binary lipid bilayer and two inclusions with opposite adsorption preferences. Top panel: side view; bottom panel: top view.

lipids repel each other. The range of the Casimir potential, ξ, is very large for T ! Tc. Even for very small concentration of the inclusions, the long-range attraction can compete with the disordering effect of entropy and lead to aggregation of the membrane inclusions into dimers or even larger clusters. Because of the strong dependence of ξ on temperature, the range of the Casimir potential can be easily changed by small temperature changes. As a consequence, small temperature changes can lead to significant differences in the distribution of the membrane inclusions. In addition to the Casimir potential, there exist different types of interactions between the membrane inclusions, such as van der Waals or electrostatic potentials, or effective interactions associated with the bending elasticity of the membrane [20–23]. These potentials have different sign, magnitude, and range, and can lead to quite complex shape of the resulting interaction between the inclusions. It is thus interesting to determine the effective potential that is the sum of all types of interactions. This is a very difficult task, and in the first step one should consider model systems, with known and controllable interactions. Experimental verification of the theoretical predictions concerning the Casimir potential is a real challenge. The force is too small to be detected directly by typical techniques such as AFM. Moreover, it is difficult to align two flat surfaces parallel to each other in the microscale. In the membranes, it is difficult to disentangle different contributions to the effective interactions. Only recently, direct measurements of the thermodynamic Casimir potential have been performed by the group of Bechinger [24–26]. They used the total internal reflection microscopy (TIRM) technique, which allows one to determine forces as small as 10 fN [27]. Since the experimental data are so far

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Fig. 3 Cartoon showing a hydrophilic and a hydrophobic particle in a near-critical mixture of water and organic liquid. The particles are surrounded by thick layers with excess concentration of the preferentially adsorbed component. Because at the critical point the two liquids start to be phase separated, the adsorbed layers tend to avoid each other and lead to effective repulsion between the particles. Critical fluctuations of the concentration are represented by large regions with excess of water or oil. Typical colloid particles are charged, and the charges are represented by the minus signs.

restricted to the 3d binary mixture, in the rest of this review we shall limit ourselves to such systems. The 3d case can shed light on the properties of the effective interactions between selective objects immersed in the critical mixture that can be relevant for the 2d case too. A cartoon with a hydrophilic and a hydrophobic particle in the near-critical water–lutidine mixture is shown in Fig. 3. The surface of the particle is curved, while the theory has been developed for parallel flat surfaces. For the separations L ≪ R, where R is the particle radius, the interaction between the particle and the substrate can be calculated from the known interactions between flat, parallel surfaces within the Derjaguin approximation [28]. Gravity, buoyancy, as well as the van der Waals and electrostatic interactions between the colloidal particle and the substrate are also present. The gravity and buoyancy can be subtracted and the van der Waals interactions can be eliminated by a refractive index matching. The particles, however, are usually charged and ions in the aqueous mixtures are also present. Thus, the electrostatic interactions have to be taken into account.

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In the case of a slit geometry, the sum of the Casimir and the electrostatic potential has the form βV ðLÞ ¼

AC 2σ 0 σ L exp ðL=λD Þ, 2 exp ðL=ξÞ + ρ ion λD ξ

(1)

where β ¼ 1/(kBT), kB is the Boltzmann constant, eσ 0 and eσ L are surface charges, e is the elementary charge, λD is the Debye screening length, and ρ ion is the number density of ions [5, 29]. The first term in (1) is attractive for like adsorption preferences, and repulsive for opposite adsorption preferences. The second term is repulsive or attractive for like or opposite surface charges, respectively. Thus, various shapes of V (L) can be obtained for different combination of the surface properties and for different ratio of the decay rates ξ/λD. The potential can be repulsive or attractive for like signs of the two terms in (1), and a minimum or a maximum for L
ξ can appear for opposite signs. Different types of the potential (1) between identical surfaces are shown in Fig. 4. The shape of the potential between identical surfaces with large surface charge and ξ/λD > 1 (strong short-range repulsion and weaker long-range attraction) is very similar to the Lennard-Jones potential. The minimum, however, occurs at the separation L
10–100 nm sufficiently close to the critical point and for a large screening length. For surfaces with an area typical for colloid particles, the depth of the minimum can be as large as a few kBT, which is enough for inducing phase transitions into the phases rich and A

1

B 0 1

0.8

2

3

4

5

L −0.2

0.6

V(L)

V(L)

−0.4 0.4

−0.6

0.2 −0.8 0 1

2

L

3

4

5 −1

Fig. 4 The characteristic shapes of the potential (1) between identical surfaces. (A) ξ/λD > 1, surfaces are strongly charged, and (B) ξ/λD < 1, surfaces are weakly charged.

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poor in the colloid particles [30]. If V (L) has a maximum (ξ/λD < 1 and the surfaces are weakly charged), the resulting short-range attraction long-range repulsion effective potential can lead to the formation of dynamic spherical or elongated clusters, a network or layers of particles, as observed in the case of depletion attraction competing with the electrostatic repulsion [31–36]. By varying the temperature and thereby changing the bulk correlation length ξ, one can cause the attractive well or the repulsive barrier in the effective potential to appear or to disappear. Thus, it seems possible to induce or to suppress a macro- or microphase separation by small temperature changes. The experimental results show, however, that the effective potential cannot be described by just a sum of the Casimir and the electrostatic potential [25, 26]. Only qualitative agreement with Eq. (1) has been obtained in Ref. [25]. A fair quantitative agreement was found only for L ≫ λD, where the electrostatic contribution can be disregarded. In this experiment, the ions are present because of a dissociation of the water molecules, and are preferentially soluble in water. More surprisingly, attraction between like charge hydrophilic and hydrophobic surfaces was measured for some temperature range when inorganic salt was added to the binary mixture [26]. Both the Casimir and the electrostatic potentials are repulsive in this case, and repulsion follows from Eq. (1) in a striking contrast with experimental results. Both potentials, however, can be modified because of different solubility of the ions in the two components of the solvent. When antagonistic salt (hydrophilic cation and hydrophobic anion) was added to the critical mixture of heavy water and 3-methylpyridine (3MP), a peak in the structure factor for the wavenumber k > 0 was observed in the one-phase region [37–41]. The peak indicates thermodynamically stable inhomogeneities on the length scale
10 nm [40, 41]. Quite different behavior of the effective potential between charged and selective surfaces can be expected in the presence of the inhomogeneities. However, no experimental results for the effective potential between surfaces confining the critical mixture with the antagonistic salt have been reported yet. Because of different solubility of the ions in the two components of the near-critical mixture, the critical concentration fluctuations and the distribution of the ions can influence each other. This coupling has to be taken into account in a theory when inorganic or antagonistic salt is present in the near-critical mixture. In this review, a mesoscopic theory developed from a microscopic description by a systematic coarse-graining procedure by Faezeh Pousaneh, Anna Maciolek, and the author is presented. The general

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version of the theory is applicable for any kind of salt. However, to make the theory tractable, further simplifying assumptions were made for the inorganic and the antagonistic salt. Different physical properties of these salts lead to different approximate theories. In Section 2, we briefly present the experimental results. In Section 3, the derivation of the theory is described. In Section 4, we focus on the case of hydrophilic ions. The cases of ξ/λD > 1 and ξ/λD < 1 are considered in Sections 4.1 and 4.2, respectively. The theory for the antagonistic salt is presented in Section 5. Section 6 contains a summary.

2. EXPERIMENTS The existence of the critical Casimir force was first confirmed experimentally through the measurement of the thickness of the wetting film of pure 4He close to the λ-point [42, 43]. Later, a film of the mixture of 3 He–4He close to the tricritical point [44], and a film of the binary mixture of methanol and an alkane formed on a silica substrate [45] were investigated. It was observed that for like or opposite adsorption preferences of the substrate and the liquid–vapor interface, the film shrinks or swells, respectively, when the critical temperature is approached. This behavior agrees with attractive and repulsive Casimir potential for like and opposite adsorption preferences, respectively.

2.1 Hydrophilic Ions in the Case of ξ > λD The first direct measurements of the critical Casimir force were carried out by the group of Bechinger, using the TIRM technique [24–26]. In the experiments, the interaction between a hydrophilic or a hydrophobic substrate and a hydrophilic or a hydrophobic particle immersed in a critical water– lutidine mixture was measured. A salt-free binary mixture of water and 2,6-lutidine with a closed-loop miscibility gap was chosen, because it has known properties and the lower critical temperature, Tc ’ 307.15 K, is easy to achieve [46]. The lutidine mass fraction was 0.28. The ions are present because of dissociation of water molecules. Negatively charged polystyrene particles with diameters 3.69 and 2.4 μm were chosen for hydrophobic and hydrophilic BC, respectively. The hydrophilic and hydrophobic particles were highly and weakly charged, respectively. Hydrophilic and hydrophobic substrates were produced by surface treatments and were negatively charged. The four particle–substrate pairs formed four types of boundary conditions, (w,w),(w,o),(o,w), and (o,o), where the first symbol concerns

69

Competition Between Electrostatic and Thermodynamic Casimir Potentials

6 4

V (kBT)

2 Tc – T (K)

0

0.30 0.21 0.19 0.18 0.16 0.14 0.12

–2 –4 –6 –8 –10 0.0

0.1

0.2

0.3

L (μm)

Fig. 5 Critical Casimir potential between a hydrophilic particle and a hydrophilic substrate in a water–lutidine mixture near the critical point [24]. (Solid lines) The first theoretical attempt to fit with the experimental data. The electrostatic potential is disregarded in these lines; therefore, the fitting only agrees for large distances. Source: Reproduced with permission from Ref. [24].

the particle and w and o denote the hydrophilic and hydrophobic surface, respectively. The gravity, buoyancy, and light pressure from the optical tweezers were subtracted from the experimentally measured potential. Far from Tc, the remaining part of the potential was repulsive and agreed with the Debye–Hu¨ckel prediction. Close to Tc, the qualitative shape of the remaining part of the potential agreed with Eq. (1) for all four combinations of the BC. Fitting of the experimental results to Eq. (1), however, failed. Only for distances L ≫ λD, a reasonable agreement was obtained, as shown in Fig. 5 for a hydrophilic substrate and a hydrophilic particle. The sum of the electrostatic potential that fitted well the experimental results far from Tc and of the critical Casimir potential that fitted well to the data for separations L ≫ λD close to Tc disagreed strongly with the measured potential for intermediate distances. The authors concluded that coupling between the critical concentration fluctuations and the distribution of ions that are soluble in water may lead to modifications of the potential. The potential shown in Fig. 5 suggests that colloid particles can undergo similar phase transitions as atoms, since by changing the temperature the depth of the potential minimum is varied. Indeed, recent experiments [30, 47, 48] confirm this expectation. In Ref. [48], a direct observation of a reversible aggregation in a colloidal system induced by the critical Casimir

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Fig. 6 Colloidal phase transitions induced by the critical Casimir forces [30]. Confocal microscope images of colloidal gas–liquid–solid transitions, (left) colloidal gas, (central) colloidal liquid aggregates, and (right) colloidal crystal. Source: Reproduced with permission from Ref. [30].

force is reported. In Ref. [30], analogs of the gas, liquid, and crystal phases were induced and destroyed by temperature changes within 0.5 °C. In this experiment, a pseudo binary mixture of 3MP, water, and heavy water with mass fractions 0.25, 0.375, and 0.375, respectively, was chosen. The lower critical point of the phase transition 3MP-rich and water-rich is Tc ¼ 325.2 K. Hydrophobic colloidal particles polyNIPAM with a radius r0 ’ 250 nm were used. By approaching the phase-separation temperature of the pseudo binary solvent, from ΔT ¼ 0.5–0.2 °C below Tc, the colloidal phase transition is observed and imaged by confocal microscopy (see Fig. 6). In the left image in Fig. 6 (far from Tc), the particles are uniformly suspended and form a dilute gas phase, while the central image for ΔT ¼ 0.3 shows that particles condense and form spherical aggregates which coexist with lowdensity colloidal gas. Closer to Tc, for ΔT ¼ 0.2, the aggregated particles form an ordered face-centered cubic lattice indicating that the colloidal liquid has frozen into a crystal. The observations provide direct evidence for analogues of gas–liquid and liquid–solid transitions in colloids, driven by the critical Casimir interactions [30]. A similar experiment done recently [47] on the 3MP–heavy water mixture, but with the critical composition (a 3MP mass fraction of 0.28), shows that upon changing the temperature close to the critical point of the solvent (Tc ¼ 325.2 K), the morphology of the aggregated colloids is changed and that they form different branched structures.

2.2 Hydrophilic Salt in the Case of ξ < λD In order to investigate the influence of an additional salt on the potential between the objects, a small amount (10 mM) of potassium bromide

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71

(KBr) was added to the water–2,6-lutidine binary mixture [26] that was previously investigated by the same group and the same method in Ref. [25]. A negatively charged hydrophilic polystyrene particle with a diameter 1.5 μm and a negatively charged hydrophobic glass surface formed BC with opposite adsorption preferences. Theoretically, both the electrostatic and the critical Casimir forces predict repulsion for this boundary condition when both surfaces are negatively charged. Indeed, for λD/ξ ≫ 1 or λD/ξ ≪ 1 the electrostatic (the second term in (1)) or the Casimir (the first term in (1)) repulsion was observed, respectively. However, for intermediate temperatures, corresponding to ξ/λD ’ 1, an attraction between the substrate and the particle was obtained in this experiment [26]; the shape of the effective interaction was similar to the one presented in Fig. 5. Therefore, Eq. (1) fails to explain this experiment completely. The experimental results evidence that it is not enough to just add the Casimir and the screened electrostatic potential in order to obtain the effective interactions between the selective and charged surfaces. This could be correct if the solubility of ions in both components of the mixture were the same. In such a case, the distribution of charges would be independent of the local solvent concentration, and also the concentration of the mixture would not be affected by the presence of the ions. However, addition of small amount of salt to a binary mixture near a demixing critical point can significantly change its properties. Common salts are soluble in water and insoluble in organic liquids. The solubility of KBr in water is well known to be 39.39% [26, 49], and in experiment [26] no indication that KBr is dissolved in lutidine was found. On the other hand, the solubility in water of the anion and the cation is not the same [49, 50]. As a result, the total potential can strongly deviate from the sum of the Casimir and the electrostatic potentials, even when no other interactions are present. Several groups tried to explain the experiment in Ref. [26]. The attraction for a range of temperatures was obtained in two different approaches. The first one is based on the theory of Onuki and Kitamura [51]. In the Onuki and Kitamura model, the critical binary mixture is described by the phenomenological Landau functional of the solvent concentration ϕ. The ions are treated as a two-component ideal gas whose particles interact with the Coulomb potential, and the corresponding entropy and electrostatic energy are added to the Landau functional. Finally, the coupling between the critical mixture and the ions of the form ϕ(w+n+ + wn), where ni and wi are the density and preferential solubility of the ith ion, is added. The attraction between the confining walls appears when the

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solubility in water of the anion and the cation differs significantly from each other and the hydrophobic surface is neutral [52, 53]. On the other hand, in the theory developed in Ref. [54] for hydrophilic ions, the concentration profile near the charged hydrophobic surface can be nonmonotonic, because the attraction of the organic particles by the hydrophobic charged surface competes with the attraction of the hydrated ions [55, 56]. When λD > ξ, excess of water surrounding ions may appear at some distance from the charged surface; therefore, it may act as a hydrophilic one. As the Casimir potential between hydrophilic surfaces is attractive, attraction can occur if the Coulomb repulsion is weak. In Section 3, a theory predicting the effective potential consistent with the above physical explanation is described, and in Section 4.2 the results concerning the case λD > ξ are presented.

2.3 Antagonistic Salt When inorganic salt is added to water and organic liquid, the two-phase region enlarges [57]. Addition of antagonistic (or amphiphilic) salt to a critical mixture leads to shrinking of the two-phase region; it can even disappear when the amount of salt is large enough [41]. Thus, the antagonistic salt has an opposite effect on the phase behavior than the hydrophilic salt discussed in Sections 4.1 and 4.2. Moreover, addition of the antagonistic salt to the near-critical mixture leads to a peak in the structure factor for the wavenumber k > 0 in the one-phase region. The peak was first observed by the group of Onuki [37] and later confirmed by different experiments [38, 40, 41]. The peak indicates thermodynamically stable inhomogeneities on the length scale
10 nm [40, 41]. In a few cases, a lamellar phase was observed for some region of the phase diagram [37, 40, 41]. In Refs. [37, 41], it was hypothesized that because of the critical concentration fluctuations, the hydrophilic ions are present mainly in the water-rich regions, and the hydrophobic ions are present in the oil-rich regions. The ions are located close to the local interfaces and partially neutralize each other, by which a compromise between the solvation and electrostatic energies, and the entropy of mixing is achieved. A cartoon showing schematically the microsegregation is shown in Fig. 7. For low salt concentration, the shape of the structure factor was described with a good accuracy by the formula (2) obtained by Onuki and Kitamura in a phenomenological theory described briefly in Section 2.2 [51]:

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Competition Between Electrostatic and Thermodynamic Casimir Potentials

D 2O

+

~ 10 nm

+

−

− + + −

Methylpyridine

−

− +

− +

+ −

+ −

− +

Fig. 7 Cartoon showing schematically the microphase separation of the near-critical mixture and the distribution of the hydrophilic and hydrophobic ions.


2 2 SðkÞ ¼ Sð0Þ 1 + ξ k 1 

γp λ2D k2 + 1

1 :

(2)

In the fitting to experimental results (see Fig. 8), γ p was treated as a fitting parameter. For larger amount of salt (when the two-phase region disappears), the experimental structure factor was described with better accuracy by the formula derived earlier for bicontinuous microemulsion or sponge phases [41]. In addition, the structure factor of the lamellar phase was fitted with a good accuracy [41] by the formula developed for a stack of membranes [41] (see Fig. 8). These observations strongly suggest that the key features of the mesoscopic structure do not depend on whether antagonistic salt or surfactant is added to a mixture of inorganic and organic solvents. The difference between the two cases concerns the thermodynamic conditions that allow for the microsegregation of water and the organic liquid. In the case of surfactant the microemulsion appears when water and oil are phase separated, whereas in the case of the antagonistic salt a structure similar to microemulsions appears in the one-phase region in the vicinity of the critical point. The effects of confinement on the near-critical mixture with antagonistic salt were not investigated experimentally yet. Theoretical investigations based on the theory of Onuki and Kitamura [51] focused very briefly on colloid particles immersed in the critical mixture with salt [39]. Oscillatory potential between the particles was predicted for some values of the model parameters. The above strong quantitative [25] and even qualitative [26, 58] disagreement between Eq. (1) and the experiments reveals that in order to design effective interactions, it is necessary to develop a more accurate

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A

B

Fig. 8 SANS intensity measurements for near-critical composition of the 3-methylpyridine, D2O, and NaBPh4 (antagonistic salt) mixture for several salt concentrations. Dashed lines—Onuki and Kitamura expression (2). Solid and dotted lines—scattering from the lamellar and sponge phases fitted to the expressions describing a stack of membranes and bicontinuous microemulsion, respectively. Source: Reprinted from Ref. [41].

theory. Several attempts have been made already [52–55, 59–62]. In the following sections, we present the theory that allows to obtain the effective interactions between charged and selective surfaces confining a critical mixture with different types of ions.

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3. FROM MICROSCOPIC TO MESOSCOPIC DESCRIPTION 3.1 The Model We consider a four-component mixture containing water, organic liquid, and salt, confined between parallel surfaces that are charged and selectively adsorb the inorganic and organic components (Fig. 9). The fluid is in contact with a reservoir with fixed temperature and chemical potentials. In equilibrium, the distribution of the components corresponds to the minimum of the grand potential Z Ω ¼ UvdW + Uel  TS  V

dr  μi ρi ðrÞ,

(3)

where Uel and UvdW are the electrostatic and the van der Waals contributions to the internal energy, respectively, and S is the entropy. μi is the chemical potential of the ith component, with i ¼ w,l corresponding to water and organic solvent (for example, lutidine or methylpyridine) and i ¼ +, corresponding to the cations and the anions. We consider dimensionless distance r* ¼ r/a and dimensionless densities, i.e., the length is measured in units of a, ρi ¼ a3 Ni =V , where a3 is the average volume per particle in the liquid phase and Ni denotes the number of the ith type molecules in the volume V. The microscopic details, in particular different sizes of molecules, are disregarded, since we are interested in the local

L Fig. 9 Cartoon with a schematic representation of the considered model in the particular case of negatively charged hydrophilic and hydrophobic confining surfaces.

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densities in the regions much larger than a. To simplify the notation, we shall omit the asterisk for the dimensionless distance and density. We neglect compressibility of the liquid and assume that the total number density is fixed, X ρi ¼ 1: (4) i¼fw , l, + , g Next we postulate the lattice gas or ideal mixing form for the entropy Z X ρi ðrÞ ln ρi ðrÞ: TS ¼ kB T dr (5) V fi¼w , l, + , g The electrostatic energy in the case of a slit geometry with parallel surfaces of area A separated by the distance L is given by [5] Z h E i Uel ¼ dr  ð5ψ el ðrÞÞ2 + eρq ðrÞψ el ðrÞ + A½eσ 0 ψð0Þ + eσ L ψðLÞ, 8π V (6) where ρq(r) is the local dimensionless charge density, ρq ðrÞ ¼ ρ + ðrÞ  ρ ðrÞ,

(7)

ψ el(r) is the electrostatic potential which satisfies the Poisson equation, 52 ψ el ðrÞ ¼ 

4πe ρ ðrÞ: aE q

(8)

We impose the Neumann boundary conditions (BC) that are appropriate in the case of fixed surface charges, 5ψ el ðzÞjz¼0 ¼ 

4πe 4πe σ 0 , 4 ψ el ðzÞjz¼L ¼ σL : E E

(9)

We neglect the dependence of the dielectric constant E on the solvent concentration [54, 60]. We assume the usual form of the internal energy U vdW , Z Z Z 1 0 0 0 0 dr dr ρi ðrÞVij ðr  r Þgij ðr  r Þρj ðr Þ + drρi ðrÞVis ðrÞ, (10) U vdW ¼ 2 V V V where Vij and gij are the vdW interaction and the pair correlation function between the corresponding components, respectively, Vis ðrÞ is the sum of

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77

the direct wall–fluid potentials acting on the component i, and the summation convention for repeated indices is used. In a slit, we consider the excess grand potential ΔΩ ¼ Ω  Ωbulk ¼ γ 0 + γ L + ΨðLÞ,

(11)

where Ωbulk is the grand potential in the bulk system of the same volume AL, γ 0 and γ L are the surface tensions associated with the two surfaces, and Ψ(L) is the effective potential between the surfaces that is induced by the confined fluid.

3.2 The Coarse-Graining Procedure The full microscopic density functional theory of a four-component mixture is more accurate and justified than a phenomenological model, but in practice it is too difficult. Moreover, such a detailed description is not necessary when the characteristic length scales are mesoscopic. On the other hand, a microscopic theory is a good starting point for a derivation of the Landau-type functional by a coarse-graining procedure. Close to the critical point and for small amount of ions, the correlation and screening lengths are both large, and the local densities vary slowly on the microscopic length scale. Thus, the density ρj(r0 ) in Eq. (10) can be Taylor expanded about r. In the case of attractive interactions, the expansion can be truncated at the second-order term [54, 63]. As a result, UvdW is given by a single integral over r with the integrand depending R on the densities and their gradients at r, and on the zeroth, Jij ¼  V drVij ðrÞgij ðrÞ, and the second, R J
ij ¼  V drVij ðrÞgij ðrÞr 2 =6, moments of Vij gij [54, 63]. Because of the universality of critical phenomena, the detailed form of the interactions is irrelevant. The density profiles at the length scale ξ ≫ a can be obtained from highly simplified models. We can further simplify the expression for UvdW by assuming appropriate relations between Jij and J
ij . Solubility of inorganic ions in water is much higher than in organic solvent, and the organic ions are much less soluble in water than in the organic liquid. We assume that the differences between the interactions of all the inorganic components are negligible; likewise, we neglect the differences between the interactions of all the organic components. In Ref. [25], ions in the solution come from dissociation of water, and any difference between the specific interactions of the ion or water molecule can be neglected. In the case of salts, the above assumption is not strictly valid, and should be considered as an

78

A. Ciach

approximation, whose validity should be verified at the later stage. After some algebra, we obtain for both inorganic and antagonistic salt the result [56, 60] Z  J  UvdW ½Φ ¼ bΦðrÞ2 + ðrΦðrÞÞ2 dr + UBC , (12) 2 V where J ¼ 14 ð Jww + Jll  2Jwl Þ is the single energy parameter relevant for the phase separation, b  2d is a dimensionless constant (recall that we consider dimensionless distance), and Φ is a difference between the local dimensionless density of the inorganic and organic components. We have disregarded contributions independent of Φ and linear in Φ while deriving Eq. (12) from Eq. (10). The former contribution is irrelevant, and the latter can be included in the modified chemical potential term. UBC is the contribution to the internal energy associated with the presence of confining surfaces. In the case of parallel confining surfaces with area A a distance L apart,
 1 2 2 (13) UBC ¼ AJ Φð0Þ + ΦðLÞ  h0 Φð0Þ  hL ΦðLÞ , 2 where Jh0 and JhL are the surface fields describing direct interactions with the surfaces, and the remaining terms compensate for the missing interactions with the fluid molecules at the solid wall that are included in the bulk part, and should be subtracted. The internal energy can be approximated by the same expression (12) for the two types of salt. However, the density of the inorganic components is ρw + ρ+ and ρw + ρion in the case of the antagonistic and the inorganic salt, respectively, while the density of the organic components in the two cases is ρl + ρ and ρl. Thus, the difference between the density of the inorganic and organic components is given by ( ΦðrÞ ¼

ρw ðrÞ  ρl ðrÞ + ρion ðrÞ, ionorganic salt ρw ðrÞ  ρl ðrÞ + ρq ðrÞ, antagonistic salt;

(14)

where ρion ðrÞ ¼ ρ + ðrÞ + ρ ðrÞ:

(15)

Competition Between Electrostatic and Thermodynamic Casimir Potentials

79

3.3 The Linearized Euler–Lagrange Equations In this theory, the thermal equilibrium for fixed temperature, total density, and chemical potentials corresponds to the global minimum of the grand potential (3) with the electrostatic and the vdW contributions to the internal energy given in Eqs. (6) and (12), respectively, and the entropy given in Eq. (5). Equation (5) should be expressed in terms of the new variables Φ, ρq, and ρion, since there are three independent variables when (4) holds. Note that because of different forms of the OP for the inorganic and antagonistic salt (see Eq. (14)), the entropy expressed in terms of the new variables has a different form for the inorganic and the antagonistic salt. For this reason, despite the same expressions for the electrostatic and van der Waals energies in terms of ρq and Φ (Eqs. (6) and (12)), the expression for the grand potential in terms of the new variables is different for the inorganic and the antagonistic salt. In the bulk ρq ¼ 0 and Φ ¼ Φ. We are interested in the critical concentration Φ ¼ Φ c . In a model of a symmetrical mixture Φ c ¼ 0, while in reality Φc6¼0. To simplify the calculations we shall assume Φ c ¼ 0; hence, Φ in the rest of this section denotes the excess concentration, Φ  Φ  Φ c . The equilibrium forms of Φ(r), ρq(r), and ρion(r) are the solutions of the Euler–Lagrange (EL) equations obtained from the extremum conditions δΩ/δρion(r) ¼ 0 ¼ δΩ/δΦ(r) ¼ 0 ¼ δΩ/δρq(r), with ψ el satisfying the Poisson equation (8). Note that neither Uel nor UvdW depends on ρion(r). For this reason, ρion(r) can be easily expressed in terms of Φ(r) and ρq(r) with the help of the equation δΩ/δρion(r) ¼ 0, and the grand potential becomes a functional of two fields, Φ(r) and ρq(r). The explicit forms of the EL equations for the inorganic and antagonistic ions are given in Refs. [56] and [60], respectively. In the linearized theory, i.e., with the contributions only up to the second order in the fields Φ, ρq, and ρion included in the Taylor-expanded entropy (5), we obtain from δΩ/δρq(r) ¼ 0 8 ρq ðrÞ > > > <  ρ , inorganic salt ion eβψ el ðrÞ ¼
 > ρq ðrÞ 1 > > : , antagonistic salt; ΦðrÞ  ρ ion ð1  ρ ion Þ where ρ ion is the number density of ions in the bulk.

(16)

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A. Ciach

In the case of the inorganic salt, Eqs. (16), (8), and the remaining linearized EL equation give us [59, 60] d2 ΦðzÞ ¼ ξ2 ΦðzÞ, dz2 d2 ρq ðzÞ ¼ λ2 D ρq ðzÞ, dz2

(17) (18)

where λD ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kB T E 4πe2 ρ ion

(19)

is the Debye screening length, and ξ∝ ðT  Tc Þ1=2 is the bulk correlation length, with Tc denoting the critical temperature. In the case of the antagonistic salt, the Poisson and the linearized EL equations give us d2 ΦðzÞ ¼ M11 ΦðzÞ + M12 ρq ðzÞ, dz2 d2 ρq ðzÞ ¼ M21 ΦðzÞ + M22 ρq ðzÞ, dz2

(20)

where the matrix elements Mij 6¼ 0 in (20) are given in Appendix A of Ref. [56]. The BC for (17) and (18) as well as for (20) are rΦð0Þ  Φð0Þ ¼ h0 , rΦðLÞ + ΦðLÞ ¼ hL

(21)

and the Neumann BC (9) with ψ el given in Eq. (16). The EL equations for the inorganic salt, (17) and (18), are decoupled in the linearized theory. Therefore in a semi-infinite system, Φ and ρq decay exponentially, with the decay rates ξ and λD, respectively. The decay rates are not affected by the coupling between the concentration and the local charge because the coupling is present beyond the linear approximation. In contrast, in the case of the antagonistic salt, the linearized EL equations (20) are coupled, and the decay rates of Φ and ρq are different than predicted by the Landau and Debye–Hu¨ckel theories. The matrix Mij is not symmetric, and a pair of complex-conjugate eigenvalues may occur, signaling oscillatory decay of Φ and ρq from a charged, selective surface.

Competition Between Electrostatic and Thermodynamic Casimir Potentials

81

4. CRITICAL MIXTURE WITH INORGANIC IONS In this section, we describe the effects of confinement on the critical mixture with inorganic ions beyond the linearized EL equations discussed in Section 3.3. To distinguish the solutions of the linearized equations (17) and (18), we shall denote them by Φ(1) and ρð1Þ q , respectively. In the semi-infinite system, we have σ 0 z=λD e λD

(22)

h0 z=ξ : 1 e 1+ξ

(23)

ρð1Þ q ðzÞ ¼  and Φð1Þ ðzÞ ¼

Beyond the linearized theory, the excess grand potential minimized with respect to ρion [56, 64] has the form Z

L

βΔΩ½Φ, ρq   βΔΩC ½Φ + βΔΩDH ½ρq   A 0

ΦðzÞρq ðzÞ2 dz , 2ρ ion

(24)

where A βΔΩC ½Φ ¼ βUvdW + 2

Z

L

dzΦðzÞ2

(25)

0

and A βΔΩDH ½ρq  ¼ βUel + 2ρ ion

Z

L

dzρq ðzÞ2

(26)

0

are the approximate Casimir and the Debye–Hu¨ckel effective potential, respectively. In Eqs. (24)–(26), terms of higher order in Φ and ρq have been neglected. The internal energies UvdW and Uel are given in Eqs. (12) and (6), respectively, and the last terms in Eqs. (24)–(26) come from the entropy (5). The effective potential is a sum of the Casimir and the electrostatic potentials R L ΦðzÞρ ðzÞ2 and the term A 0 dz 2ρ q . The above term is an extra contribution, ion negative for Φ > 0 (excess of inorganic component) and positive for Φ < 0 (excess of organic component). More importantly, when this term

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is included, the minimum of ΔΩ[Φ, ρq] is assumed for different forms of the concentration and the charge profiles. The nonlinear EL equations for the functional (24) have been solved analytically in the perturbation expansion in Refs. [56, 59]. The calculations in the slit geometry are very tedious, but further approximations are possible when either ξ ≫ λD or ξ ≪ λD. In the first case, the effect of charges on the concentration profile is irrelevant, and one can approximate Φ by the solution of the linearized EL equation, Φ(1), while ρq is approximated by the solution of the Poisson equation (8) together with kB T  ð1Þ ρq ðzÞ  ρð1Þ ðzÞΦ ðzÞ : eψ el ðzÞ ¼  (27) q ρ ion In the case of ξ ≪ λD, the concentration near the surface has a negligible effect on the charge distribution, and ρq can be approximated by the solution of the linearized EL equation, ρð1Þ q , whereas Φ is a solution of the equation T
ρqð1Þ2 ðzÞ d2 ΦðzÞ 2 ¼ ξ ΦðzÞ  : 2ρ ion dz2

(28)

The effect of the excess concentration Φ(z) on the charge distribution ρq(z), and the effect of ρq(z) on Φ(z) are described in Sections 4.1 and 4.2, respectively. The modified charge and concentration profiles lead to modified effective potential between the confining surfaces. The main contribution to the effective potential has a form similar to Eq. (1), except that both prefactors depend significantly on the ratio of the decay rates ξ/λD and on the surface charge and selectivity, and the next-to-leading order terms are present, βΨðLÞ  

Aξ L=ξ Aλ L=λD + e + βδΨðLÞ, e ξ ρ ion λD

(29)

where

βδΨðLÞ ¼

8 A ξλ L=λD L=ξ > e >

A > : 2λ e2L=λD ρ ion λD

for

(30) ξ=λD ≪1:

Terms that decay faster are neglected in (29). All the amplitudes, Aξ, Aλ, Aξλ, and A2λ, depend on ξ/λD, and on the surface charges and selectivity. The explicit expressions are given in Ref. [64].

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Competition Between Electrostatic and Thermodynamic Casimir Potentials

Note that in Eq. (1), the amplitude of the Casimir potential is independent of the charge distribution and the surface charge, and the amplitude of the DH potential is independent of the concentration profile and the surface selectivity. The mutual effect of the concentration and the charge distribution is reflected in the dependence of both amplitudes in (29) on ξ/λD and on the selectivity and charge of the surfaces. In Sections 4.1 and 4.2, we compare the effective potential (29) with the results of the experiments for ξ/λD > 1 [25] and for ξ/λD < 1 [26], respectively.

4.1 Effect of the Critical Adsorption on the Charge-Density Profile In this section, we describe the influence of the critical adsorption on the charge distribution close to the critical point of the phase separation, i.e., for ξ/λD > 1, realized in the experiments [24, 25] described in Section 2.1. The results discussed in this section have been obtained in Ref. [59]. The critical adsorption significantly influences the charge distribution near a selective surface. The charge density is enhanced in the vicinity of a hydrophilic surface and depleted in the vicinity of a hydrophobic one. The effect of the concentration profile on the charge density is shown in Fig. 10. The main goal of this section is a comparison of the experimental results with Eq. (29). There are two problems: (i) the theory has been developed for flat parallel surfaces, and in the experiment one of the surfaces is curved, and (w,o) BC

(w,w) BC 1.2

1.2

The present theory DH theory

1

0.8

0.8

The present theory DH theory

rq

rq

1

0.6

0.6

0.4

0.4

0.2

0.2 0.2

0.4

0.6

z/L

0.8

0

0.2

0.4

0.6

0.8

1

z/L

Fig. 10 Charge-density profile as a function of the scaled distance z/L. The solid line ð1Þ

represents ρq ðzÞ (the linearized DH theory result) and the dashed line is the approximate charge density with the effect of the critical adsorption included (solution of Eqs. (8) and (27)). ξ/λD ¼ 5, L/λD ¼ 5, σ L/σ 0 ¼ jhL/h0j ¼ 1 (the same charge densities and the same or opposite adsorption preferences at both surfaces), and the surface field is h0 ¼ 0.5. Plots (left) and (right) correspond to the hydrophilic–hydrophilic, (w,w), and hydrophilic–hydrophobic, (w,o), boundary conditions, respectively.

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A. Ciach

(ii) the theory is of the mean-field (MF) type, and the fluctuations lead to a modification of the Casimir potential. However, the above MF result can be corrected. As can be seen from Eq. (24), the Casimir contribution to the potential (the first term in Eq. (24)) can be considered separately, and the critical fluctuations can be incorporated in this part. The universal scaling function of the critical Casimir force has been obtained in Monte Carlo simulations [14]. The amplitude AC characterizing the long-distance decay of the potential (see the first term in (1)) has been extracted from the asymptotic behavior of this function for L/ξ ≫ 1 in Ref. [25]. In the case of the symmetrical BC AC ¼ 1.51(2), and in the case of the antisymmetric BC AC ¼ 1.82(2) [25]. We separate the contribution to Aξ/ξ that is independent of the surface charges, and replace this part by the proper Casimir amplitude, AC/ξ2. When the colloidal particle radius is much larger than the separation of its surface from the substrate, then the Derjaguin approximation can be applied, as in Refs. [24, 25]. The curved surface is approximated by a set of concentric circular rings of the infinitesimal area dS(θ). The rings are parallel to the substrate and are at the normal distance LðθÞ ¼ L + Rð1  cosθÞ (Fig. 11). For each ring, the excess grand potential per unit area is given in Eq. (29), except that the surface charge σ R of the ring differs from σ P of the colloidal particle, and the relation between them is σ R ¼ σ P = cos θ: The contribution of the ring to the potential between the substrate and the particle has the form ^ dΨðzÞ ¼ dSðθÞΨðLðθÞÞ:

(31)

dq q q R

r

r L

dr

R

L(q)

Fig. 11 Illustration of the Derjaguin approximation for the plate–sphere geometry. The left and right panels show side and top views, respectively. L is the minimal separation between the planar wall and the surface of the colloid particle with the radius R. L(θ) is the normal distance between the ring of radius r and the wall.

85

Competition Between Electrostatic and Thermodynamic Casimir Potentials

^ ^ The total potential ΨðzÞ is obtained by summing all the contributions dΨðzÞ of the circular rings up to the maximal angle π/2, ^ ΨðzÞ ¼

Z

π=2

(32)

dSðθÞΨðLðθÞÞ: 0

The results of fitting of the formula (32) with Ψ(L) given by (29), with the amplitude Aξ/ξ corrected to account for the critical fluctuations, are shown in Fig. 12. We assumed the correct dependence of the correlation length on T, ξ ¼ ξ0jτjν, with the critical exponent ν ¼ 0.63 [5]. The best recent experimental result [26] for the amplitude ξ0 for the considered mixture is ξ0 ¼ 0.2 nm [26], and it agrees perfectly with the best fits to all the (w,w) BC

(o,w) BC

4 Tc –T 8

0.25 0.28 0.30 0.32 0.34 0.43

6

0

Ψ[k BT ]

Ψ[k BT ]

2

Tc –T 0.14 0.16 0.18 0.19 0.21 0.30

–2 –4 –6 0.1

0.15

0.2

4 2 0

0.25

0

0.2

0.4 z (μm)

z (μm) (w,o) BC

(o,o) BC

Ψ[k BT ]

4

2

3

Ψ[k BT ]

0.04 0.05 0.07 0.09 0.12 0.18

6

0.8

6

Tc –T 8

0.6

0

Tc –T 0.08 0.10 0.11 0.12 0.13 0.20

–3 –6

0

–9 0.2

0.4 z (μm)

0.6

0.05

0.1

0.15 z (μm)

0.2

Fig. 12 The effective potential between a wall and a colloidal particle immersed in a water–lutidine mixture as a function of the distance z for various temperatures T [25]. Negatively charged hydrophilic and hydrophobic particles with radii R ¼ 1200 and 1850 nm, respectively, and negatively charged hydrophilic and hydrophobic flat substrates were used. The four pairs of the substrate and the particle are represented by the four BC: (w,w), (o,w), (w,o), and (o,o), where the first symbol corresponds to the particle surface, and w and o denote the hydrophilic and hydrophobic surfaces, respectively. Tc is the critical temperature of the mixture. The solid lines are the theoretical predictions (Eqs. (29) and (32)). The parameters obtained from the fitting are given in Refs. [59, 64].

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A. Ciach

experimental curves. The Debye length λD  10 nm was a fitting parameter, and it agrees with the parameters characterizing the mixture, although the number density of ions in the salt-free water–lutidine mixture could not be precisely measured. Unfortunately, the surface charges and selectivity were unknown. We required that the parameters characterizing each particle and each substrate are the same for all series of experiments. As can be seen from Fig. 12, the agreement is very good, except from the (o,o) BC, where ξ/λD  2 is not in the assumed range ξ/λD ≫ 1.

4.2 Effect of the Charge-Density Profile on the Near-Surface Concentration In this section, we discuss the effect of the charge distribution ρq(z) on the near-surface composition Φ(z), and then how the modified shape of Φ(z) influences the Casimir potential. We focus on the case ξ/λD < 1, concerning the experiment with extra salt [26]. We insert Eq. (22) in Eq. (28), and from the boundary condition (21) obtain ΦðzÞ ¼

H0 z=ξ  Bσ 20 e2z=λD , 1 e 1+ξ

(33)

where H0 ¼ h0 + ð1 + 2=λD ÞBσ 20 ,

(34)

3ðξ=λD Þ2 : ρ ion ð4ðξ=λD Þ2  1Þ

(35)

and for T  Tc B

By comparing (23) with (33), we can see that in the presence of charges the surface field h0 is renormalized, and the renormalized H0 depends on both, the surface selectivity h0 and the surface charge σ 0. The additional term in Eq. (33) has the same decay length as ρqð1Þ2 ðzÞ. The physical origin of the effect of ions on the concentration is the excess number density of ions near the charged wall that decays as ρð1Þ2 q ðzÞ [29] and the preferential solubility of the ions in the phase with Φ > 0. For ξ/λD < 1/2, the asymptotic decay of Φ(z) at large z is determined by the second term in (33). In such a case, Φ(z) > 0 for large z for both hydrophilic and hydrophobic surfaces, since  B > 0 for ξ/λD < 1/2. Moreover, it depends only on σ 0. This is because for ξ < z < λD/2 the effect of the surface selectivity is negligible, but there is excess number density of ions, and ions are soluble in water.

Competition Between Electrostatic and Thermodynamic Casimir Potentials

87

For ξ/λD > 1/2, the first term in (33) determines the behavior at large z. In the case of hydrophilic surfaces (with h0 > 0), jH0j > jh0j. In the case of hydrophobic surfaces (with h0 < 0), either jH0j < jh0j or the effective surface field changes sign, H0 > 0. H0 can be positive in the case of the hydrophobic surface when the surface charge is large, because B > 0 for ξ/λD > 1/2. Note that B ! 1 for ξ/λD ! 1/2. However, for ξ/λD ¼ 1/2 the decay rates of the two terms in (33) are the same, and the singularities in (33) cancel against each other. In order to understand why the weakly hydrophobic surface can act as an effectively hydrophilic, one recalls that near the hydrophobic surface an excess of oil in a layer of a thickness
ξ is predicted by the theory of critical adsorption [6, 10, 11, 65], and an excess number density of ions in a layer of the thickness λD/2 is predicted by the Debye–Hu¨ckel theory [29]. However, because of much lower solubility of the ions in oil than in water, a simultaneous excess of oil and of ions in a thick layer near the surface is associated with a large internal energy penalty. The distribution of the ions as well as the solvent composition near the surface must be a compromise between the bulk tendency to separate the ions from the oil, and the surface preference to attract both immiscible components. In Ref. [60], it was found that the key factor that determines the shape of Φ in a semi-infinite system is the parameter σ 20 =ðρ ion jh0 jÞ. If this parameter is large, then Φ(z) can be nonmonotonic, and near the weakly hydrophobic surface excess of water can occur. Thus, in the critical region the charged hydrophobic surface can behave as an effectively hydrophilic one. In the case of a slit with identical surfaces, the shape of Φ(z) can be qualitatively different from the concentration profile for charge-neutral surfaces. In particular, excess of water can occur in the center of the slit with hydrophobic surfaces. These strong effects of the charges again occur when the ratio between σ 20 =ρ ion and jh0j is large. The concentration profile in a semi-infinite system and in a slit with hydrophobic surfaces is shown in Fig. 13. Equation (29) for ξ/λD < 1 was investigated in detail in Ref. [56]. From this analysis, it follows that the strongly hydrophilic and hydrophobic surfaces show opposite trends. The strongly hydrophilic surface always leads to more attractive, and the strongly hydrophobic one always leads to more repulsive potential if the surfaces become charged. This is because the hydrophilic ions near the surface enhance the effect of the hydrophilicity and compete with the hydrophobicity of the surface. When the surface charge and selectivity of the two confining surfaces are both much different, then the total potential can be qualitatively different than in Eq. (1).

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A. Ciach

0.4 0.3 0 kx

0.2 Φ

Φ

0.4 0.6 0.9

0.1 0

–0.002

L 15 20 30 40

–0.1 –0.2 –0.004

1

2

3 kz

4

5

0

0.2

0.4

0.6

0.8

1

z/L

Fig. 13 The excess concentration of the inorganic components in the case of hydrophobic walls. The dimensionless number density of ions and the inverse screening length are ρ ion ¼ 103 and κ ¼ λ1 D ¼ 0:1. Left: a semi-infinite system approximated by Eq. (33). The dimensionless charge density and the surface field are σ 0 ¼ 0.007 and h0 ¼ 0.05, respectively. Right: a slit with identical hydrophobic walls. The dimensionless surface charge, surface field, and the correlation length are σ 0 ¼ 0.025, h0 ¼ 0.4, and ξ ¼ 6, respectively. From the top to the bottom line, the width of the slit is L ¼ 15,20,30,40. The length unit is the molecular size a.

Attraction can be present when both terms in (1) are repulsive, and repulsion can be present when both terms in (1) are attractive. The effective interaction may have opposite sign than predicted by Eq. (1) when one of the two surfaces is weakly hydrophobic and strongly charged. Because the hydrophilic ions attracted by the charged surface induce excess of water, such a surface behaves as a hydrophilic one, by which the sign of the Casimir potential changes. In the case of weak electrostatic interaction, the Casimir potential can dominate. In Fig. 14, the potential between like-charge hydrophilic and hydrophobic surfaces obtained by a numerical solution of the full EL equations is presented. The obtained potential is in close similarity with the experimental results [26]. Far from and close to the critical temperature the repulsion occurs, whereas for ξ/λD  1 an attractive well appears. Fitting of the experiments to our theoretical prediction has not been attempted yet. The unequal solubility of the anion and the cation in water, neglected in this theory, may play some role and influence the quantitative results.

5. CRITICAL MIXTURE WITH ANTAGONISTIC SALT In this section, we present results obtained in Ref. [60] within the mesoscopic theory outlined in Section 3 in the case of antagonistic salt added

89

Competition Between Electrostatic and Thermodynamic Casimir Potentials

(o,w) BC 2 × 10−6 kx

bY

9.12 2.88 0.912 0.288

0

2

4

6

8

kL

Fig. 14 The effective potential per microscopic area, βΨ/a2, obtained numerically from the full EL equations by Pousaneh [64]. h0 ¼ 0.16, hL ¼ 1.2, σ 0 ¼ 0.03, σ L ¼ 0.0001, κ ¼ λ1 D ¼ 0:04, and ρ ion ¼ 0:006. The length unit is the molecular size a. Note the repulsive potential far and very close to Tc, and attraction for intermediate temperatures (ξ/λD  1), in agreement with experimental results [26].

to the critical mixture of water and organic liquid. First, we discuss the bulk properties, and next the effects of confinement.

5.1 Bulk Properties We consider the excess grand potential ΔΩ associated with mesoscopic fluctuations of the concentration, number density of ions, and the charge density in a critical mixture with antagonistic salt. In the mesoscopic theory described in Section 3, ΔΩ defined in Eq. (11) and minimized with respect to the number density of ions ρion takes the form [60]





βΔΩ½Φ ðkÞ, ρ q ðkÞ ¼

1 2

Z



dk h
C ΦΦ ðkÞ Φ ðkÞ Φ ðkÞ d V ð2πÞ

i





+ 2C Φq ðkÞ Φ ðkÞρ q ðkÞ + C qq ðkÞρ q ðkÞρ q ðkÞ , (36)








where terms of higher order in Φ ðkÞ, ρ q ðkÞ are neglected, f ðkÞ denotes a


Fourier transform of f(r), Φ ðkÞ is the Fourier transform of the fluctuation of


the concentration, ΦðrÞ  Φ, and the elements of the matrix C ðkÞ are given

90

A. Ciach


in Ref. [60]. For ρ q ðkÞ ¼ 0, Eq. (36) reduces to the standard Landau functional for the mixture with the upper critical point. According to the density functional theory [66], the correlation func





tions are given by G ðkÞ ¼C ðkÞ1 . For the concentration–concentration correlations, the result obtained in Ref. [60] is 
2 2 G ΦΦ ðkÞ ¼ ξ T  1 + ξ k 1 


2

aN 2 2 λD k + aD

1 ,

(37)

where T* ¼ kBT/J, aN ¼

T  ρ ion λ2D ð1  ρ ion  Φ 2 Þð1  Φ 2 Þ

(38)

ð1  ρ ion  Φ 2 Þ : ð1  Φ 2 Þ

(39)

and aD ¼

Our formula (37) is very similar to Eq. (2) obtained in Ref. [51] in a phenomenological theory. The k-dependence is the same, but our expression for aN is somewhat different, and in Ref. [51] aD ¼ 1. In our theory, aD ¼ 1 is valid for dilute electrolyte solutions, while for higher ionic strengths aD differs from unity. The applicability of our formula for a broader range of ionic strengths is one of the advantages of the present theory. In fact, the experimental results [40, 41] fit better to Eq. (37) than to Eq. (2). We should stress that in our theory, ξ is equal to the correlation length in the
system with suppressed charge waves, ρ q ðkÞ ¼ 0, and differs from the correlation length in the presence of the charge waves.
βΔΩ in Eq. (36) can be minimized with respect to ρ q ðkÞ because





C qq ðkÞ > 0. At the minimum, ρ q ðkÞ ¼


C Φq ðkÞ



C qq ðkÞ

Φ ðkÞ and the functional takes

the form 1 βΔΩ½Φ ¼ 2

Z




dk V

ð2πÞ

d







Φ ðkÞG 1 ΦΦ ðkÞ Φ ðkÞ:

(40)

When we limit ourselves to the most probable concentration waves, with the wavenumbers near the maximum of the structure factor, k ’ k0 > 0, then we can make the approximation

Competition Between Electrostatic and Thermodynamic Casimir Potentials

 
2 2 2 , ðkÞ ’ c t + ðk  k Þ 0 G 1 0 ΦΦ

91

(41)


1 pffiffiffiffiffiffiffiffiffiffi ðk0 Þ and cT  ¼ λ2D = aN aD . We took into account that where ct0 ¼ G ΦΦ


2 2 G 1 ΦΦ ðkÞ is a function of k and truncated the Taylor expansion in k about the extremum at k20 at the second-order term. In Ref. [60], it was shown that the maximum of the structure factor satisfies pffiffi a 1 2 (42) : k0  D ’ λD ξ λD ξ

The most probable wavenumber of the concentration wave is equal to a geometric mean of the inverse correlation length in the uncharged system, and the inverse screening length. This relation allows for a quick verification if mesoscopic inhomogeneities (k0
2π/10 nm1) can occur in the investigated experimental system.


Note that the functional (40) with G 1 ΦΦ ðkÞ approximated by (41) has the same form as the Landau–Brazovskii functional [67] with terms of higher order in Φ neglected. The Landau–Brazovskii functional was successfully used for a description of the structure of systems containing amphiphilic molecules [68–70], and recently for the colloidal self-assembly [63]. In each case, the physical interpretation of the order-parameter Φ is different. In particular, in the case of ternary surfactant mixtures Φ is interpreted as a concentration difference between the polar and nonpolar components, in close analogy with the present case where Φ is a concentration difference between the inorganic and organic components. From Eq. (41), we can easily obtain the approximate expression for the correlation function in real-space representation [71],

 λ 2πr r=ζ , (43) GðrÞ ¼ sin e 2πr λ where the dimensionless correlation length and period of the exponentially damped oscillatory decay, ζ and λ, are given in Ref. [60]. ζ differs from ξ and diverges in our MF theory at the boundary of stability of the disordered phase, t0 ¼ 0. Moreover, λ  2π/k0; the equality holds when t0 ¼ 0. Beyond MF, however, ζ remains finite [67]. The similarity between our system and ternary surfactant mixtures was confirmed by the agreement of the experimental results for the former and the formulas developed for the latter case [41]. We have shown that

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starting from a simple microscopic density functional theory, one can obtain by a systematic coarse-graining procedure the same Landau–Brazovskii functional, Eqs. (40) and (41) that describe the amphiphilic systems.

5.2 Effects of Confinement In this section, we discuss the linearized EL equations (20) for the critical concentration Φ ¼ Φ c and calculate Φ  Φ  Φ c . Equation (20) can be written in the form [60] r2 r2 ΦðrÞ + a2 r2 ΦðrÞ + a0 ΦðrÞ ¼ 0

(44)

and ρq ðrÞ ¼

 ð1  ρ ion Þ  2 ξ0 ΦðrÞ  r2 ΦðrÞ , T

(45)

where r2 denotes the Laplacian, 2 a2 ¼ ðaN  aD Þλ2 D ξ

(46)

a0 ¼ aD ðξλD Þ2 :

(47)

and

The solution of (44) in a slit is a linear combination of the expopffiffi pffiffi nential terms expð λi zÞ. In Ref. [60], it was found that for ð aN  aD Þ < pffiffi pffiffi ðλD =ξÞ < ð aN + aD Þ the λi are complex conjugate numbers, for λD =ξ > pffiffi pffiffi pffiffi pffiffi ð aN + aD Þ both λi are real, while for ðλD =ξÞ < ð aN  aD Þ (i.e., t0 < 0 in (41)) both λi are imaginary. In the latter case, Φ(z) and ρq(z) are oscillatory functions. Because λ1 ¼ λre + iλim and λ2 ¼ λre iλim are complex conjugate numpffiffi pffiffi pffiffi pffiffi bers for ð aN  aD Þ < λD =ξ < ð aN + aD Þ, the concentration profile in a semi-infinite system has the form ΦðzÞ ¼ A cos ðλim z + θÞeλre z ,

(48)

with similar damped oscillatory decay of ρq(z). Similar behavior is obtained for the effective potential between confining surfaces, ΨðLÞ ¼ C cosðλim L + θÞeλre L ,

(49)

where the expressions for the amplitudes and λim,λre are too long to be given here.

93

Competition Between Electrostatic and Thermodynamic Casimir Potentials

pffiffi pffiffi For λD =ξ > ð aN + aD Þ, the two decay rates λ1,λ2 approach ξ1 and λ1 D only for low ionic strength, aD  1, and away from the critical point, ξ/λD ! 0. In this limit, Φ and ρq take the forms (23) and (22), respectively. For small surface charges, surface fields, and ion concentrations, and for temperatures far from the critical point, the above linear theory agrees very well with the numerical solutions of the full EL equations discussed in Section 3. Figure 15 shows the appearance of the periodic structure upon approaching the critical point. For bigger surface charges and surface fields, the linear theory differs significantly from the numerical results; however, the qualitative agreement is preserved. In Fig. 16, the effective potential per microscopic area a2 between identical surfaces obtained in the linearized and the nonlinear theory is presented. When the critical point of the binary mixture is approached, an oscillatory force between the surfaces is seen (Fig. 16, right). For all the considered cases, qualitative agreement between the linear theory and the numerical results was obtained. The potential between surfaces of area 400 nm 400 nm  106a2 is 6 10 Ψ(L). Note that for such a mesoscopic surface, the first two extrema in

0.02

Φ

0.01

0

–0.01

0

100

50

150

z

Fig. 15 The dimensionless concentration profile in a slit. Solid lines correspond to numerical solutions of the full EL equations discussed in Section 3 (for explicit forms of the EL equations, see Appendix A of Ref. [60]), while dashed lines show analytic solutions of Eq. (44). The dimensionless surface field, surface charge, screening length, and number density of ions are h ¼ 0.001, σ ¼ 0.001, λD ¼ 10, and ρ ion ¼ 0:005, respectively. jT/Tc  1j ¼ 0.002 (thin curves) and jT/Tc  1j ¼ 0.005 (thick curves). The length unit in the above quantities and for a distance from the left wall z is the microscopic length a  0.4 nm.

A. Ciach

1 × 10−5

1 × 10−5

5 × 10−6

Ψ[kBTc]

Ψ[kBTc]

94

0 0 0

20

40

60 L

80

100

0

50

100 L

150

200

Fig. 16 The effective potential per microscopic area a2 between two identical surfaces. Solid line corresponds to numerical solutions of the full EL equations discussed in Section 3, and dash line corresponds to Eq. (49). The dimensionless surface field, surface charge, screening length, and number density of ions are h ¼ 0.001, σ ¼ 0.001, λD ¼ 15, and ρ ion ¼ 0:005, respectively. The length unit in the above quantities and for the distance L between the walls is the microscopic length a  0.4 nm. (Left) jT/Tc  1j ¼ 0.005 and (right) jT/Tc  1j ¼ 0.002.

Fig. 16 are both of order of kBT. Potentials of such a small strength have been already measured experimentally [25, 26]. The difficulty in experimental verification of the oscillatory potential is due to a very narrow temperature range where such oscillatory potential is predicted (see Fig. 16).

6. SUMMARY We have presented the mesoscopic theory for confined critical mixtures with addition of ions developed in Refs. [54–56, 59, 60]. The theory has been developed from a microscopic density functional theory for a fourcomponent mixture by a systematic coarse-graining procedure described in Section 3. Such a strategy turned out to be successful for both the inorganic and the antagonistic salt. In derivation of the theory, the compressibility of the mixture was neglected. Moreover, it was postulated that all components interact with the van der Waals potentials, but it matters only if the component is organic or inorganic. With this assumption, the order parameter for the phase separation, Φ, is the concentration difference between the inorganic and organic components. We have postulated that the entropy has a form of the ideal entropy of mixing of a four-component mixture. After minimization of the grand potential with respect to the number density of ions, a functional of two fields, Φ and the number density of charge, ρq, was obtained.

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Our theory is similar to the phenomenological theory initiated by Onuki and Kitamura [51], but there are also significant differences. In the phenomenological theory, the van der Waals interactions between the ions are neglected, and the entropy of the four-component mixture is approximated by a sum of the entropy of the two two-component subsystems (binary solvent and ions). For this reason, the coupling between the two subsystems beyond the postulated bilinear term is not taken into account. When only the bilinear ion–solvent coupling is present, the term ∝ ρ2q Φ that plays a crucial role in our theory for the inorganic ions (see (24)) is absent. In our theory, this term comes from the entropy of a four-component mixture and is well justified. The linearized EL equations for Φ and ρq are coupled in the case of the antagonistic salt and decoupled in the case of the inorganic salt. In the absence of the coupling of the linearized EL equations, the decay lengths of Φ and ρq are the correlation length ξ and the screening length λD, respectively. In the presence of the coupling, the decay of both Φ(z) and ρq(z) is given by the decay lengths 1/λ1,1/λ2 that differ from ξ and λD. Another important consequence of the coupling between Φ and ρq in the linearized theory is the lack of a qualitative difference between the solutions of the linearized and nonlinear EL equations in the case of the antagonistic salt. In our theory for the inorganic salt, qualitatively different results in the linearized and nonlinear theories have been obtained [55, 56]. Beyond the linearized theory for the inorganic ions, the charge and concentration profiles influence each other in a very significant way. The effect of Φ on ρq dominates for ξ ≫ λD. The potential between the surfaces has the form (29) with the same decay lengths as in the simple sum of the Casimir and DH potentials (1), but with the amplitudes both depending on ξ/λD and on the surface properties. The potential was successfully fitted to the experimental results (Fig. 12). For ξ ≪ λD, the charge distribution influences the concentration very strongly, because the excess number density of hydrophilic ions enhances the effect of the surface field h0 in the case of the hydrophilic surface, and competes with h0 in the case of the hydrophobic surface. If the effect of preferential solubility of ions in water is much stronger than the selectivity of the surface due to the short-range wall–fluid interactions, then an excess of water can occur near the charged hydrophobic surface. Because the ions lead to a change of the hydrophobic surface into a hydrophilic one, spectacular violation of (1) is found when one surface is weakly hydrophobic and strongly charged, and the other surface is weakly charged and strongly

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selective. The origin of the violation of (1) is the effectively hydrophilic nature of the strongly charged and weakly hydrophobic surface. If the second surface is strongly hydrophilic and weakly charged, we obtain attraction, although both terms in (1) are repulsive. Such unexpected behavior was observed experimentally in Ref. [26]. The experimental results and our predictions (Fig. 14) agree on a qualitative level. If the second surface is weakly charged with opposite sign and it is strongly hydrophobic, we obtain repulsion, although both terms in (1) are attractive. Future experiments should verify this prediction. In the case of the antagonistic salt, a mesoscopic functional of the Landau–Brazovskii form, (40) with (41), has been derived. A functional of the same form was successfully applied to amphiphilic systems [69, 71]. Thus, our theoretical result and the experimental observations of similarity between the mesoscopic structure induced by amphiphiles and antagonistic salt [41] are complementary. We predict oscillatory effective potential, but such a behavior is expected only very close to the critical point (Fig. 16). The effect of very small amount of solute should be independent of its kind. Our functionals for the inorganic and antagonistic salt, however, differ significantly from each other. Nevertheless, we have verified that for small amount of ions and not very close to the critical point (for example for ρion ¼ 0.001 and jT/Tc  1j ¼ 0.005), the effective potential between parallel external surfaces has essentially the same form for the inorganic and antagonistic salt. For larger ρion, a quantitative difference between Ψ(L) in the presence of the inorganic or the antagonistic salt can be seen (Fig. 17). Qualitatively different shapes of Ψ(L) are obtained if the correlation length is sufficiently large compared to the period of the concentration oscillations. The same amount of antagonistic salt leads to a deeper minimum of the effective potential at shorter separation than in the case of the inorganic salt, and the repulsion barrier occurs. This shape of the potential may occur when ρion is big enough, and the critical point is approached (Fig. 17). The general version of the theory is applicable to various types of ions, but the unequal solubility of the anion and the cation in water is neglected in the approximate theories developed in Refs. [54–56, 59]. In order to investigate this effect in the case of KBr used in Ref. [26], in future studies one should remove the simplifying assumption that all the inorganic species interact with the same van der Waals forces. We conclude that effective interactions between weakly charged colloid particles immersed in a near-critical mixture with ions can exhibit very rich behavior. As a result, the particles can form different types of structures.

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2 × 10−5

Ψ[kBTc]

Ψ[kBTc]

2 × 10−5

1 × 10−5

1 × 10−5

0

0 0

100

50 L

0

100

50 L

Fig. 17 Effective potential between identical surfaces obtained from numerical solutions of the full EL equations discussed in Section 3. Solid lines correspond to the mesoscopic theory for the antagonistic salt, while the dash lines show the results of the mesoscopic theory for hydrophilic ions [56, 59]. The dimensionless surface field, surface charge, screening length, and number density of ions are h ¼ 0.001, σ ¼ 0.001, λD ¼ 10, and ρ ion ¼ 0:005, respectively. (Left) jT/Tc  1j ¼ 0.005 and (right) jT/Tc  1j ¼ 0.002. The length unit in the above quantities and for the distance L between the walls is the microscopic distance a ¼ 0.4 nm.

Small changes of the amount of ions or temperature can lead to qualitative changes of the interactions between the particles. The sensitivity of the effective interactions to the thermodynamic state is a property that may allow for manipulating with the structure of colloids, and may play a significant role for the distribution of the membrane inclusions in the lipid bilayers in living cells.

ACKNOWLEDGMENTS I would like to thank Dr. Faezeh Pousaneh and Dr. Anna Maciolek for fruitful collaboration on the problems presented in this review. The financial support by the NCN grant 2012/05/ B/ST3/03302 is gratefully acknowledged.

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CHAPTER FOUR

Effect of Dendrimers and Dendriplexes on Model Lipid Membranes M. Ionov*,1, T. Hianik†, M. Bryszewska* *

Department of General Biophysics, Faculty of Biology and Environmental Protection, University of Lodz, Poland † Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 1 Corresponding author: e-mail address: [email protected]

Contents 1. Introduction 2. Carbosilane Dendrimers 3. Phosphorus Dendrimers 4. PAMAM Dendrimers 5. Conclusions Acknowledgments References

102 104 107 109 110 111 111

Abstract In the past decades, dendrimers have gained popularity in the field of biomedicine. Dendrimers are polymeric molecules with well-defined shape and size that can successfully be used in gene therapy, medical imaging, immunology, and primarily as nanocarriers for the delivery of drugs or genes to target cells. Dendrimers are more efficient than liposomes, linear polymers, or viral vectors in transferring of many kinds of biomolecules. In this regard, the mechanisms of interaction between dendrimers and cell membranes have now become of significant interest, with an abundance of articles now being reported in the literature. We will review this experimental work on the effect of different groups of dendrimers on artificial lipid membrane matrices. This will include studies on the biophysical interaction between lipid membranes and dendrimers that could help in improving the drug delivery applications.

ABBREVIATIONS CBD carbosilane dendrimers CPD cationic phosphorus dendrimer Dendriplex complex of dendrimer with ligand

Advances in Biomembranes and Lipid Self-Assembly, Volume 23 ISSN 2451-9634 http://dx.doi.org/10.1016/bs.abl.2015.12.001

#

2016 Elsevier Inc. All rights reserved.

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DMPC 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine DPPG 1,2-dipalmitoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] DSC differential scanning calorimetry LUVs large unilamellar vesicles PAMAM polyamidoamino (dendrimer) TEM transmission electron microscopy

1. INTRODUCTION One of the major limitations in many therapies against different diseases is an inability of the drugs to cross negatively charged cell membranes. Moreover, the transfer of active biomolecules into cells can be hampered by their low solubility in water and high toxicity [1,2]. To improve the bioavailability of drugs, synthetic carriers are now being more efficiently employed [3–5]. Recently, many reports suggest using of nano-polymers to transfect a whole range of cell types [6–8]. Drug molecules complexed with polymer or polymer nanoparticles can be delivered to target cell, and are then released from the complex. In some cases, the bioavailability of drugs is improved by complexation with carrier molecules. The most promising among a range of polymeric formulations seem to be dendrimers (Fig. 1), which are well-studied molecules with defined chemical structure and physical properties [9–14]. Different classes of dendrimers have now been synthesized and their biophysical properties carefully studied generally in the area of drug and gene delivery systems [15–17]. Dendrimers possess many biological activities and can interact with gene material, proteins, enzymes, peptides, and other biomolecules [18–20].

Fig. 1 Schematic drawing of dendrimer structure.

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Based on our own experiments, we have reported on the possible use of dendrimers as effective nonviral transfecting agents [21,22]. They can be used in immunotherapy against HIV-1 infection [23–25], prions [26], and Parkinson’s and Alzheimer’s diseases [27]. We have established the ability of dendrimers to deliver anticancer siRNA cocktails to Hela and HL-60 cancer cells [28,29]. However, the biomedical applications of dendrimers require the mechanism of their interactions with cell membranes to be understood. Because of the complex structure of biological membrane, it is difficult to explore the intricacies of dendrimer–cell membrane relations. Therefore, methods of simplifying the problem by using experimental models of membranes have usually been adopted, and many experiments have already been reported. The findings have shed some light on the possible effects of dendrimers on the artificial lipid membranes, which may provide some information on interactions between dendrimers and real cell membranes. Interactions have generally been studied on liposomes that have been prepared using a well-established extrusion protocol [30,31]. Large unilamellar vesicles (LUVs) of average diameter
100 nm were formed using the 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) as a main component of the liposomal lipid composition. DMPC was chosen because it is a synthetic analog of lecithin, the main component of biological membranes in the living cell. To explore the importance of membrane surface-charge density (surface potential), we added 1,2-dipalmitoyl-sn-glycero-3-[phosphorac-(1-glycerol)] (DPPG) to the lipid mixture. Thus, to prepare the negatively charged liposomes, mixtures of DMPC and DPPG phospholipids at selected molar ratios were used. Interactions between dendrimers and dendriplexes with lipid membranes were examined by the following biophysical methods: Differential scanning calorimetry (DSC) was used to analyze the thermotropic properties of the lipid bilayer in the presence of dendrimers [32]. Phase transition temperatures of lipids can be affected by dendrimers or their complexes with biomolecules (dendriplexes), and the character of these changes can give information about the effect of dendrimers on lipid membrane. Dynamic light scattering (DLS) technique was used to monitor the size of species formed during dendrimer–liposome interaction. The experiments determined the hydrodynamic diameter of the liposomes following their interaction with dendrimers or dendriplexes [33]. Phase analysis light scattering (PALS) was used to measure the zeta potential of the liposomes in the presence of dendrimers. The electrophoretic mobility of samples at the applied electric field gives information about the surface charge of the complexes formed [34,35].

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Spectrofluorimetry was used to measure steady-state fluorescence anisotropy of the probes embedded in the lipid bilayer of liposomes. Membrane fluidity was examined with fluorescent probes (DPH and TMA DPH) located at different depths in the lipid bilayer [36–39]. These probes provide time-averaged information on the structure and dynamics of the hydrophobic and hydrophilic regions of the liposomal membrane in the presence or absence of dendrimers. Langmuir–Blodgett technique was used to monitor interactions between dendrimers or dendriplexes and lipid monolayers. Homogeneous lipid films of accurate thickness were formed. Monolayers were assembled at an air– water interface composed of phospholipid molecules with hydrophilic heads and hydrophobic tails [40–42]. This method gives information on dendrimer–lipid monolayer interactions and makes it possible to explore the role of surface charge. Transmission electron microscopy (TEM) was used to analyze the morphological characterization and size of liposomes interacting with dendrimers or their complexes [43]. The present review focuses generally on the aspects of the molecular mechanism of interaction of complexed and noncomplexed dendrimers with model lipid membranes. Here, we summarize our view on the perspectives of using dendrimers as carriers for biomolecules in drug delivery.

2. CARBOSILANE DENDRIMERS Among a wide range of nanoparticles representing drug carriers, the cationic dendrimers seem to be the most promising candidates to deliver the bioactive molecules into cells [44–47]. Positively charged dendrimers form complexes with nucleic acids, peptides, and numerous drugs by binding to positively charged surface groups [48]. In a class of cationic dendrimers, carbosilane dendrimers (CBD) are of special interest. CBDs have been synthesized with the aim of using them in DNA and RNA delivery systems [49–51]. Shcharbin et al. [45] found that CBDs form complexes with siRNA. The ability of CBDs to deliver the HIV-derived peptides has been reported [52]. Interactions between dendrimers and peptides or genes are electrostatic in nature due to the negative charge of complexed biomolecules and positively charged surface groups of dendrimers. CBDs can form stable complexes with biomolecules, allowing their time-dependent release after 4 and 24 h [53]; they showed good toxicity profiles in primary cell lines [54]. The ability of CBDs to protect the peptides and oligonucleotides from

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degradation has also been noted [47,55]. We are discussing here the CBDs of second generation with carbon–silicon bonds (CBD-CS) or oxygen–silicon bonds (CBD-OS), focusing on interactions between these dendrimers, along with their complexes with HIV-derived peptides or siRNAs [43,56–58], and model lipid membranes. The different lipid composition of liposomes formed with DMPC and DPPG phospholipids modifies the surface charge of the LUVs, which is important in dendrimer–membrane interactions. For liposomes purely made of DMPC, the presence of dendrimers did not change the particle size due their neutral charge, suggesting weak interactions between dendrimers and DMPC membranes. For the vesicles prepared from DMPC/DPPG lipid mixture or from pure DPPG, the average size of liposomes significantly increased on addition of dendrimers, an effect that was more pronounced for LUVs containing pure DPPG. This suggests that positively charged CBD-CS and CBD-OS interact strongly with negatively charged lipid membrane. Increase in liposome size can be explained by formation of the liposome–dendrimer aggregates. The physical properties of the liposome bilayer were modified by dendrimers under these conditions. The presence of CBDs in liposomal suspension also altered the surface charge of vesicles, which increased the zeta potential to positive values for all lipid formulations that were examined. The presence of dendrimers increased the surface charge of the lipid vesicles in a similar manner, and the changes did not seem to depend on the initial zeta potential of liposomes of different lipid compositions. Dendriplexes (complexes of siRNA with dendrimers) affect the size and zeta potential of phospholipid vesicles [56]. Adding CBD-OS/siRNA dendriplexes significantly increased the zeta potential of membranes of pure DMPC, DPPG, or DMPC–DPPG mixtures. In contrast, the presence of CBD-CS/siRNA dendriplexes in liposomal suspension changed zeta potential values in the opposite direction leading to a gradual decrease in surface charge of LUVs. Taking into account the different nature of our dendrimers, we proposed the scheme shown in Fig. 2 to explain the differences between the effect of CBD/siRNA dendriplexes on liposomal bilayer. The effect of dendriplexes formed by dendrimers with HIV-derived peptides on LUVs has also been explored. The ways in which these dendriplexes (dendrimer/HIV peptide) affect the physical properties of lipid membranes has been reported [43]. Interestingly, the naked peptides did not significantly change the parameters measured in lipid bilayer. In contrast, peptides complexed with positively charged dendrimers affected fluidity, size, and surface charge of liposomes prepared from DMPC or DMPC–DPPG mixtures due to

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Dendrimer

−

siRNA

−

+ +

+

− CBD-CS

CBD-OS

Fig. 2 Scheme of possible interactions between CBD-CS/siRNA or CBD-OS/siRNA dendriplexes and negatively charged liposome bilayers. Modified from Ref. [56] with permission from Elsevier.

the strong adsorption of positively charged peptide–dendrimer complexes at the liposome surface. For LUVs containing negatively charged DPPG, the mean diameter and surface charge increased markedly, suggesting that these CBD-CS and CBD-OS dendriplexes interact mostly with negatively charged components of the lipid membrane. These findings show the importance of membrane lipid composition in the interactions between dendriplexes and lipid bilayer. Studies on monolayers show the increase in surface pressure for all the examined lipid formulations treated with dendriplexes, but not with naked peptides, corroborating the results obtained by fluorescent anisotropy [43]. TEM images of the liposomes show that the morphology of lipid vesicles was affected by presence of dendriplexes, indicating that HIV peptide–dendrimer complexes do interact with liposomal membranes (Fig. 3). For all lipid formulations, liposome morphology was changed by the presence of dendriplexes. In the case of DMPC, driplexes unattached to liposomes were seen, confirming previous results of the weak interactions between dendrimer–peptide complexes and the neutral bilayer. Recent results show that CBDs have the potential to deliver siRNA and HIV-derived peptides to their targets. We propose that they can also be used as carriers for other anionic biomolecules. HIV peptides and siRNAs complexed with CBDs interact with negatively charged model lipid membranes. However, these dendrimers and dendriplexes did not significantly affect LUVs composed of DMPC. These data suggest that CBDs contact DMPC membranes in random manner. In contrast, negatively charged lipid formulations interact electrostatically with CBD-CS and CBD-OS by attaching the dendrimers to the negatively charged membrane surface, which induces the formation of large liposome aggregates. Analyzing the results, we suggest that CBD-CS is a better at delivering negatively charged biomolecules to target cells. This dendrimer not only gives better bioavailability of biomolecules but also more stable in water when compared with SBD-OS.

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Fig. 3 TEM images of DMPC liposomes. (A) The same liposomes treated with [p24/CBDCS] dendriplex. (B) Magnification  100,000; bar ¼ 100 nm. According to Ref. [43] with permission from Elsevier.

3. PHOSPHORUS DENDRIMERS There are many kinds of dendrimers that can be used efficiently in nanotechnology and biomedicine. Among them, the cationic phosphorus dendrimers (CPD) are well-studied cationic nanoparticles that have high pharmacological potential [59,60]. The potential use of these dendrimers in gene therapy against HIV infection has been reported [23,61]. Phosphorus dendrimers can affect the Alzheimer’s protein aggregation [19,27], and their antimicrobial and antifungal properties have also been recognized [62]. CPDs can be used as efficient nonviral transfecting agents [21,23]; their ability to deliver siRNAs to cancer cells has been reported [28,29]. Phosphorus dendrimers have a hydrophobic backbone and a hydrophilic surface that allows them to penetrate efficiently lipid membranes [21,63]. These dendrimers have on their surface protonated terminary amine end-groups, the

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number depending on the dendrimer generation [26]. The main characteristics and synthesis of CPD-G3 (48 surface end-groups, generation 3), and CPD-G4 (96 surface end-groups, generation 4) have already been described [64]. To use them as drug carriers requires an understanding of how they interact with biological membranes. Many drug delivery systems including dendrimers have been examined by thermal analysis [32]; calorimetric analysis of phosphorus dendrimers was made with multilamellar membrane models. Effects of CPD-G3 and CPD-G4 dendrimers on the DMPC lipid systems were different. Adding dendrimers significantly changed the main transition enthalpy and phase-transition temperature of lipid multilayers. The pretransition peak was also affected, suggesting that dendrimer molecules interact both with polar head regions and the hydrophobic part of lipid membranes. Both dendrimers altered the thermotropic behavior of the membranes in a dose-dependent manner by affecting the melting cooperativity, confirming the findings of Demetzos [65] and Gardikis et al. [66]. These authors showed that dendrimers interact with model lipid membranes, and are dependent on dendrimer concentration and generation. The effect of phosphorus dendrimers on negatively charged lipid (DMPC/DPPG) membranes was more pronounced, an increase in membrane fluidity being detected. This could be explained by the negative charge of membrane surface, promoting a stronger effect of dendrimers through electrostatic interactions. In both cases for neutral and positively charged lipid formulations it is noteworthy that the thermotropic properties of membranes were affected by lipidphase separation [67], which has never been recorded, even in high dendrimer/lipid molar ratios [68]. The zeta potentials of neutral or negatively charged liposomes after addition of phosphorus dendrimers are significantly positive. The hydrodynamic diameter of LUVs increased in the presence of CPDs, mostly CPD G3, suggesting that generation of dendrimers is involved in dendrimer– membrane interactions [68]. We previously noted (not published data) that CPD dendriplexes (complexes of phosphorus dendrimers with HIV-derived peptides) interact well with LUVs composed of DMPC or DMPC–DPPG mixtures. The presence of CPD-G3 or CPD-G4 affects liposome morphology as seen by TEM. A similarity between results obtained for CBDs and phosphorus dendrimers has also been found. Thus, both CBD and CPD dendrimers interact better with negatively charged lipid systems. These results show that dendrimers interact with neutral membranes in a random contact manner. In contrast, negatively charged LUVs led to electrostatic

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interaction of positively charged dendrimers with hydrophobic part of the membrane. The results in Ref. [68] suggest a higher mixing affinity of the CPDs in the liquid-crystalline phase, and this may be of particular importance, indicating that phosphorus dendrimers can be used in the incorporation of molecules with low therapeutic index, for example, doxorubicin [69].

4. PAMAM DENDRIMERS Polyamidoamino (dendrimer) (PAMAM) dendrimers, first synthesized in Tomalia’s group, have been proposed as low toxic, highly efficient cationic carriers for the delivery of drugs or genes to different kinds of cells [70,71]. In a wide group of dendrimeric nanoparticles that are commercially available, PAMAMs are hyperbranched polymers with sufficient biodegradable profile that allow controlled drug release [72]. Moreover, PAMAM dendrimers have weak binding properties to transport proteins [72–74]. There are many reports on the mechanisms of interaction between PAMAM dendrimers and lipid vesicles. Thus, PAMAMs are the most studied dendrimers, but the mechanisms by which they penetrate lipid membrane remains unclear. Despite a rigid structure, the poly(amidoamine) dendrimers interact well with model membranes. In high dendrimer/lipid molar ratios, PAMAMs could form micelles that strongly affect the structure of liposomal membrane, while low dendrimer concentrations can lead to dendrimer penetration of the membrane [75–77]. PAMAM dendrimers can form pores in lipid bilayers, producing holes suggesting that dendrimers are internalized by the cells in the form of passive transport [78,79]. Penetration of dendrimers across the lipid bilayer depends on their generation and size; larger generations and concentration of dendrimers lead to increase in bilayer damage due to holes being produced [78,80]. Wang et al. [80], analyzing molecular simulations, suggested that PAMAM dendrimers are inserted into the cell without the formation of pores. Others have also reported that interactions between PAMAM dendrimers and lipid membranes made of zwitterionic lipids are hydrophobic in nature [81,82]. These associations might be due to the interactions between lipid acyl chains and the hydrophobic cores of dendrimers [78]. NMR studies [83] indicate that some PAMAMs dendrimers are thermodynamically stable in the membrane interior and do not alter the membrane head groups, in agreement with data suggesting hydrophobic interactions of incorporated dendrimers with lipid tails of the membrane. In contrast, other reports [1,84] suggest that negatively charged lipid

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membranes interact electrostatically with cationic PAMAMs by binding of positively charged dendrimers to the negative surface of LUVs, with the formation of larger liposomal aggregates. Descriptions of mechanisms of entrance of PAMAMs complexed with DNA into the cells suggest that incorporation of dendriplexes might be accomplished through passive transport due to membrane perturbations caused by the interactions of dendrimers with the membrane or some endocytotic activity [85,86]. On the basis of the data, we have discussed, it is possible to conclude that dendrimers alone and those complexed with different kinds of biomolecules can interact with lipid bilayer in different manners; these interactions are strongly dependent on the kind of dendrimer and lipid composition of the membrane.

5. CONCLUSIONS The reviewed data could lead to a better understanding of the advantages of combining drugs and polymer nanoparticles (dendrimers) to create and improve novel and efficient drug formulations. Knowledge of interactions between dendrimers and model membranes are of a high importance because they can be considered as the earliest interplay of dendrimer/biomolecule formulations with cells following drug administration. For pharmaceutical investigations, appropriate biological membranes should be considered; however, some simplification leads to a better understanding of the mechanisms of interaction of dendrimers and their complexes with biomolecules with cells. Model membranes are the most common tools for the research of molecular interactions characterized by lipid arrangement that can mimic lipid organization in biological membranes. The presence of drug molecule may well affect the physicochemical properties of lipid bilayers. Some amphiphilic molecules can induce detergent-like effects on lipid bilayers that lead to membrane degradation and malfunctioning. Examination of the different interactions between membrane models and dendrimers show that dendrimers interact strongly with membranes but do not necessarily destroy them. The importance of the electrostatic behavior of dendrimer or dendriplex interaction with model lipid systems has been emphasized. This interaction of cationic dendrimers or dendriplexes with neutral membranes is due to casual contacts leading to disturbances in the hydrophobic

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domains of bilayer, whereas significant effect on negatively charged lipid membranes is due to electrostatic interactions between negatively charged membranes and cationic dendrimers/dendriplexes. In conclusion, succinctly the data suggest that some of the dendrimers we have discussed can be considered as carriers for delivery of drugs or another biomolecules into target cells.

ACKNOWLEDGMENTS Research was supported by the Polish-Slovak 2013–2014 bilateral cooperation project. Conflict of Interest: The authors declare that there is no potential conflict of interest relevant to this chapter.

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CHAPTER FIVE

The Membrane Bending Modulus in Experiments and Simulations: A Puzzling Picture D. Bochicchio*, L. Monticelli†,1 *Physics Department, University of Genoa, Genoa, Italy † Molecular Microbiology and Structural Biochemistry (MMSB), University of Lyon, CNRS UMR 5086, Lyon, France 1 Corresponding author: e-mail address: [email protected]

Contents 1. Introduction 2. Experiments 2.1 Experimental Techniques 2.2 Experimental Values 3. Simulations 3.1 Computational Techniques 3.2 Bending Modulus from Atomistic Simulations 3.3 Bending Modulus from Coarse-Grained Simulations 4. Discussion and Conclusions References

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Abstract The bending modulus is one of the most important material properties of lipid membranes, playing an important role in a number of biological processes including exo- and endocytosis, vesicle fusion, and the regulation of membrane protein activity. Different experimental techniques have been developed to estimate the bending modulus of simple lipid membranes, but unfortunately they provide different results for the same lipid membranes in very similar conditions. Similar issues have been found in simulations, where different methods (and different energetic models) provide different results. In this review, we collect results from both experiments and simulations, and discuss possible reasons for the discrepancies among different techniques.

1. INTRODUCTION The lipid bilayer is the base structure of the cell membrane of every living organism. It is a self-assembled object that can be considered as Advances in Biomembranes and Lipid Self-Assembly, Volume 23 ISSN 2451-9634 http://dx.doi.org/10.1016/bs.abl.2016.01.003

#

2016 Elsevier Inc. All rights reserved.

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two dimensional, if observed on length scales larger than the lipids size. It has been shown that, in terms of elastic properties, the bilayer obeys a simple continuum theory characterized by a very small number of effective material parameters [1]. The bending modulus is a mechanical macroscopic constant that describes the tendency of a certain material to oppose bending. In the case of a lipid membrane, it is defined as the energy required to deform the bilayer from its intrinsic curvature to some other curvature, and is undoubtedly one of the most important properties of the bilayer. In fact, it is known to play an important role in many biological phenomena, including endocytosis [2], the organization of membrane trafficking [3], and membrane fusion [4]. Given the importance of this physical parameter, it is a shame to have to admit that measuring it is not easy at all. Many measurements have been performed in the past decades [5–19], resulting in a set of values often not consistent with one another. As recently pointed out by Nagle et al. [20], a correlation appears to exist between the experimental technique used to determine the bending modulus and the expected result, which raises major questions. Simulations also are somewhat problematic for similar reasons: different results have been obtained using different theories and algorithms. Moreover, the choice of the force field also affects simulation results. Let us define the bending modulus of a membrane more precisely. We refer to the theory of Helfrich, which is more than 40 years old [1]. If the membrane is modeled as a two-dimensional elastic sheet, the curvature energy per unit area can be expressed as E¼

Kc
ðc1 + c2  c0 Þ2 + kK 2

(1)

where c1 ¼ 1/R1 and c2 ¼ 1/R2 are the two main curvatures, c0 is the spontaneous curvature, K the Gaussian curvature, k
the Gaussian modulus, and Kc the bending modulus. If the membrane topology is fixed, the second term is constant, and if the bilayer is symmetric c0 is equal to zero. Thus, in the simplest case, the only parameter characterizing membrane rigidity is the bending modulus Kc, and the optimum configuration is the flat one. However, thermal undulations lead to local displacements. We can call u(r) the vertical displacement of each point of the membrane, identified by r, with respect to the horizontal plane of the flat membrane. These displacements can be expressed in terms of plane waves. Taking into account the membrane surface tension γ, and working in the reciprocal space, the power spectrum < juqj2 > dependence on the wavevector q can be derived, using the equipartition theorem [21]. The very famous result reads

The Membrane Bending Modulus in Experiments and Simulations: A Puzzling Picture

< juq j2 >¼

kB T , AðKc q4 + γq2 Þ

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(2)

with A being the area of a squared piece of membrane. Thus, in the case of vanishing (or negligible) surface tension, a simple q4 dependence is found. Since the only parameter left is Kc, this result gives rise to the most common experimental and numerical methods to determine the bending modulus from the thermal undulation spectrum. Although seemingly simple, measuring (or calculating from simulations) the undulation spectrum poses several practical problems. A different approach to derive the bending modulus consists in actively bending the membrane and measuring (or calculating) its response. The latter approach gives rise to different experimental and numerical techniques. The present review has three main objectives. Our first objective is to collect the values of Kc reported in the literature for single component lipid membranes, from both experiments and simulations. Second objective is to discuss why those values span a rather wide range (4–16  1020 J), highlighting, when possible, if there is a correlation between the technique and the value obtained. Third, we will discuss the similarities and differences between computational and experimental results on the bending modulus of single-component lipid membranes. The review is structured as follows. In the first section, we describe briefly the most commonly used experimental techniques, and resume the results of experimental measures. The second section focuses on the bending modulus values obtained from simulations. After a description of the main calculation techniques in use, we gather all the computational values of Kc we found in literature, and classify them in three tables according to the energetic model used in the simulations: atomistic, coarse grained (MARTINI [22]), and implicit solvent. In the final section, we discuss similarities and differences between the values found in the literature, and suggest ideas to interpret conflicting results.

2. EXPERIMENTS 2.1 Experimental Techniques The techniques to experimentally determine the bending modulus rely essentially on two different kinds of setup: giant unilamellar vesicles (GUVs) and bilayer stacks. GUVs are liposomes consisting of a single bilayer, with a diameter up to 100 μm, that can be formed in aqueous media in

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appropriate conditions (e.g., by using an alternate electric field [23]). The term “giant” is used to stress that GUVs are much bigger than liposomes formed with standard techniques, and this allows a direct observation by optical microscopy. The use of GUVs is in general preferred over bilayer stacks, because the latter are known to exhibit slightly different properties due the steric interactions between the layers [24]. In the present section, we briefly describe three methods: the Shape Fluctuation Optical Analysis, Micropipette Aspiration, and X-ray Scattering. All three methods are based on measuring deviations of the bilayers from the flat geometry due to thermal fluctuations, and on the assumption that the membrane curvature energy is given by Eq. (1). 2.1.1 Shape Fluctuations Optical Analysis The analysis of thermal fluctuations of a giant vesicle is based on the idea that the vesicle is a two-dimensional object that conserves its volume and area. Under these assumptions, a formula can be derived to express the amplitude of the thermal fluctuations, using spherical coordinates and spherical harmonics functions, as explained in the work by Faucon et al. [25]. The mean squared value of the fluctuations for a given spherical harmonic (defined by n and m) depends essentially on three quantities: the bending modulus Kc, the membrane surface tension γ, and the hydrostatic pressure p
, as indicated in the following: < jUnm ðtÞj2 >¼

kB T 1 Kc ðn  1Þðn + 2Þ½γ + nðn  1Þ + 2ð2γ  p
Þ

(3)

where kB is the Boltzmann constant and T the temperature. In practical cases, when the fluctuations are not too big and the quadratic approximation used in the derivation is still valid, the last term of the denominator can be omitted, being much smaller than the first one. Thus, in the simplified expression, only the mean surface tension γ must be known for deriving Kc. One way to obtain it is by recognizing that the product < jUnm ðtÞj2 > ðn  1Þðn + 2Þ½γ + nðn  1Þ ¼

kB T Kc

(4)

is independent of n, and can be calculated for different values of n. The only missing point is now how to relate the quantity < jUnm ðtÞj2 > to experimentally measurable quantities. This can be done by connecting it to the autocorrelation function of the vesicle radius [25], which can be calculated from

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Fig. 1 Two images of a fluctuating GUV at different times, obtained from phase-contrast microscopy. Reprinted with permission from [26].

the coordinates of the vesicle contour. The latter can be obtained directly from optical microscopy images (see Fig. 1), after digitalization. The shape fluctuation method is advantageous because it is not very demanding in terms of experimental setup and it does not require the addition of exogenous molecules into the membrane. The main disadvantage is that, since the membrane should exhibit well visible fluctuations, it cannot be applied in the case of high surface tension (e.g., vesicles in the gel phase) [27]. 2.1.2 Micropipette Aspiration The Micropipette Aspiration technique is a mechanical manipulation method introduced by Evans and Needham in the 1980s [28]. The experimental setup includes a large membrane vesicle and a small-caliber suction pipette. The vesicle is at first slightly deflated and then aspirated into the pipette. During the aspiration process, the volume encapsulated by the membrane remains constant. In these conditions, the change in length of the vesicle projection ΔL inside the pipette (see Fig. 2) is connected with a projected area expansion that has two contributions: a reduction of membrane undulations and a direct dilation of area per lipid. It can be demonstrated that the total area expansion, defined as Δa ¼ 1=2½ðRp =R0 Þ2  ðRp =R0 Þ3 ΔL=Rp ,

(5)

where Rp is the pipette radius and R0 the exterior vesicle radius, is a function of the membrane tension γ: Δa ¼

kB T γ ln ð1 + cγAÞ + , 8πKc Ka

(6)

where c is a coefficient assuming different values depending on the approximations used and Ka is the direct area expansion modulus (also known as

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A

10 μm

Tension ≈ 0.2 mN/m B

ΔL

Tension ≈ 6.2 mN/m

Fig. 2 Micrograph of a vesicle area expansion test. (A) The vesicle at low tension. (B) The vesicle at high tension. The change in projection length ΔL is related to the area subtracted to the vesicle undulations, and thus can be used to derive the bending modulus. Reprinted from [8], Copyright 2011, with permission from Elsevier.

area compressibility modulus). Thus, in the so-called low tension regime, the first term dominates and the slope of the logarithm of the tension versus the area expansion is proportional to the bending modulus Kc. To achieve a higher precision in measuring the length of the portion of vesicle aspirated in the pipette, the use of fluorescent dyes can be helpful. Unfortunately, fluorescent dyes (like most other impurities) can alter membrane elastic properties. Another problem of this technique stems from the possible adhesion of the membrane to the pipette: according to the theory, the membrane should slide freely along the walls. An appropriate coating of the pipette walls is therefore needed. Finally, significant amounts of sugars (sucrose and glucose) are typically added to the vesicle solution, to maintain constant volume. Again, there is a possibility that such sugars affect the rigidity of the membrane.

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2.1.3 X-ray Scattering The first use of X-ray scattering to derive the bending modulus of lipid membranes dates back to 1995 [29], and more recently the technique has been refined by Lyatskaya et al. [30]. In X-ray scattering, stacks of bilayers are mounted on solid substrates (usually glass, mica or silicon) and oriented with their normals aligned along one axis. What is measured is the scattered X-ray beam intensity obtained from bilayers with normal parallel to z, that can be written as IðqÞ ¼ SðqÞjFðqz Þj2 qz 1

(7)

where S(q) is a structure factor and F(qz) a form factor. The Kc value is contained in the expression of two parameters, the Caille parameter η1 and the in-plane correlation length ξ, which is given by ξ4 ¼ Kc =B,

(8)

with B being the inter-bilayer compressibility modulus. Membrane height fluctuations are coherent between layers for distances greater than ξ, while they are incoherent for smaller distances. Lyatskaya et al. showed how both η1 and ξ (and thus Kc) can be obtained from the dependence of S(q) on qr (in-plane wavevector) at large values of qz (regions of the data where the fluctuations and diffuse scattering dominate). In practice, two measures at two different qr are sufficient to determine Kc. However, the determination of S(q) requires pair correlation functions, not only between points in the same bilayer, but also between points in different bilayers, which requires some additional calculation [30].

2.2 Experimental Values In 2012, in its introductory lecture to the Faraday Discussion 161 (Lipids and Membranes Biophysics) [31], John Nagle tried to cast some light on the numerous discrepancies found in the literature about the value of the experimentally measured bending modulus. The focus was on the three techniques described in the previous section: Shape Fluctuation Analysis, Micropipette Aspiration and X-ray scattering. Values obtained with the tethers (or tube pulling) technique were reported too, but not discussed, since their number was too low to find any significant trend. The main conclusion of Nagle’s analysis was that values obtained from Shape Fluctuation Analysis tend to be higher than values obtained with Micropipette Aspiration, by a factor of about two [31]. However, some uncertainty remains

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about the results from Micropipette Aspiration, due to the possibility of artifacts. Indeed values obtained with the Micropipette Aspiration technique are generally significantly lower (softer membrane) than with all other techniques, and the softening could in principle be due to the presence of sucrose and glucose, typically used in the experiments. To investigate this point, Nagle et al. recently measured the bending modulus (using the X-ray scattering technique) of membranes in the presence of different concentrations of sucrose and glucose. Their conclusion was that glucose does not reduce the value of Kc, and sucrose probably neither [20]. If the effect of sugars is ignored, X-ray scattering and Micropipette Aspiration appear to agree on values of Kc that are smaller than the ones obtained by Shape Fluctuation Analysis. It is, however, important to note that all these methods rely on the assumption that the membrane is a thin sheet lacking any internal structure. This approximation is reasonable when one focuses on long wavelengths, but it breaks at length scales comparable to the bilayer thickness. In this second case, the internal degrees of freedom of each single lipid become important (e.g., lipid tilt, defined as the orientation of the lipid respect to the bilayer normal). Lipid tilt oscillations contribute to the undulation spectrum, adding a new term that scales as q2 and thus dominates at short wavelengths. For what concerns Shape Fluctuation Analysis, the typical wavelengths are of the order of 10 μm, and the surface tension is kept low (of the order of 104 mN/m); for such values, the effect of tilt on the fluctuation power spectrum should be negligible, and the analysis should give the correct value of Kc [20]. As for X-ray scattering, the situation is different. The undulations of bilayers in a stack are constrained by neighboring bilayers, and this reduces the amplitudes of the undulations when the wavelength exceeds the lateral correlation length ξ, which is typically of the order of 5 nm—comparable to the length scale at which lipid tilt becomes important (around 2 nm). Indeed, Nagle et al. observed small but systematic differences between the X-ray scattering data and fits made without taking into account lipid tilt. The differences become more important as the signal-to-noise ratio increases [20], confirming the relevance of lipid tilt in the analysis of X-ray data. Concerning the Micropipette Aspiration technique, Nagle et al. analyzed existing data using a refined theory that includes the contribution of lipid tilt. Their analysis shows that, in the low tension regime, including a tilt degree of freedom does not alter the value of Kc. Thus the Micropipette Aspiration method by itself cannot provide experimental evidence for or against including tilt in studying lipid bilayers elastic properties.

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Considering all this, the situation can be summarized as follows. X-ray scattering and Micropipette Aspiration tend to give smaller bending moduli compared to Shape Fluctuation Analysis. As for X-ray scattering, the discrepancy may be explained by the contribution of lipid tilt to the undulation spectrum, since in experiments on bilayer stacks the amplitude of undulations is limited by the presence of neighboring bilayers. The addition of a contribution due to lipid tilt would, in principle, increase the value of Kc; unfortunately, a detailed theory taking into account lipid tilt in the interpretation of X-ray data is not available at present, and it would require some major theoretical development. As for Micropipette Aspiration, the discrepancy with Shape Fluctuation Analysis has been historically ascribed the effect of sucrose/glucose added to the sample. However, this has been recently challenged, thus the mystery remains.

3. SIMULATIONS Molecular simulations can be used to provide a molecular-level interpretation of experiments. In the case of experimental measurement of the bending modulus of lipid membranes, simulations could in principle be used to find out the origins of the discrepancies discussed in the previous section. Unfortunately, some limitations make the analysis of simulations not straightforward. First of all, in simulations, an important degree of freedom has to be taken into account: the force field that models the lipid species. Lipid force fields have been notoriously difficult to parameterize, and many different force fields are available for a variety of lipid species, both at the atomistic and at the coarse-grained level [22, 32–42]. The value of the bending modulus will, to a certain extent, depend on the chosen parameterization. This makes the analysis of values from the literature quite difficult: even if the number of values that can be found is quite high, the statistics for a given membrane composition and a given force field is usually very low (if available at all). A second problem, important for atomistic simulations, is the computational cost; results on small membranes, that can be easily simulated, are difficult to interpret using approaches based on the continuum approximation. Finally, a third problem concerns the different results obtained using different theories linking the bending modulus to quantities directly observed in simulations. In this case, the situation is very similar to the one described for experimental determinations. The number of different techniques available today to calculate the bending modulus is rapidly increasing, with numerous cases in which old

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methods are slightly refined. The most used methods are, however, essentially four: the analysis of the thermal undulation spectrum [43], the lipid orientation method [44], the analysis of response to buckling [45], and the simulation of tethers [46]. In the next sections, we describe the main techniques available. We briefly expose the basic theory behind each method, and then outline its pros and cons. Then we describe the results from atomistic simulations, followed by results obtained with the MARTINI coarse-grained force field. Finally, we summarize and discuss the simulation results.

3.1 Computational Techniques In simulations, the bending modulus can be calculated using different approaches. Historically, the first method to be introduced is the one based on the thermal undulation spectrum [43]—in analogy with the experimental case. This is by far the oldest and thus the most used to date. Then more recently other techniques have been proposed. The ones we describe in the following are based on the analysis of lipid orientation fluctuations [47], on the stretching of tethers [46], and on the buckling of membranes [45]. 3.1.1 Thermal Undulation Spectrum The analysis of undulation spectrum as a method to derive the bending modulus from simulations was introduced by Lindahl and Edholm in 2000 [43]. The starting point of this method is the Helfrich theory [1], that describes the bilayer as a single surface u(x,y), represented by 1 uðx,yÞ ¼ ðz1ðx,yÞ + z2ðx, yÞÞ, 2

(9)

where z1(x,y) and z2(x,y) are the two monolayer surfaces. The analysis of thermally induced fluctuations is performed through a Fourier expansion X uðrÞ ¼ uðqÞeiq  r (10) q

where r ¼ (x,y) is a real space two-dimensional vector and q ¼ (qx,qy) is a reciprocal space two dimensional vector. Using the equipartition theorem it can be shown that the power spectrum of fluctuations (per unit area A) follows the law SðqÞ ¼

< juðqÞj2 > kB T , ¼ A ðKc q4 + γq2 Þ

(11)

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where Kc is the bending modulus and γ the surface tension, and with the angular brackets indicating averages over simulation times. Thus, in the tensionless state (γ ¼ 0, which is generally the case in NPT simulations of flat membranes with periodic boundary conditions), S(q) should scale as q4, and Kc should be obtainable from a simple fit. However, some limitations have to be discussed. The first limitation concerns the use of a box with periodic boundary conditions, which discretizes the values of q and establishes a small-q cutoff at 2π/L, where L is the length of the box. This limits the maximum wavelength observable. A second limitation comes from the presence of a high-q limit, above which strong deviations from a behavior of the type q4 can be observed. These deviations have been originally ascribed to protrusion modes [43], and lately they have been proposed to be related to lipid tilt [48]. It has been suggested that a spurious q2 behavior could also be due to real space filtering [49]. In practical cases, if the size of the box is kept small, deviations from the q4 behavior appear already at a few q-values from the smallest one, which leaves only few q values available for the fit of Kc. As an alternative, relatively large length scales should be used in the simulations (at least a few tens of nm), but these are computationally expensive. Moreover, sampling large-scale undulation modes requires relatively long simulations, as relaxation times are of the order of hundreds of nanoseconds [45]. The combination of large length scale and long time scale makes thermal undulation analysis computationally very costly. 3.1.2 Lipid Orientation Fluctuations In 2011, Watson et al. [44] started analyzing the mechanical properties of lipid bilayers taking into account all the internal degrees of freedom of the lipids. Their mechanical free energy is thus no more the simple Helfrich one (Eq. (1)), but is written as a functional of various shape fields connected with changes in membrane shape and thickness, together with changes in lipid orientation. Including all these effects, and using the approximation of protrusions decoupled from bending, they derived   kB T 1 1 1 SðqÞ ¼ , (12) + + 2 Kc q4 Kθ q2 Kλ + γq2 where Kλ is the protrusion elastic modulus and Kθ the tilt modulus. The bending modulus, together with the other moduli, was derived from multiple fits to all the fluctuation spectra extracted from the simulations.

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One year later the same group introduced a new method to extract the bending modulus [47], based on the analysis of a single spectrum, connected with the orientation of lipids. This method relies on identical simulations and similar analyses as the ones used in the case of thermal undulations. In addition, it requires the definition of a vector n representing the orientation of each individual lipid; the choice of the orientation vector is not unique, but it has been shown that changing the definition of such vector leads to results that differ by no more than 5% [47]. The expression of the mechanical free energy can be reformulated through a linear transformation that makes it almost diagonal. Using once again a Fourier representation and the equipartition theorem, it can be demonstrated that < j^ n jjq j2 >¼

kB T , Kc q2

(13)

where n^jjq is the component longitudinal to q of the vector m, obtained as the difference between the orientation of pairs of lipids. Thus, a simple relation directly connects fluctuations in lipid orientation to Kc. In their letter, Watson et al. show in a few representative cases that theory and simulation are in good agreement down to short wavelengths, shorter than in the case of the undulations spectrum. 3.1.3 Tethers Stretching A quite different approach from the two described above is the one introduced by Harmandaris and Deserno in 2006 [46]. Such method requires deforming a membrane to create a tether (i.e., a cylindrical tube) and measuring the tensile force originated by the deformation. The latter is connected to the bending modulus by a very simple relation. In simulations, a cylindrical tether can be stabilized by periodic boundary conditions—i.e., making an infinite, periodic bilayer tube. The curvature energy, in this case, is given by   Kc 1 2 πKc Lz (14) E¼ 2πRLz ¼ 2 R R where Lz is the size of the box in the direction of the infinite cylinder, and R is the cylinder radius. Under the assumption that the total surface of the membrane A ¼ 2πRLz remains fixed, the axial force can be obtained as Fz ¼ ðδE=δLZ ÞA ¼

2πKc R

(15)

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and thus Kc ¼

Fz R : 2π

(16)

Since in simulations Fz is easily obtainable from the zz component of the stress tensor, the bending modulus can be extracted from this simple ground state relation. Thermal fluctuations are here completely neglected, since their effect on the axial force is very small, as can be deduced for instance from a simple plane wave ansatz for the cylindrical modes [46]. This method solves the issue of large length and time scales present in the undulation spectrum analysis, and has proven successful for simple implicit solvent lipid models [46, 50]. Unfortunately, also this method suffers from some serious technical limitations. First of all, the infinite (periodic) membrane tube divides the simulation box in two distinct space compartments, in and out of the cylinder, possibly leading to a pressure difference between in and out that must be relaxed. Second, the area per lipid could differ between the two leaflets, and has to be equilibrated. Since lipid flip-flop is a very rare event, equilibrating of the number of lipids in the two leaflets would be cumbersome or costly for most available models. A possible solution lies in introducing a hole (i.e., a toroidal pore) in the cylinder, allowing free equilibration of the number of lipids in each leaflet. Such pore can be generated, for example, using a Mean Field Boundary Potential, as implemented by Risselada et al. [51], but the implementation of such potential into commonly available simulation code is not straightforward. Considering all this, despite its simplicity, the tether stretching method has been used only rarely [52]. 3.1.4 Membrane Buckling The theory connecting membrane buckling with the bending modulus dates back to 2011 and is due to Noguchi [53], but the method has become popular only after Deserno and coworkers showed its applications in 2013 [45]. The method relies on the relationship between stress and strain in buckled membranes. Buckled membranes can be described as homogeneous sheets, as shown in fig. 3, exerting forces against the simulation box in the x and y directions. The derivation of the stress–strain relation requires expressing the curvature energy as a function of the shape of the sheet, parametrized through the angle ψ(s) (see Fig. 3). The energy reads

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Fig. 3 Top panel: membrane representation as a 2D elastic sheet in its buckled configuration inside a rectangular box. Its shape is specified though the angle ψ(s) along the arc length s. Bottom panel: snapshot taken from our simulation of a buckled DPPC membrane (strain of γ  0.2). Top panel reprinted with permission from [45] (Copyright 2013, AIP Publishing LLC).

Z E½ψ ¼ Ly 0

L

   1 Lx 2 ds Kc ψ + fx cos ψ  , L 2

(17)

where L is the total length of the membrane contour and fx a Lagrange multiplier needed to fix the length of the box in the x-direction at a given value of the overall membrane area. Having defined the strain as γ :¼ (L  Lx)/L, and after quite a long mathematical journey that involves functional variations and elliptic functions, one finds that Fx ðγÞ ¼ 4π 2 Kc

1 Ly X bi γ i , L 2 i¼0

(18)

where the bi are numeric coefficients given in the original paper. This equation allows the calculation of Kc through a simple procedure. The buckled configuration can be generated via simulations using anisotropic pressure

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coupling, with higher pressure in the x direction. Once the desired strain is achieved, the production run can be started fixing the box sizes in the x and y directions. Then, the force exerted by the membrane in the x-direction can be immediately deduced from the xx component of the stress tensor, averaged during the production run. As for the tether stretching method, also the buckling method is a ground state approach, and thus it does not require sampling of fluctuations, which may require long simulation times—an important advantage over the analysis of the thermal fluctuation spectrum. In fact, in the buckling approach, thermal fluctuations are only a correction to the ground state. This correction has negligible effects on the force along x [45]. The method can be applied to both atomistic and coarse-grained systems, is computationally cheap, and therefore appears very promising. Anyway, one must pay attention that buckling does not induce phase transitions, leading for instance to gelification of parts of the membrane. Another limitation regards the requirement for homogeneous membranes—i.e., the absence of phase separations. When simulating mixtures, the local composition can couple with the local curvature, and can lead to strong compositional inhomogeneities, which make the method not applicable. We notice that the same limitation is also valid for all other calculation and experimental methods: when the membrane contains areas with different chemical composition, the central assumption of the membrane as a homogeneous elastic sheet is not valid anymore, and the meaning of forces, pressures, and other metrics related to membrane elasticity becomes unclear.

3.2 Bending Modulus from Atomistic Simulations In this section, we discuss the Kc values obtained from atomistic (all-atom or united atoms) force fields available in the literature. Such values are gathered in Table 1. The small number of values, together with the use of different force fields, makes the comparison between the techniques rather problematic. However, we provide some comments. For DPPC, the oldest reported value is based on the analysis of the thermal undulation spectrum by Lindahl et al. [43]. The value of 4  1020 J obtained with the Berger force field for lipids [32] agrees with a more recent value obtained by Hofsass et al. with the same method [54]. In both cases, the value seems to be severely underestimated, possibly due to disregard of degrees of freedom relative to lipid tilt. Furthermore, the short total simulation time (10 ns) is definitely not sufficient to correctly sample the longest undulation modes in the system [45].

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Table 1 Bending Moduli of Single Component Membranes (DPPC, DOPC, and DMPC) Obtained from Atomistic Simulations Kc (10220J) T (K) Method Year Ref. LT and FF NL 2 time

DPPC(BERGER) DPPC(BERGER) DPPC(BERGER) DPPC(CHARMM36)

1024  10 ns 1024  10 ns 256/2304  80 ns 648  100 ns

4 4.5  1 6.1 15.6  0.5

DOPC (CHARMM36)

648  100 ns

11.4  0.3 298 LOF

2014 [56]

DMPC(BERGER) DMPC(BERGER) DMPC(BERGER)

256/2304  80 ns 6.5 303 SCM 1024 N.A. 15 300 LOF 934 N.A. 10.3  0.4 300 BU

2009 [55] 2012 [47] 2013 [45]

323 323 323 323

TUS TUS SCM LOF

2000 2003 2009 2014

[43] [54] [55] [56]

The results reported in the table are obtained with two force fields: CHARRM36 [38] and BERGER [32]. In the second column, NL stands for “number of lipids.” N.A. stands for not available. The methods are indicated with acronyms: Thermal Undulation Spectrum (TUS), Slope of Compressibility Modulus (SCM), Lipid Orientation Fluctuations (LOF), and Buckling (BU).

Levine et al. in 2014 [56], calculated Kc of DPPC and DOPC with the technique based on lipid orientation fluctuations, from simulations performed with the CHARMM36 atomistic force field [38]. The values obtained for both lipids are in agreement with experimental results obtained with shape fluctuation analysis [57–58], and the value for DPPC is nearly identical to the one obtained with the MARTINI coarse-grained force field using the same method [47]. Waheed and Edholm obtained a value of 6.5  1020 J for DMPC [55], from atomistic simulations with the Berger force field. They derived the bending modulus from the slope of the compressibility modulus versus system size, which depends on the undulation spectrum [55]. Since they did not include the tilt degree of freedom in their treatment of undulations, their value is possibly underestimated. The same problem affects the value obtained for DPPC. Analyzing lipid orientation fluctuations, Watson et al. obtained the same value of Kc for DMPC (simulated with the Berger united-atom force field) and DPPC (simulated with the MARTINI coarse-grained force field); a very similar value was also obtained from all-atom simulations of DPPC (simulated with the CHARMM36 force field) [47].

3.3 Bending Modulus from Coarse-Grained Simulations Coarse-grained force fields offer the advantage of a significantly lower computational cost, particularly important when calculations require large lipid

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bilayers and long time scales. One of the most popular coarse-grained force fields for lipid membrane simulation is the MARTINI force field. The popularity of MARTINI is such that most of the available coarse-grained calculations of the membrane bending modulus in the literature have been performed with MARTINI. In the following, we thus propose a critical reading of the results obtained with the MARTINI force field. This approach allows us to focus on the correlation between the calculated Kc and the methods used, neglecting further complications arising from the use of different model potentials. We report in Table 2 all the values found in the literature for single component membranes simulated with the MARTINI force field. In Table 4, instead we report values obtained

Table 2 Bending Moduli of Single Component Membranes (DPPC,DOPC, DMPC, and POPC) Obtained from MARTINI Coarse-Grained Simulations LT NL 2 time Kc (10220J) T (K) Method Year Ref.

DPPC 6400  150 ns 4  2

323 TUS

DPPC 3200  1 μs

21

323 TUS (+ tilt) 2007 [48]

DPPC 256  100 ns

8

323 TUS

2004 [35]

2007 [63]

DPPC 2048  2.4 μs 13.4 (13.2–22) 323 TUS (+ FS) 2011 [44] DPPC 2048  2.4 μs 15

325 LOF

2012 [47]

DPPC 2048  7.5 μs 9.5  0.5

320 CU

2013 [64]

DPPC 640  4 μs

14.6  0.4

323 BU

2015 Present work

DMPC 8192 N.A.

15

300 TUS

2011 [49]

DMPC 8192  2 μs

16.6  0.5

300 TUS

2012 [65]

DMPC 1120 N.A.

12.0  0.5

300 BU

2013 [45]

DMPC 8192  2 μs

14  1

310 TUS

2014 [59]

DMPC 640  4 μs

12.6  0.3

300 BU

2015 Present work

DOPC

10

DOPC 640  4 μs

15.5  0.4

POPC 8000  2.1 μs 8.7  0.5

TP

2012 [66]

300 BU

2015 Present work

320 CU

2013 [64]

In the second column NL stands for “number of lipids.” N.A. stands for not available. The methods are indicated with acronyms: Thermal Undulation Spectrum (TUS), Lipid Orientation Fluctuations (LOF), Tethers Pulling (TP), Buckling (BU), Coupled Undulatory (CU), and Fluctuation Spectra (FS). With the last one, we indicate the use of multiple different spectra that are fitted with six independent parameters [44].

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with other coarse-grained and solvent-free force fields: Dry-MARTINI [59], Wang [60], Brannigan [61], and Cooke [62]. Let us start with the values concerning DPPC bilayers. This lipid presents a gel–liquid phase transition at a relatively high temperature (41 °C), and is therefore still in the gel phase at room temperature. For this reason, bending modulus calculations on DPPC are generally performed at a temperature around 323 K. Only a few values of Kc have been published before 2010, and they were all obtained analyzing the undulation spectrum [35, 48, 63], although with important differences. Indeed it can be noticed that the three values of the bending modulus do not agree at all, ranging from 4 to 21  1020 J. The first value was obtained by Marrink et al. by fitting the spectrum at low q values, where a simple dependence on q4 is expected (Eq. (11)). May et al., instead, explicitly included a tilt modulus in their analysis, claiming that, for the bending modes accessible to simulations, this is necessary to avoid underestimating Kc. Indeed the latter authors found a much higher value. Furthermore, in the original work by Marrink, the total simulation time (150 ns) was probably too short to achieve good statistics on longer (and thus slower) undulation modes. Shkulipa et al. reported an intermediate value, but their calculation appears less reliable, given the very small simulation box and the short total simulation time. More recently, the DPPC bending modulus was calculated by Watson et al. with two different techniques [44, 47]. A value of 13.4  1020 J was obtained using a refined analysis of fluctuation spectra, taking into account tilt, thickness, and orientation fluctuations [44]. In this case, Kc was obtained through a fit with four free parameters, and thus the resulting uncertainty is rather high (13.2–22). A year later [47] the same authors used their newly proposed method, based on the analysis of lipid orientation fluctuations, and obtained a value of 15  1020 J, consistent with the previous one. Tarazona et al. used a novel approach to analyze thermal fluctuations, introducing a new coupled undulatory mode which describes the correlated movement of the two leaflets [64]. They obtained a value of 9.5  1020 J, considerably smaller than the value obtained with orientation fluctuations by Brown et al. [47]. The discrepancy between these values is discussed in the article, and possibly attributed to subtleties in the analysis of tensionless membranes. The authors provide some evidence of the influence of an effective surface tension, created by the fluctuations and thus present also in the tensionless state, on the results at low q (under 0.5 nm1). They claim that extrapolating at q ¼ 0 from low q values can lead to an overestimation of Kc.

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However, it is not completely clear why the lipid orientation fluctuation method would be affected by this problem, since the spectrum obtained by Watson et al. is consistent with the theory up to at least q ¼ 0.7 nm1. Finally, we calculated ourselves the bending modulus for DPPC at 323 K using the membrane buckling technique, and found a value of 14.6  1020 J, in excellent agreement with the value obtained by Watson et al. [47]. In conclusion, it appears that the “standard” undulation analysis, orientation fluctuations, and buckling methods provide rather consistent results for DPPC at 323 K, if simulations are performed on sufficiently long length and time scales. We now consider the case of DMPC/DLPC. These two lipids are not distinguishable at the MARTINI coarse-grained level. The values reported in the literature are more recent than for DPPC, and are obtained with two techniques: undulation spectrum [49, 59, 65] and buckling [45]. The values range from 12 to 16.6  1020 J, showing reasonable agreement. Using the buckling technique, we obtained a value of 12.6  1020 J, compatible with the original calculation by Hu et al. [45]. Unfortunately no calculations have been reported using the orientation fluctuation method nor the new approach by Tarazona et al., so the question on discrepancy between methods remains open. For DOPC, we found only one value of bending modulus in the literature, obtained by Baoukina et al. [66] with a technique similar to tether stretching. In this case, a tether was created by pulling on a planar membrane, and the force needed to extend the tether was calculated. The dependance of this force on Kc is given by Eq. (16). The value obtained was 10  1020 J. We also calculated the bending modulus for DOPC, at the same temperature as in [66], using the buckling method, and obtained a value of 15.5  0.4  1020 J. The two values appear quite different, but a rigorous comparison is not possible since Baoukina et al. did not provide error estimates. We also notice that the tether response to the pulling force contains both static and viscous friction contributions, which can affect the results, as shown by the dependence of the bending modulus on the pulling rate. It is well known that the bending modulus increases with increasing the thickness of the membrane [31], and thus it generally decreases with the rate of unsaturation of the lipid acyl chains. A comparison of the values we obtained with the buckling method for three different lipids (DMPC, DPPC, and DOPC) is not immediate, since simulations reported in the literature were carried out at different temperatures. To allow a quantitative comparison, we performed additional simulations for DOPC and DPPC

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at 323 K. For DOPC, we tried both the new [67] and the old [22] MARTINI topologies. The results are gathered in Table 3. All the right trends are reproduced: DMPC is softer than DPPC (DMPC chains are one bead shorter), the new DOPC is softer than DPPC (same number of beads but unsaturated chains for DOPC) and also softer than the old DOPC, that had one more bead in the chains. We now discuss the values of the bending modulus obtained with solvent-free coarse-grained models (reported in Table 4). In this case, the force fields use an implicit treatment of the solvent, and the effect of hydration is included in the interaction parameters. The Cooke force field [62] is a very general model, in which each lipid is represented by three beads: one for the head and two for the tail. The properties Table 3 Bending Moduli Obtained with the Buckling Technique, from Simulations Using the MARTINI Coarse-Grained Force Field at 323 K LT Kc (10220J)

DMPC

10.5  0.2

DPPC

14.6  0.4

DOPC (old)

12.8  0.2

DOPC (new)

9.6  0.2

Table 4 Bending Moduli Obtained from Solvent-Free Coarse-Grained Simulations LT Kc (10220J) Method Year Ref.

4.9  0.1

TS

2006

[46]

5.2  0.4

TUS

2006

[46]

5.2  0.1

TS

2012

[50]

5.3  0.2

BU

2013

[45]

28(22–36)

TUS (+ tilt)

2006

[68]

32(30–42)

TUS (+ FS)

2011

[44]

36

LOF

2012

[47]

Wang(DOPC)

2.3  0.2

BU

2013

[45]

D-MART(DMPC)

11  1

TUS

2014

[59]

Cooke

Brannigan

The results reported in the table are obtained with different force fields: Dry-Martini (D-MART) [59], Wang [60], Brannigan [61], and Cooke [62]. The methods are indicated with acronyms: Thermal Undulation Spectrum (TUS), Tethers Stretching (TS), Buckling (BU), and Fluctuation Spectra (FS). With the last one we mean the use of multiple different spectra that are fitted with six independent parameters [44].

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of the bilayer (bending modulus included) are tunable by the choice of a single interaction parameter. All the Kc values reported here, obtained with a particular choice of that parameter, are within 10% of each other, despite having been obtained with different techniques. One possible reason for the good agreement observed is sampling: implicit solvent models are computationally cheap, and simulations used for the calculations reported here used a large number of lipids and long simulation times; for systems with large size, the deviations of the undulation spectrum from the simple q4 behavior are small. Good agreement was also found between the different values obtained with the model by Brannigan [61]. In this case, all the values obtained from the undulation spectrum were refined taking into account other bilayer fluctuations. Interestingly, the values obtained with the Cooke and the Brannigan models show significant differences compared to values obtained from atomistic and MARTINI CG simulations, as well as from experiments. In the case of the Cooke model, values are lower, while for the Brannigan model values are higher. An even larger discrepancy is shown by the model of Wang [60]. These discrepancies are justified by the lower resolution of the models. The bending modulus reported for DMPC with the DryMARTINI model is of 11  1020 J. This value is slightly smaller than the value obtained by the same authors with the standard MARTINI force field, and is much closer to results of atomistic simulations as well as experimental results (ranging between 5 and 11  1020 J for DMPC). In conclusion, it appears that low-resolution solvent-free coarse-grained models tend to give values significantly different from the experimental data; Dry-MARTINI, having the same resolution as the standard MARTINI model, yields better agreement with experiments.

4. DISCUSSION AND CONCLUSIONS Our analysis of experimental and simulation literature regarding the determination of lipid membrane bending modulus shows a complex picture. As for experiments, it appears clearly that Kc values correlate with the technique used for the measures. Recent X-ray scattering and micropipette aspiration measures provide consistent values of the bending modulus of single component bilayers (DOPC and DMPC). However, both techniques generally give values smaller than those obtained by shape fluctuation analysis. For both techniques, different authors speculated about the possible systematic underestimation of Kc. In the case of X-ray scattering analysis, the

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underestimation might be due to the use of stack of bilayers, which poses limits to the amplitude of the undulation modes. Corrections to the current interpretation would require taking into account the contribution of lipid tilt to the undulation spectrum, which in turn would require important theoretical advances. In the case of micropipette aspiration, Kc might be underestimated (according to some authors) due to the use of sugars (sucrose or glucose) in the experimental preparation. Nagle recently showed by X-ray scattering analysis that neither sucrose nor glucose influence the value of Kc obtained with the same technique. However, it is still possible that the sugars affect the results obtained by micropipette aspiration, without changing the real bending modulus. Shape fluctuation analysis appears to be the least problematic technique to determine membrane bending rigidity. Contour analysis, that is probably the most problematic point in shape fluctuation analysis, has been recently refined [16]. Moreover, the technique does not require additives and is applied directly on vesicles (as opposed to bilayer stacks), and is therefore the most direct method available. Estimates of the bending moduli obtained by shape fluctuation analysis lie in the range 9–12  1020 J for DOPC and 12–14  1020 J for DMPC (at 300 K, in both cases). As for DPPC, the only available value is 15  0.9  1020 J, obtained at 320 K [57]. As for simulations, a historical trend emerges from our analysis, for both the atomistic and coarse-grained models: older values of Kc values are generally smaller than the more recent values. The older values were in general affected by two related problems: the use of small simulation boxes and/or small total simulation times, and at the same time the use of thermal undulation analysis without taking into account fluctuations in lipid tilt. Figure 4 shows the average results obtained from atomistic and MARTINI simulations (excluding the values reported before 2010), alongside with the average results from the most common experimental techniques. Values obtained from MARTINI and atomistic simulations are very similar, and fairly independent of the technique used to extract Kc from the simulations. For DMPC, Kc is in the range 10–15  1020 J in atomistic calculations, and in the range 12–16  1020 J in MARTINI calculations. For DPPC, Kc is 15  1020 J according to the only available atomistic simulation, and is in the range 13–15  1020 J in MARTINI simulations. For DOPC, the values obtained from atomistic simulations with lipid orientation fluctuations shows reasonable agreement with values from MARTINI simulations with the buckling method (considering the most recent modification of MARTINI DOPC, using four particles in oleoyl chains), and

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Fig. 4 Bending moduli obtained from experiments and simulations for DMPC, DOPC, and DPPC. The point represents the average of the results found in the literature for each specific technique: X-Ray (XR), Aspiration Pipette (AP), and Shape Fluctuations Optical Analysis (SFOA). The asymmetric error bars indicate the minimum and maximum value. In the case of simulations, the results from all the different techniques are merged, but only the ones obtained after 2010 are taken into account.

both are within the range of experimental values obtained by shape fluctuation analysis. The analysis above excludes the recent results by Tarazona et al. [64], using a peculiar “coupled undulations” approach. Tarazona et al. claim that values around 15  1020 J are overestimated, and identify the reason in subtleties associated with undulations and their effect on the effective surface tension. However, we find these claims not fully convincing, since the buckling approach shows good agreement with the lipid orientation fluctuation approach, and both techniques show good agreement with experimental results from shape fluctuation analysis. In conclusion, recent simulations analyzed with the buckling method and the lipid orientation fluctuation method provide similar results, particularly for atomistic force fields like CHARMM36 and Berger and for the MARTINI coarse-grained force field. Such results are in good agreement with experimental results obtained by shape fluctuation analysis, while micropipette aspiration and X-ray scattering provide consistently lower values of the bending rigidity. The reasons for the discrepancies among experimental techniques are still not fully understood. Given the length scale relevant for micropipette aspiration, lipid tilt is very unlikely to contribute. On the contrary, lipid tilt might actually be relevant for the interpretation of X-ray scattering data, but unfortunately a theory is not yet available to include this contribution in the analysis.

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CHAPTER SIX

Bicontinuous Phases of Lyotropic Liquid Crystals W. Góźdź*,1 *

Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland Corresponding author: e-mail address: [email protected]

1

Contents 1. 2. 3. 4.

Introduction The Model and the Computational Method Cubic Phases of Lyotropic Liquid Crystals The Structure of the Interface Between the Cubic Phase and the Isotropic Phase 4.1 Computational Setup 4.2 The Structure of the Interfaces Between the Diamond and the Isotropic Phase 4.3 The Structure of the Interfaces Between the Gyroid and the Isotropic Phase 5. Conclusions Acknowledgments References

145 146 152 156 157 159 164 166 166 166

Abstract The bicontinuous lyotropic cubic phases and their properties are investigated within the framework of the Landau–Brazovskii free energy functional. Cubic phases of different symmetries and topology are examined. The structure and stability of the interfaces between the cubic phases and the isotropic phases are described.

1. INTRODUCTION Bicontinuous cubic lyotropic phases are liquids with crystalline order, periodicity in x, y, and z directions having the length scale much larger than the size of molecules. They are formed in systems with competing interactions [1–3], such as diblock copolymers, ternary mixtures of oil, water, and surfactants, or binary mixtures of lipids and water [4–7], and they can be encountered in biological cells in endoplasmic reticulum and organelle [8]. We focus on bicontinuous phases in mixtures of lipids and water. The amphiphilic lipid molecules self-assemble into a bilayer with the hydrocarbon chains isolated from the water molecules. The bilayer divides the Advances in Biomembranes and Lipid Self-Assembly, Volume 23 ISSN 2451-9634 http://dx.doi.org/10.1016/bs.abl.2015.12.003

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2016 Elsevier Inc. All rights reserved.

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volume into two disjoint networks of channels filled with water and behaves as an elastic membrane. For a fixed topology, the elastic energy of the membrane depends on the mean curvature, H, of the surface describing the center of the bilayer according to the Helfrich formula [9]: Z Fb ¼ 2κ H 2 dA (1) where κ is the bending rigidity and dA is the infinitesimal area element. The formula (1) may be applied for the systems with fixed topology where according to Gauss–Bonnet theorem the surface integral of the Gaussian curvature is constant. In equilibrium, the elastic energy assumes the minimum. In the bulk, the minimum of (1) corresponds to triply periodic minimal surface, because the minimal surfaces have zero mean curvature at every point. The surface with zero mean curvature has saddlelike shape at every point (except flat points). A plane is a special case of the minimal surface. The functional (1) has been successfully applied to the studies of vesicles built of lipid bilayers. The agreement between experimental results and the calculations performed for different shapes of vesicles was excellent [10–14]. The mathematical modeling of the bicontinuous phases in terms of the functional (1) is however very difficult, especially in the presence of the interface. It requires minimization of the functional (1) for functions describing the location of the bilayer. These functions are not known a priori and cannot be easily parameterized. Therefore, we decided to perform the calculations within the framework of a relatively simple Landau–Brazovskiitype model with one scalar order parameter related to the local concentration of water [15–16].

2. THE MODEL AND THE COMPUTATIONAL METHOD The free-energy functional for systems inhomogeneous on the mesoscopic length scale can be written in the form Z   F ½ϕðrÞ ¼ d 3 r ΔϕðrÞ2 + g½ϕðrÞrϕðrÞ2 + f ½ϕðrÞ : (2) This functional successfully describes systems as diverse as binary or ternary surfactant mixtures, block copolymers, colloidal particles with competing attractive and repulsive interactions of different range, or magnetic systems with competing ferromagnetic and antiferromagnetic interactions

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[2, 3, 15, 17–20]. The order-parameter ϕ(r) in (2) depends on the physical context. In the case of block copolymers or ternary water-surfactant-oil mixtures ϕ(r) is the local concentration difference between the polar and the nonpolar components. In the case of lipids in water ϕ2(r) describes the local concentration of water. At the center of the lipid bilayer ϕ(r)¼0. The bilayer divides the space into two disjoint water channels, one of them on one side of the bilayer, where ϕ(r) > 0, and the other one on the other side of the bilayer, where ϕ(r) < 0. The sign of ϕ(r) allows to distinguish between the two disjoint channels of water. The fluid in each channel, however, has the same physical nature. For this reason in the case of lipids in water the functional (2) must be an even function of ϕ. In homogeneous phases, the concentration of water is independent of the position. In such a case, ϕ(r)¼const and rϕ¼Δϕ¼0; therefore, f [ϕ] is the free-energy density of the homogeneous phases. In the case of the phase coexistence between water- and lipid-rich phases, we can postulate for f [ϕ] the form with three minima of equal depth, where ϕ¼1 both represent the water-rich phase, f [ϕ(r)]¼(ϕ(r)21)2(ϕ(r))2. The inhomogeneous distribution of the components, in particular the formation of the bilayer, is possible when the corresponding free energy is lower than for any homogeneous structure. When the concentration ϕ(r) becomes position dependent, then (rϕ)2 >0. F can decrease for (rϕ)2 increasing from zero when g[ϕ(r)] λD, 68–70 like-type inclusions, 63–64 microscopic to mesoscopic description coarse-graining procedure, 77–78 linearized Euler–Lagrange equations, 79–80 model, 75–77 quantitative agreement, 67 TIRM technique, 64–65 water–lutidine mixture, 69f EL equations. See Euler–Lagrange (EL) equations Endosomal sorting complex required for transport (ESCRT), 190–191 Endothelial cells HUVECs, 42 viability of, 47f

Enthalpy effect, 2–3 ESCRT. See Endosomal sorting complex required for transport (ESCRT) Euler–Lagrange (EL) equations confinement effects, 92–94, 93–94f linearized, 79–80 nonlinear, 82 EV-depleted growth medium, 191 Exosomes, 188–189 Extracellular vesicles (EVs), 187–188 biogenesis, 190–191 cargo sorting, 190–191 culture medium of CRC cells, 191 for discard of unnecessary miRNAs, 192–194 drug delivery system for RNAi, 198 EV-depleted growth medium, 191 5-FU treatment, 192–194 genetic information, 188–189 heterogeneous forms, 188–189 from mouse and human plasma, 192 nanoparticle tracking analysis, 192, 193f PML, 196–197 for proangiogenesis, 194–198 secretion, 190–191

F Fluorescent dyes, 18–20, 122 Functional groups, on surface, 36–37

G Gaseous plasma AFM, surface topography by, 40–41 biomaterials, 27–29 chemical composition, 46 endothelial cells interaction, 47 fourth state of matter, 31–36 functional groups on surface, 36–37 HUVECs, 42, 47 interaction of platelets, 47–51 morphological changes, 35–36 roughness, 37–38 surface morphology, 37–38, 43 treatment, 40 WCA measurements, 41 wettability, 38–40, 43–46 XPS, 41 Gauss–Bonnet theorem, 145–146

208 Gaussian curvature, CPPs, 4–8, 16–18 Giant unilamellar vesicles (GUVs), 119–120 pore formation, 14–18 thermal fluctuations, 120–121, 121f utilization, 9–11 Gyroid phase lyotropic liquid crystals, 155f, 159f, 164–165 structure of, 164–165, 165f

H Helfrich theory, 118–119, 126–127, 145–146 Heterogeneous nuclear ribonucleoprotein A2B1 (hnRNPA2B1), 190–191 Human plasma, EVs from, 192 Human umbilical vein endothelial cells (HUVECs), 42 on polystyrene surfaces, 47 viability and proliferation of, 47, 47f Hydrophilic ions in case of ξ < λD, 70–72 in case of ξ < λD, 68–70

I Intraluminal vesicles (ILVs), 189f, 190–191 Isotropic phase lyotropic liquid crystals, 159–165 structure of, 159–164

K Kosmotropic solute, CPPs, 13f Kruppel-like factor 2 (KLF2), 195–196

L Lampert rule, 39 Landau–Brazovskii functional, 91–92 Landau–Brazovskii-type model, 146 Langmuir–Blodgett technique, 104 Laplace equation, 2–3 relative pressure, 3f Large unilamellar vesicles (LUVs), 2–3 carbosilane dendrimers, 105–106 dendrimers, 102–103 hydrodynamic diameter, 108–109 surface charge, 104–105 LC. See Liquid crystal (LC)

Index

Linearized Euler–Lagrange (EL) equations, 79–80 Lipid bilayer bending modulus, 119–120 biophysical phenomena, 170 elastic properties, 117–118 living cells, 62 mechanical properties, 127 Lipid membrane bending modulus, 117–118 CPPs on phase transition, 9f dendrimers, 102–103 Lipid orientation fluctuations, bending modulus, 127–128 Liposomes dendrimer and, 103–105 DMPC, 104–105 formation, 171–172 functionality, 170–171 surface charge, 105–106 TEM, 105–106 Liquid crystal (LC) bicontinuous cubic, 6–8 cell-penetrating peptides, 5–6 LUVs. See Large unilamellar vesicles (LUVs) Lyotropic liquid crystals computational setup, 157–158 computational tetrahedron, cubic unit cell, 148f cubic phase, 152–156, 152–153f diamond phase, 158f, 159–164 Euler characteristics, 150 gyroid phase, 155f, 159f, 164–165 in homogeneous phases, 147 hydrophobic effect, 156 isotropic phase, 159–165 mean-field approximation, 147–148 model and computational method, 146–151

M

MD. See Molecular dynamics (MD) Mean curvature, CPPs, 5–11 Mean Field Boundary Potential, 129 Mean-square displacement (MSD), 180 Membrane bending modulus from atomistic simulations, 131–132

209

Index

coarse-grained simulations, 132–137, 133t, 136t computational techniques lipid orientation fluctuations, 127–128 membrane buckling, 129–131, 130f tethers stretching, 128–129 thermal undulation spectrum, 126–127 dipalmitoylphosphatidylcholine, 131–132, 132t, 134–135 experimental values, 123–125 experiments, 119–125, 139f Helfrich theory, 118–119, 126–127 in lipid membrane, 117–118 Micropipette Aspiration technique, 121–122 shape fluctuations optical analysis, 120–121 X-ray scattering, 123 Membrane buckling, 129–131, 130f, 135 Micropipette Aspiration technique, 121–122 MicroRNAs (miRNAs) anti-oncogenic downregulation, 194 dysregulation, 187–188 EU-based tracing, 197f EVs for discard, 192–194 extracellular, 188–189, 195f hnRNPA2B1 binds with, 190–191 types of, 189f miR-1246, 194–197 miR-92a, 194–196 Molecular dynamics (MD) coarse grain, 172 computational methodology, 174–177 dedicated particle placing, 173–174 energy minimization, 175–176 mean-square displacement, 180 radial distribution function, 177, 180, 181f results and discussion, 177–182 self-assembling objects, 171–172 Molecular simulations, 125 bending modulus atomistic simulations, 131–132, 132t coarse-grained simulations, 132–137, 133t, 136t lipid orientation fluctuations, 127–128 membrane buckling, 129–131, 130f

tethers stretching, 128–129 thermal undulation spectrum, 126–127 Mouse plasma, EVs from, 192 MTS assay, 42, 47 Multivesicular bodies (MVBs), 188–191

N Nagle’s analysis, 123–124 Nanoparticle tracking analysis (NTA), EV, 192, 193f Nonequilibrium cold plasma, 31–35

O Osmotic pressure CPP translocation, 9–11, 11f effect, 10f, 18–20

P

PET. See Polyethylene terephthalate (PET) Phase analysis light scattering (PALS), 103 Phase diagram binary mixture, 62, 62f lamellar phase, 72 local/global, 5–6 Pheochromocytoma (PC12) cells, 190 Phosphorus dendrimers, 107–109 Plasma categories, 31–35 definition, 31–35 fourth state of matter, 31–36 functionalization, 35–36 nonequilibrium cold, 31–35 RF technique, 35, 40f thermal near-equilibrium, 31–35 treatment, 40 Platelets activation degree, 30–31 adhesion on surfaces, 42 artificial surface, 32f interaction of, 47–51 on PET surfaces, 47–51, 51f with respect to O/C ratio, 52–53, 53f SEM, 47–51, 49f PML. See Promyelocytic leukemia protein (PML) Polyamidoamino (PAMAM) dendrimers, 109–110

210 Polyethylene terephthalate (PET) plasma treatment, 40 platelet on, 47–51 polymer, 29f, 43 SEM analysis, 42 topographic changes, 40–41 vascular grafts, 37–38, 38f Polymers morphological changes on, 35–36 polyethylene terephthalate, 29f, 43 sensitive biomaterials, 31–35 surface, biological system, 34f Pore formation, 14–18 Preexosomes, 190–191 Proangiogenesis, extracellular vesicles for, 194–198 Promyelocytic leukemia protein (PML), 196–197

R Radial distribution function (RDF), 177, 180, 181f Radio frequency (RF) plasma technique, 35, 40f Refined theory, 124 RNAi, drug delivery system for, 198 Roughness, 37–38

S Scanning electron microscope (SEM) platelets interaction, 47–48, 49f polyethylene terephthalate, 42 Shape fluctuations optical analysis, 120–121 Shed microvesicles (SMVs), 188–190 Spectrofluorimetry, 104 Surface morphology results, 43 roughness, 37–38, 44f Surfactant parameter (SP), 5–6, 6f Systematic coarse-graining procedure, 67–68

T

TEM. See Transmission electron microscopy (TEM)

Index

Tethers stretching (TS), 128–129 Thermal fluctuations giant vesicle, 120–121, 121f novel approach, 134–135 tether stretching method, 131 Thermal near-equilibrium plasma, 31–35 Thermal undulation spectrum, 118–119, 126–127 Thermodynamic Casimir potential antagonistic salt, 72–74 characteristic shapes, 66, 66f definition, 63 electrostatic and (see Electrostatic and thermodynamic Casimir potentials) experimental verification, 64–65 feature, 63 like-type inclusions, 63–64 quantitative agreement, 67 TIRM technique, 64–65 water–lutidine mixture, 69f Total internal reflection microscopy (TIRM) technique, 64–65, 68–69 Transmission electron microscopy (TEM) dendrimers, 104 DMPC liposomes, 105–106, 107f

U Unilamellar membrane, 8f

W Water contact angle (WCA) measurements, 41, 43–46 Wettability biomaterials, 38–40 hemocompatibility of materials, 39–40 results, 43–46

X X-ray photoelectron spectroscopy (XPS), 41 X-ray scattering bending modulus, 123 stacks of bilayers, 123