Biophysical Chemistry [Revised ed.] 1781830037, 9781781830031

Table of contents :
Cover
Foreword
Preface
Acknowledgement
Contents
Chapter 1. Biological Cell and its Constituents
1.1 Biological Cell
1.2 The Major Complex Biomolecules of Cell
1.3 Structure and Function of Proteins and Enzymes
1.4 Nucleic Acids
Chapter 2. Bioenergetics
2.1 Introduction
2.2 Free Energy Change
2.3 Standard Free Changes in Biochemical Reactions
2.4 Hydrolysis of ATP-Bioenergetic Significance of ATP
2.5 Biochemical Reactions in a Cell
2.6 The Actual Free Energy Change in Living Cells is Much Higher Than the Standard Free Energy Change
2.7 Biological Phosphate Compounds Other Than ATP -- Conversion of ADP to ATP
2.8 Biological Oxidation-Reduction Reactions (Oxidative Phosphorylation ATP Synthesis)
2.9 Glycolysis is a Pathway Which Produces ATP (ATP Formation Coupled to Glycolysis)
Chapter 3. Statistical Mechanics in Biopolymers
3.1 Chain Configuration and Conformation of Macromolecules
3.2 Statistical Distribution-end to end Dimensions and Biopolymer Structure
3.3 Calculation of Average Dimensions for Different Chain Structures
Chapter 4. Forces Involved in Biopolymer Interactions
4.1 Introduction
4.2 van der Waals Forces
4.3 Electrostatic Interactions (Ionic Bond, Salt Linkage, Salt Bridge or Ion Pair)
4.4 Hydrophobic Interactions
4.5 Hydrogen Bonding
4.6 Hydrogen Ion Titration Curves
Chapter 5. Cell Membrane and Solute Transport
5.1 Introduction and Function of Cell Membranes
5.2 The Chemical Composition of Membranes
5.3 Formation of Bilayer Lipid Aggregates--The Bilayer Membrane Structure
5.4 Fluid Mosaic Model of Membrane Structure
5.5 Transport Across Membranes
5.6 Nerve Conduction--Propagation of Impulse Along a Nerve
5.7 More on Transport of Ions Through Membranes
Chapter 6. Biopolymers and Their Molecular Weights
6.1 Introduction
6.2 Molecular Weight of Macromolecules
6.3 Methods of Determination of Molar Masses of Macromolecules
6.4 Electrophoresis
Chapter 7. Thermodynamics of Biopolymer Solutions
7.1 Introduction and General Principles
7.2 Thermodynamics of Biopolymer Solutions
7.3 Thermodynamics Principles and Dissolution of Crystalline and Amorphous Polymers
7.4 Heat of Dissolution and the Solubility Parameter
7.5 The Flory-Huggins Theory of Polymer Solutions
7.6 Donnan Membrane Equilibrium
7.7 Muscular Contraction and Energy Generation in Mechanochemical System
7.8 Osmotic Pressure
Chapter 8. Diffraction Methods
8.1 Introduction--General Principles of Light Scattering
8.2 Light Scattering by Macromolecules and Measurement of Average Molar Mass
8.3 X-ray Diffraction and Three Dimensional Structures of Macromolecules
8.4 Photon Correlation Spectroscopy (PCS) also Called the Dynamic Light Scattering (DLS)
Index

Citation preview

BIOPHYSICAL CHEMISTRY

BIOPHYSICAL CHEMISTRY (SECOND EDITION)

P S KALSI Former Dean of Colleges Punjab Technical University Jalandhar, INDIA

N MAHANTA Assistant Professor Department of Chemistry, J B College Jorhat (Assam), INDIA

New Academic Science Limited NEW ACADEMIC SCIENCE

27 Old Gloucester Street, London, WC1N 3AX, UK www.newacademicscience.co.uk e-mail: [email protected]

Copyright © 2014 by New Academic Science Limited 27 Old Gloucester Street, London, WC1N 3AX, UK www.newacademicscience.co.uk • e-mail: [email protected]

ISBN : 978 1 781830 76 5 All rights reserved. No part of this book may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the copyright owner. British Library Cataloguing in Publication Data A Catalogue record for this book is available from the British Library Every effort has been made to make the book error free. However, the author and publisher have no warranty of any kind, expressed or implied, with regard to the documentation contained in this book.

Dedicated to Prof. Dr. P.T. Manoharan (FNA) Former Vice Chancellor, Madras University and Presently Raman Chair Professor Indira Gandhi National University, New Delhi for the rare devotional temper of his knowledge of chemistry and his keen interest in the development of educational system in the country.

Ph. No. Fax email

: +91-361-2570412 (O) : +91-361-2675515 : [email protected]

GAUHATI UNIVERSITY

Prof. O. K. Medhi

Gopinath Bardoloi Nagar

Vice-Chancellor

Guwahati - 781 014 Assam :: India

FOREWORD Polymers like DNA, RNA, Proteins and polysaccharides existed in natural form since life began and these play crucial roles in plants and animal life. Since earliest times, man has been exploiting naturally occurring polymers as materials for providing clothing, shelter, tools, weapons, writing materials and other requirements. Ever since the continued research on polymers has led to vulcanization of natural rubber, cellulose nitrate as an explosive and the viscose process for dissolving and regenerating cellulose. By early 1930s most scientists were convinced at the macromolecular structure of polymers. The theoretical and experimental work of Paul Flory was prominent as the years passed and he was awarded the Nobel prize for chemistry in the year 1974. In the present book, Prof. Kalsi and Dr. Nivedita have presented the physical chemistry of biological macromolecules and have provided extensive material to show how to study this subject at the master’s level. They have presented a rigorous theoretical understanding and have brought it to a mature level. I take this opportunity to congratulate the authors who have dared and successfully entered the biological territory. I am extremely confident to say that all the students and professionals who want to attain the conceptual knowledge of interplay between organic chemistry, physical chemistry and biology will appreciate the present work of Prof. Kalsi and Dr. Nivedita.

Prof. O.K. Medhi

vii

ACKNOWLEDGEMENT

One of us (PSK) is indebted to Prof. Dr. V.N. Rajasekharan Pillai, Hon’ble Vice Chancellor of Indira Gandhi National Open University, New Delhi, for initiating him to write a series of books for IGNOU. The wisdom and loyalty of the Vice Chancellor to upgrade the educational system in the country is a singular example of its kind in the country. Dr. Nivedita Mahanta was discovered during lectures by (PSK) during refresher course at North Eastern Hill University (NEHU) Shillong. She is a wonderful teacher with many years of teaching and research experience in chemistry and biology. The support and inspiration of the following colleagues is acknowledged: Prof. Suhail Sabir (Aligarh), Prof. P.J. Das (Guwahati), Prof. Aswar (Amravati), Prof. Shobna Menon, (Ahmedabad), Prof. I.K. Sharma (Jaipur), Prof. Charanjit Kaur (Bhopal), Prof. Anamik (Rajkot), Prof. Malkani (Nainital), Prof. Monika Datta (Delhi), Prof. Nasreen (Tezpur), Prof. Shailesh, R. Shah (Vadodara), Prof. V.K. Singh (Nawalgarh), Prof. Saroj Agarwal (Indore), Profs. K. Mohan Rao and Profs. G. Bez and Askari (Shillong), Prof. S.C. Ameta (Udaipur), Prof. Uma Sharma (Ujjain), Prof. K.M. Gangotri (Jodhpur), Prof. M.S. Shingare, C.H. Gill and R.A. Mane (Aurangabad), Prof. S. Kumbhat (Jodhpur), Prof. U.V. Desai (Kolhapur), Prof. Raval (Anand), Prof. A.V. Bajaj (Indore), Prof. Rashmi Saxena (Jabalpur) and Prof. C.P. Bhasin (Patan). We specially thank Prof. S. Malhotra, Former Director, School of Sciences, Indira Gandhi National Open University (IGNOU), New Delhi, a person with rare qualities of academic and administrative leadership. Recently interaction with some brilliant students of chemistry, K. Bavya Devi (Chennai), Poonam (Sudhar), Sheetal (Indore) and Parul and Sheenam (Banasthali) was a great experience. Thanks are due to Dr. V.K. Kapoor, Principal G.H.G. Khalsa College of Pharmacy Gurusar Sadhar (Ludhiana) and Dr. K.S. Jain, Principal Sinhgad College of Pharmacy, (Sinhgad Technical Education Society) Pune. They provided assignments to teach M. Pharm. classes at their respective colleges, to generate interest of the author in application of organic chemistry to molecular biology. This testifies the statement ‘Great ability develops and reveals itself increasingly with every new assignment’ (Baltasar Gracian). xi

xii

ACKNOWLEDGEMENT

One of us (PSK) have been lucky enough to have worked with some wonderful teacher friends both before, and after, his days as a Poona University and NCL (Pune) student during Ph.D. programme. Prof. M.S. Wadia and Prof. S.K. Paknikar were surely largely responsible for setting me on my way. More importantly I discovered an intellectual atmosphere in their company that affected me forever. My wife Jagdish bore much of the brunt of the writing of this book. Too many absences, a large preoccupation, all coped with. Great thanks to her. One of us (NM) pays her gratitude to her mother, Mrs. Devajani Mahanta and her husband Mr. Mayur Bordoloi and all family members who stood by her during preparation of this book. A large part of the book was written during a period of study leave, I thank the Principal of J.B. College Dr. B.C. Sarma for his support and cooperation during this period. Special thanks are to Dr. D.R. Saikia Vice Principal of J.B. College for his moral support and all well wishers. Last but not the least, the authors place on record, the excellent service they got from AIU and its guest house during the past two decades. During visits to other universities in the country, stay at the guest house was very comfortable. The facility was gainfully used by us in the preparation of text material of books. Mrs. Vijaya Sampath had been very considerate and kind.

CONTENTS Foreword Preface Acknowledgement

vii ix xi

1. BIOLOGICAL CELL AND ITS CONSTITUENTS 1.1 1.2 1.3 1.4

1 –50 50

Biological Cell The Major Complex Biomolecules of Cell Structure and Function of Proteins and Enzymes Nucleic Acids

2. BIOENERGETICS

1 12 13 38

51 78 51–78

2.1 2.2 2.3 2.4 2.5 2.6

Introduction Free Energy Change Standard Free Changes in Biochemical Reactions Hydrolysis of ATP–Bioenergetic Significance of ATP Biochemical Reactions in a Cell The Actual Free Energy Change in Living Cells is Much Higher Than the Standard Free Energy Change 2.7 Biological Phosphate Compounds Other Than ATP — Conversion of ADP to ATP 2.8 Biological Oxidation–Reduction Reactions (Oxidative Phosphorylation ATP Synthesis) 2.9 Glycolysis is a Pathway Which Produces ATP (ATP Formation Coupled to Glycolysis)

3. STATISTICAL MECHANICS IN BIOPOLYMERS

51 54 61 63 66 66 67 69 76

79 104 79–104

3.1 Chain Configuration and Conformation of Macromolecules 3.2 Statistical Distribution–End to End Dimensions and Biopolymer Structure 3.3 Calculation of Average Dimensions for Different Chain Structures xiii

79 95 102

xiv

CONTENTS

4. FORCES INVOLVED IN BIOP OL YMER INTERACTIONS BIOPOL OLYMER 4.1 Introduction 4.2 van der Waals Forces 4.3 Electrostatic Interactions (Ionic Bond, Salt Linkage, Salt Bridge or Ion Pair) 4.4 Hydrophobic Interactions 4.5 Hydrogen Bonding 4.6 Hydrogen Ion Titration Curves

5. CELL MEMBRANE AND SOLUTE TRANSPORT 5.1 5.2 5.3 5.4 5.5 5.6 5.7

105 106 111 116 121 125

136 161 136–161

Introduction and Function of Cell Membranes 136 The Chemical Composition of Membranes 137 Formation of Bilayer Lipid Aggregates—The Bilayer Membrane Structure 140 Fluid Mosaic Model of Membrane Structure 141 Transport Across Membranes 142 Nerve Conduction—Propagation of Impulse Along a Nerve 156 More on Transport of Ions Through Membranes 160

6. BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS 6.1 6.2 6.3 6.4

105 135 105–135

Introduction Molecular Weight of Macromolecules Methods of Determination of Molar Masses of Macromolecules Electrophoresis

7. THERMODYNAMICS OF BIOPOLYMER SOLUTIONS 7.1 Introduction and General Principles 7.2 Thermodynamics of Biopolymer Solutions 7.3 Thermodynamic Principles and Dissolution of Crystalline and Amorphous Polymers 7.4 Heat of Dissolution and the Solubility Parameter 7.5 The Flory-Huggins Theory of Polymer Solutions 7.6 Donnan Membrane Equilibrium 7.7 Muscular Contraction and Energy Generation in Mechanochemical System 7.8 Osmotic Pressure

162 180 162–180 162 162 165 177

181 199 181–199 181 182 187 187 189 193 195 198

CONTENTS

8. DIFFRACTION METHODS

xv

200 222 200–222

8.1 Introduction—General Principles of Light Scattering 8.2 Light Scattering by Macromolecules and Measurement of Average Molar Mass 8.3 X-ray Diffraction and Three Dimensional Structures of Macromolecules 8.4 Photon Correlation Spectroscopy (PCS) also Called the Dynamic Light Scattering (DLS)

Index

200 201 205 210

223 228 223–228

BIOLOGICAL CELL AND ITS CONSTITUENTS

1

C H A P T E R

 1.1

BIOLOGICAL CELL AND ITS CONSTITUENTS

BIOLOGICAL CELL

(A) INTRODUCTION The cell is the basic structural unit of living systems, as glucose is the structural unit of starch and cellulose and adamantane is the structural unit of diamond. The nutrients absorbed by the human body are used by cells and most of the chemistry which takes place in the body occurs within cells. Thus in summary, the cell is the structural and functional unit of biological activity. The cells of living kingdom are basically of two types. 1. Prokaryotes The prokaryotic cell is smaller and simpler and is typical of bacteria. The E. coli cell is around 2 µm long and 1 µm in diameter. The prokaryotes have typically: 1. A cell membrane 2. Cytosol (containing metabolites) 3. Cell wall and perhaps an outer layer 2. Eukaryotes The eukaryotic cells are larger, more complex cells and are found in plants and animals. These are 5 to 100 µm in diameter with cell volumes thousand to million times larger compared to those of bacteria. In addition to a cell membrane, cytosol, and perhaps cell walls, eukaryotes have following distinguishing characteristics (compared to prokaryotes): 1. A nucleus 2. Different membrane bound, organelles which have specific functions (mitochondria, endoplasmic reticulum, Golgi complexes and lysosomes) 1

E. coli is found in the human intestinal tract.

A cell is the basic unit of life and represents a smallest piece of a living organism which can carry out life processes on its own.

Organelle is a structure within a cell which carries out one or more functions of the cell. Prokaryotic cells (bacteria) are smaller, simpler, lack a nucleus and these have a cell membrane. Eukaryotic cells are layer, more complex with different membranous organelles and have a true nucleus. Antibiotics used in medicine adversely affect bacteria with little or no effect on human cells.

2

Typically eukaryotic cells possess a true nucleus, the organelle where DNA is located in bacteria, the DNA is not located in a separate organelle but it is simply suspended in the cytosol. In bacteria the DNA is often termed nucleoid.

BIOPHYSICAL CHEMISTRY

(B) DESCRIPTION

OF

ORGANELLES

The diagrammatic representation of a typical eukaryotic cell is given in (Scheme 1.1). The structural components of the cell are described in detail. Plasma membrane separates the cell from environment and regulates movement of substances into and out of cell

A gene is a small region of a DNA.

Mitochondrion (Oxidises fuels e.g., glucose to produce ATP)

Ribosomes

Lysosome Nucleus (Contains the genes)

Rough endoplasmic reticulum

Nucleolus

Smooth endoplasmic reticulum

Golgi apparatus

Peroxisome (Destroys peroxides)

Cytoskeleton

Cytosol (The fluid interior of the cell)

Schematic representation of a cell: Some of the more unique structures are explained SCHEME 1.1

The plasma membranes provide barriers which protect the cell and the subcellular organelles from the external hostile environment. The basic structure of a membrane is a lipid bilayer on which globular proteins are irregularly embedded.

1. Nucleus Nucleus is the largest cellular organelle. It contains the genes and it is here where the information required for cell growth, division and maintenance is located. It is here where the DNA of the eukaryote is found. DNA is associated with proteins in larger structures termed chromosomes. Chromosomes represent rather complex structures which contain genetic material (DNA) and protein. The nucleus is bounded by two membranes which fuse together at the nuclear pores from which molecules e.g., mRNA (messenger ribonucleic acid), proteins, ribosomes etc., can move between the nucleus and cytosol.

BIOLOGICAL CELL AND ITS CONSTITUENTS

2. Nucleolus It is a dense structure in the nucleus of eukaryotic cells. It is rich in RNA and ribosomal RNA which enter the cytosol through the nuclear pores. 3. Plasma Membrane (For Details See Chapter 6) The plasma membrane is the cell structure which separates the contents of the cell from the external environment. The plasma membrane is not a rigid structure, it also is not a passive barrier between the internal and external environment. It is a selectively permeable barrier for controlling the entry of nutrients and the departure of waste products. The membranes are composed of lipids, proteins and carbohydrates and these biological membranes are relatively impermeable. These membranes provide a selectively permeable barrier because of the presence of specific transport proteins and the receptor proteins which can only bind specific ligands. Thus one protein may be involved in the transport of glucose while others are involved in the transport of ions e.g., a sodium ion. In summary considering only the two principal classes of compounds found in membranes i.e., polar lipids and proteins, the overall outlines of a membrane structure are in (Scheme 1.2).

3

When two aqueous compartments with different concentrations of a soluble compound or an ion are separated by a membrane the solute moves by simple diffusion from the region of higher concentration to the region with lower concentration. In the case of a charged solute the movement across a membrane depends on chemical gradient (the difference in solute concentration) as well as the electrical gradient (Vm) across the membrane. Taken together these two factors are called electrochemical gradient or electrochemical potential and the behaviour of solutes follows the second law of thermodynamics.

Structurally the biological membranes are bilayer sheets with hydrophilic regions immersed in water while the hydrophobic regions of phospholipids are protected from the aqueous environment. Membranes also contain integral and peripheral proteins. The membranes selectively allow adjustments of cell composition and function. Membrane structure: (I) Diagram of a section of a bilayer membrane formed from phospholipid molecules. (II) Fluid mosaic model of biological membranes with proteins embedded in the lipid matrix. SCHEME 1.2

4

Membrane proteins are integral, if these are firmly embedded in the bilayer and are called peripheral when these are attached loosely to the inner or outer surface of the membrane. The plasma membranes are selectively permeable barriers because of the presence of specific transport proteins and also due to the presence of other receptor proteins which can only bind specific ligands.

BIOPHYSICAL CHEMISTRY

The lipids prevent movement of polar molecules and ions across the membrane while some membrane proteins act as specific transport systems for these polar species. Considering two common methods for passing substances through a membrane one is facilitated transport while the other is active transport. Facilitated diffusion (transport) is speeded up by proteins which act as channels. Movement of the molecules or ions is from a region of higher concentration on one side of membrane to one of lower concentration to the other side. The process occurs quickly because the proteins allow passage across the nonpolar core of the membrane (Scheme 1.3). Facilitated diffusion is independent of externally applied energy.

Facilitated transport: A membrane protein acts as a channel or carrier. It is like a channel or pore in the membrane from which the molecules or ions pass through SCHEME 1.3

During the active transport external energy is needed. This energy is provided by ATP or electrochemical gradients (see Chapter 6). Active transport moves molecules against a concentration gradient (from low concentration to high concentration) (Scheme 1.4).

Active transport: This process requires energy when a substance is pumped from one region to another even against its gradient. SCHEME 1.4

BIOLOGICAL CELL AND ITS CONSTITUENTS

5

The free energy change (for details also see Sec. 2.8) for transport through a membrane may be considered from the following points: l The free energy change during a chemical process converting a substrate (S) to a product (P) is given by (Eqn. I Scheme 1.5). ∆G = ∆Go′ + RT ln

[P] [S]

(I)

where R = gas constant K and T is the absolute temperature ∆Gt = RT ln

where

C2 C1

(II)

C  ∆Gt = RT ln  2  + ZF ∆ψ  C1  Z = charge on the ion F = Faraday constant (96, 480 J/v. mol) ∆ψ = transmembrane electrical potential in volts SCHEME 1.5

In case the reaction in a simple transport of a solute from a region of C1 concentration to a region of C2 concentration, the standard free energy change ∆G°′ is zero and then the free energy change for such a transport is given by (Eqn. II, Scheme 1.5). l In case the solute is an ion, the energy cost for its transport is related to the electrochemical potential which is the sum of both chemical as well as electrical gradients and is then given by (Eqn. III, Scheme 1.5). 4. The Mitochondrion (Plural—Mitochondria) The mitochondria (Greek: mitos-thread; chondros-granule) are regarded as the power houses of the cell where much of the energy production of the cell takes place. This organelle functions in the oxygen-requiring process (oxidative phosphorylation) in which energy contained within electrons is conserved in a form of energy usable by the cell, i.e., as the nucleotide adenosine triphosphate (ATP). For this reason, the mitochondria may be described as the power houses of the cell. Mitochondria are therefore, generally located where energy demand is highest in the cell. All mitochondria have two separate membranes an inner and outer membrane which

6

BIOPHYSICAL CHEMISTRY

The transport of electrons through electron transport chain (ETC) is linked with the release of free energy. The synthesis of ATP from ADP and Pi coupled with the electron transfer chain is termed oxidative phosphorylation. Members of the electron transport complexes are housed in the inner mitochondrial membrane.

are chemically and functionally distinct. The principal features of the structure of the mitochondrion are: l Outer membrane l Intermembrane space (or ‘O’ compartment) l Inner membrane l Matrix (or ‘M’ compartment) (Scheme 1.6)

l The outer membrane of a

mitochondrion is freely permeable to small molecules and ions.

l The inner membrane is

impermeable to most small molecules and ions including H+ . The structure of mitochondrion with some of the enzymes SCHEME 1.6

The outer membrane is freely permeable to small molecules and ions and maintains the shape of organelle and contains open pores which are generated by transmembrane protein called porin. The diameter of the pore may be adjusted by either positive or negative voltages across the outer membrane, i.e., the channel of mitochondrial porin is voltage gated. The ‘O’ compartment separates the outer and inner membranes. The inner membrane (cristae) is the site of oxidative phosphorylation and members of electron transport complexes and ATP synthesising enzymes are housed here.

BIOLOGICAL CELL AND ITS CONSTITUENTS

The inner membrane is less permeable to most small molecules and ions including H+. The species which cross the membrane need the help of specific transporters. The inner membrane is folded to form cristae. The central matrix which is surrounded by inner membrane (Scheme 1.6) is a site of several metabolic reactions including citric acid cycle and fatty acid breakdown. Within the matrix is found discrete double helical strands of circular DNA and ribosomes. The mitochondrial matrix contains several enzyme systems (Scheme 1.6): l Pyruvate dehydrogenase complex l Enzymes of the citric acid cycle l The fatty acid β-oxidation pathway and l The pathway of amino acid oxidation All these systems are needed for fuel oxidation. Glycolysis however occurs in cytosol (scheme 1.6a) and involves a series of ten enzyme-catalysed reactions by which glucose is oxidized to two molecules of pyruvate. β-oxidation involves a series of four enzyme catalysed reactions which cleave two carbon atoms at a time until the entire fatty acid chain is degraded to acetyl CoA. Pyruvate, fatty acids and amino acids are brought into the matrix by specific transporters to undergo citric acid cycle (Scheme 1.6b). ADP and Pi then get transported specifically into the matrix and newly synthesised ATP is transported out. β-Oxidation of Fatty Acids Fatty acids after their release from triglycerides are activated in the cytoplasm by formation of thioesters with coenzyme A and transport of activated fatty acids across the inner mitochondrial membrane exposes them to β-oxidation enzymes.

Glycolysis occurs in cytosol SCHEME 1.6(a)

7

The mitrochondrial matrix is rich in enzymes which are involved in citric acid cycle, β-oxidation of fatty acids and oxidation of amino acids

The citric acid cycle (krebs cycle or tricarboxylic acid TCA cycle) represents the key metabolic pathway for the energy supply to the body. The cycle e.g., oxidises pyruvate (formed during the glycolytic breakdown of glucose) to CO 2 and H 2O with the production of energy. It represents the final common oxidative pathway for carbohydrates, fats and amino acids. This cycle utilises nearly 2/3 of total oxygen consumed by the body to generate nearly 2/3 of total energy in the form of ATP.

The NADH is an energy rich molecule since it contains electrons with high transfer potential.

8

Oxidative phosphorylation needs a supply of NADH, O2, ADP and Pi. Electrons flow from fuel molecules to O2 only if ATP is required to be synthesised.

BIOPHYSICAL CHEMISTRY

In mitochondria the hydride ions (from NADH e.g.,) donate electrons to the electron transfer chain (ETC) which subsequently transfers the electrons to O2 to form water which is an exergonic process and releases energy. This free energy of oxidation (see, Scheme 1.7) is used for the synthesis of ATP.

NADH (and also FADH2) are formed in glycolysis, fatty acid oxidation (β-oxidation), and citric acid cycle are rich in energy since these have a pair of electrons with high transfer potential. Shuttle systems transfer reducing equivalents from cytosolic NADH to mitochondrial NADH.

Conversion of food energy into ATP in mitochondrion. Oxidation of the major food stuffs leads to the formation of reducing equivalents e.g., NADH. Electrons from these sources are collected by ETC for oxidation and coupled formation of ATP SCHEME 1.6(b)

BIOLOGICAL CELL AND ITS CONSTITUENTS

9

As discussed above a major role of the inner membrane is that it is the site of oxidative phosphorylation. It houses the electron transport chain and ATP synthesising system. One may consider the energetics of oxidative phosphorylation. The transport of two electrons from the redox pair NAD+/ NADH to the redox pair ½O2/H2O can be written as (Eqn. I, Scheme 1.7). This net reaction is highly exergonic. For details of energetics of oxidative phosphorylation see Sec. 2.8 and Table 2.2. + 1 O + NADH + H 2 2 +

ADP + Pi + H

Electrons e.g., from NADH are transferred in mitochondrial membranes through a chain of three large protein complexes. The electron carrying groups in these enzymes are flauins, iron sulphur dusters, hemes and copper ions. Each redox couple e.g., NAD +/NADH and ½O2/H2O is associated with a redox potential (∆E0′) and a calculated ∆G°′ (see Table 2.2 and Scheme 2.29).

+

H2O + NAD + (exergonic) (I) ATP + H2O (endergonic)

(II)

NADH transfers two electrons (through the respiratory chain) to molecular oxygen in an exergonic process. This free energy of oxidation is used in the synthesis of ATP (Eqn. II) which is an endergonic process SCHEME 1.7

The redox potential difference ∆E0′ between these two redox pairs in 1.14 V [NAD+/NADH (E0′ = – 0.32 V) while for the pair O2/H2O (E′0 = +0.82)]. Thus when NADH is oxidixed most of the energy released is trapped to form ATP. The standard free energy change for the reaction (I, Scheme 1.7) is given by Nernst equation (Scheme 1.8, for details see Scheme 2.30). ∆G0′ = –nF ∆E0′ = –2 (96.5 kJ/V. mol) (1.14 V) = –220 kJ/mol (of NADH) SCHEME 1.8

Thus in summary electrons flow from NADH to molecular oxygen (Eqn. I, Scheme 1.7) is an exergonic process to release energy. This free energy of oxidation is used for the synthesis of ATP (Eqn. II, Scheme 1.7) which is an endergonic process. 5. Endoplasmic Reticulum (ER) It is a complex network of membrane enclosed spaces and some of these thread like structures extend from the nuclear pores to the plasma membrane. It is often studded with ribosomes leading to granular appearance which is than called rough endoplasmic reticulum. Ribosomes are the sites of protein biosynthesis.

Sequence of electron carriers in the respiratory chain (ETC). Protons are pumped by the three protein complexes shown in circles

10

Mitochondria uses its arrangement of electron carriers for the mediation of the transfer of electrons from a low to a high redox potential. As a consequence of this electron flow free energy is released which is utilized to form ATP in the process of oxidative phosphorylation. Cytoplasm is the portion of cell contents which is outside the nucleus, but within the plasma membrane and includes organelles like mitochondria.

Ribosome is a supramolecular complex of rRNAs and proteins. It is the site of protein synthesis. The digestive enzymes of cellular compounds are kept confined to the lysosomes. If these enzymes escape into cytosol these will lead to destruction of cells by their own enzymes. Some diseases like arthritis, muscles diseases and allergic disorders are partly due to the release of lysosomal enzymes.

BIOPHYSICAL CHEMISTRY

The smooth endoplasmic reticulum which is not studded with ribosomes is the site of biosynthesis of lipids (triacylglycerols, phospholipids, sterols) and is where several detoxification reactions (e.g., of drugs) take place. The smooth endoplasmic reticulum besides its involvement in metabolism of drugs also supplies Ca2+ for the cellular functions. 6. Golgi Apparatus It represents a complex membranous organelle of eukaryotic cells. It acts as the sorting and processing centre of the cell. The Golgi apparatus catalyses the addition of carbohydrates lipids or sulphate moieties on the newly synthesised proteins. These modification on the proteins are necessary for the transport of proteins across the plasma membrane or incorporation into the plasma membrane. Golgi apparatus also encloses some proteins and enzymes which are secreted from the cell after appropriate signals. 7. Lysosomes Lysosome is a membrane bounded organelle in the cytoplasm of eukaryotic cells and is regarded as the digestive tract of the cell. It contains several hydrolytic enzymes (hydrolases) and lysosomes are involved in the digestion of cellular substances like lipids, carbohydrates, proteins and nucleic acids. The internal pH of lysosomes is mildly acidic (pH = 4– 5) than the cytosol (pH = 7). The mildly acidic pH of lysosome is maintained by integral proteins which pump H+ ions into them. This mildly acidic pH of lysosomes makes the hydrolases optimally active to facilitate the degradation of different compounds. Proteases degrade proteins, lipases degrade lipids, phosphatases remove phosphate groups from nucleotides and phospholipids and nucleases degrade RNA. 8. Peroxisomes

Catalase is a hemoprotein containing four heme groups. It uses one molecule of H2O2 as a substrate electron donor and another molecule of H2O2 as an oxidant or electron acceptor.

Peroxisomes are also microbodies have a single boundary membrane and contain the enzyme catalase. The enzyme catalase protects the cell from the toxic hydrogen peroxide (H2O2) by converting it into harmless H2O and O2 (Scheme 1.9). Catalase 2H2O2

2H2O + O2

Toxic

Harmless SCHEME 1.9

BIOLOGICAL CELL AND ITS CONSTITUENTS

9. Cytosol and Cytoskeleton Cytosol represents the continuous aqueous phase of the cytoplasm which is not included within any of the subcellular organelles. Cytosol contains several enzymes, metabolites and salts in aqueous gel like medium several reactions e.g., glycolysis, (see Scheme 2.31) gluconeogenesis. The pentose phosphate pathway and fatty acid synthesis all occur in cytosol. Cytosol also holds in addition to many proteins, metabolic enzymes, cytoskeletol proteins and intracellular transport proteins many small organic molecules e.g., amino acids and nucleotides which are involved in metabolic processes. It also contains coenzymes, cations (Mg2+, Ca2+) and anions (HCO3– and HPO42–). Recall that glycolysis involves several reactions which occur in cytoplasm. The role of glycolysis is to generate energy both directly and also by the supply of substrates for the citric acid cycle and oxidative phosphorylation. Glycolysis also generates several intermediates for biosynthetic pathways. The cytosolic NADH (i.e., electrons from NADH) enters mitochondria by shuttles instead, because the inner mitochondrial membrane is impermeable to both NADH and NAD+. One carrier is glycerol 3-phosphate (Scheme 1.10).

SCHEME 1.10

The first step in this shuttle involves the transfer of electrons from NADH to dihydroxyacetone phosphate which is converted into glycerol 3-phosphate (Scheme 1.11) catalyzed by the enzyme (cytosolic) glycerol 3-phosphate dehydrogenase. The product glycerol 3-phosphate than diffuses in the membrane and the electrons thus carried are not transferred to mitochondrial NAD+ but to FAD bound as a prosthetic group to a different enzyme, mitochondrial glycerol 3-phosphate dehydrogenase. Subsequent oxidation of glycerol 3-phosphate gives dihydroxyacetone phosphate which diffuses back into cytosol to complete the shuttle.

11

Peroxidases are also heme enzymes which catalyse an analogous reaction where on alkyl peroxide is reduced to water and alcohol by a reductant (AH2). ROOH + AH2 ROH + H2O + A The reductant could be cytochrome or ascorbate.

NADH is also formed by glycolysis in the cytosol (also see, Scheme 2.26), however the inner mitochondrial membrane is quite impermeable to both NADH and NAD+. It is the electrons from NADH rather than NADH itself which are carried across the mitochondrial membrane. At the subcellular level glycolysis occurs in the cytosol while citric acid cycle in the mitochondria.

In the first stage of glycolysis a C6 molecule of glucose is divided into two different C3 molecules dihydroxyacetone phosphate and glyceraldehyde 3-phosphate.

12

BIOPHYSICAL CHEMISTRY

The glycerol phosphate shuttle predominates in the cells of mammalian skeletal muscle and brain.

SCHEME 1.11

The cytoplasm contains a rather complex network of protein filaments which provide structure as well as organisation to the cytoplasm.

1.2 Viruses are essentially only DNA with a protective coat of protein. All life forms contain DNA which is species specific.

THE MAJOR COMPLEX BIOMOLECULES OF CELL

Carbon is the key and most versatile element of life. Carbon can form stable covalent bonds and C—C chains of unlimited length and thus forms infinite number of compounds. More than 90% of compounds of biological origin invariably contain carbon. Some of the major complex biomolecules with their functions are listed in (Table 1.1). TABLE 1.1: The major complex biomolecules of cells

An internal protein network called the cytoskeleton is responsible to maintain the cellular shape and physical integrity.

Biomolecule 1.

Proteins

Building block (repeating unit) Amino acids

Major functions Represent the major structural substances of skin, blood, muscle, hair and other tissues of the body. Proteins called enzymes are required to catalyse almost all the reactions in the cell.

BIOLOGICAL CELL AND ITS CONSTITUENTS

13

2. Deoxyribonucleic acid (DNA)

Deoxyribonucleotides

Contains the genetic information.

3. Ribonucleic acid (RNA)

Ribonucleotides

Involved in protein biosynthesis.

4. Polysaccharide (glycogen)

Monosaccharides (glucose)

Storage form of energy for short term demands.

5. Lipids

Fatty acids, glycerol

Storage form of energy for long term demands; structural components of membranes.

1.3

Glucose is the major metabolic fuel of mammals and is the precursor for the synthesis of other carbohydrates in the body e.g., glycogen for storage, ribose and deoxyribose in nucleic acids, galactose in milk etc.

STRUCTURE AND FUNCTION OF PROTEINS AND ENZYMES

Protein is the key and most abundant class of biomolecules in the cells. Protein makes up one-half of the dry mass of a cell. The name protein is derived from the Greek word proteios, which means of the first rank or importance. Proteins are indeed of the first rank, because they are directly responsible for most of the chemical activity and for much of the physical structure of a cell.

(A) STRUCTURAL OUTLINES

OF

PROTEINS

1. What are Proteins? Proteins are special type of polypeptides made of primarily 20 different specific amino acids (structures of amino acids are given in Table 1.2). Proteins are large molecules with molecular weights from 6000 to more than 1,000,000 (from nearly 50 to more than 8,000 amino acids per molecule). 2. Proteins and Amino Acids Proteins are important biological macromolecules and these play a variety of roles in the functions of living systems. These control cell growth and differentiation and recognize foreign substances. The monomeric subunits in proteins are a variety of amino acids and 20 of these with their structures, and abbreviations are given (Table 1.2). TABLE 1.2: Common amino acids Name Non-polar R group Alanine

Abbreviation Ala or A

Structure

14

BIOPHYSICAL CHEMISTRY

Valine

Val or V

Leucine

Leu or L

Isoleucine

Ile or I

Phenylalanine

Phe or F

Tryptophan

Trp or W

Methionine

Met or M

Proline

Pro or P

Polar but neutral R group Serine

Ser or S

Threonine

Thr or T

Tyrosine

Tyr or Y

Cysteine

Cys or C

Asparagine

Asn or N

BIOLOGICAL CELL AND ITS CONSTITUENTS Glutamine

Gin or Q

Glycine

Gly or G

15

Acidic R groups Glutamic acid

Glu or E

Aspartic acid

Asp or D

Basic R groups Lysine

Lys or K

Arginine

Arg or R

Histidine

His or H

Peptides, also called polypeptides are amino acid polymers. In organic chemistry the bond formed between the carbon atom of the carbonyl group of a carboxylic acid and the nitrogen atom of an amino group is called an amide bond. When this bond involves amino acids, it is called a peptide bond (Scheme 1.12). Peptide bond connects amino acids together in peptides and proteins. For example, the peptide formed from two amino acids is a dipeptide. Like an amino acid it is amphoteric and exists as a Zwitterion (Scheme 1.12). A tripeptide contains three amino acid building units, and so on. Adding more units to the chain, a polymer of any length, i.e., a polypeptide can be obtained (Scheme 2.2). Thus peptides (polypeptides) are amino acid polymers. The individual amino acids are connected by amide linkages (a peptide bond) from the amino group of one unit to the carboxy group of other. A +

polypeptide will contain a free NH3 group— the N-terminal

The Primary (1°) protein structure is the linear sequence of amino acids from N-to C-terminus.

The Secondary (2°) protein structure is the arrangement of a polypeptide chain into an organized structure, such as an α-helix or β-pleated sheet, stabilized by hydrogenbonding between peptide bonds.

16

BIOPHYSICAL CHEMISTRY

end and a free COO– group,—the C-terminal end. It is the usual convention to write the structure of a peptide with N-terminal end on the left and the C-terminal on the right.

SCHEME 1.12

Primary structure of a protein shows the amino acid sequence SCHEME 1.13

3. Primary Structure of a Protein The primary structure of a protein is simply the amino acid sequence on their order in the polypeptide chain from N- to C-terminus. Peptide bonds are the only covalent bonds that hold adjacent amino acid residues in a peptide/protein/ enzyme (see Scheme 1.13). 4. Secondary Structure of a Protein α-Helical structure The secondary structure is a result of the conformation that the polypeptide chain can take. If the polypeptide chain of proteins was totally composed of single bonds as the primary structure is usually written (see Scheme 1.13) then each molecule would have an infinite number of conformations.

BIOLOGICAL CELL AND ITS CONSTITUENTS

However, resonance in the amide (i.e., peptide) group gives a partial double bond character to the C—N bond (Scheme 1.14). This restricts rotation around these bonds and thus the number of stable conformations is restricted. The four atoms of the peptide bond and the two connective α-carbons i.e., all the six atoms in a peptide bond lie in the same plane (II, Scheme 1.14). The peptide bond is rigid, however, the planes can rotate about the α-carbon atoms Cα—C and Cα—N (H and O atoms are placed trans to each other).

SCHEME 1.14

The linear polypeptide chain can adopt different secondary structures depending on the nature of R groups attached. A partial rotation of about 45° allows the peptide bonds to arrange so that every fourth peptide bond comes under another to get a common arrangement called the α-helix. Hydrogen bonding can occur between peptide bonds located above and below each other in a direction almost parallel to the long axis of the helix (Scheme 1.15). Thus the α-helix is stabilized by intrachain hydrogen bonds between the —C = O group of each peptide bond and the —NH group of the peptide bond four residues away (Scheme 1.16).

17

An α(alpha)-helix is a spiral protein secondary structure stabilized by hydrogen-bonding between the peptide bonds of every four amino acids.

The stability of an α-helix primarily results from hydrogen bond formation between the carbonyl oxygen of the peptide bond and the amide hydrogen atom of the peptide bond of the fourth residue down the polypeptide chain (see, Schemes 1.15 and 1.16). The ability to form the maximum number of hydrogen bonds, supplemented by van der Waals interactions in the core of this tightly packed spiral structure provides the thermodynamic driving force for the formation of the helical structure.

18

BIOPHYSICAL CHEMISTRY

The hydrogen attached to the amide nitrogen is electropositive (δ+) while the oxygen of the carbonyl group is electronegative (δ–). Thus, the amide hydrogen is said to be a hydrogen-bond donor and the carbonyl oxygen is a hydrogen-bond acceptor.

An α-helix—A right-handed spiral secondary structure of many proteins SCHEME 1.15

The polypeptide chain rotates around the tetrahedral carbons in order to align amide hydrogens with carbonyl oxygens (hydrogen-bond donor-acceptor pairs).

C

O N

C

A proline residue in a polypeptide can lead to difficulties to fit into an α-helix. The amino nitrogen is also the part of the substituent ring and restricts rotation. Thus a proline residue forces a bend in α-helix.

O H

N α-Helical structure in keratin, the term α was coined to specify the X-ray pattern of keratin and to distinguish it from other proteins. The helical shape is responsible for strong, fibrous and flexible product. (non-participating R’s and H’s not shown in diagram).

C

C C

H

C

H

N

C

O

O- -

N

H

C N C

O

Keratin

SCHEME 1.16

5. Prevention of α-helix Formation A stable α-helix is not formed by all polypeptides and an important constraint on the formation of α-helix is the presence of proline residues on the polypeptide chain (Scheme 1.17). There is no rotation about the α carbon since the nitrogen atom is part of the rigid ring. Moreover, no hydrogen atoms are present on the nitrogen of a proline residue and thus interchain hydrogen bonds cannot form. Successive serine residues also disrupt the α-helix formation due to the tendency of its OH group to form strong hydrogen bonds with water. Thus stretches of proline and serine may coil into helical arrangements other than an α-helix and proline e.g., is only rarely found within an α-helix.

BIOLOGICAL CELL AND ITS CONSTITUENTS

19

“The presence of a proline residue on a polypeptide chain” SCHEME 1.17

One knows that in an helix the substituents (R) on the α-carbons of the amino acids protrude outward at right angles from the helix so that steric interactions are minimum, this further stabilizes the structure (I, Scheme 1.18). Two adjacent amino acids that have more than one substitutent on a β-carbon (valine, isoleucine, or threonine) cannot fit into a helix because of steric crowding between the R groups. Two adjacent amino acids with like-charged substitutents cannot fit into the helix because of electrostatic repulsion between the R groups. This is so if a polypeptide chain has a long block of glutamic acid (Glu) residues. This portion of the chain does not form an α-helix at pH 7.0. Similarly when there are several adjacent lysine (Lys) and/or arginine (Arg) residues with positively charged R groups at pH 7.0, they repel each other and prevent the α-helix formation. The percentage of amino acid residues coiled into an α-helix varies from protein to protein, but overall about 25% of the residues in globular proteins are in α-helices.

A segment of a protein in an α-helix when viewed up the longitudinal axis of the αhelix. The side chains of the amino acids (R) are positioned on the outside of the helix. The van der Walls radii of the atoms on the helix (not shown) are large and there is in infact no free space inside the helix.

β (beta)-pleated sheet is layered protein secondary structure stabilized by sideto-side hydrogen-bonding between peptide bonds located in different chains or parts of a chain. In a parallel β sheet a β sheet has its polypeptide strands aligned N-to Cterminus. In a antiparallel β sheet a β sheet has its polypeptide strands which run N to C and C to N.

SCHEME 1.18

20

BIOPHYSICAL CHEMISTRY

β-pleated sheet structures With the repeating sequences of amino acids with small compact R-groups e.g., glycine and alanine the formation of a β-pleated structure is favoured. Such a structure has the polypeptide backbone extended in a zigzag structure like a series of pleats. In this arrangement the polypeptide strands may be alligned N- to C-terminus (parallel β sheet) or N- to C- and C- to N-(antiparallel β sheet). The hydrogen bonding in a β-pleated sheet occurs between neighbouring peptide chains (Scheme 1.19). Silk is a protein with β-pleated structure. In such an arrangement the substituents (R) on the α-carbons of the amino acids on adjacent chains are close to one another. For effective hydrogen bonding the steric hindrance caused by closeness of (R) groups should be minimum. Significantly, therefore, the silk fibrion contains 46% glycine (no side chain), and 38% a mixture of alanine and serine (small side chains).

SCHEME 1.19

6. Protein Tertiary Structure—Fibrour and Globular Proteins Proteins can bend and fold to adopt a variety of structures that may be long and fibrous like hair or more compact, that is, globular, like egg white (albumin). The R side chains participate in both covalent and non covalent interactions in order to stabilize the protein in its final three-dimensional structure or tertiary (3°) conformation. The common and the only covalent side chain bond that can hold together remote regions of the protein is the disulphide bond formed between two cysteine residues. The -SH groups on two cysteines are oxidized to form a covalent disulphide bond or bridge. (Scheme 1.20)

BIOLOGICAL CELL AND ITS CONSTITUENTS

SCHEME 1.20

Several factors (Scheme 1.20) stabilise tertiary structure of a protein and more often by noncovalent interactions. Principal among these are hydrophobic interactions that drive most hydrophobic amino acid side chains into the interior of the protein and thus shield them from water. Other significant forces include hydrogen bonds and salt bridges between the carboxylates of aspartic and glutamic acid and the oppositely charged side chains of protonated lysyl, argininyl, and histidyl residues. Although individually weak relative to a typical covalent bond of 80–120 kcal/mol, collectively these interactions confer a high degree of stability to the tertiary conformation of a protein.

21

22

BIOPHYSICAL CHEMISTRY

7. Quaternary Structure of a Protein The Quaternary structure of a protein represents an association of several protein chains or subunits into a closely packed arrangement Scheme 1.21. Each of the subunits has its own primary, secondary, and tertiary structure. The subunits fit together as a result of their shape and are held together by forces other than covalent bonds. Single-chain proteins have no quaternary structure. The subunits in a quaternary structure must be specifically arranged for the proper the entire protein. Any change in the structure of the subunits or how they are associated causes marked changes in biological activity.

SCHEME 1.21

(B) FUNCTION R — SH + HSR Thiol Thiol Reduction

Oxidation

R—S—S—R Disulphide

OF

PROTEINS

AND

ENZYMES

1. Biological Activity and Nature State of a Protein The biological activity of a protein depends on the threedimensional shape of the molecule, called its native state or native conformation. Any alteration of this structure due to breaking any type of bond destroys the physiological function of the protein. Protein structure is described at four levels: primary, secondary, tertiary, and quaternary. Each of these divisions is somewhat arbitrary because it is the total structure of the protein that controls function. Disulphide bridges are covalent bonds between cysteine residues which help a protein to maintain its tertiary structure. One method to destroy the secondary or tertiary structure is to break. The disulphide bonds which leads to loss of biological activity. On air oxidation the disulphide bridges re-form and the original bio activity is reestablished (Scheme 1.22).

BIOLOGICAL CELL AND ITS CONSTITUENTS

23

SCHEME 1.22

2. Some of the more Important Proteins and their Functions These are summarised in table 1.3. TABLE 1.3: Some proteins and their functions Name and class Structural α-Keratin Collagen Contractile Myosin Actin Transport Hemoglobin Serum albumin Cytochrome c Protective Antibodies Fibrinogen and thrombin Regulation Insulin Growth hormone Storage Myoglobin Ovalbumin

Function Found in skin and hair Fibrous connective tissue Thick muscle filaments Thin muscle filaments Transports oxygen in blood Fatty acid transport in blood Transport of electrons React with foreign invaders Blood clotting proteins Involved in regulation of metabolism Involved in regulation of metabolism Stores oxygen in muscles Protein of egg white. Supplies amino acids to developing young

3. The Role of Proteins and Enzymes in the Body l

Structural roles

Some proteins have structural roles. Collagen is the most abundant protein in animals which is a component of skin, bone, teeth, ligaments, tendons, and other extracellular connective structures.

24

BIOPHYSICAL CHEMISTRY

Regulation of body functions Some proteins play a role in regulation of body function. Insulin, glucagon, and growth hormone help control cellular and body activities. Several examples of these assorted functions are presented in (table 1.3).

l

Enzymes are protein catalysts involved in biochemical reactions in the cell. The commonly used nomenclature of enzymes describes the type of reaction catalysed followed by the suffix ase. The broad classification is: l Oxidoreductases (catalyse oxidations and reductions) l Transferases (catalyse the transfer of moieties e.g., methyle, phosphoryl) l Hydrolases (catalyse the hydrolytic cleavage of e.g., C—C, C—O, C—N bonds) l Lyases (catalyse the cleavage of bonds like C—C, C—O, C—N by an atom elimination. l Isomerases (bring about geometric or structural changes in a molecule) l Ligases (catalyze the condensation of two groups coupled to the hydrolysis of ATP). Prosthetic groups, cofactors and coenzymes Structurally many enzymes cannot catalyze a reaction without the help of small non protein molecules and metal ions. These are termed prosthetic groups, cofactors and coenzymes. Cofactors which are organic molecules are called coenzymes. Several of these cofactors are derivatives of B-vitamins. An example is of an enzyme yeast alcohol dehydrogenase which has a hydride donating coenzyme NADH (see, Scheme 1.26) at the active site where the catalysis occurs.

Protective roles in the body Some proteins have protective roles in the body. Antibodies are proteins that bind to specific foreign invadors e.g., viruses and bacteria. The antibody–particle complexes can then be more easily destroyed by various mechanisms.

l

Genetic information Via proteins genetic information is expressed. The two type of nucleic acids i.e., DNA and RNA serve as repositories and transmitters of genetic information. The genes control the protein synthesis (amino acid sequence) via the involvement of RNA (Scheme 1.23).

l

The genes control the protein synthesis through the mediation of RNA SCHEME 1.23

Transport of the materials in the blood Proteins are also involved in transport of materials in the blood. Hemoglobin helps transport oxygen and carbon dioxide, and lipoproteins transport lipids that would otherwise be insoluble. Various membrane proteins are involved in movement of substances across membranes via active transport or facilitated diffusion.

l

Catalytic role An important class of protein catalysts are the enzymes which act as catalysts for a variety of reactions that occur in the body. The enzymes are essential to bring about the break down of nutrients for the supply of energy and the chemical building blocks for the synthesis of proteins, DNA, membranes, cells and tissues. Lysozyme is an enzyme that cleaves or lyses the cell wall of some bacterial species and provides a protective role. Some proteins play a role in movement, such as actin and myosin which are two contractile proteins in muscles. Some proteins function as storage proteins. Myoglobin stores oxygen in

l

BIOLOGICAL CELL AND ITS CONSTITUENTS

muscle, and casein is a protein in milk that stores amino acids for the nursing young. 4. Functions of Enzymes as Catalysts The enzymes are chiral catalysts which catalyse the conversion of a substrate(s) into a product(s). The enzymes enhance the rates when compared with an uncatalysed reaction by a rate around 106. As true catalysts enzymes are neither consumed nor altered during their participation in a reaction. Enzymes display stereoselectivity and stereospecificity: Unlike synthetic chemistry enzymes are highly selective for the type of reaction to be catalysed, for the substrate (or a set of closely related substrates). Enzymes also display stereospecificity and catalyse the reactions of only one stereoisomer e.g., D-but not L- sugars and also Lbut not D-amino acids. This is due to fact that enzymes bind substrates through atleast three points of attachment. Thus an enzyme with specific bonding sites for three of the four groups on a stereocenter can make a distinction between a molecule and its enantiomer (or one of its diastereomers). From (Scheme 1.24), one can see that one enantiomer (a) can be absorbed at its three bonding sites while the other enantiomer (b) cannot.

SCHEME 1.24

The considerations (Scheme 1.24) explain as to how the enzyme catalysed reactions of an achiral substrate can produce one enantiomer and not the racemic mixture. When two atoms e.g., 1 and 4 of a substrate are identical and after atoms 2 and 3 are bound to their complementary sites on the enzyme than only atom 1 can bind and once it is bound, the apparently identical atoms become distinguishable to allow a stereoselectivity (Scheme 1.25) by the enzyme.

25

When the enzymes react with one of the enantiomers of a racemic mixture these are said to display stereospecificity. When these are in contact with a prochiral molecule react with only one of the enantiotopic ligands a property called stereoselectivity. When a carbon is bonded to two identical ligands (e.g., H atoms) and two different ligands, the two hydrogens are enantiotopic.

The carbon to which enantiotopic ligands are attached is called a prochiral carbon since it becomes a stereo center when one of the H atom is replaced by a group other than CH 3 or OH (already present in the molecule).

26

BIOPHYSICAL CHEMISTRY

Enantiotopic ligands e.g., H atoms of ethanol are not chemically equivalent towards chiral reagents e.g., an enzyme Ha CH3

C

4 3

C

1 2

OH

1

3

Enzyme site

2 Substrate (achiral)

Hb Alcohol Dehydrogenase

SCHEME 1.25

O C Hb

H3C 100%

Similarly unlike the equivalent faces of formaldehyde the faces of acetaldehyde are enantiotopic and enzymes react with only one of these enantiotopic faces. Example of another compound with enantiotopic faces is pyruvate (CH3COCOO–)

When one considers the reduction of e.g., acetaldehyde-1d with enantiotopic faces (Scheme 1.26) with the enzyme yeast alcohol dehydrogenase in the presence of hydride donating coenzyme NADH the hydride is only transferred to one of the faces (Re face), and the product is optically active. Thus the enzyme reacts with only one face of acetaldehyde-1-d. Thus one diastereomeric transition state during this reduction is greatly favoured over the other during the transfer of the hydride from the coenzyme to one face of the substrate with this enzyme system.

The enzyme yeast alcohol dehydrogenase

B B+ O

O

H

pro-R

pro-S

H H

O

H

H2N

O H2N N R NADH

D

H

CH3

Acetaldehyde-1-d Substrate

+ N R + NAD

Coenzyme NADH

SCHEME 1.26

D H

CH3

(s)-ethanol-1-d Product

BIOLOGICAL CELL AND ITS CONSTITUENTS

Enzymes follow several mechanisms for their catalytic action. l

Acid base catalysis

The enzymes carry out the catalysis at their active sites which is a cleft or a pocket. The substrate fits into the pocket and only those portions are aligned for catalytic reactivity that will undergo a change. An example of an acid-base catalysis is by an enzyme chymotrypsin. At the active site of the enzyme the histidine molecule behaves both as an acid and a base catalyst (Scheme 1.27). In the first step of catalytic activity it removes a proton from serine so that OH group becomes a stronger nucleophile to attack the peptide bond of the substrate. A transient tetrahedral intermediate is formed from which by proton donation by histidine the RNH2 group is liberated when the peptide bond is cleaved.

Covalent and general acid base catalysis—the outlines of the peptide bond cleavage by the enzyme chymotrypsin in its active site SCHEME 1.27

l

Catalysis by proximity

The enzyme binds its substrate at the active site in a way so as to orient the substrate in a position which is ideal for their interaction as seen in the case of chymotrypsin (see Scheme 1.27).

27

Enzyme catalysed carbonyl additions. During an enzyme-catalyzed addition to a carbonyl compound, only one of the enantiomers is formed. The enzyme blocks one face of the carbonyl compound so that it cannot react or the enzyme positions the nucleophile so that it is able to attack the carbonyl group from only one side of the substrate.

C

O Nucleophile

28

Histidine as an acid and a base catalyst. Protonation of the doubly bonded nitrogen in histidine gives a resonance stabilized cation. At pH7, imidazole of histidine can exist half protonated and halfdeprotonated. Thus histidine is found frequently at the active site of enzymes where it can act as an acid or a base. The basicity of imidazole ring of histidine is crucial in biology (Scheme 1.27).

BIOPHYSICAL CHEMISTRY

l

Covalent catalysis

During covalent catalysis there is a formation of a covalent bond between the enzyme and one or more substrates. The enzyme is modified which then becomes a reactant. Covalent catalysis introduces a new reaction pathway whose lower activation energy makes it faster. The chemical modification of the enzyme is only transient. On completion of the reaction, the enzyme returns to its original unmodified state and its role thus remains catalytic (see page 30). An example of covalent catalysis is found in (Scheme 1.27). l

Catalysis by strain

Often binding of a substrate to the enzyme leads to conformational changes in the substrate leading to strain which stretches or distorts the targeted bond or part of the substrate. This strain helps in cleavage of the substrate (Scheme 1.28). Substrate molecule in normal conformation

Conformational change

Induced fit of enzyme to strained substrate Enzyme in normal conformation

Cleavage of the substrate

Koshlands induced fit model assisting in cleavage of the substrate SCHEME 1.28

BIOLOGICAL CELL AND ITS CONSTITUENTS

An example of the Catalysis by strain is found in the cleavage of bacterial cell wall by the enzyme lysozyme (Scheme 1.29). The mechanism involves the formation of a planar carbocation at anomeric carbon is ring A of the bacterial cell wall (substrate). The enzyme stretches the substrate so as to bring the anomeric carbon from its tetrahedral shape (in the initial chair) towards planar sp2 shaped to accommodate the future carbocation (Scheme 1.30).

SCHEME 1.29

29

30

BIOPHYSICAL CHEMISTRY

N

CH2

Asp 52

–

COO

O

–

NH A

O

O

O HO H

O

OH

OAc

OH +

:

O

O

O

: :

Covalent catalysis—an example from organic chemistry laboratory during nucleophilic substitution when both the nucleophile and the leaving group are poor, the substitution rates are rather poor. R

O NH

O–

O

O + N

Glu 35

CH2R

A slow substitution reaction Asp 52

COO–

–

O NH

O O

A

: :

Under these circumstances iodide ion is added as a nucleophilic catalyst. Recall that the iodide ion is both a stronger nucleophile and a better leaving group (compared to pyridine and acetate ion respectively). Note that the nucleophilic catalyst acts by forming a covalent bond with the substrate.

O +

CH

O (I)

O

OH

O–

Carbocation O

Glu 35

SCHEME 1.30

(C) ENZYME ACTIVITY

AND

KINETICS

OF

ENZYMES

1. Introduction Enzymes display maximum activity under optimal conditions. The activity of an enzyme is markedly affected by several factors, like temperature, pH, concentration of the enzyme or the substrate, and the presence of the activator or the inhibitor. 2. Effect of Temperature A fast substitution reaction

The effect of temperature on an enzyme-catalyzed reaction is similar to the effects on other reactions (up to a point). The rates for most chemical reactions shows regular increase with increasing temperature (the higher speed and increased energy of molecules). Collisions between reactants become more frequent, and a larger proportion of these collisions

BIOLOGICAL CELL AND ITS CONSTITUENTS

possess enough energy to break old bonds and make new ones. The rate of an enzyme-catalyzed reaction also increases with temperature until the enzyme denatures. Above this temperatures, the rate drops. For most of the enzymes, optimum temperature is near the body temperature, i.e., between 37–40°C, where an enzyme is stable. With further rise in the temperature of the reaction mixture, the enzyme is denatured i.e., there is loss of its normal shape and its function. At higher temperatures the enzyme therefore, does not act as a catalyst leading to a drop of reaction rate dramatically (Scheme 1.31).

SCHEME 1.31

3. Effect of pH Each enzyme has an optimum pH range at which its activity is maximal; at higher or lower pH, activity decreases. Amino acid side chains in the active site may act as weak acids and bases for critical catalytic functions that depend on their maintaining a certain state of ionization, and elsewhere in the protein ionized side chains may play an essential role in the interactions that maintain protein structure. The enzyme activity depends on several factors and one of these is the acceptance and donation of protons during catalysis. Thus in a serine protease a serine residue (acid) attains the more reactive anionic form by donating a proton to the nearby histidine (base). If the pH is too high or too low, then these groups will be unprotonated or protonated too much of the

31

32

BIOPHYSICAL CHEMISTRY

time. The enzyme will function much less efficiently. The pH range over which an enzyme undergoes changes in activity may provide a clue to the type of amino acid residue involved. A change in activity near pH 7.0, for example, often reflects titration of a His residue. Pepsin, a digestive enzyme of the stomach, is most active under acidic conditions like those found in the stomach (optimum pH 1.6, the pH of gastric juice is between 1–2). Trypsin, a digestive enzyme of the small intestine, is most active at neutral to slightly alkaline pH, the pH range of the small intestine (Scheme 1.32).

SCHEME 1.32

4. Substrate Concentration (Michaelis-Menten Equation) The substrate concentration effects the rate of enzyme catalysed reactions and the relationship between the substrate concentration and reaction rate can be expressed quantitatively. The following points may be considered: The rate of enzyme-catalyzed reactions also varies with the concentration of the substrate. But the rate varies with substrate concentration in a way that is substantially different from ‘ordinary’ chemical reactions. Generally in many nonenzymic reactions, the rate is directly proportional to the concentration of the reactant. Doubling the concentration of the reactant doubles the rate of the reaction. Doubling the concentration of S in an enzymecatalyzed reaction appears to double the rate provided the concentrations of S is small, but doubling relatively large concentrations of S actually yields only a slight increase in reaction rate (Scheme 1.33). The relationship between rate and substrate concentration expressed by the Michaelis–

BIOLOGICAL CELL AND ITS CONSTITUENTS

Menten equation is explained by the formation of an enzymesubstrate complex. In turn, this complex may break down to yield free E and S or product P and free E. E + S P ES → E + P. This leads to a hyperbolic graph. At higher concentrations of S, many of the enzyme molecules already have S bound to them. Many of the collisions of S with enzyme molecules therefore, only involve unproductive collisions with ES rather than with E. Since the number of enzyme molecules is normally small, at high concentrations of S most of the E molecules already have S bound to them; they exist as ES, not E. Doubling the concentration of S increases the amount of ES and decreases the amount of E. Ever increasing concentrations of S yield even smaller increases in rate, which produces the hyperbolic graph.

SCHEME 1.33

Accordingly, Michaelis and Menten derived an equation called Michaelis-Menten equation, which is written as follows: Vo =

Vmax [S] K m + [S]

where Vo is the initial reaction velocity, Vmax is the maximum velocity of a reaction, [S] is concentration of the substrate and Km is a constant, called as Michaelis constant, which is defined as the concentration of S that yields half maximal velocity.

5. Michaelis Constant (Km)–Lineweaver-Burk Plot Two methods are presented which one can use to determine the value of Km.

33

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BIOPHYSICAL CHEMISTRY

(i) Vmax method: The Michaelis-Menten equation (I, Scheme 1.34) can be rewritten as (II) from which Km is determined. In other words, the substrate concentration corresponding to half the maximum velocity is numerically equal to Km (Scheme 1.33). Vo = Km + [S] = When

Vmax [S] K m + [S]

...(I)

Vmax (S) Vo

...(II)

Vmax = 2Vo, one has Km + [S] = 2 [S] or Km = [S] SCHEME 1.34

The enzyme succinate dehydrogenase catalyses the removal of a hydrogen atom from each of the two methylene carbons of succinate. The structural analog of succinate is matonale (–OOC — CH2 – COO–) which like succinate can also bind to the active site of succinate dehydrogenase and acts as a competitive inhibitor.

(ii) Lineweaver and Burk method: By taking the reciprocal of both sides of Michaelis Menten equation (I, Scheme 1.34) one gets the relationship (Scheme 1.35).

K m × [S] 1 = Vo Vmax [S] Km 1 1 1 × + = Vo Vmax [S] Vmax

SCHEME 1.35

This is linear equation of the type of y = ax + b. As Km and Vmax are constants, the plot of 1/Vo against 1/[S] will give a straight line (Scheme 1.35). Its intercept on the y-axis is 1/Vmax and that on x-axis (after extrapolation) is – 1/Km (from which Km can be calculated) the slope being Km/Vmax.

BIOLOGICAL CELL AND ITS CONSTITUENTS

35

The Lineweaver-Burk plot of enzyme reaction rates is very useful to distinguish between some types of enzymatic reaction mechanisms and to study enzyme inhibition.

(D) ENZYME INHIBITION—REVERSIBLE OF ACTIVE SITE)

AND IRREVERSIBLE

(NATURE

1. Introduction Enzyme inhibitors are molecular agents which interfere with catalysis, to slow or eliminate enzymic activity. Enzymes catalyze virtually all cellular processes, thus enzyme inhibitors are among the most important pharmaceutical agents (drugs). The study of enzyme inhibitors provides valuable information about enzyme mechanisms and has helped define some metabolic pathways. There are two main classes of enzyme inhibitors: reversible and irreversible. 2. Reversible Inhibitors (Competitive, NonCompetitive and Uncompetitive Inhibition) A competitive inhibitor competes with the substrate for the active site of the enzyme. The inhibitors bind reversibly to the enzyme; they remain associated with the enzyme for a period of time, then diffuse away. Since a permanent association is not formed, the inhibitor can be removed and activity restored. A competitive inhibitor resembles the substrate and combines with an enzyme to form a EI complex (instead of an enzyme-substrate complex ES) however, a catalysis does not occur (Scheme 1.36). (active) E + I P EI (inactive). A competitive inhibitor thus reduces concentration of the free enzyme available for the substrate binding. The binding of the enzyme with the inhibitor or with the substrate depends on their relative concentrations. Since the inhibitor binds reversibly to the enzyme, the substrate binding will be favoured on adding more substrate. The presence of a competitive inhibitor, therefore, increases the apparent Km for the substrate, without any change in Vmax (Scheme 1.37).

36

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A competitive inhibitor resembles a substrate. The effect of a competitive inhibitor can be overcome by raising the concentration of the substrate. SCHEME 1.36 When [S] far exceeds [I], the probability that an inhibitor molecule will bind to the enzyme is decreased and the reaction displays a normal Vmax. However, the [S] at which

1 V , the apparent Km, 2 max increases in the presence of inhibitor. This increase on apparent Km, combined with the absence of an effect on V max , is diagnostic of competitive inhibition and is readily revealed in a doublereciprocal plot. Vo =

Non competitive inhibitors lower Vmax but have no effect on Km.

The Lineweaver-Burk Plot for a competitive inhibitor (+) [Vmax not altered, Km is increased] SCHEME 1.37

Enzyme kinetics plays a key role in drug discovery. One can easily identify a molecule which can be used as a drug if it selectively inhibits specific enzymes.

Methanol is only mildly toxic, in the liver. However, the enzyme alcohol dehydrogenase, convertes it into highly toxic formaldehyde. This toxicity of methanol, is overcome by giving ethanol. Which competes with methanol for binding to the active site of the enzyme and slows down the conversion of methanol to formaldehyde, methanol is excreted out from the body with the urine harmlessly. Ethanol thus is used in the treatment of methanol poisoning due to its competitive inhibition of the enzyme alcohol dehydrogenase.

BIOLOGICAL CELL AND ITS CONSTITUENTS

There are some reversible inhibitors which, however, do not bind to the active site of an enzyme. These are called noncompetitive inhibitors (Scheme 1.38) because they do not compete with the substrate for the active site and do not prevent S from binding, to the enzyme. Noncompetitive inhibitors bind to the enzyme and cause a conformational change in it. The enzyme thus becomes inactive. It now binds S less efficiently or not at all, or the catalytic groups of the active site are no longer aligned properly for efficient catalysis. Noncompetitive inhibitors reduce Vmax for the reaction, but do not change Km.

SCHEME 1.38

37

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An example of a non-competitive inhibitor is the drug 5-fluorouracil (5-Fu) which is used to treat breast and liver cancers: 5-Fu interferes with DNA synthesis. The target enzyme is thymidylate synthase (this enzyme converts uracil to thymine by methylation). Uncompetitive inhibition occurs on binding of the inhibitor after the substrate has bound to the enzyme, and then stops the reaction. The uncompetitive inhibitor thus binds directly to the enzyme-substrate complex and not to free enzyme. Such an inhibitor does not necessarily resemble the substrate. The uncompetitive inhibitor affects catalytic function of the enzyme but not the substrate binding. Both, Km and Vmax are lowered (Scheme 1.39).

Nucleic acids contain a chain of five-membered-ring sugars linked by phosphate groups. Each sugar (D-ribose in RNA, 2’– deoxy -D- ribose in DNA) is bonded to a heterocyclic amine in a β-glycosidic linkage.

The Lineweaver-Burk Plot for an uncompetitive inhibitor (+). [Both Vmax and Km are decreased] SCHEME 1.39

1.4

NUCLEIC ACIDS

(A) STRUCTURE

OF

NUCLEIC ACIDS (DNA

AND

RNA)

The following points may be noted: 1. Basic Structural Features Nucleic acids (DNA and RNA) are polymers of nucleotides. A nucleotide has three structural units. l A sugar l A nitrogen base l A phosphate group The sugar in RNA is the β-anomer of D–ribose, which accounts for the name ribonucleic acid. The sugar in DNA is the β–anomer of D–2 deoxyribose. Thus name deoxyribonucleic acid.

BIOLOGICAL CELL AND ITS CONSTITUENTS

39

2. Nucleotides A nucleoside is a nitrogen glycoside formed when the hemiacetal center of the sugar and an –NH of the base join with the elimination of a molecule of water. The configuration in both DNA and RNA is β at the anomeric carbon atom of the sugar. The ring atoms in the base are numbered; primed numbers indicate the carbon atoms of the carbohydrate. The nitrogen base is always attached to the 1′ carbon atom of the carbohydrate, and there is a primary hydroxyl group located at the 5′ carbon atom. Ribonucleosides have secondary hydroxyl groups at the 2′ and 3′ carbon atoms, whereas deoxyribonucleosides have a secondary hydroxyl group only at the 3′ carbon atom. A nucleotide is an ester of a nucleoside and phosphoric acid. The hydroxyl group at the 5′ carbon atom acts as the alcohol to form the ester. The two protons of the monophosphate ester are ionized at physiological pH. Thus the ester exists as an ion with a – 2 charge in solution.

The bases in DNA and RNA are substituted purines and substituted pyrimidines.

3. Bases in Nucleic Acids The structures of the four bases found in DNA are in Scheme 1.38. RNA also contains four bases, three adenine, guanine and cytosine are the same as in DNA but the fourth base in RNA is uracil instead of thymine.

Recall that a β-linkage is one where the substituents at C1 and C4 are on the same side of the furanose ring.

Ribonucleosides are named by modifying the name of the nitrogen base. Purine derivatives have the ending osine; pyrimidine derivatives end in -idine. A similar convention is used for deoxyribonucleosides along with the prefix deoxy.

SCHEME 1.40

40

Thymine and uracil differ only by a methyl group. Thymine is 5–methyluracil.

BIOPHYSICAL CHEMISTRY

4. The Primary Strand Nucleotides are joined covalently through phosphodiester linkages to give the primary structure of both RNA, and DNA molecules. Phosphodiesters are formed between the 3′ hydroxyl group of one nucleotide and the 5′ phosphate ester of another nucleotide. Thus both DNA and RNA have a backbone of alternating sugar and phosphate units. Note that each

Each organism transmits hereditary information involving chromosomes contained in the nucleus of the cell. A chromosome represents a single large DNA molecule along with its proteins. A chromosome stores and transmits genetic information. Each chromosome contains a series of hundreds to thousands of genes which contain information for a limited function e.g., synthesis of a specific enzyme. Surprisingly, only four bases (Scheme 1.39) and their sequence determines. The vast difference in heredity among species, carrot seets produce only carrot and not radish, mice give birth to only to mice and not cats.

SCHEME 1.41

BIOLOGICAL CELL AND ITS CONSTITUENTS

phosphodiester has one acidic hydrogen atom; hence the name nucleic acids. However, at physiological pH the nucleic acids are ionized. The differences in structure are in the sugar (deoxyribose in DNA and ribose in RNA) and in the order of the bases. Recall that thymine exists only in DNA, and uracil exists only in RNA. The sugar units and phosphate groups are same in all the nucleotides thus the structural abbreviations represent only the sequence of the nitrogen bases. By convention one starts at the left working in the 5′ → 3′ direction. Thus a , when it is tetranucleotide can be referred to as clear that the reference is to DNA. On may often write these abbreviations for the base sequence in DNA by putting a . lower case d in front of the base sequence i.e., This shows that all the sugar units of the sugarphosphodiester backbone of the molecule are deoxyribose in DNA (since the phosphate ester bridges holding the nucleotides together each contain two phosphate ester linkages, these bridges are called phosphodiesters). 5. DNA Double Helix The following points may be noted: l DNA is composed of two strands of polynucleotide and each base of one strands forms hydrogen bonds with a base of the opposite strand to give a base pair, commonly between the lactam and amino tautomers of the bases. l Because A in one strand pairs with T in the other strand while G pairs with C, the strands are complementary. In any DNA molecule, A = T and G = C. l The reason for adenine to pair with thymine rather than with cytosine (the other pyrimidine) is that base pairing is dictated by hydrogen bonding. That bases exist in the keto form allowed Watson to explain the pairing. Adenine forms two hydrogen bonds with thymine but would form only one hydrogen bond with cytosine. Guanine forms three hydrogen bonds with cytosine but would form only one hydrogen bond with thymine (Scheme 1.42).

41

42

BIOPHYSICAL CHEMISTRY

The DNA base pairs SCHEME 1.42

The major and minor grooves as seen in the double helix interact with proteins specifically.

The strands of DNA run in opposite directions i.e., these are antiparallel. Each end of double-stranded DNA is made up of the 5′ end of one strand and the 3′ end of another. This base pairing, thus enables two complementary strands of DNA to form a duplex. Whose shorthand structure may be represented as (I, 1.43) l The duplex is in fact a right-handed double helix (II) (Watson and Crick, the Noble prize 1962) where the two helical polynucleotide chains wrap around each other (two stranded helical structure around a common axis). Thus the DNA molecule can be imagined as a ‘ladder’ which has been twisted into a helix. l The purine and pyrimidine bases are on the inside of the helix while the sugar-phosphate units on the nucleotide are on the outside of the DNA molecule. The planes of the bases are perpendicular to the helix axis, while the plane of the sugars are almost at right angles to those of the bases. l The precise sequence of bases carries the genetic information while the Watson-Crick pairing rules for bases that adenine (A) must pair with thymine (T); and guanine (G) with cytosine (C), (specificity for the pairing of bases) reflect on the double helical structure regarding steric and hydrogen bonding factors. l

BIOLOGICAL CELL AND ITS CONSTITUENTS

43

SCHEME 1.43

There is the right amount of space in the center of the helix for one purine and one pyrimidine to fit across from each other (III, Scheme 1.43). In contrast the room is insufficient for two purines, there is more than enough space for two pyrimidines and in that case these would be too far apart to form effective hydrogen bonding. Thus out of the base pair in a DNA helix one must always be a purine and other pyrimidine (steric factors). The base pairing in further restricted by hydrogen bonding requirements.

(B) RNA RNA is much shorter than DNA and is generally singlestranded. Compared to DNA molecules which can have billions

Proteins have unique amino acid sequences which are specified by genes.

mRNA carries instructions for protein synthesis in a code or codon made of a series of nitrogen bases. The sequence of bases in mRNA determines the sequence of amino acids in the protein to be synthesised.

44

BIOPHYSICAL CHEMISTRY

of base pairs, RNA molecules rarely have more than 10,000 nucleotides. There are three kinds of RNA—messenger RNA (mRNA) whose sequence of bases determines the sequence of amino acids in a protein, ribosomal RNA (rRNA), a structural component of ribosomes, and transfer RNA (tRNA), the carriers of amino acids for protein synthesis. The biosynthesis of proteins occurs on particles known as ribosomes. A ribosome is composed of about 40% protein and about 60% rRNA. There is increasing evidence that protein synthesis is catalyzed by rRNA molecules rather than by enzymes.

(C) FUNCTION rRNA combines with about 50 proteins to give complex structures termed ribosomes which are the sites of protein synthesis.

tRNA molecules are small and their roles are both the delivery and positioning of amino acids in correct order in the growing poly peptide chain according to the mRNA template.

n

OF

NUCLEIC ACIDS

The Flow of Genetic Information

Genes, which are segments of DNA, are responsible for control of the synthesis of proteins and DNA codes for formation of an amino acid sequence in a protein. DNA in the nucleus also controls protein synthesis that occurs in the cytoplasm. The “message” is translated from one molecular language into another by an intermediate molecule, mRNA, that is formed in the nucleus and moves to the cytoplasm. The flow of genetic information is commonly called the central dogma. The following points may be noted: l DNA stores and transmits all hereditary information, including the instructions for the synthesis of all proteins. DNA is replicated in the cell nucleus when the cells are ready to divide. l Replication process is complex in however some general features can be described. In replication, DNA must unwind so that the new complementary chain can form. The enzyme DNA helicase works its way in between the two strands and then moves along the helix, temporarily separating the strands as it goes. This process exposes the bases at a point in the double helix called the replication fork. In this process, the DNA unwinds, and each strand serves as a template for the synthesis of its complementary strand. When replication is completed, two identical versions of the original DNA helix are present (Scheme 1.44).

BIOLOGICAL CELL AND ITS CONSTITUENTS

SCHEME 1.44

The enzyme DNA polymerase catalyzes the replication by binding to each unwound strand. This enzyme recognizes each base in the DNA chain and matches it with a free nucleotide according to the base pairing rules. Then it binds the nucleotides into a growing strand by bonding the 5′ position of one unit to the 3′ position of another unit to form the backbone. This process is known as 5′ → 3′ replication. The two DNA polymerases must enter the fork and move in opposite directions on each strand to replicate DNA.

(D) PROTEIN SYNTHESIS The transformation of the information in a DNA strand into a protein sequence involves steps. First an RNA polymer, called messenger RNA (mRNA), that is complementary to the DNA is synthesized in much the same manner as the synthesis of new DNA described earlier. This process is called transcription. l Most tRNA molecules have less than 100 nucleotides and serve to bind and deliver individual amino acids

45

46

The primary structure of tRNA represents the nucleotide sequence which undergoes extensive folding via intrastrand complementarily to create a secondary structure which when viewed in two dimensions looks like a cloverleaf (see, Scheme 1.44). A tRNA is often drawn as shown for simplicity

Protein synthesis involves the following steps: l A particular amino acid is converted into an amino acyl tRNA. l The anticodon of tRNA associates with the codon of mRNA, so that the correct amino acid is brought to the codon site of mRNA where base pairing takes place.

BIOPHYSICAL CHEMISTRY

from pool to the site of protein synthesis. There are atleast 20 species of tRNA molecules in each cell and a specific (and often several) tRNA carries one type of amino acid. Each specific tRNA differs from the others in its sequence of nucleotides, however tRNA molecules have several features in common. A tRNA which carries alanine is designated as tRNA. A typical tRNA molecule contains four main arms (Scheme 1.45). The acceptor arm in every tRNA molecule has a CCA sequence at 3′ end where an amino acid gets attached and it is critical that the correct amino acid is attached to tRNA, otherwise correct protein will not be synthesised. l The anticodon arm has three nucleotides in its loop, which form base pairs with the complementary codon in mRNA during translation.

SCHEME 1.45

l

Messenger RNA then serves as a template for protein synthesis in a process called translation. Individual amino acids are attached to relatively small RNA molecules called transfer RNA (tRNA). Each amino acid has its own type of tRNA that has a three-base region, known as the anticodon, that is complementary to the codon for that amino acid. The tRNA with the correct amino acid forms three base pairs with the mRNA and brings the amino acid into position for attachment to the growing protein chain.

BIOLOGICAL CELL AND ITS CONSTITUENTS

A Codon The information for the amino acid sequence of a protein is stored in the base sequence of DNA. However, 20 amino acids are found in proteins, while only 4 bases are present in DNA. Thus a single base cannot code for an individual amino acid. Similarly a two base code, which provides 4 × 4 = 16 combinations, still is not large enough to specify 20 different amino acids. The genetic code is infact based on a series of three bases, called a codon codon, which provides 43 = 64 different possibilities. A codon for a particular amino acid is designated by listing the first letters of the three bases that compose it. Thus, one codon for serine is UCA, which designates a base sequence of uracil, cytosine, and adenine. The code is degenerate; that is most amino acids are specified by two or more codons. For example, the codons CCC, CCU, CCA, and CCG all specify the amino acid proline. Moreover, the codons UAA, UAG and UGA all specify a stop signal; that is, they indicate the end of the protein chain. Protein synthesis involves the following steps: 1. Amino Acids are Activated for Reaction ATP reacts with the carbonyl carbon atom to yield an activated acyl derivative in which adenosine monophosphate (AMP) is bonded to the amino acid. The product is an aminoacyl adenosine monophosphate (an aminoacyl adenylate). The reaction is catalyzed by enzymes known as aminoacyl synthetases, and a specific enzyme is required to activate each amino acid Scheme 1.46.

SCHEME 1.46

47

48

BIOPHYSICAL CHEMISTRY

2. Esterification of tRNA Aminoacyl adenosine monophosphates of amino acids react with a molecule of tRNA. Although each tRNA has a unique structure, they all terminate in the sequence CCA. The carbonyl carbon atom of the amino acid forms an ester with a hydroxyl group of the terminal adenylic acid (Scheme 1.47). After formation of the proper aminoacyl RNA molecule, the anticodon of tRNA associates with the codon of mRNA. Thus the correct amino acid is brought to the codon site of mRNA, where base pairing occurs (Scheme 1.48).

SCHEME 1.47

The process for attaching a proline, followed a phenylalanine, to a growing polypeptide chain is shown in (Scheme 1.48). The tRNA for proline (the anticodon GGG) makes hydrogen bonds to the CCC codon for proline in the mRNA and positions its attached proline amino acid for attachment to the growing protein chain. Then the tRNA for phenylalanine hydrogen bonds to the codon for phenylalanine in the mRNA

BIOLOGICAL CELL AND ITS CONSTITUENTS

and similarly brings its attached phenylalanine into position for attachment to the proline. This process continues until a stop signal is reached.

SCHEME 1.48

PROBLEMS AND EXERCISES 1. Describe a cell and explain its role in organisms. 2. Name different organelles of a eukaryotic cell and explain their functions. 3. What is plasma membrane? Outline its structural features. How a membrane acts as a barrier? 4. On what factors the transport of solutes across a membrane depends? Discuss the free energy changes during a transport through a plasma membrane. 5. What are chemical and electrochemical gradients? Discuss the free energy change during the transport of a simple solute and an ion through a plasma membrane. 6. Where is the site of oxidative phosphorylation in a cell? Discuss the energetics when two electrons are transferred from NADH through the respiratory chain to molecular oxygen. 7. What enzyme systems are present in the matrix of mitochondria? How diet is converted into energy via citric acid cycle?

49

50

BIOPHYSICAL CHEMISTRY

8. How NADH formed during glycolysis in the cytosol enters the impermeable inner membrane of mitochondria? 9. Detail the structure of a protein. 10. Give an example to show that biological activity of a protein is associated with its native conformation. 11. What are enzymes? Out line their functions with appropriate examples. 12. What are the uses of Michaelis-Menton equations? 13. Write a short note on Lineweaver-Burk plot. 14. Write a short note on enzyme kinetics and its role in the study of enzyme inhibitors? 15. Write a short note on the role of enzyme kinetics in the evaluation of molecules as drugs. 16. Give examples to show that enzymes are both stereospecific and stereoselective reagents. 17. Write short notes on (a) Protein structure (b) Protein function 18. Derive the structure of DNA and explain its various functions. 19. How DNA replicates itself? How precise sequence of bases carries genetic information? 20. Write notes on (a) Enzyme kinetics (b) α-helix (c) mRNA 21. How the molecule of DNA differs from that of RNA? 22. What role tRNA plays during replication? 23. Draw the gross structure of tRNA and specify different roles played by its different structural units.

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51

C H A P T E R

BIOENERGETICS

2.1

INTRODUCTION

The reactions of the body either produce or require energy which is defined as the capacity to do work or the capacity to effect change. Energy is utilized by living organisms for three major changes: l Biosynthetic or chemical work for building and to sustain the molecules for life. l Transport work for bringing molecules and ions, into, out-or around the cells. l Movement or mechanical work. Cells use energy to do work. A large number of reactions occur simultaneously in a living cell and these are wellintegrated and organised. These chemical reactions are collectively called metabolism. Metabolism is broadly divided into two categories. l Catabolism is a energy yielding process and reactions of catabolism cleave larger dietary molecules into smaller ones. l Anabolism involves biosynthetic reactions by using energy to form complex molecules from simple precursors. The energy produced by catabolism is first stored in the cell in several ways and the most important form of energy storage is via adenosine triphosphate (ATP). ATP is obtained from adenosine diphosphate ADP and inorganic phosphate which requires the input of 7.3 kcal (30.5 kJ) of energy per mol (Scheme 2.1). Thus inorganic phosphate is covalently bonded to the terminal phosphate of ADP via an anhydride 51

Biological systems utilize chemical energy to power its various living processes. Catabolism is an energy yielding process. The most important form of energy storage is ATP which is a high energy compound.

On hydrolysis ATP releases a large amount of energy which is utilised e.g., during muscle contraction and active transport.

52

Glycolysis is the principal metabolic pathway (Catabolic) which converts glucose to pyruvate with production of energy, a part of which is conserved as ATP. ATP is the most important and major storage form for metabolic energy. This energy is used as required to drive energy requiring reactions.

BIOPHYSICAL CHEMISTRY

bond. One can broadly say that a mole of ATP has 7.3 kcal more energy compared to a mole of ADP and Pi. With formation of each mole of ATP in the body, 7.3 kcal (30.5 kJ) of useful energy is stored. ATP allows the coupling of thermodynamically unfavourable reactions to favourable ones. SCHEME 2.1

Thermodynamics involves the study of energy dynamics and shows that energy can both be a reactant and a product of chemical reactions (Scheme 2.1a). Exothermic reaction

A C + Energy

B + Energy D

Endothermic reaction

SCHEME 2.1(a)

The first and second laws of thermodynamics are combined in the thermodynamic function, free energy (G). The unit of energy is the joules/mole or calories/mole (recall that 1 cal = 4.184 J). DNA and RNA e.g., are biopolymers. DNA encodes an organism’s entire hereditary information and is involved in the control of growth and division of cells. The genetic information which is stored in DNA is transcribed into RNA which is then translated to bring about the synthesis of all proteins which are needed for cellular structure and function. Chemical energy is needed not only for the formation of covalent bonds between the subunits in these biopolymers, but cell has also to invest energy so that these subunits follow a correct sequence. Living cells need energy for their survival, differentiation, function and reproduction. This energy is acquired in chemical form from nutrient molecules. Cellular metabolism comprises of chemical processes occurring within the cell. Cellular metabolism brings about the synthesis of monomeric units e.g., nucleotides, amino acids, monosaccharides and fatty acids for the biosynthesis of macromolecules, nucleic acids, proteins polysaccharides and lipids respectively. In summary, metabolism involves several interconnected reactions which bring about the interconversion of cellular metabolites. The needs for energy and building materials differ widely across different cell types and within the same cell under

BIOENERGETICS

53

different conditions. The sequence of each cellular metabolic activity is precisely regulated in order to provide for the fluctuating needs of the cell at a given time and to expend energy only when required. These sequences in the cells are managed to maintain the balance/concentration of key compounds within strict limits. These processes involve both the synthesis of enzymes and the regulation of the activity of existent enzymes for a particular metabolic pathway. The flow of electrons provides energy for organisms. Photosynthesis is the ultimate source of all molecules on this universe. Plants, algae and certain bacteria use light as their energy source via the chemical process called photosynthesis which is light driven reduction of carbon dioxide (Scheme 2.1b). During photosynthesis the photosynthetic cells absorb light energy (as the energy source) for driving electrons from water to CO2 to yield energy rich nutrient molecules e.g., glucose and release oxygen to the atmosphere. Thus carbon dioxide is reduced to yield glucose (or some other carbohydrate) and water is oxidized to oxygen.

SCHEME 2.1(b)

Non-photosynthetic cells and organisms (e.g., humans, other animals and fungi and many bacteria) extract their energy by biological oxidation from food (energy rich products of photosynthesis) and then releasing electrons to atmospheric O2 to give products like water and carbon dioxide (Scheme 2.2). Oxidation refers to addition of oxygen, loss of hydrogen or loss of electrons and its reverse is termed reduction, and therefore, oxidation, reduction are processes which involve electron flow (Scheme 2.3). Thus oxidation is defined as the loss of electrons and reduction as the gain of electrons as e.g., Extraction of energy by the oxidation of glucose

C6H12O6 + 5O2

6CO2 + 6H2O + Energy

Glucose

SCHEME 2.2

54

BIOPHYSICAL CHEMISTRY

during the interconversion of ferrous ion (Fe2+) to ferric ion (Fe3+).

SCHEME 2.3

The electron lost in the oxidation is accepted by an acceptor which is said to be reduced. Thus the oxidationreduction is a coupled process and in a chemical reaction one has two oxidation-reduction systems a compound X gets oxidized while an equivalent amount of other compound Y is simultaneously reduced. In a biological system X and Y refer to two compounds one of which is the substrate while the other is generally a cofactor (Scheme 2.4). The oxidation of alcohols in biological systems by NAD+ within the active site of an alcohol dehydrogenase enzyme in an example.

SCHEME 2.4

2.2

FREE ENERGY CHANGE

The energy which is actually available to do work (utilizable) is termed free energy(G). Gibbs developed the theory of energy changes during chemical reactions. Changes in the free energy

BIOENERGETICS

55

(∆G) have significance to predict whether a chemical reaction will be energetically favourable or not. The following points may be noted: l A biochemical reaction can occur spontaneously only provided ∆G is negative. l A system is at equilibrium if ∆G is zero. l A reaction cannot occur spontaneously in case ∆G is positive. An input of energy is required to drive such a reaction. l The ∆G of a reaction is independent of the path of the transformation. l ∆G does not give any information about the rate of a reaction.

(A) ENERGY CHANGES DURING

A

REACTION

The diagram (Scheme 2.5) describes the reaction of A–B with C to give A and B–C. An activation barrier representing the transition state must be overcome during this interconversion even though the products are more stable compared with the reactants (as shown by large negative free energy change ∆G. As the reactants are converted into products, a particular biochemical reaction passes through a maximum energy state called a transition state. The structure of the transition state lies somewhere between the structure of the reactants and the structure of the products.

SCHEME 2.5

The Gibbs free energy change ∆G reflects on both the direction in which a chemical reaction is likely to proceed and the concentration of both reactants and products which will be present at equilibrium. Moreover, ∆G is independent of reaction mechanism and provides no information about the rate of reactions.

56

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In every reaction there is an energy barrier which has to be overcome in order for the reaction to proceed. This is the energy required to transform the substrate molecules into the transition state. The transition state has the highest free energy compared to any component in the reaction pathway. Bonds which break and bonds that form when reactants are converted to products are partially broken and partially formed in the transition state. Dashed lines indicate partially broken or partially formed bonds. The energy needed to overcome the activation barrier is the activation energy (∆G≠). One may note that ∆G is not related to ∆G≠. The following points may be noted: l

∆G and ∆G≠ are not related.

l

The ∆G of a reaction is not dependent on the reaction path.

l

The ∆G gives no information regarding the rate of a reaction which is governed by ∆G≠.

l

A negative ∆G shows that the reaction is thermodynamically favourable in the indicated direction, and the reaction is likely to proceed without any input of energy.

l

When the free energy change (∆G) is represented by a positive sign, it shows that the reaction is not thermodynamically favourable and input of energy is needed so that it can occur in the direction indicated.

l

In biochemical reactions this input of energy is brought about by coupling the energetically unfavourable reactions with energetically favourable ones. These type of coupled reactions are central to the energy exchanges in living systems.

l

The enzymes catalyze reactions by lowering ∆G≠ (Scheme 2.5). Thus an enzyme stabilizes the transition state and increase the rate at which the reaction occurs, however it has no effect on the overall change in energy of the reaction.

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Coupled Reactions—An Introduction When the free energy change (∆G) is indicated by a positive sign, the input of energy is needed so that a reaction can proceed in a direction indicated. In a biochemical reaction this input of energy is generally achieved by coupling otherwise unfavourable reaction with a more energetically favourable one. The conversion of glucose to glucose 6-phosphate, the first reaction in the pathway for the oxidation of glucose is taken as an example (Scheme 2.6).

SCHEME 2.6

One simple way of conversion of glucose into its 6-phosphate is the reaction in (Scheme 2.6). This reaction however, does not occur spontaneously since ∆G is positive. A reaction (Scheme 2.7) on the other hand has negative ∆G. The common intermediate (Pi) is consumed in reaction. (Scheme 2.6). While it is generated in reaction (Scheme 2.7). The

SCHEME 2.7

coupling of these two reactions lead to a third reaction (Scheme 2.8) which is the sum of first two involving a common intermediate (Pi) which is omitted. More energy is released in reaction (Scheme 2.7) that is consumed in reaction (Scheme 2.6). The overall free energy change for reaction (Scheme 2.8) has a negative sign. Thus this reaction provides a pathway for the synthesis of glucose 6-phosphate. SCHEME 2.8

Further details are in (Schemes 2.11–2.20)

(B) PROGRESS

OF A

REACTION

1. Progress of a Reaction and Free Energy As a chemical reaction proceeds, heat may be released or absorbed. Enthalpy (∆H) is a measure of the change in heat

Chemical energy is required by biological systems to power the living processes e.g., muscular contraction, nerve impulse conduction, synthetic reactions etc. This energy is provided by chemical linkage or coupling to oxidative reactions. The terms exergonic and endergonic indicate that a reaction is accompanied by loss or gain of free energy respectively (not necessarily as heat). Unlike exergonic reactions which take place spontaneously with loss of free energy endergonic reactions require the gain of free energy. Endergonic reactions occur only when these are coupled to exergonic reactions. In a coupled exergonic endogonic reaction the overall net change is exergonic.

Catabolism is the breakdown or oxidation of fuel molecule by exergonic reactions. The synthetic reactions to build up substances is called anabolism. Metabolism is a combination of catabolic and anabolic processes.

content of the reactants compared to products. Enthalpy, the total energy of the system consists of entropy and free energy (G). Entropy (S) represents a change in the randomness of reactants and products and tends to increase as free energy is released during reactions. Free energy is available to a system for performing useful work until equilibrium is achieved.







Entropy attains a maximum as the reaction approaches equilibrium. Changes in free energy accompany the concomitant changes in enthalpy and entropy and the relation between changes of free energy (G), enthalpy (H) and entropy S) is given (Scheme 2.9). G = H – TS ( denotes change) T denotes the absolute temperature in Kelvin K = 273 + ºC SCHEME 2.9

2. The Term Standard Free Energy Change (G°) G for any chemical reaction is a function of the standard free energy change G°, a constant which is characteristic of each specific reaction (note the superscript°). Thus the difference between the free energy of the products and the free energy of the reactants under standard conditions of temperature 298 K (25°C), a pressure of 1.0 atmosphere, with reactants and products at a concentration of 1 M is called the free energy change G° (Scheme 2.10). G º = (free energy of products) – (free energy of the reactants) SCHEME 2.10

3. Exergonic Reactions Consider equation (Scheme 2.10), G° will have a negative value in case the products have a less free energy (more stable) than the reactants. Thus in such a reaction (Scheme 2.11), there is release of free energy available to do work and the reaction is said to be exergonic and it proceeds spontaneously. The hydrolysis of ATP is a classic example of exergonic reaction (Scheme 2.11).

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SCHEME 2.11

4. Endergonic Reactions In an endergonic reaction ∆G° is positive i.e., the products have a higher free energy (less stable) compared to the reactants (Scheme 2.12) such reactions which require an input of energy are called endergonic reactions. The reversal of reaction (Scheme 2.11) is in (Scheme 2.12) is endergonic. This reaction can occur only with an input of energy of at least 7.3 cal/mol (∆G° is positive).

SCHEME 2.12

Exothermic and Endothermic Reactions The enthalpy change (∆H°) represents a measure of the relative strength of bonding in the products and reactants. Heat is evolved on bond formation and heat is consumed on bond breaking. Two factors contribute to the change in free energy, the change in enthalpy and the change in entropy multiplied by the temperature (Scheme 2.13).

The terms exergonic and endergonic are used for reactions which have a negative ∆G° or a positive ∆G° respectively. One knows that changes in free energy reversal are accompanied by concomitant changes in enthalpy and entropy ∆G° = ∆H° – T ∆S°, ∆H° (change in enthalpy) is the amount of heat evolved or consumed due to bond making and bond breaking during the course of a reaction. An exothermic reaction has a negative ∆H° while an endothermic reaction has a positive ∆H°.

 G = H º – TSº  H º = (Energy of the bonds broken) – (Energy of the bonds formed) SCHEME 2.13

The enthalpy term (H°) is usually much larger than the entropy term (–T S°) at lower temperatures and the entropy term is then usually ignored. When weaker bonds are cleaved and stronger bonds are formed then heat is evolved and the reaction is exothermic (negative value of H°). In an exothermic reaction, the enthalpy term makes a favourable negative contribution to G°. When, however, stronger bonds are broken and weaker bonds are formed, then energy is consumed in the reaction, and the reaction is endothermic (positive value of H°). In an endothermic reaction, the enthalpy term makes an unfavourable positive contribution to G°. 5. G° is Related to Equilibrium Constant, Keq For a general reaction A + B  C + D the equilibrium constant Keq is defined by equation (Scheme 2.13(a). Keq =

Brackets are used to indicate concentration in moles/liter i.e., molarity (M)

[C] [D] [A] [B]

SCHEME 2.13(a)

At a constant temperature and pressure, G depends on the actual concentration of reactants and products. For the general reaction, A + B  C + D, the actual change in free energy (G) is related to the standard free energy change (G°) by the approximation (Scheme 2.14). G = G° + RT In where

[C] [D] [A] [B]

G° = Standard free energy change R = Gas constant T = Absolute temperature 273 + ºC In = Natural logarithm



SCHEME 2.14

One can thus determine G° when the system is at equilibrium because when the reaction has reached equilibrium, G° = 0 and the equation (Scheme 2.14) can be rearranged to (Scheme 2.15). As the system is at equilibrium

(eq), the concentration component is the equilibrium constant Keq and one has equation (Scheme 2.16). This relationship shows whether reactants or products are favoured at equilibrium either by the equilibrium constant (Keq) or by the change in free energy (G°). Gº = – RT ln







[C] [D] [A] [B]



SCHEME 2.15





Gº = – RT ln Keq SCHEME 2.16 

Thus in summary a reacting system tends to proceed towards equilibrium and is then associated with a driving force whose magnitude may be expressed as a free energy change G for that system. Two points may be noted: It is often convenient to refer to G under a set of standard conditions:



To comply with several biochemical reactions which liberate or consume protons, [H+ ] = 1 M or pH = 0, the standard conditions demand these reactions to proceed at pH = 0. However, this is not so since most biochemical reactions occur in vivo around pH = 7.0. Most biochemical reactions take place in well-buffered aqueous solutions around pH = 7.0. Therefore, both the pH and the concentration of water (55.5 M) remain constant. Biochemists (unlike chemists) define a different standard state donated as G° i.e., G° written by a prime and thus, follows the relationship between Keq and G° (Scheme 2.17) for a biochemical reaction A + B C + D. Recall from (Schemes 2.13a – 2.16) that when a reaction is at equilibrium G is 0.

 









 





  





[C] [D]  G = Gº + RT ln [A] [B]

 

At equilibrium G = 0 0 = G = Gº + RT ln

[C]eq [D]eq [A]eq [B]eq

OR

Remember that the actual free energy change (G) is a variable which depends on Gº and the concentration of reactants and products.

Gº = – RT ln K eq SCHEME 2.17



Standard free energy changes are additive, for pathways















Each reaction in the sequence A B and B C has its own equilibrium constant as well as its own characteristic standard free energy change G° and G. Since these two reactions are sequential, B cancels out to give the overall reaction A C with its own equilibrium constant and consequently its own standard free energy change Gt°otal Biochemical pathways often involve a series of reactions. For these reactions the G° values are additive. As long as the sum of overall standard free energy change G° of individual reactions is negative the pathway can operate. This happens despite the fact that some of the individual reactions may have a positive value of G° In summary a thermodynamically favourable reaction (exergonic reaction) may be linked to an unfavourable reaction (endergonic reaction) so that the free energy liberated during the exergonic reaction may be employed to drive an energy consuming reaction. Such interconnected endergonic and exergonic reactions are termed coupled reactions. ATP + H2O

ADP + Pi

G° = –7.3 kcal/mol or –30.5 kJ/moll A highly exergonic reaction, G °  is –7.3 kcal/mol or –30.5 kJ/mol SCHEME 2.18



An example of an energetically favourable reaction which has a large negative G° and is generally used to drive less energetically favourable reactions in the hydrolysis of adenosine triphosphate ATP to form adenosine diphosphate (ADP) and free inorganic phosphate. The major link in cells between exergonic and endergonic reactions is ATP (Scheme

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63

2.18). Glucose 6-phosphate may be thought to be produced by the reaction of glucose with inorganic phosphate (Pi = HPO4–2) as shown (Scheme 2.19). This reaction, however, does not occur spontaneously, since now ∆G°′ is positive.

SCHEME 2.19

When the two reactions are added together (the species occurring on both sides of the reaction arrow cancel), the net reaction is exergonic (∆G°′ = –4.0 kcal/mol or –16.7 kJ/mol). Thus, the energy released from the hydrolysis of ATP is sufficient to drive the phosphorylation of D-glucose. Two reactions in which the energy of one is used to drive the other are known as coupled reactions (Scheme 2.20 also see Scheme 2.31).

SCHEME 2.20

2.4

HYDROLYSIS OF ATP–BIOENERGETIC SIGNIFICANCE OF ATP

Recall from earlier discussion that free energy change of ATP hydrolysis is large and negative and ATP provides a major link in cells between exergonic and endergonic reactions. Within a cell magnesium ions are found at a relatively high concentration so that ATP and ADP due to their electronegativity can exists as their magnesium complexes (Scheme 2.21). The following points may be considered:

BIOENERGETIC SIGNIFICANCE OF ATP Bioenergetic significance of ATP (adenosine 5′triphosphate) is reflected in the fact that the free energy change associated with its hydrolysis is large and negative. ATP is known as the universal carrier of chemical energy, since the energy of hydrolysis of ATP converts endergonic reactions to exergonic reactions. ATP therefore, has the ability to release a large amount of energy on hydrolysis and this energy is used to drive an endergonic reaction.

CHEMICAL BASIS FOR THE FORMATION OF GLUCOSE 6-PHOSPHATE The simplest way for the formation of glucose 6-phosphate by the reaction of glucose with inorganic phosphate. Such a reaction is however, impossible since the nucleophilic attack on phosphorus will require the displacement of highly basic OH–.

64

BIOPHYSICAL CHEMISTRY

ATP—The most Important High Energy Compound

Adenosine Triphosphate ATP is a unique high energy molecule in the living cells. Structurally it contains an adenine, a ribose and a triphosphate moiety. Recall from basic organic chemistry that the hydrolysis of a carboxylic acid anhydride is exothermic. Phosphoric acid anhydrides found in di- and triphosphates are very similar to carboxylic acid anhydrides.

SCHEME 2.21

l

ATP functions as the energy currency of the cell.

At pH 7.0, the triphosphate portion of ATP is almost fully deprotonated. The four electronegative charges repel each other vigorously, on hydrolysis of ATP e.g.,

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65

at the γ carbon (Scheme 2.22). The electrostatic repulsion is reduced. The electrostatic repulsion is also partially reduced by binding with magnesium ions. l Moreover, greater stability is also conferred on the product of hydrolysis — inorganic phosphate Pi via resonance.

The reactions of ATP are mostly S N 2 nucleophilic displacements at phosphorus. The nucleophile gets phosphorylated by the consequent release of energy.

The low rate of ATP hydrolysis (nucleophilic attack by H2O) in the absence of enzymes has biological significance (negative charges on ATP repel the approach of nucleophiles). Carboxylic acid anhydrides hydrolyze quickly, however, ATP is extremely slow to hydrolyze. Biologically ATP must exist in cell till it is needed by an enzyme catalyzed reaction. While at the active site of the enzyme these negative charges are stabilized on complex formation with Mg2+ and by arginine and lysine residues at the active site of the enzyme.

SCHEME 2.22

l

In most of its reactions ATP displays SN2 type of reactivity when any of the three phosphorus atoms (α, β or γ) could be the electrophilic target for the

Triphosphate portion of ATP on the active site of enzyme

66

BIOPHYSICAL CHEMISTRY

On chemical basis one can explain the large free energy change during the hydrolysis of ATP. Firstly the vigorous electrostatic repulsion among four negative charges in ATP is reduced in the product ADP. The other product of hydrolysis, the inorganic phosphate (Pi) is stabilized via resonance (Scheme 2.22) O HO

–

P

O –

O

–

O HO

P

O

–

O

–

O HO

P

2.5

BIOCHEMICAL REACTIONS IN A CELL

Recall from above discussion on ATP, that in the absence of an enzyme (a catalyst) a biochemical reaction may be extremely slow. The enzyme provides a reaction pathway which has a lower activation energy compared to the uncatalyzed reaction (see Scheme 2.5). Thus enzymes accelerate the attainment of the equilibrium position but do not shift its position. The free energy change of a reaction is not dependent on the pathway of the reaction, but depends only on the nature and concentration of the reactants and the products. Enzymes, thus do not change equilibrium constants, however they can increase the rate of the reaction in the direction dictated by thermodynamics. The flow of phosphoryl groups e.g., from ATP to glucose to give glucose-6-phosphate is catalyzed by enzymes called kinases.

O

2.6

O–

–

O + HO

nucleophilic attack. However the negative charges on ATP (pH = 7) repel the approach of the nucleophiles. When ATP is bound with the active site of the enzyme, it complexes with Mg2+ and this decreases the overall charge on ATP. In this state ATP can be readily approached by nucleophiles.

P

O

–

O– Resonance forms of Pi

THE ACTUAL FREE ENERGY CHANGE IN LIVING CELLS IS MUCH HIGHER THAN THE STANDARD FREE ENERGY CHANGE

Recall that free energy change for ATP hydrolysis is –30 kJ/mol under standard conditions (see Scheme 2.22). However, it is found that in living cells e.g., human erythrocytes the free energy of hydrolysis is much higher (–52 kJ/mol). The reasons are due to the following factors. l In cells the concentrations of ATP, ADP and Pi are unequal and are much lower as compared to the standard concentrations (1 M). l In the cells, ATP and ADP during enzymatic reaction exist as complexes with Mg 2+ so that the actual substrate is not ATP4– but MgATP2– (see Scheme 2.21). l In human erythrocytes, the concentrations of ATP, ADP and P i are 2.25, 0.25 and 1.65 mM and substituting these values in the equation (Scheme

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67

2.23) one can reach the actual value of G for ATP hydrolysis. G Free energy change in cells

[ADP] [Pi ] [ATP] [ADP] [Pi ] – 30.5 kJ/mol RT In [ATP] – 52 kJ/mol

Gº + RT In

= = =

SCHEME 2.23

Recall the additive free energy changes of sequential reactions and their role in the formation of glucose 6-phosphate (see, Scheme 2.20). The phosphate of the enol of pyruvic acid (phosphoenolpyruvate) PEP is a product of the metabolism of glucose (see Scheme 2.31). The cleavage of P i from PEP generates much more energy than is required to drive the condensation of Pi with ADP to form ATP (Scheme 2.24). The hydrolysis to phosphate and pyruvate (highly exergonic) has a very favourable free energy change of –14.8 kcal/mol (–61.9 kJ/mol) and can be used to drive the formation of ATP from ADP (G° = + 7.3 kcal/mol). When this reaction is coupled with the conversion of ADP to ATP, the overall process has a favourable free energy of –7.5 kcal/mol (–31.4 kJ/mol, Scheme 2.24). Phosphoenolpyruvate drives the formation of ATP. O

–

CO2 CH2

C

–

+ H2O 2–

OPO3

Phosphoenolpyruvate (PEP)

ADP

2–

CH3CCO2 + HPO4 G° = –14.8 kcal/mol (–61.9 kJ/mol) Pyruvate

2–

ATP + H2O

+ HPO4

Phosphoenolpyruvate + ADP

G° = +7.3 kcal/mol (+30.5 kJ/mol)

Pyruvate + ATP

G° = –7.5 kcal/mol (–31.4 kJ/mol)

SCHEME 2.24

ATP is often termed a high energy phosphate compound and it serves as the principal immediate donor of free energy

68

PEP is a Phosphate

BIOPHYSICAL CHEMISTRY

High

Energy

This represents the phosphate of the enol of pyruvic acid, a product of the metabolism of glucose. PEP is a high energy compound because it is a phosphate ester of an enol, the unstable tautomer of a ketone.

in biological systems rather than long-term storage form of the free energy. In a living cell ATP molecule is consumed immediately (within a minute) after its formation. Thus ATP acts as energy currency of the cell as is evident from the ATP – ADP cycle (Scheme 2.25) which provides the fundamental mode of energy exchange in biological systems. ATP is continuously formed and consumed and the turnover of ATP is very high. It is shown that a resting human utilizes around 40 kg of ATP during 24 hours. The rate of utilization of ATP may go up as high as 0.5 kg per minute during exertion. Often one writes a reaction in which ATP supplies energy by its conversion to ADP and Pi. This reaction thus seems to be a simple hydrolysis of ATP where water replaces Pi. However, in general it is the transfer of a phosphoryl group from ATP to the substrate or the enzyme molecule which couples the energy of ATP breakdown to drive endergonic reactions. Various other phosphorylated compounds in biological systems also have large free energies of hydrolysis (Table 2.1). ATP acts as an energy link between the catabolism (degradation of molecules) and anabolism (synthesis) in a biological system. Phosphocreatine (creatine phosphate) is an energy rich compound which is stored in vertebrate muscle and brain.

Given below are some compounds (high energy compounds) which liberate more energy than that of ATP

SCHEME. 2.25

TABLE 2.1: Standard free energies of hydrolysis of some phosphorylated compounds ∆G′′ ° Phosphoenolpyruvate Phosphocreatine ADP + Pi) ATP ( Glucose 1-phosphate Fructose 6-phosphate Glucose 6-phosphate Glycerol 1-phosphate

(KJ/mol)

(kcal/mol)

– 61.9 – 43.0 – 30.5 – 20.9 – 15.9 – 13.8 – 9.2

– 14.8 – 10.3 – 7.3 – 5.0 – 3.8 – 3.3 – 2.2

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69

The following points may be noted regarding synthesis of ATP: l Oxidative phosphorylation: This is the major source of ATP in aerobic organisms. It is linked with the mitochondrial electron transport chain. l Substrate level phosphorylation: ATP may be directly synthesized during substrate oxidation in the metabolism. The high energy compounds such as phosphoenolpyruvate can transfer high energy phosphate to ultimately produce ATP (see Scheme 2.24). Designation of High Energy Phosphate Bonds The symbol ~ is used to represent high energy bond and high energy phosphates are designated by ~ P . This symbol indicates that the group attached to the bond when transferred to an appropriate acceptor results in transfer of large quantity of free energy. Thus ATP and ADP is designated (Scheme 2.26), and the shorthand scheme for ATP/ADP cycle in the transfer of high energy phosphate is shown in (Scheme 2.26a).

Nicotinamide is the operative part of the molecule in oxidationreduction reactions. O

SCHEME 2.26

CNH2 +

+ H + 2e – N

+

R + NAD (Oxidized form) Oxidant

O H

H CNH2

SCHEME 2.26(a) N

2.8

BIOLOGICAL OXIDATION–REDUCTION REACTIONS (OXIDATIVE PHOSPHORYLATION ATP SYNTHESIS)

The NADH and FADH2 (reduced coenzymes) are energy rich molecules because each contains a pair of electrons with high transfer potential. Both NADH and FADH2 are formed during

R NADH (Reduced form) Reductant

Nicotinamide adenine dinucleotide NAD + is a biological oxidizing agent.

70

Flavin adenine dinucleotide a biological oxidizing agent

ATP is formed from the energy of electrons which are released when the reduced coenzymes NADH and FADH 2 are reoxidized. In summary electrons flow from NADH to molecular oxygen in an exergonic process and releases energy. This free energy of oxidation is used for the synthesis of ATP which is an endergonic process (Scheme 2.26c).

BIOPHYSICAL CHEMISTRY

glycolysis, fatty acid oxidation and citric acid cycle. On donation of these electrons to molecular oxygen a huge amount of free energy is released which can be used to form ATP. In oxidative phosphorylation, ATP is formed (from ADP and Pi) as a result of electron transport from NADH or FADH2 to O2 – by distinct carriers (also see Schemes 1.7 and 1.8). Thus in short electron transport and oxidative phosphorylation reoxidize NADH and FADH2 and the energy released is trapped as ATP (Scheme 2.26a). The following points may be noted: l A hydrogen atom contains a single electron, thus the transfer of a hydrogen atom effects electron transfer. l A hydride ion is made of a hydrogen atom and an additional electron. Thus the transfer of a hydride ion e.g., during the reduction of NAD + to NADH translocates two electrons. l The energy released from the oxidation of food materials (carbohydrates, fats, proteins) is made available within mitochondria as reducing equivalents (H or electrons). Thus mitochondria are the centers to generate reduced coenzymes e.g., NADH. The reducing equivalents are utilized in the ETC and are directed for their final reaction with oxygen to form water (Scheme 2.26b).

Conversion of food energy to ATP. Reducing equivalents are collected by the respiratory chain for oxidation and coupled formation of ATP. The reaction occurs in the mitochondrial matrix and the inner membrane. SCHEME 2.26(b)

SCHEME 2.26(c)

l

The flow of electrons from NADH to O2 is an exergonic

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71

process. The free energy of oxidation is utilised for the synthesis of ATP which is an endergonic process (Scheme 2.26c) l The oxidation and phosphorylation are coupled by a proton motive force (p.m.f.). The chemiosmotic hypothesis proposed by Mitchell (1961) explains the transport of electrons through the respiratory chain to produce ATP from ADP + Pi. l According to this hypothesis the electron transport ejects protons from the mitochondrial matrix into the intermembrane space (Scheme 2.26d) where the proton concentration increases (a decrease in pH). Since the inner mitochondrial membrane is impermeable to protons a gradient of protons is established across the membrane. This proton gradient provides the energy in the form of proton-motive force (by analogy to electromotive force) for ATP synthesis from ADP and Pi. In summary the protons attempt to flow back across the membrane to equilibrate their concentrations on both sides. The p.m.f. which drives protons back into the matrix provides the energy for ATP synthesis (also see Schemes 1.8 and 2.30).

SCHEME 2.26(d)

l

Electron transport creates a proton gradient across a membrane as shown by measuring the changes in pH and electrical potential across the inner mitochondrial membrane. Both the pH and membrane potential (Em) contribute to the p.m.f. which is calculated from the

Oxidation is loss of electrons and reduction is gain of electrons. The oxidationreduction reactions involve the transfer of electrons. In the oxidation-reduction reaction: NADH + H+ + 1/2 O2 S

NAD+ + H2O NADH is oxidized to NAD+, it loses electrons, while the molecular oxygen is reduced to water, it gains electrons. Synthesis of ATP via phosphorylation takes place when NADH and FADH2 are oxidized via electron transport through the respiratory chain. This process is termed oxidative phosphorylation. The oxidation process begins in mitochondrion (in the matrix) when pyruvate and fatty acids (from food) are converted into acetyl CoA. In the citric acid cycle the acetyl group of acetyl CoA is oxidised to form end-products NADH and FADH2, which are the starting products for the respiratory chain (ETC) and redox reactions in the mitochondrial inner membrane. Electrons are transported through the respiratory chain and molecular oxygen is reduced to water. Oxidation and phosphorylation are coupled by a proton gradient that is used to drive ATP synthesis.

72

ATP is synthesised when a pH gradient is imposed on mitochondria. Electron flow is accompanied by proton transfer across the membrane to produce both a chemical and an electrical gradient. The proton-motive force (p. m. f.) which drives protons back into the matrix provides the energy for the synthesis of ATP from ADP and Pi. The bioenergetic reactions in the mitochondrion take place in the matrix region and the inner membrane surrounding it. The complete oxidation of glucose yields about 30 ATP. The redox potential E 0 is directly related to the change in the free energy by Nernst equation. The passage of electrons through the ETC leads to loss of free energy. In biosystems a part of this free energy is used to form ATP from ADP and Pi. Redox reactions involve the loss or gain of electrons (see Table 2.2). One cannot measure electron concentrations directly. However, the measurement of redox potential is possible. The redox potential reflects on the measure for a species to either gain or lose electrons. Electron transport to O2 takes place only (through the electron transport chain ETC) provided there is a need for ATP. Oxidative phosphorylation needs a supply of e.g., NADH, O2, ADP and Pi. In summary electrons do not flow from fuel molecules to O2 to generate energy (see, Scheme 2.26b) unless there is a need for the synthesis of ATP.

BIOPHYSICAL CHEMISTRY

equation (scheme 2.26e). ∆p = Em – 2.3

RT i ∆ F

where ∆p Em R T F i ∆°pH

= = = = = =

proton motive force in V membrane potential in V gas constant temperature in K the Faraday constant the difference in pH from the inside the membrane to its outside SCHEME 2.26(e)

The equation simplifies to: ∆p = Em – 59 i∆° pH when expressed in mV. Note that ∆p and Em are negative values. Experimentally it has been shown that electron transport may generate an i∆° pH of approximately 1.4 units and an Em of –140 mV. The p.m.f. generated (–223 mV) is sufficient to account for the synthesis of three molecules of ATP. The mitochondria are the centers for metabolic oxidative reactions to form reduced coenzymes NADH and FADH2 which are subsequently utilized in electron transport chain (ETC) which consists of distinct protein complexes to liberate energy in the form of ATP. Electron transport is generally tightly coupled to ATP synthesis. Electrons do not flow through the electron transport chain to oxygen unless ADP is simultaneously phosphorylated to ATP. When ADP is available then electron transport proceeds and ATP is formed. When the concentration of ADP falls, electron transport slows down. This process of respiratory control as it is called ensures that electron flow occurs only when ATP synthesis is needed. The process (Scheme 2.26b) provides a major source of ATP in eukaryotes. The process of oxidative phosphorylation of glucose e.g., when it is completely oxidized to CO2 and H2O generates 26 of the 30 molecules of ATP. There are several distinct electron carriers (protein complexes) through which the reduced coenzymes NADH and FADH2 pass and finally reduce oxygen to water (Scheme 2.26b). Mention here may be made of one complex carrier that participates in the electron transport chain (ETC). This complex constitutes cytochromes which are conjugated proteins

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73

containing heme group. The iron of heme in cytochromes is alternately oxidized (Fe3+) and reduced (Fe2+).

(A) REDOX POTENTIAL The oxidation reduction potential E (or redox potential) of a substance is a measure of its affinity for electrons. The standard redox potential in biological systems (E0′) is a constant. For a redox couple which is measured under standard conditions, at pH = 7 is expressed in volts. Estimated standard redox potentials of some carriers are in (Table 2.2). The redox potentials are measured in volts and chemists designate this by E°. The redox potential of a half reaction is measured relative to a reference (the hydrogen electrode) it is found that at pH = 7, the redox potential of the hydrogen electrode converts to – 0.42 V, a value used by biologists as a standard redox potential when the value of a measured redox potential E°′ is negative, the tendency is to loose electrons (oxidation) while a positive value of E°′ indicates a gain in electrons (reduction). Thus e.g., a strong reducing agent like NADH is poised to donate electrons and has a negative reduction potential, while a strong oxidizing agent e.g., O2 is ready to accept electrons and has a positive reduction potential. *TABLE 2.2: Standard reduction potentials of some biologically important reactions (systems) Oxidant

Reductant

Number of electrons transferred (n)

E0′ (v)

2H+ + 2e–

—

H2

2

1/2 O2 + 2H+ + 2e–

—

H2O

2

0.815

NAD++ H+ + 2e–

—

NADH

2

– 0.32

Acetaldehyde + 2H+ + 2e– —

ethanol

2

– 0.197

Cytochrome c (Fe3+) + e– —

Cytochrome cFe2+

1

0.07

*

– 0.42

Standard redox potentials refer to reactions oxident + electron(s)

Reductant.

One can estimate the actual redox potential (E′) of a particular couple from the standard redox potential and the concentrations of the oxidized and reduced species by the relationship (Scheme 2.27). E′ = E′0 + RT In (oxidized species) nF (reduced species) Where: E′ = actual redox potential at pH = 7

Oxidation/reduction reactions which occur in living cells occur through specialized electron carriers and an example is of cytochrome C. Electron carriers transport electrons from the reduced coenzymes e.g., NADH to oxygen. During several biological oxidations (dehydrogenations) one or two hydrogen atoms (H+ + e–) are transferred from a reactant to a hydrogen acceptor (see Scheme 2.4) Transfer of a hydride ion is equivalent to the transfer of a proton, (H + ) and two electrons, H– = H+ + 2e–. The reduction of NAD + involves a hydride ion (see Scheme 2.4) A single electron can directly reduce a transition metal e.g., Fe 3+ (ferric ion) to Fe 2+ (ferrous ion). A hydrogen atom has a single electron, thus transfer of a hydrogen atom effects electron transfer.

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E 0 R T n F

= = = = =

standard redox potential gas constant temperature in K number of electrons transferred The Faraday constant 96.5 kJV–1 mol–1 In = natural logarithm

(E  and E 0 are in volts) SCHEME 2.27





(B) REDOX REACTIONS AND FREE ENERGY One can use standard redox potentials to calculate the free energy change of an oxidation/reduction reaction. The magnitude of the free energy release during the spontaneous electron flow depends on the difference in the standard redox potentials, E0 between the two redox couples. The change in standard redox potential can be calculated from the equation (Scheme 2.28).



 

E 0 = E 0 (electron acceptor) – E 0 (electron donor) SCHEME 2.28

The standard free energy change Go for any oxidation - reduction reaction is calculated from the Nernst equation (Scheme 2.29), from the values of E 0 (Table 2.2). G o  = –nFE0 (Nernst equation) Where: G o  = standard free energy change. n and F have their usual meaning (see Scheme 2.27) SCHEME 2.29

One may consider the reduction of acetaldehyde by the biological electron carrier NADH which comes out to be an exergonic reaction (Scheme 2.30). CH3CHO + NADH + H+  C2H5OH + NAD+



Acetaldehyde

(I)

Ethanol

Reduction potential of the reaction are: CH3CHO + 2H+ + 2e–  C2H5OH (E0 = – 0.197 V)  





NAD+ + 2H+ + 2e–  NADH + H+ (E 0 = – 0.32 V) [The change in the reduction potential ( E0) by convension is E0 of the electron donor]

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75

Thus  E0 of the reaction (I) is given by –0.197 V – (– 0.320 V) = 0.123 V. With n = 2 (The number of electrons involved in the reaction). The standard free energy change is given by Nernst equation.

G º  = – nF E0



(Nernst equation) = – 2(96.5 kJ/V mol) (0.123 V) = – 23.7 kJ/mol

 

SCHEME 2.30

Energy for Life—ATP Synthesis Recall (Sec. 2.8) that in oxidative phosphorylation the synthesis of ATP is coupled to the flow of electrons from NADH to O 2 by a proton gradient across the intermitochondrial membrane. One may consider again here that the driving force of oxidative phosphorylation is the electron tansfer potential of NADH compared to that of O2. The following points may be noted:  NADH provides an example of a biological electron carrier and such molecules which can accept or donate electrons are called electron carriers.  A series of electron carriers form an electron transport chain when these are arranged on the basis of their redox potentials.  Electrons flow from a low redox potential (i.e., with more negative E0) to a higher redox potential (i.e., more positive E0). This flow of electrons through electron transport chain is associated with a free energy change. A part of this free energy is used in the synthesis of ATP from ADP and Pi.  The redox potential E0 is directly related to the change in free energy Gº.  By convention a change in the reduction potential (E0) is –E0 of the electron acceptor –E0 of the electron donor.  At one end of the electron transport chain (ETC), NADH which is formed in the cell via catabolic pathways (see Scheme 2.26b) on oxidation provides two electrons. These pass down the chain from one carrier to the other and finally reduce oxygen to water.



 





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BIOPHYSICAL CHEMISTRY



One calculates the free energy of oxidation of this reaction as in (Scheme 2.30a). The oxidation of NADH (relatively low redox potential, E0 = – 0.32 V) and reduction of oxygen (relatively high redox potential, E0 = + 0.815) creates a potential difference of +1.13 volt between NADH and O2 (This potential difference drives electron transport through the electron transfer chain). Reduction potential of the reactions involved are :

+ – E 0 = + 0.815 V  1/2O2 + 2H + 2e  H2O  + + – E 0 = – 0.32 V  NAD + H + 2e  NADH Thus E 0 of the overall reaction: 1/2O2 + NADH + H+  H2O + NAD+ is given by + 0.815 V – (– 0.32 V)

= + 1.13 V From Nernst equation G º = – nF  E0 = – 2 (96.5 kJ V–1 mol–1) (1.13 V) = – 218 kJ mol–1 A highly exergonic reaction SCHEME 2.30(a) 6

CH 2 5

H

2–

OPO 3

The large negative free energy (Scheme 2.30a) is used in the synthesis of ATP.

O

OH

H

1

4

OH OH 3

H

H

H

2

OH

Glucose 6-phosphate

Glycolysis is a cytosolic process which converts glucose to two molecules of pyruvate with the liberation of two molecules of CH2 OH H

O

OH

H

OH OH H

H

H

O Glycolysis

O 2CH3CCOO– + 2H

2CH3CCOOH Pyruvic acid

+

Pyruvate

OH

Glucose

Glucose + 2 ADP + 2 Pi + 2 NAD

+

Glycolysis

2 Pyruvate + 2 ATP + 2 NADH

SCHEME 2.31

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77

ATP and two molecules of NADH (Scheme 2.31). Glycolysis is the principal catabolic pathway for glucose. A part of the energy thus released is conserved in ATP (Scheme 2.31) while the rest remains in the product pyruvate (see Scheme 2.24). Thus when a molecule of glucose is degraded to pyruvate two molecules of ATP are generated. It comes out that formation of pyruvate from glucose is exergonic (Scheme 2.32). Recall that formation of ATP from ADP and Pi is endergonic (Scheme 2.33). The overall standard free energy change of glycolysis is obtained from the sum of equations (Schemes 2.32 and 2.33) which comes out to be – 85 kJ/mol.

SCHEME 2.32

SCHEME 2.33

PROBLEMS AND EXERCISES 1. What is free energy? How negative and positive ∆G have significance on the outcome of a reaction? 2. How is free energy (∆G) related with free energy of activation (∆G ≠)? Draw a reaction coordinate diagram. Why a biochemical reaction in a cell in the presence of biocatalysts greatly enhance the rate of a reaction? 3. Write a short note on coupled reactions in relation to negative and positive free energy change. 4. What are exergonic and endergonic reactions? How these differ from exothermic and endothermic reactions? 5. Deduce a relationship from which one could know if the reactants or products are favoured at equilibrium either from equilibrium constant or by the change in free energy. 6. Define a relationship between ∆Gº and ∆Gº′ and the relationship ∆Gº′ = – RT In K′eq as used for biochemical reactions. 7. What are exergonic and endergonic reaction? Explain by taking the example of ATP and its role to converts glucose into its 6-phosphate. 8. How do you explain that the free energy change of ATP hydrolysis is both large and negative?

Glycolysis is almost considered a universal pathway which brings about the oxidation of a glucose molecule to two molecules of pyruvate. Partly the energy thus released is conserved as ATP and NADH. During glycolysis six carbon glucose splits into two molecules of 3 carbon pyruvate. This is followed by phosphorylation of ADP to ATP and the transfer of a hydride ion (H:–) to NAD+ to give NADH.

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9. What is redox potential? Derive a relationship to derive free energy change. 10. What is catabolism? How the energy from catabolism is stored in the cell? 11. Write a brief note on the process of glycolysis. How during this catabolic pathway ATP is formed? 12. How ATP is synthesised in mitochondria? 13. How a proton gradient is created in mitochondria? How p.m.f. is utilized in the synthesis of ATP? 14. Write short notes on (a) Redox potential (b) The free energy and redox potential as related by Nernst equation. 15. Using data of redox potentials (table 2.2). How will you calculate ∆Gº′ for the reduction of oxygen to water? 16. How free energy of a redox reaction can be calculated directly from its E′0?

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79

C H A P T E R

! 3.1

STATISTICAL MECHANICS IN BIOPOLYMERS

CHAIN CONFIGURATION AND CONFORMATION OF MACROMOLECULES

(A) INTRODUCTION—MAIN CHAIN CONFORMATION

OF

PROTEINS

Two terms are used to describe molecular structure: configuration and conformation. The configuration of a molecule are stereo-arrangements that are related to one another by symmetry but cannot be converted into one another without cleaving bonds. For example, cis- and trans-2-butene are the two configurations of this achiral molecule (Scheme 3.1).

SCHEME 3.1

Another example of configurational isomers is found in the case of trans-1,2-dichlorocyclopropane, the mirror image is not superposable on the original. It is, therefore, a chiral molecule and two resolvable enantiomers exist (Scheme 3.1(a)). Proteins are optically active as they are dissymmetric (cannot be superimposed on their mirror images). Two kinds of dissymmetry are present in proteins–configurational and conformational. Amino acid residues other than glycine are optical activity (L configuration about their α carbon atom). 79

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Threonine and isoleucine have an additional stereocenter. Electronic interactions between different residues in a protein also contribute to optical activity. The right-handed α helical component for example, gives rise to a large conformational and configurational contribution to optical activity.

SCHEME 3.1(a)

D-Amino acids are found only in special instances such as bacterial cell walls and peptide antibiotics. Free rotation (conformation) is possible around only two of the three covalent bonds of the polypeptide backbone— the α-carbon (Cα) to the carbonyl carbon (CO) bond, and the Cα to nitrogen bond. The partial double-bond character of the peptide bond which links CO to the αnitrogen requires that the carbonyl carbon, carbonyl oxygen, and α-nitrogen to be coplanar to prevent rotation (configuration).

Conformation represents the spatial arrangement of substituent groups that freely rotate to assume different positions in space, without breaking any bonds as in ethane [Scheme 3.1(b)].

SCHEME 3.1(b)

Recall from the details (Chapter 1) that proteins are polymers of specific sequences of L-amino acids which are linked together by covalent peptide bonds [amide bonds, Scheme 3.1(c)]. Two planar peptide groups are shown (Scheme 3.2). The following points may be noted:

SCHEME 3.1(c)

STATISTICAL MECHANICS IN BIOPOLYMERS

l

81

The C–N bond has significant double-bond character (~ 40%). Thus, rotation about this bond is restricted by an activation energy of about 40 to 80 kJ mol–1. Rotation about the Cα–C and Cα–N bonds can take place freely (The Cα–N and Cα–C are the bonds on either side of the peptide bond) and this allows adjacent peptide units to be at different angles.

SCHEME 3.2

The backbone of a polypeptide is a linked sequence of rigid planar peptide groups and the backbone conformation of a polypeptide is specified by the rotation angles or torsion angles (also called dihedral angles) about the Cα–N bond (phi, φ) and Cα–C bond (psi, ψ) of each of its amino acid residues. A polypeptide chain is in its planar, fully extended (all-trans) conformation, the φ and ψ angles are both defined as 180°. l The trans configuration is more stable than the cis configuration due to the steric interaction between the groups of the Cα atoms in the cis isomers (Scheme 3.3). l

Restricted rotation around the single bond

C

C C

O

C

N

H C

H

s-cis configuration

O

N C

s-trans configuration

SCHEME 3.3

l

The backbone or main chain of a protein (polypeptide) refers to the atoms which participate in peptide bonds

Conformation versus configuration The terms configuration and conformation are often confusing. Configuration refers to the geometric relationship between a given set of atoms, for example, those that distinguish L- from D-amino acids. Interconversion of configurational isomers requires breaking of covalent bonds. Conformation refers to the spatial relationship of every atom in a molecule. Interconversion between conformers occurs without covalent bond cleavage with retention of configuration, and typically via rotation about single bonds. Proteins contain only Lamino acids, for which a right-handed α helix is by far the more stable, and only right-handed α helices are present in proteins. Configuration is the spatial arrangement of an organic molecule that is conferred by the presence of either (1) double bonds, a ring system about which there is no freedom of rotation, or (2) stereocenters around which substituent groups are arranged in a specific sequence. Configurational isomers donot interconvert without breaking one or more covalent bonds.

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(Scheme 3.4), ignoring the side chains of the amino acid residues. 1

R H2N

C

C

H

O

H N



H C



3

R

O H N

C

2

R

n

C

C

H

O

OH

Extended conformation of a polypeptide showing rotatable φ/ψ angles. The planar peptide (amide) bonds are shown in bold, which are generally trans. SCHEME 3.4

Due to rotational flexibility in the polypeptide backbone around the N—Cα(φ) and Cα—C(ψ) angles, there is a very large number of possible conformations which a polypeptide molecule may adopt. However, unlike most synthetic polymers proteins have the ability to fold up (under the right conditions) into specific conformations, and these are the conformations which give rise to their individual properties. l The conformational freedom and thus the torsion angles of a polypeptide backbone are sterically constrained. Rotation around the Cα—N and Cα—C bonds leading to certain combinations of φ and ψ angles may cause the amide hydrogen, the carbonyl oxygen, or the substituents of Cα of adjacent residues to collide. Certain conformations of longer polypeptides in a similar way can lead to collisions between residues which are far apart in sequence. l

(B) ALLOWED CONFORMATIONS DIAGRAM

OF

PROTEINS—RAMACHANDRAN

The following points may be noted: l From the above discussion it follows that the conformational range of torsion angles φ and ψ in a polypeptide backbone are restricted by steric hindrance. Sterically forbidden conformations have φ and ψ values which would bring atoms closer than the corresponding van der Waals distance (the distance of closest contact between nonbonded atoms). This information is displayed in a Ramachandran map (Scheme 3.5) (named after its inventor, G.N. Ramachandran). The Ramachandran diagram indicates allowed conformations of polypeptides.

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83

Since the amide group is essentially planar, the polypeptide chain has only two degrees of rotational freedom the rotation about the Cα–N bond, characterized by (angle φ) and the rotation about the C α –C bond, characterized by (angle ψ). The three-dimensional picture of the polypeptide chain can be completely defined in terms of these two angles. For a right-handed α helix, φ = –57° and ψ = –47°. All possible combinations of φ and ψ do not, however, yield stable conformations. Severe steric hindrance between amide hydrogen atoms for example, would result if φ = 0° and ψ = 0°.

The Ramachandran Plot of main chain φ and ψ angles of proteins (non-glycine). The shaded areas represent the allowed combination of φ and ψ angles and the blank spaces represent their prohibited combinations. SCHEME 3.5

l

The sterically allowed values of φ and ψ can be found by calculating the distances between the atoms of a tripeptide at all values of φ and ψ for the central peptide unit. These values are indicated in a conformation map or Ramachandran plot. It can be seen from (Scheme 3.5) that most areas of the Ramachandran plot (most combinations of φ and ψ) are conformationally inaccessible to a polypeptide chain and represent forbidden conformations of a polypeptide chain. Only three small regions of the diagram are physically accessible to most residues of a polypeptide chain. The observed φ and ψ values of accurately determined structures almost always fall within these allowed regions of the Ramachandran plot. These three regions represent the φ-ψ values which generate:

For amino acids other than glycine, most combinations of phi and psi angles are not allowed due to steric hindrance. The conformations of proline are further restricted due to the absence of free rotation of the N—Cα bond. Regions of ordered secondary structure are observed (Scheme 3.5) when a series of aminoacyl residues adopt phi and psi angles of same magnitude. Extended segments of polypeptide (e.g., loops) can have a variety of such angles. The angles which define the two most common types of secondary structure, the α helix and the β sheet, fall within the lower and upper left-hand quadrants of a Ramachandran plot, respectively.

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(E) A right-handed α-helix (EE) The parallel and anti-parallel β-sheets and (EEE) The collagen helix. The following are the two notable exceptions: (E) The cyclic side chain of Pro limits its range of φ values to angles of around –60º, to make it the most conformationally restricted amino acid residue. (EE) Gly, the only residue without a Cβ atom is far less sterically hindered than the other amino acid residues. Thus, its permissible range of φ and ψ covers a larger area of the Ramachandran diagram. At Gly residues, polypeptide chains generally adopt conformations that are forbidden to other residues.

(C) THE LEVELS OF STRUCTURES FOUND IN PROTEINS

IN

PROTEINS–CONFORMATIONS

1. Primary Structure of Proteins Proteins function as enzymes i.e., biological catalysts, antibodies, messengers, carriers, receptors, structural units and so on. Their chemical structure and conformation is described in terms of primary, secondary, tertiary and quaternary.

The primary level of structure in a protein (see Scheme 1.13) is the linear sequence of amino acids as joined together by peptide bonds. This sequence of amino acids is determined by the sequence of nucleotide bases in the gene encoding the protein. The sequencing of nucleic acids is easy and faster than

Proteins must be flexible to undergo conformational change to bind substrates, interact with other proteins, and carry out catalysis. Proteins rapidly switch between different conformational states to act as signal transducers and energy converters.

SCHEME 3.6

STATISTICAL MECHANICS IN BIOPOLYMERS

85

protein sequencing, this method is very attractive and followed wherever it is feasible. Recall that disulphide bonds (see, Scheme 1.22) are also included under primary structure, these are bonds between cysteine residues (Scheme 3.6) which are adjacent in space and are not in the linear amino acid sequence. These covalent cross-links between separate polypeptide chains or between different parts of the same chain are formed as a result of oxidation of the SH groups on cysteine residues which are juxtaposed in space. The resulting disulfide unit is termed a cysteine residue. Disulfide bonds are generally present in extracellular proteins and are rarely found in intracellular proteins. Some proteins, such as collagen, have covalent crosslinks formed between the side-chains of Lys residues. The amino acid sequence of a polypeptide is also determined by hydrolysis with various proteases. Some of these are general while others are more specific (papain, pepsin, thermolysin, trypsin etc.). The amino acids thus formed are then analyzed. Automated amino acid sequencing is carried out either by ion exchange chromatography or by reverse-phase HPLC via Edman’s degradation method. A protein with more than 50 amino acids is cleaved to obtain smaller fragments (enzymatically or chemically). Trypsin is highly specific and cleaves peptide bonds after positively charged residues (Lys and Arg) if the next residue is not proline. Similarly, cyanogen bromide (CNBr) is specific to cleave peptide bonds after methionine residues. Peptide fragments obtained after cleavage are separated and purified by standard biochemical methods. This is followed by the reassembling of amino acid sequences of several fragments into a single frame. 2. The Secondary Structure of a Protein–α α-Helical and β-Pleated Sheet

α-Helical structure The secondary structure of a protein is the regular folding of regions of the polypeptide chain to generate a regular secondary structure element. The two most common types of protein fold are the α-helix and the β-pleated sheet. In the rod-like α-helix, the amino acids arrange themselves in a regular helical conformation (see, Scheme 1.15). The carbonyl oxygen of every peptide bond is hydrogen bonded to the hydrogen on the amino group of the fourth amino acid away (Scheme 1.16) with the hydrogen bonds running almost parallel to the axis of the helix. In an α-helix there are 3.6

The peptide bond nitrogen of proline lacks a hydrogen atom and thus cannot be involved in a hydrogen bond. Proline thus can only be stably accommodated within the first turn of an α helix. When present elsewhere, proline disrupts the conformation of the helix to generate a bend. Due to small size, glycine also often induces bends in α helices.

86

Ribbon diagrams are used to depict the conformation of the polypeptide backbone. Cylinders and arrows indicate regions of α-helix and β-sheet respectively.

Motif It is the distinct folding pattern for elements of secondary structure in a given protein. It is also called a fold or super-secondary structure.

A Domain A domain is a section of protein structure sufficient to perform a particular chemical or physical task such as binding of a substrate or other ligand. Other domains may anchor a protein to a membrane or interact with a regulatory molecule that modulates its function.

BIOPHYSICAL CHEMISTRY

amino acids per turn of the helix which cover a distance of 0.54 nm, and every amino acid residue represents an advance of 0.15 nm along the axis of the helix (see Scheme 1.16). Why proline is rarely found in α -helical regions— Disruption of helical conformation Proline is rarely found in α-helical regions due to reasons already explained (see Scheme 1.17) Proline therefore, is found at the end of the α-helix and it is here that proline alters the direction of polypeptide chain and the helical structure is terminated. β-Pleated structure The β-sheet (the second, hence “beta”) is the other regular secondary structure in proteins, for details (see Scheme 1.19). Compared to the compact backbone of the α helix, the peptide backbone of the β sheet is highly extended. However, like the α helix, β sheets also derive much of their stability from hydrogen bonds between the carbonyl oxygens and amide hydrogens of peptide bonds. In contrast to the α helix, these bonds are formed with adjacent segments of β sheet. (see Scheme 1.19). Interacting β sheets can be arranged either to form a parallel β sheet, when the adjacent segments of the polypeptide chain proceed in the same direction amino to carboxyl, or an antiparallel sheet, in which they proceed in opposite direction. Ribbon cartoons are generally used to symbolize secondary protein structure. The α helix is easily recognized as a spiral, whereas β structure is indicated by an arrowhead to indicate the N- to C- orientation of the chain (Scheme 3.7). Studies on protein conformation, function, and evolution have shown the significance of two other levels of organization. Supersecondary structure refers to clusters of secondary structure, a β strand separated from another β strand by an α helix. This feature (Scheme 3.8) is found in many proteins and this motif is

SCHEME 3.7

STATISTICAL MECHANICS IN BIOPOLYMERS

called a βαβ unit. Some polypeptide chains fold into two or more compact regions joined by a flexible segment of polypeptide chain. These compact globular units are termed domains with about 100 to 400 amino acid residues. β Strands get paired in a parallel fashion provided a crossover connection is made. The connector links opposite ends of the sheet and thus must be much longer than is required for antiparallel association. The crossover connector is normally an α helix (Scheme 3.8). In this βαβ motif the hydrophobic side of the β strands packs tightly against the hydrophobic face of the α helix.

SCHEME 3.8

Left handed α-helices cannot be formed using L-amino acids The α-helix is right-handed and is composed of L-amino acids. The left handed α-helices cannot be realized using L-amino acids due to the steric hindrance involving R groups. However, a left handed α-helix may be observed when the α-helical stretch is very short—three to five residues in length. What leads to a secondary structure of a protein? Recall that the amide group is rigid and planar due to resonance. The peptide bond, C–N, has about 30–40% double bond character, therefore, rotation about the C–N bond is not feasible. This leads to only two rotational degrees of freedom per peptide, which are about the single bonds N–Cα (φ) and Cα–C (ψ). The conformation angles φ, ψ are referred to as Ramachandran angles (see Scheme 3.5). The secondary structure of a protein deals with the ordered segments, of which α-helix and β-sheet are the most common examples. Repetition of the same φ/ψ angles from one amino acid to the next leads to a regular secondary structure element, of which α-helix and β-sheet are the most predominant. In these structures the φ/ψ angles repeat in such a way that hydrogen bonds may form between different peptide groups to stabilize the structure.

87

All portions of proteins are not necessarily ordered. Proteins may contain “disordered” regions, often at the extreme amino or carboxyl terminal and are characterized by high conformational flexibility. In many cases, these disordered regions assume an ordered conformation on binding of a ligand. The structural flexibility enables such regions to act as ligandcontrolled switches which affect protein structure and its function.

88

Haemoglobin Haemoglobin, is made up of four globular subunits–two of one kind (α) and two of another (β)–which combine to form a tetramer quaternary structure. Interaction between these subunits controls the delicate uptake of oxygen and its release by the haem groups in this protein.

BIOPHYSICAL CHEMISTRY

A β-turn—Its utility in protein folding in a typical globular protein The helices and sheets are called ‘ordered’ structures since their residues have repeating backbone torsion angles φ, ψ and their N-H and C=O groups have periodic patterns of hydrogen bonding, turns and loops do not have regular repeating secondary structural features. β-Turns are the regions in proteins where the backbone folds back on itself at ~ 180º i.e., the polypeptide chain reverses direction to make a hairpin (Scheme 3.9).

Native Conformation Native conformation of a protein is its biologically active conformation. Protein Folding Proteins are conformationally dynamic systems—which can fold and unfold in a time frame of milliseconds. Folding into the native state is not an exhaustive search of all possible structures. Denatured proteins do not represent just random coils. Native contacts are favoured and regions of native structure persist even in the denatured state of a protein. Partial Unfolding of Proteins Partial unfolding allows proteins to be transported across membrane barriers. The transport of a protein from one cellular compartment to another e.g., from the cytosol into a mitochondrion can take place only provided the protein can unfold sufficiently to enable it to thread through a membrane channel.

SCHEME 3.9

Proteins have varying degrees of both the α helix and the β structure according to Pauling and Corey’s theory. Proteins are normally divided into two categories, globular and fibrous. Globular proteins are characterized by their compactness. In these molecules, the polypeptide chain is folded up to fill most of the space within its domain, leaving relatively little empty volume. A β-turn provides an opportunity to fold tightly into the compact shape of a globular protein. Thus the reversal of direction by the polypeptide chain to make a β-turn gives a protein globularity and not linearity. A β-turn contains a tetrapeptide unit with the Cα-atoms of the first and the fourth residues ~ 4.8 Å apart and a hydrogen bond between the C=O group of the first and the N-H group of the fourth residue

STATISTICAL MECHANICS IN BIOPOLYMERS

(Scheme 3.9). The hydrogen bond between the 1st and 4th residues is not however a necessary condition for the β-turn and there are several types of β-turns, type I is the most common. Normally half of the residues in a globular protein reside in α helices and β sheets and half in loops, turns, bends, and other extended conformational features. 3. Loops and Bends The role of a β-turn to give globularity to a protein has been explained. Along with a turn a bend also refers to short segments of amino acids that join two units of secondary structure, such as two adjacent strands of an antiparallel β sheet (Scheme 3.9). Proline and glycine and asparagine are often present in β-turns in which the polypeptide chain abruptly changes direction by 180 degrees. Loops represent those regions which contain residues over the minimum number needed to connect adjacent regions of secondary structures. Loops have irregular conformations but have significant biological roles. Motifs that arise by the association of α helices or β strands play a fundamental role in protein folding. They are termed folding motifs or supersecondary structures as e.g., in a helixloop-helix motif. Many structural elements like loops turns or other motifs e.g., helix-loop-helix are intermediate between secondary and tertiary structures. They do not have a regular repeating φψ signatures, but are unique for biological activity.

(D) PROTEIN FOLDING PROBLEMS The formation of α-helix and β-strands is at the heart of the protein folding which generally occurs via a orderly and guided process. In the first stage, as the newly synthesized polypeptide is released from the ribosomes (whose primary structure is dictated by an mRNA) short segments fold into secondary structural units which lead to local regions of organized structure. Folding is limited to the selection of an appropriate arrangement of this relatively small number of secondary structural elements. The following points may be noted: 1. Main Chain Conformation of a Protein can be Determined from Circular Dichroism (CD) Spectra Protein folding can be studied from spectral methods, particularly circular dichroism is useful to monitor

89

The participation of ribosomes in the initial protein folding is recognized. Ribosomes may have no further role in subsequent folding after the protein is translocated onto an organelle. The biologically active (native conformation) of a protein is normally the most energetically favoured.

90

Traditional animal glues are made from denatured skin and bone. The main connective tissue protein, collagen, takes its name from the Greek word for glue.

Denaturation and Renaturation of Ribonuclease The amino acid sequence in ribonuclease specifies its complex three dimensional structure and this principle holds for other proteins as well. Purified ribonuclease is denatured with complete loss of activity, in the presence of concentrated urea solution in the presence of a reducing agent. The four disulphide bonds are cleaved leading to disruption of stabilizing hydrophobic interactions to give a completely unfolded conformation. Refolding occurs with great accuracy on removing urea and reducing agent to give its correct tertiary structure with complete restoration of biological activity. Significantly the interchange disulphide bonds are formed exactly at the same positions as in the parent native ribonuclease (although more

BIOPHYSICAL CHEMISTRY

conformational changes in proteins near the region 220 nm. In this region CD spectra of α-helices, β-structure motifs and random coils have distinct features. The α helix displays negative CD bands at 208 and 222 nm, and α positive band at 192 nm. A randomly arranged polypeptide chain has a negative CD band centered at 199 nm. Estimates of the α helix content of proteins derived from CD spectra are in good agreement with values obtained from X-ray crystallographic studies. The content of β structures can also be determined from CD spectra, but the uncertainty is greater because β structures are less regular than the α helices and contribute somewhat less to the CD spectrum. For detailed discussion on ORD and CD refer to chapter 7.

CD spectra can differentiate between an α-helix, a β-pleated sheet and a random coil region conformations of a polypeptide chain. SCHEME 3.10

2. Significance of Protein Folding Protein folding involves mechanisms by which the linear sequence of amino acid that residues in an unfolded polypeptide must fold to its native conformation. In the native state of the protein, each residue is spatially fixed relative to the others in a unique three-dimensional structure. This loss of three dimensional structure leads to loss of function of the protein and is termed denaturation. In a pure and properly folded protein all the molecules will have the same

STATISTICAL MECHANICS IN BIOPOLYMERS

conformation, give or take a little bit of variation due to thermal fluctuation. Folded proteins can unfold (“denature”) easily, especially with a change in temperature, pH or on addition of chemical denaturants such as urea, guanidine hydrochloride or alcohols. Denatured proteins may, however, retain some secondary structural features and under most conditions exist in a set of partially folded states. They rarely approach the true random coil state. Thermodynamic measurements show that the native protein is only marginally (20–40 kJ mol–1) stable than the denatured one. This small value is typical of a hydrogen bond. The fact that native proteins are only marginally stable than denatured proteins enables them to change their conformations rapidly, as in allosteric interaction. Proteins that can change their conformations easily can also diffuse across cell membranes more readily. Flexibility is essential for protein folding, function and removal. 3. Defective Protein Folding and Human Health Unfolded or misfolded proteins may be the molecular basis for several human genetic disorders. An unfolded protein is also quite sticky stuff with a tendency to aggregate with other denatured proteins or to stick to surfaces. This intrinsic stickiness of unfolded proteins appears to be one of the causes of prion diseases and other amyloidrelated conditions such as mad cow disease, CJD, Alzheimer’s, etc. In these situations unfolded or misfolded proteins aggregate into lumps or “plaques” that interfere with normal cell function. 4. The Folding of Protein A completely unfolded polypeptide chain in water is unstable since many non-polar side chains are in contact with the aqueous medium. These hydrophobic groups spontaneously come together to avoid water—this condensation is called a hydrophobic collapse. The polypeptide chain thus folds spontaneously to allow the hydrophobic residues to be burried to minimize their exposure to water. Moreover, most of the burried groups i.e., the main chain NH and CO groups are involved in hydrogen bonding. These features lead to formation of an α-helix and or β-sheet. Recall that more than 60% of the secondary structure of most proteins consists of α-helices and β-strands.

91

than 100 ways are available to reform these disulphide bonds). Thus the amino acid sequence of a polypeptide chain has the information to bring about the folding to its native three dimensional structure.

92

Molten Globule Molten globule is an early intermediate in protein folding. The spontaneous collapse of a polypeptide chain into a compact state mediated by hydrophobic interactions (stabilizing interactions) among nonpolar residues initiates protein folding. The collapsed state is often called a molten globule. The molten globule has most of the secondary structure of a native protein i.e., α-helices and β-sheets but not tertiary structure. The term globule points to its condensed state, and the adjective molten emphasizes the fluctuating nature of the interactions between secondary-structure units. The molten globule state is a readily observed intermediate between the unfolded and native (folded) forms of several proteins.

These structural elements come together to form folding motifs (supersecondary structure) e.g., four-helix bundles, β hairpins, and βαβ units. Thus in summary during folding of several proteins molten globule represents an early intermediate. The driving force for its formation are the hydrophobic interactions which stabilize proteins. A molten globule contains much of the secondary structure but only little well packed tertiary structure of the native form. The mechanisms of protein folding (a) Hydrophobic interactions among non-polar residues The initial step brings the hydrophobic residues out of contact with water and into contact with one another. This step, which is accompanied by a large decrease in Gibbs energy, largely reduces the number of possible conformations that need to be explored. This partial folding leads to the formation of α helices and β sheets i.e., a molten globule. One may depict the Gibbs energy during folding of a protein with the intermediate formation of molten globule. (Scheme 3.11)

Fast

Random coil RC

Gibbs energy

The process by which an unfolded chain folds into the native biologically active form of the protein takes place in times of seconds to minutes by the progressive stabilization of intermediates that resemble parts of the final folded state.

BIOPHYSICAL CHEMISTRY

Slow

Native protein

Molten globule M

N

RC MG N Folding progress

Depiction of a molten globule as in intermediate during protein folding SCHEME 3.11

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93

(b) The folding sequence in proteins containing disulphide bonds Proteins containing disulfide linkages can be unfolded by reducing these cross-links to sulphydryl groups –SH. The protein now exists in unfolded form. Folding is then initiated by removing the denaturant when —S—S— bonds start reforming. As the protein refolds the intermediates which have disulfide bonds that do not exist in the final molecule appear and disappear. The folding pathway can be tracked by trapping the intermediates covalently by blocking the uncombined cysteines with iodoacetate, an alkylating agent. These intermediates are separated by chromatography and analysed to throw light on folding sequence (Scheme 3.12). CH2COO– S

HS

HS

SH Air

CH2COO–

Iodoacetate S

HS

S

SH

O2

S S

S

SH SH + ICH2COO–

–

SCH2COO + HI

Determination of sequence of formation of —S—S— bonds in a protein by trapping free cysteine residues (SH groups) with iodoacetate.

SCHEME 3.12

(c) Use of pulsed-label NMR spectroscopy in protein folding A protein is denatured (unfolded) and placed in D2O, when the amide NH groups change to ND groups i.e., all the labile H atoms are replaced by D atoms (I, Scheme 3.13). Then the denaturant is removed and the folding of the protein starts and most of the ND groups become protected due to the formation of secondary structure (II, Scheme 3.13). This is followed by the addition of H2O and any deuterium atoms which are not protected are exposed to the solvent and are replaced by H atoms (III, Scheme 3.13). By using 2D NMR spectroscopy individual NH resonances can be detected. Thus the precise locations of exchangeable sites can be identified and consequently, those regions of the compact protein which contain protected deuterium can be recognized. Generally the sites protected from a fast H—D exchange are located in αhelices, β-sheets and β-turns.

94

Chaperones Chaperone proteins assist in the folding of over half of mammalian proteins. The hsp 70 (70-kDa heat shock protein) family of chaperones binds short sequences of hydrophobic amino acids in newly synthesized polypeptides, to shield them from solvent. Chaperones prevent aggregation, to provide an opportunity for the formation of appropriate secondary structure and its subsequent coalescence into a molten globule.

BIOPHYSICAL CHEMISTRY

D D

D

D

D

D D D

D D D

folding in D2O

D Denatured protein (unfolded) in D2O

(I)

H

D

Dilute with H 2O

D D D H

D H

D Partially folded protein in D2O

Partially folded protein in H2O

(II)

(III)

SCHEME 3.13

(d) Protein folding in vivo is catalysed by isomerases and chaperone proteins Protein disulfide isomerase (PDI) catalyzes disulfide interchange reactions, thereby facilitating the shuffling of the disulfide bonds in a protein until the bonds of the native conformation are formed by achieving their correct pairing. Many proteins, do not however, fold spontaneously after being synthesized in the cell. Folding of these proteins requires the action of specialized proteins. Molecular chaperones are proteins that interact with partially folded or improperly folded polypeptides to assist folding. (e) Proline–cis, trans-isomerase Recall that partial double bond character of amides increases the torsional barriers. Consequently it may become practicable to separate conformers at room temperature (Scheme 3.14). All X-Pro peptide bonds (where X represents any residue) are synthesized in the trans configuration. However, X-Pro bonds of mature proteins, approximately 6% are cis. The cis configuration occurs commonly in β-turns. The barriers in peptidylprolines are so important in protein folding, that there is a very widespread enzyme, peptidylprolyl-cis, trans-isomerase (PPI), to catalyse the rotation.

SCHEME 3.14

STATISTICAL MECHANICS IN BIOPOLYMERS

3.2

95

STATISTICAL DISTRIBUTION–END TO END DIMENSIONS AND BIOPOLYMER STRUCTURE

In the present section we try to give a more analytical treatment of polymer conformations. There is no good theory of solvent structure and solvent-polymer interactions that allows us rigorously to introduce solvent effects into our mathematical treatment of protein conformations. Hence, we focus on the configurational statistics of chain molecules. Here, the treatment is based on statistical evaluation of chain properties made by averaging over all conformations, (with weighting factors determined by the chain’s bond rotational potentials). The evaluated conformational properties so obtained reflects the chain geometrics, i.e., bond angles and bond lengths as well as of the hinderances to backbone rotations. Here we are calculating the average properties of “statistically coiling” chains which are to be distinguished from the single unique conformations that one comes across with many biologically active macromolecules. This is the procedure of averaging over all conformations.

(A) CONFIGURATIONAL STATISTICS (CHAIN DIMENSIONS)

OF

POLYMER CHAINS

Chain dimensions relate the sizes and shapes of individual polymer molecules to their chemical structures, chain length and the molecular environment. To treat chain statistics emphasis is largely laid on calculation of intrachain distances. This amounts to the determination of average distance between chain segments e.g., chain termini. This is carried out by averaging the distance over all conformations based on the principles of statistical mechanics. The valuable insight to the protein folding problem can be obtained from the configurational statistics of polypeptides. The statistics of homopolymers and copolymers of glycine, alanine and proline give clues to the ways of how these residues can influence protein conformation. The hydrodynamic and other physical properties (e.g., intrinsic viscosities and sedimentation coefficients) of a coil have an important connection with the extensions of chains i.e., the mean square end to end distance. These hydrodynamic

Configuration and Conformation Studied Together Two configurations are possible for the atoms of a planar peptide bond. The trans configuration is more stable (see Scheme 3.3). Secondary structures result partly from restricted rotation around the C—N peptide bond (see Scheme 3.2). However, there is conformational freedom (about single bonds N—Cα and Cα—C) leading to two degrees of freedom per peptide. Proteins display secondary and tertiary structures, which constitute localised conformations and the overall shape.

96

Random coil conformation of a protein has no defined secondary structure. A random coil formation (denaturation) is a result of breaking the stabilising hydrogen bonds.

BIOPHYSICAL CHEMISTRY

properties are major sources of understanding of flexible coils, as well as worm like chains as high molecular-weight DNA. This discussion lays emphasis on both artificial and real chains. The knowledge of both are interdependent. 1. Freely-Jointed Chains The simplest way to measurement of chain dimensions is to measure the length of the chain along its backbone. This is known as the contour length. If we have a chain of n backbone bonds each having a length l, then the contour length is nl. It is more usual and more realistic for linear flexible chains, to consider the dimensions of the molecular coil in terms of the distance separating the chain ends, i.e., the end-to-end distance r. (Scheme 3.15)

A macromolecule can have a disorderly coiled shape (Scheme 3.15). It may adopt

a straightened out form. A study of end to end distances is made by considering a model of freely jointed chain which is closely related to random walk model (see Scheme 3.28). The following mathematical symbols are used: l A chain contains n units. l The length of each unit is l. l The chain may thus consist of N independent random sections. l The thermodynamic segment d is related to hydrodynamic length L (see Scheme 3.31). l The end to end distance of a coiled polymer is represented by r.

SCHEME 3.15

When we consider an isolated polymer molecule it is not possible to assign a unique value of r because the chain conformation (and hence r) is continuously changing due to rotation of backbone bonds. Meanwhile, each conformation has a characteristic value of r, while certain different conformations give rise to the same value of r. Thus some values of r are more probable than others and the probability distribution of r can be represented by the root mean square (RMS) end-to-end distance, 〈r 2〉1/2 , where 〈 〉 indicates that the quantity is averaged over time.

STATISTICAL MECHANICS IN BIOPOLYMERS

97

The use of the techniques of statistical mechanics to calculate 〈r 2〉1/2 necessitates the assumption of a model for the polymer molecule. The simplest model is that of a freelyjointed chain of n links (i.e., backbone bonds) each of length l for which there are no restrictions upon either bond angle or bond rotation. The study of this model is a simple extension of the well-known random-walk calculation which was first initiated to describe the movement of molecules in an ideal gas. The only difference being, in case of a freely-jointed chain, each step is of equal length l. A three-dimensional rectangular co-ordinate system is used as shown in Scheme 3.16. z

r O

y

x

A polymer molecule represented in a coil form, indicating end-to-end distance (r) in a rectangular coordinate system, where one chain end is fixed at the origin O. SCHEME 3.16

One end of the chain is fixed at the origin O and the probability, P(x, y, z) of finding the other end within a small volume element dx, dy, dz at a particular point with coordinates (x, y, z) is calculated. This calculation gives (Eqn. I, Scheme 3.17) P(x, y, z) = W(x, y, z)dxdydz

...(I)

where: W(x, y, z) is a probability density function (a probability per unit volume) SCHEME 3.17

In case however, r nl, a condition which is physically impossible (i.e., the end-to-end distance cannot exceed the contour length). However, as W(r) is small for r > nl the errors creeping in are insignificant. ∞

∫ W (r )dr

= 1

...(V)

0

SCHEME 3.23

The second moment of the radial distribution function 2

〈r 〉 (The mean square end-to-end distance) is given by the integral (Eqn. VI, Scheme 3.24). 〈r 2 〉 =

∞

∫ r W (r )dr 2

...(VI)

0

SCHEME 3.24

On combining (Eqns. IV, Scheme 3.21 and VI, Scheme 3.24) followed by integration gives the result (Eqn. VII, Scheme 3.25) 〈r 2〉 = 3/2β2 SCHEME 3.25

...(VII)

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BIOPHYSICAL CHEMISTRY

As β2 = 3/2nl2, the RMS end-to-end distance is given by (Eqn. VIII, Scheme 3.26) = n1/2l 〈r 2 〉1/2 f

...(VIII)

f stands for a freely-jointed chain SCHEME 3.26

This expression (Eqn. VIII, Scheme 3.26) is very important and shows that 〈r 2〉1/2 is a factor of n1/2 smaller than the f Random–Walk Chain The following points may be noted: l It is a freely jointed chain model (Scheme 3.28). l There is no restriction on the free rotation at the joints or on the angle between any two segments. l The polymer may be completely stretched out or it may be wound on itself like a ball of string. l In the random-walk model a polymer has no preferred orientation.

contour length. As n is large, this highlights the highly coiled nature of flexible Gaussian polymer chains. For example, a freely-jointed chain of 10,000 segments each of length 3 Å will have a fully-extended contour length of 30,000 Å whereas its RMS end-to-end distance will be only 300 Å. Dimensions of Branched and Cyclic Macromolecules One often studies the dimensions of linear chains in terms of RMS distance of a chain segment from the center of mass of the molecule. This represents the quantity of the RMS radius of gyration 〈s2〉1/2 . These determinations are in addition to the RMS end-to-end distance. The RMS radius of gyration, 〈s2〉1/2 has the additional advantage that it also can be used to characterize the dimensions of branched macro-molecules (which have more than two chain ends) and cyclic macro-molecules (which have no chain ends). Moreover, properties of dilute polymer solutions which are dependent upon chain dimensions can be controlled by 〈s2〉1/2 rather than 〈r 2〉1/2 . For linear Gaussian chains 〈s2〉1/2 is related to 〈r 2〉1/2 by (Eqn. IX, Scheme 3.27) 〈s 2 〉1/2 = 〈r 2 〉1/2 /61/2

...(IX)

SCHEME 3.27

2. The Freely Jointed or Random-Walk Chain (Random Walk Model) The earlier discussion (Schemes 3.15–3.21) gives a fairly clear picture as to how a polymer chain in a solution may look like. A random-walk model i.e., the freely jointed or random-walk chain is an artificial model which is a two dimensional presentation of a freely jointed polymer chain containing identical units. One is then interested to find out the distance

STATISTICAL MECHANICS IN BIOPOLYMERS

101

between the two ends of the chain (r). This will give some information about the size of the molecule. The lines joining the successive steps quite accurately represent the arrangement of a polymer chain. The random-walk model is a two dimensional representation (two dimensional floor) of a polymer which has a three dimensional structure. This type of a two dimensional random-walk model is represented in (Scheme 3.28).

r

The random-walk (freely jointed) chain. It is a two dimensional model where the orientation of every bond is completely random when compared to its predecessor. SCHEME 3.28

The statistical calculations averaged over many different random walks reveal that the average of the square of the distance r is given by (Eqn. I, Scheme 3.29) r 2 0 = nl2

...(I)

n = number of bonds l = length of each bond SCHEME 3.29

The root mean square distance is given by (Eqn. II, Scheme 3.30). rrms =

r2  l n

...(II)

SCHEME 3.30

This equation (Eqn. II, Scheme 3.30) leads to a result which is similar to displacement of diffusing gas molecules as a function of time. In the latter situation, the rootmean-square displacement is directly proportional to the square root of the time; in the present situation r 21/2 is 0 proportional to n 1/2, where n is similar to time in the diffusing-gas case.

102

BIOPHYSICAL CHEMISTRY

One can calculate the most probable end-to-end distance of a freely jointed chain from the Gaussian distribution curve (Scheme 3.22). Recall that W/r = 0 according to conditions for maximum. Thus (Eqn. IV, Scheme 3.21) can be written as (Eqn. I, Scheme 3.31). In Eqn. I, Scheme 3.31, d represents the thermodynamic segment (Kuhn segment) whose position is independent of that of adjacent units. One may note that, d infact is the segment of chain or statistical element, and is related to the hydrodynamic length L of the chain by (Eqn. Ia, Scheme 3.31). N represents number of independent segments. 2 2 Nd 3 L = Nd

r2m =

...(I) ...(Ia)

where: 2 rm , corresponds to the maximum of a curve. (The most probable end-to-end distance of a freely jointed chain) SCHEME 3.31

One can obtain the mean value rcoil and the root-meansquare value

1/2

  r 2coil

from (Eqns. Scheme 3.32). 1/2

 8 2 rcoil =  Nd   3  1/ 2

r  2 coil

r 2coil

or

...(II)

= N1/2d

...(III)

= Nd2

...(IV)

SCHEME 3.32

The size of the macromolecular coil can be expressed as statistical parameters e.g., root-mean-square distance between its ends

1/ 2

r  2 coil

, or from the value of the radius of gyration,

s2 (rotation radius). This represents the mean-square of the distances of all the elements of the mass of the coiled chain from its centre of gravity. The root-mean-square distance and the radius of gyration are interrelated (Eqn. V, Scheme 3.33). 1 2 (s 2 )1/2 = 6 r coil

1/ 2

 

SCHEME 3.33

...(V)

STATISTICAL MECHANICS IN BIOPOLYMERS

103

2

Both r coil and (s2 ) depend on d which represents the length of each independent segment. One can relate the mean-square end-to-end distance and square of radius of gyration by (Eqn. VI, Scheme 3.34) in the case of linear macromolecules which are not appreciably extended beyond their most probable shape. In the case of r 2coil = 6s 2

...(VI)

SCHEME 3.34 2 2 extended chains (r coil > 6s ). The degree of coiling of a chain

can be obtained from the ratio of the hydrodynamic length L of the chain to the root-mean-square end-to-end distance, (r 2coil )1/2 (Eqn. VII, Scheme 3.35). L

( ) r 2coil

1/2

=

Nd (Nd 2 )1/2

...(VII)

= N1/2

SCHEME 3.35

The following points may be noted regarding (Eqn. VII, Scheme 3.35) l

With the larger value of N, the coiling of the chain is more.

l

With larger N the molecular mass of the macromolecule is large.

l

The end-to-end distance is proportional to the square root of the number of links in the macromolecules. A reference to (Eqn. III, Scheme 3.32) leads to another relation (Eqn. VIII, Scheme 3.36)

(r ) 2

1/2

f

= N1/2d

...(VIII)

SCHEME 3.36

The subscript, f represents the random-flight end-to-end distance, i.e., coil. Thus

(r ) 2 f

1/2

∝ M 1/2 , or rf2/M is a

characteristic property of the macromolecule chain structure which is independent of molecular mass or length.

104

BIOPHYSICAL CHEMISTRY

PROBLEMS AND EXERCISES 1. How both configuration and conformation lead to secondary structure of proteins? 2. Write short notes on: (a) Conformation and configuration (b) Allowed conformations of proteins. 3. How Ramachandran diagram throws light on the conformations of proteins? 4. Write a short note on protein folding. How different structural features in a biopolymer contribute to it? 5. Discuss the consequences of protein folding. What leads to protein folding? 6. What is the statistical distribution end-to-end distance of a biopolymer? 7. How one can calculate the average dimensions for different chain structures of a macromolecule? 8. Write short notes on: (a) Protein folding (b) β-Turns (c) Partial unfolding of proteins. 9. Derive a mathematical expression which will throw light on the extended or coiled nature of a macromolecule.

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

105

C H A P T E R

" 4.1

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

INTRODUCTION

The covalent bond is essential and constitutes the strongest force which holds the molecules together. Noncovalent forces e.g., electrostatic bonds, hydrogen bonds and van der Waals bonds are weak but these participate in maintaining molecular structure stability and functional competence of macromolecules in living cells and some examples are: l Replication of DNA. l The folding of proteins into intricate three-dimensional forms for biological activity. l The specific recognition of substrates by enzymes and l Detection of signal molecules. Consider the molecule of methane in which the atoms are held together by covalent bonds. In the vapour state, these molecules are well separated and can be regarded as having little effect on one another. This is one of the criteria of an ideal gas, but in reality gas behaviour deviates from ideality because the molecules interact with each other. On liquification of methane, the molecules come closer together, and when the liquid is solidified, an ordered structure is formed in which there are intermolecular interactions between liquid and liquid solid the CH4 molecules. The vapour phase changes are endothermic, however, the intermolecular interactions are only weak: ∆vapH = 8 kJ mol–1 and ∆fusH = 1 kJ mol–1. The covalent bonds within the CH4 molecule remain intact, during different phases of methane. The strength of these intermolecular (van der Waals) interactions (Table 4.1) vary depending upon their precise nature. The weakest interactions occur between the electron 105

The noncovalent forces may be either attractive or repulsive. These forces involve interactions both within a molecule and also within it and water molecules which is the most abundant component in the surrounding biological environment. The noncovalent forces play a central role to enforce the structure and stability required for the function of biomolecules. Every biological activity involves noncovalent molecular interactions. Molecules must interact (bind) to initiate a reaction and then separate. Whether the event is an enzyme binding to its substrate, a hormone binding to its receptor on a membrane, or RNA being transcribed on a DNA template, all have to be bound in a precise orientation for a short duration. Such events are also termed molecular recognition which are made possible through intermolecualr interactions.

106

BIOPHYSICAL CHEMISTRY

The effective sizes of atoms in molecules are expressed in terms of their van der Waals radii. The van der Waals radius of a hydrogen atom is 1.2 Å. Nonbonding interactions between molecules or between different parts of the same molecule result in van der Waals attractions, as long as the interacting atoms do not come too close to each other. At distances which are shorter than the van der Waals radii of the atoms, repulsion occurs. In the gauche conformation of butane, the hydrogen atoms of the two methyl groups are too close to result in close van der Waals repulsions. Consequently, the gauche conformations are less stable than the anti form by approximately 0.9 kcal/mol. 60°

CH3

H3C

H

H

clouds of adjacent molecules and are called London dispersion forces. These interactions are involved between molecules of methane in the solid state. The enthalpies of fusion and vaporization (and melting and boiling points) of molecular species reflect the extent of intermolecular interaction. Consider an ionic solid in which ions interact with one another through electrostatic forces, the amount of energy needed to separate the ions is often far much more than that needed to separate covalent molecules. Enthalpies of fusion of ionic solids are far higher than those of covalent solids. TABLE 4.1: van der Waals types of intermolecular forces Interaction London or dispersion forces Dipole-dipole interactions Ion-dipole interactions

Acts between Most molecules Polar molecules Ions and polar molecules

The forces of attraction between the small molecules of methane are so weak that methane exists as a gas at room temperature. Molecules of hexane are larger than those of methane, and the attractive forces between hexane molecules are increased enough that hexane is a liquid. The still larger molecules of icosane attract each other so strongly that the compound is a solid at room temperature.

H

H Gauche conformer

4.2

(A) CH3 H

H

H

H CH3 Anti conformer

VAN DER WAALS FORCES

INDUCED DIPOLE/INDUCED DIPOLE INTERACTIONS (LONDON FORCES)

The van der Waals forces or dispersion forces are the same interactions which provide the cohesive force in a liquid hydrocarbon and may be regarded as examples of the like dissolve like phenomenon. The weak forces of attraction which exist between nonpolar molecules are called van der Waals interactions. These forces are due to the constant motion of electrons within bonds and molecules, giving rise to effects known as London dispersion forces. The motion of electrons generates small distortions in the distribution of charge in nonpolar molecules. A small and transient dipole results. This small dipole in one molecule can then create a dipole with the

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

opposite orientation, an induced dipole, in another molecule (Scheme 4.1). The induced dipoles constantly change, however, the net result is a slight attraction between molecules. As the number of carbon and hydrogen atoms increases, the additive effect of these weak intermolecular forces becomes more significant, as evidenced by the increase in boiling and melting points from methane to hexane to icosane. van der Waals interactions can act only through the parts of different molecules that are within a certain distance of each other. The three-dimensional shapes of molecules, therefore, determine to some extent the intermolecular interactions between molecules (see Scheme 1.4). For example, the isomers, butane and 2-methylpropane, both with the molecular formula C4H10, have different boiling points.

107

Non-bonded molecular interactions 1. Induced/dipole–induced/ dipole are called London forces and these forces are weakest of all. 2. Dipole/Dipole 3. Dipole induced dipole are all together called van der Waals interactions. – 1

+

–

CH3

–

CH3

–

+

–

+

–

CH3

+

–

CH3

+

Instantaneous dipole

–

+ + +

Induced dipole

At any given moment a nonpolar molecule like CH 3 CH 3 can develop an uneven distribution of electrons—an instantaneous dipole. This dipole can induce a dipole in a nearby molecule.

SCHEME 4.1

A good example of such van der Waals forces which leads to base stacking (vertically) in DNA molecules leads to stability of DNA (see, Scheme 4.8). For London interactions (which are also called dispersion forces) a quantum mechanical treatment (interactions between nonpolar molecules) was given in 1930 by the German physicist Fritz London (1900–1954), who showed that the potential energy V arising from the interaction of two identical atoms or non-polar molecules is given by expression (Scheme 4.1(a)). 3 I α2 4 r6 I is the first ionisation energy of the atom or a molecule α is the polarizability of the molecule r is the separation distance. V = −

where

London equation SCHEME 4.1(a)

Dipole-dipole interactions are weaker

The dipole of the water molecule induces an uneven electron distribution in the I2 molecule. This dipole-induced dipole interaction is quite weak.

108

The repulsion between atoms or groups directly reflects on the Pauli exclusion principle, according to this principle electrons are prevented from sharing the same region in space.

BIOPHYSICAL CHEMISTRY

When the nuclear distances are very short, the atoms or molecules must repel each other and thus repulsive forces operate. The fusion is prevented by strong repulsive forces between electron clouds and between nuclei. The potential energy of repulsion is extremely short range and is proportional to 1/rn, where n is between 8 and 12. The British physicist Sir John Edward Lennard-Jones (1894–1954) gave the expression [Scheme 4.1(b)] to represent the attractive and repulsive interactions in nonionic system. A B + r 6 r 12 A and B are constants for two interacting atoms or molecules r is the distance between atoms or center of the molecules. Lennard–Jones expression

V = −

where

SCHEME 4.1(b)

In [Scheme 4.1(b)], the first term represents attraction. (Recall, the dipole-dipole, dipole-induced dipole, and dispersion interactions all have 1/r6 dependence.) The second term, which is very short-range (depends on 1/r12), represents repulsion between molecules.

(B) DIPOLE/DIPOLE INTERACTIONS Nitriles are often used as solvents since they are polar, but do not have reactive hydroxyl or amino groups.

Dipole/Dipole interactions have importance in protein folding. A dipole-dipole type intermolecular interaction occurs between polar molecules with permanent dipole moments. Consider the electrostatic interaction between the two dipoles µ1 and µ2 separated by distance r. In extreme cases, these two dipoles can be aligned [I, Scheme 4.1(c)] the potential energy of interaction then is given [II, Scheme 4.1(c)]. ...(I) V = −

2µ1µ 2 εr 3

...(II)

...(III) V = −

µ1µ2 εr 3

...(IV)

where ε is the dielectric constant The negative sign indicates attractive interaction (energy is released when the two species interact) SCHEME 4.1(c)

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

109

For the arrangement [III, Scheme 4.1(c)]. The energy of interaction is given by [IV, Scheme 4.1(c)]. On reversing the charge sign of one of the dipoles V is positive quantity and thus the interaction becomes repulsive. In a macroscopic system with all possible orientations of the dipoles the mean value of V is expected to be zero because there would be as many repulsions as attractions. But even under conditions of free rotation in liquid or gaseous state, arrangements which lead to a lower potential energy are favoured over those of higher potential energy. The average energy of interaction of permanent dipoles (randomly distributed) is then given by the expression [Scheme 4.1(d)] V = − where

2 2 2 µ1µ 2 1 . . 3 εr 6 KT

K is a constant T is absolute temperature. SCHEME 4.1(d)

A consideration of [Scheme 4.1(d)] needs following points to be considered: l V is inversely proportional to the sixth power of r to show that the energy of interaction falls off rapidly with distance. l Moreover, V is inversely proportional to T as well, since at higher temperatures the average kinetic energy of the molecules is greater. This is the condition which does not favour aligning dipoles for attractive interaction. l In summary, therefore, the dipole/dipole interaction with increasing temperature will gradually average out to zero.

(C) DIPOLE/INDUCED-DIPOLE INTERACTION Recall a permanent dipole of water which induces a dipole moment in a neutral polarizable molecule e.g., iodine. In the same way an ion e.g., a positive ion can lead to distribution of charge density in a neutral nonpolar species e.g., helium atom. In helium atom the electron charge density is spherically symmetrical about the nucleus and the charged ion can generate a dipole moment in helium atom. [Scheme 4.1(e)]

A helium atom (in isolation) has electron density and is spherically symmetrical.

A permanent dipole induces a dipole moment in helium.

110

BIOPHYSICAL CHEMISTRY

SCHEME 4.1(e)

The magnitude of the induced dipole moment µind is directly proportional to the strength of the electric field E [Eqn. I, Scheme 4.1(f)] and the energy of interaction V of a dipole and an induced dipole is given by (Eqn. II, Scheme 4.1(f)). Generally, the larger the number of electrons and the more diffuse the electron charge cloud in the molecule, the greater is its polarizability.

µind ∝ E

...(I)

= αE V = −

2αµ2 εr 6

...(II)

where E is the electric field ∝ is the polarisability ε is the dielectric constant of the medium (permitivity). SCHEME 4.1(f)

Polarizability reflects on how easily the electron density is a molecule or in an atom can be distorted by an external electric field. In case the dielectric constant of a substance is large then its molecules are polar with high polarizability. When molecules with asymmetric charge distribution e.g., HCl are present, the neighbouring molecules are affected. The molecular alignment is opposed by thermal motion while the molecular polarization Pm and relative permitivity εr (dielectric constant) are related by the expressions [I and II, Scheme 4.1(g)].  µ2   α + 3K T  B   Debye equation

NA Pm = 3ε 0

where

M ρ NA ε0 KB

is is is is is

 εr − 1  M Pm =  ε + 2  ρ  r  Clausius-Mossotti equation molecular mass density of sample Avogadro’s number permitivity in vacuum Boltzmann constant SCHEME 4.1(g)

...(I)

...(II)

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

111

One can determine the Pm values from the measured values of εr of a molecular species at different temperatures. A plot of Pm against 1/T enables the determination of the permanent dipole moment, µ, from the slope, and the polarisability, α, from the intercept. One can also determine Pm as a function of frequency. At high alternating frequencies the molecule has no time to align. Therefore, Pµ = 0 and Pm = Pα. A light beam can be used as the rapidly alternating field. The Maxwell expression [Scheme 4.1(h)] relates the refractive index n and the dielectric constant. Thus [Eqns. I and II Scheme 4.1(g)] when considered in terms of molecular refractive index Rm become [Scheme 4.1(i)] from which α is deduceable. ε = n2 Maxwell equation SCHEME 4.1(h)

 n2 − 1 Rm =  n 2 + 1  . M /ρ   3ε0 α = N R A m SCHEME 4.1(i)

4.3

ELECTROSTATIC INTERACTIONS (IONIC BOND, SALT LINKAGE, SALT BRIDGE OR ION PAIR)

(A) ELECTROSTATIC INTERACTIONS Electrostatic interactions between oppositely charged groups within or between molecules are often termed salt bridges. An example is of a charged group on a substrate when it attracts an oppositely charged group on an enzyme. The force (F) of such an electrostatic attraction is given by Coulomb’s law [Scheme 4.1(j)]. q1q2 εr 2 q1 and q2 are the charges of the two groups r is the distance between them F =

where

ε is the dielectric constant of the median SCHEME 4.1(j)

Salt bonds, hydrogen bonds, hydrophobic interactions and van der Waals forces participate to maintain structure of biopolymers and are key to their bioactivity. Na+

Cl–

Na+

Cl–

Na+

Cl–

Ion-ion interactions are very strong. This is what is called an ionic bond. H Na+

O H

Ion-dipole interactions are moderately strong.

112

BIOPHYSICAL CHEMISTRY

The attraction is strongest in a vacuum (where ε is 1) and is weakest in a medium like water (where ε is 80). This attraction is also often called an ionic bond, salt linkage, salt bridge, or ion pair. The distance between oppositely charged atoms in an optimal electrostatic attraction is about 2.8 Å.

(B) ELECTROSTATIC INTERACTION THE ENZYME

IN

BINDING

OF A

SUBSTRATE

TO

An example of a salt bridge formation (Eqn. I, Scheme 4.2) is found during the hydrolysis of peptide bonds in proteins when some enzymes use the guanidinium ion of arginine to bind substrates with carboxylate and phosphate groups. The following points may be noted:

...(I)

...(II)

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

113

...(III) SCHEME 4.2

The guanidine group (present in amino acid arginine) is remarkably basic. l After protonation (Eqn. II. Scheme 4.2), the guanidinium ion is remarkably resonance stabilized. l Thus a carboxylic group and a guanidine group form a good steric match (Eqn. III, Scheme 4.2). l Carboxypeptidase A (Scheme 4.3) is an enzyme which catalyzes the hydrolysis of the C-terminal peptide bond l

SCHEME 4.3

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BIOPHYSICAL CHEMISTRY

Dielectric constants at 20°C Substance

Dielectric constant

Benzene Chloroform Acetone Ethanol Water

2.3 5.1 21.4 24 80

Water being a polar solvent, readily dissolves biomolecules, which are generally charged or polar compounds. Compounds which dissolve easily in water are hydrophilic (Greek, “water-loving”). Nonpolar solvents such as chloroform and benzene are poor solvents for polar biomolecules but easily dissolve nonpolar molecules such as lipids and waxes, which are called hydrophobic.

in peptides and proteins and releases the C-terminal amino acid. One of the groups at the active site of this enzyme is Arg 145 which helps to bind the substrate in the optimum position for reaction. l The guanidine group, a functionality which is a part of the side chain of arginine provides a good steric match for a carboxylate ion, and it has the advantage that it is readily protonated. This feature leads to especially strong interactions with the negatively charged RCO2– group as a result of both hydrogen bonding and an electrostatic attraction. Many proteins (enzymes) use the guanidinium ion of arginine to bind substrates with carboxylate and phosphate groups. This binding is shown with the Ang 145 at the active site of carboxypeptidase with the C-terminal amino acid of the substrate (Scheme 4.3).

(C) WATER WEAKENS ELECTROSTATIC INTERACTIONS Water solvates (hydrates) polar molecules (Scheme 4.4) to weaken the electrostatic interaction between them. This leads to weakening of the otherwise normal electrostatic interactions between them. Water is highly effective to weaken electrostatic interaction between polar molecules due to its high dielectric constant (see, Scheme 4.1).

Biological systems are known to create water-free microenvironments where polar interactions have maximal strength and specificity. Such interactions are of key importance in protein structure and function.

Water weakens electrostatic attractions between charged groups e.g., —COO– and —NH3+ SCHEME 4.4

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

(D) INCREASE IN ENTROPY PROVIDES SOME DRIVING FORCE THE FORMATION OF ENZYME—SUBSTRATE COMPLEX

115

FOR

Consider the binding of a polar substrate with the complementary polar surface of the enzyme (Scheme 4.5). Separately each of them has a shell of water molecules in an ordered fashion. When the substrate binds to the enzyme some of the ordered water molecules are released at the site of contact. In thermodynamic terms this leads to an increase in entropy which is favourable for the formation of the enzyme—substrate complex.

...(I)

 



 



...(II)

SCHEME 4.5

Electrostatic interactions are noncovalent interactions between charged groups. A typical electrostatic interaction involves the attraction of a protonated positively charged

116

BIOPHYSICAL CHEMISTRY

An ionic bond between —COO– and — +NH3 within a protein molecule to maintain its tertiary structure.

C =O

+

O– NH3 CH2

The free-energy change for dissolving a nonpolar solute in water is unfavourable: ∆G = ∆H – T ∆S, where ∆H has a positive value, ∆S has a negative value, and ∆G is positive.

The strength of hydrophobic interactions is not due to any attraction between nonpolar groups. The system achieves thermodynamic stability by minimizing the number of ordered water molecules which would be otherwise required to surround individual hydrophobic portions of the biopolymer.

amino group and a nearby ionised negatively charged carboxylate ion. These interactions are operative between the groups within a protein and help to maintain the tertiary structure.

4.4

HYDROPHOBIC INTERACTIONS

(A) WHAT

ARE

HYDROPHOBIC INTERACTIONS?

Most biopolymers are amphipathic that is, they have regions rich in charged or polar functional groups as well as regions with hydrophobic character. One has seen that interactions between charged groups help shape biomolecular structure. They thus often facilitate the binding of charged molecules and ions to proteins and nucleic acid. Hydrophobic interaction refers to the tendency of nonpolar compounds to cluster together in an aqueous environment, to minimise their contact with water. Consider the mixing of an amphipathic compound like a phospholipid with water. The polar, hydrophilic region tends to dissolve, but the nonpolar, hydrophobic region tends to avoid contact with water. The nonpolar regions of the molecules cluster together and are shielded from water. The polar regions are arranged to maximize their interaction with the solvent and are immersed in the aqueous environment. These stable structures of amphipathic compounds in water lead to a lipid bilayer which satisfies the thermodynamic requirements of amphipathic molecules in an aqueous requirement. The forces that hold the nonpolar regions of the molecules together are called hydrophobic interactions (Scheme 4.6). The following points may be noted: l Fatty acids are linked to glycerol and phosphate to give phospholipids, the major constituent of biological membranes. The highly polar phosphate group makes these amphipathic molecules. l The closed bilayer provides one of the key properties of membranes. These are impermeable to most watersoluble molecules, since they would be insoluble in the hydrophobic core of the bilayer. l Lipid bilayers are formed by self-assembly, driven by the hydrophobic effect. When lipid molecules come together in a bilayer, the entropy of the surrounding water molecules increases.

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

117

–

O O

–

O

P O

Polar

H2C

C

O

O

C

C

CH2 Hydrophilic

P O

P

P

P

O Hydrophobic

Shown in shorthand as Nonpolar

P

P

P

P

Hydrophilic

CH3 CH3 A phospholipid

Amphipathic phospholipids are major constituents of biological membranes

A possible structure of methane trapped in a cavity in water (methane hydrate). Creation of cavity disrupts some initial hydrogen bonds

SCHEME 4.6

The strength of hydrophobic interaction is not due to any mutual attraction or any attraction between nonpolar moieties which is sometimes incorrectly referred to as “hydrophobic bonds”. The strength of the hydrophobic interactions is based on the need to minimize energetically unfavourable interactions between nonpolar groups and water. Thus the strength of hydrophobic interactions is the achievement of thermodynamic stability by the system by decreasing the number of ordered water molecules needed to surround the hydrophobic moieties present in the system. l Recall that the entropy of hydrogen—bonded bulk water is very high. When a nonpolar molecule enters the aqueous medium, some of the hydrogen bonds have to break to make room (cavity) for its trapping. This is an endothermic process since the broken hydrogen bonds are far stronger than the dipole-induced dipole and dispersion interactions. The nonpolar molecule thus gets trapped in an ice like cage structure. One may consider the structure of methane hydrate where l

in water molecules. The displaced water molecules reorient to form new hydrogen bonds. This cavity formation is an unfavourable process due to large decrease in entropy. Due to hydrophobic interaction, the nonpolar molecules come together, releasing some of the ordered water molecules in the cavity structure and thus increasing entropy. This is a thermodynamically favourable process.

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BIOPHYSICAL CHEMISTRY

The immiscibility of nonpolar systems in water in an entropy driven process.

methane molecule is trapped in a highly structured (ordered) cage of water molecules held together by hydrogen bonds. This is an entropically unfavoured step. This leads to an appreciable decrease in entropy. Thus the nonpolar molecules self anociate (hydrophobic interactions) in order to minimize energetically unfavourable interactions between their nonpolar groups and water.

(B) HYDROPHOBIC INTERACTIONS Hydrophobic attractions are the major driving force in the folding of macromolecules, the binding of substrates to enzymes, and the formation of membranes which define the boundaries of cells and their internal compartments. Stabilizing interactions can occur between peptide groups (atoms in the backbone of the protein), between side-chain groups (α-substituents), and between peptide and side-chain groups. Since the side-chain groups help determine how a protein folds, the tertiary structure of a protein is determined by its primary structure. The polar residues such as the carboxy groups of aspartic acid or the amino groups of lysine interact with polar residues or with water are called hydrophilic residues. – OOC

CH2

CH

– COO

+

NH3 Aspartic acid CH2 CH2

CH2 CH2

COO +

+

NH3

–

CH

Lysine

NH3

AND

MEMBRANES

The ‘hydrophobic effect’ is of major importance in biology. Biological membranes form a hydrophobic barrier which defines a cell, or cellular organelle.

(C) HYDROPHOBIC I NTERACTIONS STRUCTURE OF PROTEINS

IN

R ELATION

TO

T ERTIARY

Protein molecules undergo folding in order to adopt threedimensional structures, driven by the ‘expulsion’ of hydrophobic groups from water. The hydrophobic groups in proteins are found buried within the protein’s interior, where there is no water. The tertiary structure of a protein reflects the threedimensional arrangement of all the atoms in the protein. Proteins fold spontaneously in solution in order to maximize their stability. A stabilizing interaction between two atoms leads to the release of free energy. With the release of more free energy (the more negative the ∆Gº) a protein becomes more stable. A protein molecule therefore, folds in a way so that the number of stabilizing interactions increases. Recall that the stabilizing interactions are: l Disulphide bonds l Electrostatic interactions l Hydrogen bonds and l Hydrophobic interactions. Of these interactions disulphide bonds which are covalent bonds are formed only when a protein folds. The other three are much weaker but since their number is large they are key in determining as to how a protein folds. Since most of the proteins exist in aqueous environments, therefore, they tend to fold in a way that exposes the maximum number of polar groups to the aqueous environment. The nonpolar groups then get burried in the interior of the protein, away from

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

119

water. These type of hydrocarbon like residues are sometimes called hydrophobic groups (nonpolar groups, Scheme 4.7).

A protein conformation drawn straight for simplicity

Alanine Isoleucine Leucine Methionine Proline Valine Phenylalanine

Ionic bond Aspartate or glutamate

Amino acids involved in hydrophobic interactions

Cysteine

S

–ve +ve

Amino acids involved in ionic bonds

S

Lysine or arginine

Cysteine

Stabilizing interactions responsible for the tertiary structure of a protein

H3C CH3

COO–

CH

CH H3C

+

COO–

CH +

NH3

NH3

Alanine

Valine

Nonpolar (hydrophobic) residue of some amino acids

CH2

CH +

NH3 Phenylalanine

– COO

CH2 N

COO–

CH +

NH3

H Tryptophan

SCHEME 4.7

The hydrophobic interactions increase the stability of a protein by increasing the entropy of water molecules. With hydrophobic interaction the nonpolar groups come together into a single cavity, the surface area in contact with water decreases. Since water molecules which surround nonpolar groups are highly ordered, this response destroys part of the cage structure decreasing the amount of ordered water. This

Unlike when a nonpolar molecule (group) occupies different cavities in water, an energetically more favourable system arises when this molecule instead occupies a single large cavity. The

120

BIOPHYSICAL CHEMISTRY

nonpolar groups thus come together and are involved in hydrophobic interactions. Ordered water molecules around a nonpolar molecule making a cavity

Nonpolar molecule

Water molecules lose entropy

Water

results in an increase in ∆S and hence a decrease in ∆G. A decrease in free energy increases the stability of a protein since ∆Gº = ∆Hº – T ∆Sº.

(D) IMPORTANCE

IN

NUCLEIC ACIDS

The following points may be noted: l In double helical DNA structure the two strands of the duplex are held together via hydrogen bonding between heterocyclic bases on opposite strands. l The bases represent planar aromatic systems which stack on top of one another vertically (like coins on top of each other, Scheme 4.8).

(I)

P

P S

C

G

S P S

Fewer Molecules of water around hydrophobic cluster, overall increase in entropy

This arrangement releases some of the ordered water around each cavity initially present in (I). The end result is increase in entropy of water —a thermodynamically favourable process.

A P

G

S

C

S

= Adenine

G

= Guanine

T

= Thymine

C

= Cytosine

S P

= Sugar

P

P T

S

A

P

S

P S P

P S

C

G

= Phosphate

S P

P G

S P The two helical strands in DNA are held together by the hydrogen bonds between complementary base pairs. Additional stability arises from vertical hydrophobic interactions between adjacent nonpolar heterocyclic bases which generate stacking throughout the duplex structure.

T

S P

A

Pyrimidines

S P

Purines

P

P

3¢

C

S

P

5¢

Base stacking (shaded) in DNA and hydrophobic association of bases in the inside of helix. SCHEME 4.8

l

Several forces like van der Waals interaction between the mutually induced dipoles (see, Scheme 4.1) of adjacent pair of bases lead to interactions called as stacking interactions. Though these are weak but added together these lead significantly to the stability of the double helix. The stacking interactions between two purines are the strongest while these are weak between two pyrimidines.

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

l

121

Apart from hydrogen bonding and van der Waals interactions discussed above, the DNA molecule confines these bases to the inside of the helix away from water to generate hydrophobic interactions. This leads to an increase of the entropy of the water surrounding the DNA molecule and thus stabilises the DNA molecule. A linear expression (Scheme 4.9) exists between ∆Gtransfer and the water-accessible surface area for completely nonpolar side chains. Recall that the driving force for the formation of hydrophobic environment is entropy driven (positive entropy change) –RT ln K = ∆Gtot = ∆Hch = ∆Hsol – T∆Sch – T∆Ssol where ch = chain and sol = solution.

One may imagine a DNA double helix where each base pair is slightly rotated with respect to the next pair. Stacking interactions are between these pair placed vertically which give the look of a partially spread-out hand of cards.

SCHEME 4.9

For nonpolar region, ∆Hch and ∆Hsol are small (∆Hch is positive and ∆Hsol is negative) and ∆Ssol is positive and large. Thus ∆Ssol from a nonpolar group gives the largest single contribution to protein stability. Whereas in polar regions, ∆Ssol is cancelled by ∆Hch (that is ∆G ≈ 0).

4.5

HYDROGEN BONDING

Hydrogen bond is an important, and relatively strong, form of intermolecular interaction. A well known example of hydrogen bonding is between water molecules (Scheme 4.9). H

H O

H H

+

H

H O

Hydrogen bond

H

H

H

+

Polar (covalent) bond

O

O

H O

H

H

H O

O

O

–

Water

H

H

H

Association of two dipolar water molecules by a hydrogen bond, shown as a dotted line.

Hydrogen bonded cluster of four water molecules. Water can serve simultaneously both as a hydrogen donor as well as a hydrogen acceptor. SCHEME 4.9

Carboxylic acids have relatively high boiling points since they form intermolecular hydrogen bonds, giving them larger effective molecular weights.

122

Hydrogen bonds are formed whenever a strongly electronegative atom (O, N or F) approaches a hydrogen atom which is covalently attached to a second strongly electronegative atom.

Hydrogen bonds are stronger than van der Waals interactions.

BIOPHYSICAL CHEMISTRY

Hydrogen bonding in water involves the oxygen atom of one molecule of water sharing a lone pair of electrons with the slightly positively charged hydrogen atom of another molecule of water. Water molecules thus interact with each other through hydrogen bonding. Hydrogen bonds rapidly form and break in water but in ice a lattice-like arrangement is formed. This property of hydrogen bonding in water is paramount in determining its unique characteristics as the ‘solvent of life’. Hydrogen bonds are formed whenever a strongly electronegative atom (e.g., oxygen, nitrogen and fluorine) approaches a hydrogen atom which is covalently attached to a second strongly electronegative atom. For example, a hydrogen bonding is formed between a carbonyl and amino group (Scheme 4.10) and an example is found in proteins where the peptide bonds are involved in hydrogen bonding. Hydrogen bond

C

d+

O d–

H

d+

N

d–

Carbonyl

amino

O R Hydrogen bonding between an amide and a carbonyl group in an α helix of a protein.

C

O N H

R

C

d+

H

d–

O R

N H

C

N Hydrogen bond

O R

N

C

H Hydrogen bonding in proteins involving polypeptides SCHEME 4.10

Additional polar groups involve themselves in hydrogen bonding and these polar groups occur in biological molecules. In a hydrogen bond, a hydrogen atom is shared by two other atoms. The atom to which the hydrogen is more tightly linked is called the hydrogen donor, while the other atom is the hydrogen acceptor. The acceptor has a partial negative charge that attracts the hydrogen atom. Moreover, an important

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

feature of a hydrogen bond is that it is highly directional. The strongest attraction between the partial electric charges is when the three atoms involved e.g., O, H and O (Scheme 4.11) lie in a straight line. When the hydrogen-bonded moieties are structurally constrained e.g., as parts of a single protein molecule, this ideal linear geometry may not be attainable and the resulting hydrogen bond is weaker.

123

The optimum hydrogen bond has a distance of about 2.8 Å. Hydrogen Hydrogen donor acceptor

O

H

N

2.88 Å Hydrogen Hydrogen donor acceptor

SCHEME 4.11

The hydrogen bond energies range between 3–7 kcal/mol and these bonds are far stronger than van der Waals interactions. Lastly mention may be made of DNA strands where it is hydrogen bonding between purine and pyrimidine bases that forces these bases on opposite strands to lie flat i.e., planar and to maintain a defined distance from each other. Moreover, it is the hydrogen bonding that determines that only thymene bonds with adenine and cytosine with guanine (Scheme 4.12).

SCHEME 4.12

N

H

O

3.04 Å

124

BIOPHYSICAL CHEMISTRY

SUMMARY The following points may be noted:

The most stable conformations of biopolymers are those in which hydrogen bonding is maximized within the biopolymer and between the biopolymer and the surrounding water, and in which hydrophobic moieties cluster in the interior of the biopolymer away from water. Moreover other noncovalent interactions namely ionic and van der Waals interactions are of equal significance to decrease the free energy of the biopolymer to make it stable.

l

Van der Waals forces are nonspecific attractive forces which come into play when any two atoms are 3 to 4 Å apart. These are weaker and less specific compared with electrostatic and hydrogen bonds. Van der Waals bonds have however equal significance in biological systems. The van der Waals forces arise due to the changes in distribution of electronic charge around an atom with time. At any instant, the charge distribution is not perfectly symmetric. This transient asymmetry in the electronic charge around an atom initiates a similar asymmetry in the electron distribution around its neighboring atoms. The resulting attraction between a pair of atoms tend to increase as they come close to each other, until they are separated by the van der Waals contact distance. At a shorter distance, the strong repulsive forces become dominant because the outer electron clouds overlap.

l

The van der Waals bond attraction energy of a pair of atoms is around 1 kcal/mol and is weaker than a hydrogen or electrostatic bond (3 to 7 kcal/mol).

l

Covalent bonds are strong, which need significant amount of energy to break. Intermolecular interactions are relatively weak, and in water form and break rapidly in a reversible manner. Weak though they are, intermolecular interactions are collectively strong and vitally important in understanding the interactions of biological molecules.

l

Biopolymers e.g., proteins, DNA and RNA contain very many sites of potential hydrogen bonding or ionic, van der Waals, or hydrophobic interactions. The total combined effect of these, otherwise weak binding forces can be enormous. The generation of each of these weak interactions contributes to a net decrease in the free energy to make the system stable.

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

4.6

125

HYDROGEN ION TITRATION CURVES

(A) SHAPE OF A BIOPOLYMER IN RELATION HYDROGEN IONS IN AQUEOUS MEDIUM

TO

CONCENTRATION

OF

Generally biopolymers exist within the cell in an ionised charged state. The ionic state is determined by the concentration of hydrogen ions in the aqueous medium. Any change in the [H+] of this environment may affect the state of ionization of these molecules to result in a change in their structural shape. This change in shape may lead to a modification in their biological activity, e.g., the effect of [H+] on enzymes. Cells and body fluids of living organisms use buffer systems to regulate the free [H+] within the limits which allow normal function of their constituent biomolecules. The following points may be noted: l Non covalent bonds within a biopolymer stabilize the biological molecules. Interaction with water which is the major component of the surrounding environment influences the structure of biopolymers as well. l Electrostatic interactions between charged residues is pH dependant i.e., these interactions depend on the degree of ionisation, on the local dielectric environment and also on the ionic cloud of the counter charge. l Consider the thermodynamic stability during the interaction between ionised residues of opposite charges in an aqueous environment, ∆G is negative, whereas ∆H and ∆S are both positive. Thus the enthalpy change is not favourable since energy is required to displace solvating water molecules. However, the entropy and the free energy changes are favourable as the displaced ordered water molecules are released.

(B) WATER MOLECULES TO DISSOCIATE

HAVE A

SLIGHT

BUT IMPORTANT

TENDENCY

The ability of water to ionize to a small extent is of central importance for life. Water can act both as an acid and as a base and thus its ionization may be represented as an intermolecular proton transfer that forms a hydronium ion (H3O+) and a hydroxide ion (OH–) (Eqn. I, Scheme 4.13).

126

BIOPHYSICAL CHEMISTRY

The transferred proton is infact associated with a cluster of water molecules and thus can exist in solution not only as H3O+, but also as multimers such as H5O+2 and H7O3+. However, in a routine way proton is represented as H+. One H2O molecule dissociates to yield one H+ and one OH– ion. H3O+ + OH–

H2O + H2O +

...(I)

−

[H ][OH ] [H2O]

...(II)

Kw = [H+][OH–]

...(III)

Keq =

where KW is the dissociation constant of water. SCHEME 4.13

The degree of dissociation is measured from the equilibrium constant. Equilibrium constant is the ratio of the concentration of the dissociated ions to the undissociated molecules. The equilibrium constant (Keq) for the dissociation of H2O is in (Eqn. II, Scheme 4.13). As the concentration of water [H2O] is constant and is simply equivalent to the density of water, the relationship between KW and Keq is given by (Eqn. III, Scheme 4.13). In pure water the concentration of hydrogen ions and hydroxide ions must be same and is found experimentally to be equal to 1.0 × 10–7 M at 25ºC, thus [H+] = [OH–] = 1.0 × 10–7 M From these considerations (Eqn. III, Scheme 4.13) is written as in (Scheme 4.14). KW = [H+][OH–]

KW = [H+][OH–] = 1.0 × 10–7M × 1.0 × 10–7 M = 1.0 × 10–14 M2

This relation tells: Very little pure water exists as its ions. KW is a constant at a specific temperature, with the decrease in the concentration of H3O+, the concentration of OH– must increase and vice versa. SCHEME 4.14

At 25 °C, KW = (10–7)2, or 10–14 (mol/L)2. At temperatures below 25 °C, KW is slightly less than 10–14, and at temperatures above 25 °C it is somewhat more than 10–14. Within these limitations of the effect of temperature KW equals 10–14 (mol/L)2 for all aqueous solutions, even solutions of acids or bases. One uses KW to calculate the pH of acidic and basic solutions.

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

(C) pH

OF

127

WATER

pH is the negative log of the hydrogen ion concentration (Scheme 4.15). Low pH values correspond to high concentrations of H+ and high pH values correspond to low concentrations of H+. pH = –log [H+] To calculate pH, first: + l Calculate hydrogen ion concentration [H ]. + l Calculate the base 10 logarithm of [H ]. l pH is the negative of the value found in second step. Thus pH of pure H2 pH = –log [H+] If [H+] is equal to 1.0 × 10–7 M pH = –log(1.0 × 10–7 M) = –(–7) = 7 SCHEME 4.15

(D) FUNCTIONAL GROUPS WHICH ARE WEAK ACIDS BIOLOGICAL SIGNIFICANCE (pKa AND pH)

HAVE

GREAT

A knowledge of the dissociation of weak acids and bases is key to the understanding the effect of pH on structure of a biopolymer and its biological activity. The biopolymers have functional groups which can act as weak acids and bases. Recall that carboxyl groups, amino groups and phosphate esters have a second dissociation which falls within the phisiological range. These functional groups are present e.g., in proteins and nucleic acids. The dissociation behaviour of functional groups have applications in separation techniques like electrophoresis and ion exchange chromatography. When hydrogen chloride which is a strong acid is dissolved in water, almost all the molecules dissociate to give ions, thus products are favoured at equilibrium. When a much weaker acid, such as acetic acid, is dissolved in water, very few molecules dissociate, therefore, reactants are favoured at equilibrium (Scheme 4.16). Whether a reversible reaction favours reactants or products at equilibrium is indicated by the equilibrium constant of the reaction, Keq. Brackets are used to indicate concentration in moles/litre, i.e., molarity (M) (Eqn. I Scheme 4.16). The degree to which an acid (HA) dissociates is normally determined in a dilute solution, so the concentration of water remains nearly constant. The equilibrium expression,

Conjugate acid and conjugate base When a compound loses a proton, the species thus obtained is called its conjugate base. Thus, Cl– is the conjugate base of HCl and H 2O is the conjugate base of H 3 O + . When a compound accepts a proton, the resulting species is called its conjugate acid. Thus, HCl is the conjugate acid of Cl–, and H3O+ is the conjugate acid of H2O.

128

BIOPHYSICAL CHEMISTRY

Very strong acids pKa < 1 Moderately strong acids pKa = 1–5 Weak acids pKa = 5–15 Extremely weak acids pKa > 15

therefore, can be rewritten using a new constant called the acid dissociation constant, Ka (Eqn. II Scheme 4.16). Thus for a weak acid like acetic acid one writes the dissociation (Eqn. III) and in the equilibrium expression the concentration of water is not included, since it is in large excess and the value [H2O] is a constant. +

HA + H2O +

Keq =

–

H3O + A –

[H3O ] [A ] [H2O] [HA]

...(I)

Equilibrium constant

Larger stronger Smaller stronger

the value of K a , the acid. the value of pK a, the acid.

Acid dissociation constant

+

–

[H3O ] [A ] Ka = Keq = [H2O] [HA]

CH3COOH(aq) + H2O(I) (Weak acid)

–

...(II) +

CH3COO (aq) + H3O (aq) (Conjugate base)

Ka =

– (aq)

[CH3COO

+

] [H3O

(aq)]

...(III)

[CH3COOH(aq)]

4–5 9–10 6.4 7.2 = = = = R—CH2—COO– R—CH2—NH2 HCO–3 HPO4–2 R—CH2—COOH R—CH2—NH3+ H2CO3 H2PO4–

Some weak acids

Conjugate bases

pKa pKa pKa pKa

pKa

SCHEME 4.16

The acid dissociation constant is the equilibrium constant multiplied by the molar concentration of water (55.5 M). The following points may be noted: l The larger the acid dissociation constant, the stronger is the acid since then there is greater tendency to give up a proton. Hydrogen chloride, with an acid dissociation constant of 107, is a stronger acid than acetic acid, with an acid dissocation constant of only 1.74 × 10–5. l For convenience, the strength of an acid is generally indicated by its pKa value rather than its Ka value (Scheme 4.17) pKa = –log Ka

Since: The numeric values of Ka for weak acids are negative exponential numbers, one expresses Ka as pKa. pKa is related to Ka as pH is to [H+], thus stronger the acid, the lower its pKa value. SCHEME 4.17

This expression (Scheme 4.18a) is a relationship among pH, the buffering action of a mixture of a weak acid with its conjugate base and the pKa of the weak acid. The concentration of an acid and its conjugate base in aqueous solution can be calculated from its Ka or pKa. Ka =

[H3O+ ][A − ] [HA]

pKa = –log

and

pKa

[H3O+ ][A − ] [HA]

[A − ] = – log[H3O+] – log [HA] [A − ] = pH – log [HA]

[A − ] pH = pKa + log [HA] (Henderson-Hasselbalch equation)

From this equation, when pH = pKa, then [A − ] log [HA] = 0

and

[HA] = [A–] SCHEME 4.18(a)

Beer Gastric juice

Acidic

Household bleach

In a compound acidic form will predominate if the pH of the solution is less than its pKa.

and pKa = –log Ka (From Scheme 4.16)

Thus

0

(E) THE HENDERSON-HASSELBALCH EQUATION

Neutral Milk of magnesia

9 3

4

5

6

7

8

Egg white

1

Acidic solutions have pH values less than 7; basic solutions have pH values greater than 7. The pH of a solution can be changed by the addition of acid or base to the solution.

Human blood tears

SCHEME 4.18

Coffee

pH = –log [H+]

2

The pKa of hydrogen chloride is –7 and the pKa of a far weaker acid, acetic acid is 4.76 (the smaller the pKa the stronger is the acid) l The pH of a solution shows the concentration of positively charged hydrogen ions in it. The concentration can be indicated as [H+] or, because a hydrogen ion in water is solvated, as [H3O+]. The lower the pH, the more acidic is the solution. The term pH is defined by the expression (Scheme 4.18). l

Basic

129

10 11 12 13 14 pH

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

A compound will exist primarily in its basic form if the pH of the solution is greater than its pKa.

130

Solutions of weak acids or bases and their conjugates display buffering (the ability to resist a change in pH following addition of strong acid or base) Several metabolic processes are accompanied by the release or uptake of protons. Oxidative metabolism produces CO2, the anhydride of carbonic acid, which if not buffered would produce severe acidosis. Maintenance of a constant pH involves buffering by phosphate, bicarbonate, and proteins, which accept or release protons to resist a change in pH.

BIOPHYSICAL CHEMISTRY

This equation (Scheme 4.18a) shows that the pKa of an acid is numerically equal to the pH of the solution when the molar concentration of the acid equals that of its conjugate base. The pH of a solution can be known from the HendersonHasselbalch equation provided the molar concentrations of A– and HA, and the pKa of HA are known. Similarly, the pKa of an acid can be calculated if the molar concentrations of A– and HA, and the pH of the solution are known.

(F) BUFFERS—TITRATION CURVES An acid-base conjugate pair e.g., acetic acid and acetate (see eq. III, Scheme 4.16) is able to resist changes in the pH of a solution. That is, it can act as a buffer. On adding hydroxide (OH–) to a solution of acetic acid one has the reversible equilibria (Eqn. Scheme 4.19). –

CH3COO + H2O

Conjugate base SCHEME 4.19

Weak acid

A graph of the dependence of the pH of this solution on the amount of OH– added is called a titration curve (Scheme 4.20). There is an inflection point in the curve at pH 5.0 which is the pKa of acetic acid. In the vicinity of this pH, a relatively large amount of OH– (or H+) produces little change in pH as the added OH– (or H+) reacts with CH3COOH (or CH3COO–), respectively. Weak acids are very effective in buffering against changes in pH within 1 pH unit of the pK often referred to as pK ± 1, the buffering capacity. 1.0

[CH3COO– ]

pKa ± 1 pH = pKa = 5

–

Equivalents of OH added

At physiological pH most polyprotic biomolecules exist as ionic species.

–

CH3COOH + OH

0.5

[CH3COOH] = [CH3COO– ]

[CH3COOH] 0 0

3

4

pH

5

6

Titration curve of acetic acid, of type HA. The heavy dot indicates the pK a

SCHEME 4.20

7

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

(G) TITRATION CURVES

OF

131

AMINO ACIDS

–

Equivalents of OH added

Consider the Following Points: l Every amino acid has two acid-base groups: the αamino and α-carboxyl groups attached to the Cα atom. Few other amino acids with an ionizable side-chain (Asp, Glu, Arg, Lys, His, Cys, Tyr) have an additional acid-base group. l The carboxyl group of these amino acids have pKa values of approximately 2, and the protonated amino groups have pKa values near 9. l At low pH (pH ~ 0) i.e., in a very acidic solution, both the amino group and the carboxyl group of glycine e.g., are fully protonated and glycine exists almost entirely in the cationic form (I, Scheme 4.21).

Biological fluids e.g., the cytosol and blood, are buffered. The pH of the blood is carefully controlled at pH 7.4. The major buffering components in most biological fluids are the phosphate ion (H2PO4–, pKa 7.2) and the carbonate ion (HCO3–, pKa 6.4) because they have pKa values in this range. Several biopolymers e.g., amino acids proteins, nucleic acids and lipids have multiple acid base groups and these therefore, are effectively involved at buffering in the physiological range (pH = 6–8)

pKa1

pKa2

–

OH

H2N

Cationic form pKa1 = 2.3 (I )

– COO

H2N

Dipolar form pKa2 = 9.8 (II) Gyline in various forms at different pH values

SCHEME 4.21

Now the amino acid solution is titrated with increasing amount of a strong base (NaOH) and the titration curve is in (Scheme 4.21). l On increasing the pH the cationic form gives up a proton from the carboxylic acid group (the carboxylic acid is a stronger acid than the ammonium group) to give the dipolar ion. From the Henderson-Hasselbalch l

–

COO

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BIOPHYSICAL CHEMISTRY

The Isoelectric Point The isoelectric point (pI) of an amino acid is the pH at which it has no net charge, it is the pH at which the amount of positive charge on an amino acid exactly balances the amount of negative charge: pI (isoelectric point) = pH at which there is no net charge

The form of an amino acid at different pH values. O R

CH +

NH3

C

CH

OH

pH = 0

+

C

O–

NH3 a zwitterion pH = 7

O R

CH NH2

C

1 (2.3 + 9.8) = 6.1. This pH 2 is called the isoelectric point (pI) because the amino acid has an overall charge of zero; that is, it is neutral. Several important clues may be obtained from the above discussion. Firstly, glycine (and other amino acids) is never present in aqueous solution in a neutral form with uncharged carboxylic acid and amino groups. It is present as a cationic form, a dipolar ion, or an anionic form, depending on the pH. Secondly since the pH of most physiological solutions is near 7, which is close to the isoelectric point of glycine, it is commonly present as a dipolar ion in biological fluids. Thirdly, on comparison of pKa1 (= 2.3) of glycine with pKa (= 4.76) of acetic acid shows that the carboxyl group of glycine is about 100 times more acidic than that of acetic acid. This is due to the presence + of the positively charged amino group (—NH3) of glycine. An inspection of the titration curve of α-amino acid reveals that glycine has two regions which can act as buffers. One is around pK1 = 2.3 indicating that glycine is a good buffer, near pH 2.3, and the second is centred around pH 9.8 (pKa2 = 9.8).

of pKa1 and pKa2, or pH =

O R

equation the concentration of the cationic form equals the concentration of the dipolar ion when the pH is equal to pKa1—that is, at pH = 2.3. l A further increase in pH leads to an increase in the concentration of the dipolar ion which increases until nearly all of the glycine is present in that form. Now the ammonium group begins to give up its acidic proton to give the anionic form. The concentration of the dipolar ion equals that of the anionic form when the pH is equal to pKa2—that is, at pH = 9.8. At higher pH, glycine is present predominantly in its anionic form. l In the case of glycine the concentration of the dipolar ion is at its maximum at a pH equal to the average

O–

pH = 7

(G) THE EFFECT POLYMERS When the amino acids are linked together in proteins only the side chain groups and the terminal α-amino and α-carboxyl groups are free to ionize.

OF

pH

ON

STRUCTURE

AND

BIOACTIVITY

OF

Recall that while working with proteins and other biological molecules, control of pH is significant to avoid denaturation and thus loss of activity. It has been found that the enzyme lysozyme works best between pH values 3 and 8. The cleavage of the bacterial cell

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

wall at the active site of the enzyme requires the protonation of the acetal oxygen atom (Scheme 4.22) by glutamic acid and after the removal of the alcohol fragment the intermediate carbocation must be stabilized by the negatively charged carboxylate ion of aspartic acid (Scheme 4.23).

SCHEME 4.22

For activity a optimum pH 3–8 provides a carboxylic acid group as well as a carboxylate ion at the active site of the enzyme. At lower pH both aspartate and glutamate will be protonated and the carboxylate ion will not be available. At higher pH than 8, both aspartic acid and glutamic acid residues will be deprotonated and thus a proton wil not be available to initiate the first step. Asp

COO–

COO– NHAc

O O OH

+

O HO H COO– Glu

OH O NHAc

133

134

BIOPHYSICAL CHEMISTRY

Asp

COO– –

COO

OH

NHAc

+ O HO O H – OH COO

O

O NHAc

Glu

Asp COO– O Intermediate carbocation

COO– NHAc HO + HO O+

OH O NHAc

OH

COO–

Glu

SCHEME 4.23 .

PROBLEMS AND EXERCISES 1. Describe different noncovalent van der Waals forces involved in various biopolymers. Give a brief description of each of these forces. 2. Describe the structure of DNA. How van der Waals forces explain the stability of DNA? 3. Write a short note on van der Waals forces. Draw the London equation and discuss attractive and repulsive interactions in nonionic systems. 4. Draw a mathematical expression to explain dipole-dipole interactions between polar molecules. How these interactions have significance in protein folding?

FORCES INVOLVED IN BIOPOLYMER INTERACTIONS

5. What are dipole/induced dipole interactions? Explain their role in stability of biopolymers. 6. Explain how hydrophobic interactions increase the stability of a protein molecule? 7. Explain hydrogen bonding by taking simple molecules as your examples. How hydrogen bonding helps to explain the shape of biopolymers? 8. Discuss the tendency of water molecules to dissociate. 9. Discuss the dissociation of a weak acids and bases. How such information is useful in understanding the structure of a biopolymer? 10. Discuss in detail the utility of Henderson-Hesselbalch equation. Explain how this equation fits the titration curve of a weak acid? 11. Taking the example of acetic acid, show that titration curves reveal the pKa of weak acids. 12. Discuss the titration curve of glycine. What important information is generated from such a curve? 13. How the titration curve of a monoprotic acid compares and contrasts with that of glycine?

135

136

BIOPHYSICAL CHEMISTRY

C H A P T E R

5

CELL MEMBRANE AND SOLUTE TRANSPORT

5.1 Cytoplasm is that portion of the cell’s contents, which is outside the nucleus, but within the plasma membrane. Cytoplasm contains organelles e.g., mitochondria.

INTRODUCTION AND FUNCTION OF CELL MEMBRANES

The plasma membrane is an envelope which surrounds the cell and defines cellular boundaries to permit cellular individuality. These membranes divide cells into discrete compartments and have selective permeabilities to act as barriers in maintaining the difference in composition between the inside and outside of cell. The selective permeabilities are due to the presence of channels and pumps (e.g., Na+/K+ ATPase) for ions and substrates. In summary the plasma membrane encapsulates the cell and brings about a physical separation of the cytoplasm from the external hostile environment. All substances which either enter or leave the cell must pass through the plasma membrane and therefore, it plays an important role for the selective uptake of nutrients from the extracellular medium and the discharge of waste products of metabolism from the cell. Membranes are also involved in signalling processes. They have specific receptors for external stimuli and thus generate chemical as well as electrical signals within the cell. Membranes are involved in the organisation of cellular processes e.g., synthesis of lipids and certain proteins. The basic structure of all membranes is derived from the lipid bilayer. The membranes are rather very thin and essentially two-dimensional. The two dimensional space makes the intermolecular collisions far more probable than in a threedimensional space. Thus the enzyme catalysed processes which occur within membranes are largely increased.

136

CELL MEMBRANE AND SOLUTE TRANSPORT

5.2

137

THE CHEMICAL COMPOSITION OF MEMBRANES

The biological membranes are rather complex structures and are overall composed of lipids, proteins and carbohydrates. From one membrane to another the composition of lipids, proteins and carbohydrates differ. The major lipids in mammalian membranes are: l Phospholipids l Glycospingolipids and l Cholesterol.

A biological membrane consists of a phospholipid bilayer with proteins, carbohydrates and other lipids embedded on the surface and in the bilayer.

(A) PHOSPHOLIPIDS Phosphoglycerides are the most common of the two major phospholipid classes that occur in membranes. These contain a glycerol backbone esterified with two fatty acid residues and one phosphoric acid residue (Scheme 5.1). The fatty acid constituents are normally even-numbered, carbon molecules commonly having 16 or 18 carbons. These are unbranched and may be saturated or unsaturated. A simple example of a phosphoglyceride is phosphatidic acid (Scheme 5.1). Polar hydrophilic group

O– O

The various cellular membranes have different compositions e.g., lipid to protein ratio. This difference is reflected in their divergent functions.

P

OH

Polar head group Glycerol

O H2C

O

CH

CH2

O

O

C

C

Hydro carbon tails

º O

A symbol used to designate a phospholipid or other membrane lipids e.g., a glycolipid

Apolar hydrophobic tails Apolar hidrophobic tails

Phosphatidic acid SCHEME 5.1

In other phosphoglycerides an alcohol moiety is attached to the phosphoric acid residue i.e., the phosphate group is

138

BIOPHYSICAL CHEMISTRY

General structure of a phosphoglyceride

Some typical glycerides

further esterified to the hydroxyl group of one of the several alcohols (choline, ethanol amine, glycerol, inositol or serine and thus represent phosphoric acid diesters). A typical member is phosphatidylinositol (Scheme 5.2). Although phosphatidate (diacylglycerol 3-phosphate) is a minor component in membranes, the major phosphoglycerides are derived from it. In these major phosphoglycerides, the phosphate is further esterified and phosphatidylinositol (Scheme 5.2) is one example.

phospho-

O

Alcohol-Inositol

Fatty acids

R1

C

O

CH2

R2

C

O

CH

O R¢

C

O

CH2

R²

C

O

CH CH2

O

–

O O

P O

H2C

O

O O

OH O

P

R¢² –

O R¢² = H = Phosphatidic acid +

R¢²= –CH2CH2N(CH3)3 = Phosphatidyl choline

Glycerol

O

H H H OH

OH H H OH OH H

Phosphatidylinositol A typical phosphoglyceride showing phosphorylated alcohol (inositol), glycerol and fatty acids R1 and R2

SCHEME 5.2 OH H R¢²= H H OH

OH H OH H

H = Phosphatidyl inositol OH

The second major class of phospholipids contains sphingosine backbone rather than glycerol. Sphingomyelin represents the only phospholipid in biological membranes which is not derived from glycerol. In sphingomyelin, the backbone is sphingosine an amino alcohol which contains a long unsaturated hydrocarbon chain. In sphingomyelin the amino group of the sphingosine backbone

SCHEME 5.3

CELL MEMBRANE AND SOLUTE TRANSPORT

is linked to a fatty acid via an amide bond. Moreover, the primary hydroxyl group of sphingosine is esterified to phosphoryl choline (Scheme 5.3). The sphingomyelins occur in the plasma membrane of most cells and are present in large quantities in the myelin sheath which surrounds nerve cells.

139

The common alcohol moieties of phosphoglyceride +

HO—CH2—CH2 NH3 Ethanolamine +

HO—CH2—CH2— N(CH3)3 Choline

(B) GLYCOLIPIDS Many membranes also contain glycolipids i.e., sugar containing lipids. These are also derived from sphingosine, however in place of phosphorylated head group they have one or more sugar residues. A typical example is of cerebrosides (Scheme 5.4). In galactocerebrosides there is one galactose unit and these glycolipids are found in the neuronal cell membranes of the brain.

Inosito

R

R

–

CH3 (CH2)12 Sphingosine

SCHEME 5.4

(C) CHOLESTEROL The sterol cholesterol is a major constituent of animal plasma membranes, however it is absent in prokaryotes. The fused ring system of cholesterol (Scheme 5.5) makes it more rigid

SCHEME 5.5

Phospholipids represent the major class of membrane lipids. The major classes of membrane lipids are: l Phospholipids l Glycolipids and l Cholesterol

140

BIOPHYSICAL CHEMISTRY

compared to other lipids of membranes. Plants contain little cholesterol while other sterols e.g., stigmasterol and β-silosterol are major components, these sterols differ from cholesterol only in the structure of their aliphatic chains at C–17.

Phospholipids and glycolipids readily arrange to form bimolecular sheets in aqueous media.

Representation of hydrophilic head group (polar) of a phospholipid or a glycolipid molecule O O

5.3

–

P

Membrane lipids are made from hydrophobic fatty acid chains and a hydrophilic polar head group as has been shown for phosphatidic acid using a general symbol (see, Scheme 5.1). In the case of sphingolipids, the fatty acid chain (R1, Scheme 5.3) and the hydrocarbon chain of sphingosine are hydrophobic while the phosphorylated or sugar head group provide the hydrophilic portion. Cholesterol is a vital component of cell walls and helps in the fluidity of membranes (Scheme 5.6). Cholesterol is entirely hydrophobic but for the C–13 hydroxyl group.

–

O

O CH2

Hydrocarbon tails

CH

CH2

O

O

C

OC

CH2

CH2

CH2

CH2

CH2

CH2

FORMATION OF BILAYER LIPID AGGREGATES—THE BILAYER MEMBRANE STRUCTURE

O

Hydrophilic surface exposed to water

Cholesterol is a common constituent of the outer membranes of cells. The amphipathic character of this molecule is due to the hydroxyl group, which orientates this end of the molecule to the surface of the membrane in contact with water. The hydrophobic fused ring structure along with the side chain are anchored within the hydrophobic interior of the cell membrane.

Hydrophobic interior fatty acid tails

Hydrophilic surface

SCHEME 5.6

Membrane lipids, thus provide amphipathic molecules which contain both hydrophilic (water loving) and hydrophobic (water hating regions). In aqueous solution the amphipathic molecules will organise themselves in such a way as to prevent the hydrophobic region coming into contact with the water molecules. In aqueous solution the formation of a lipid bilayer from glycolipids and phospholipids is a spontaneous and rapid process (Scheme 5.6). The following points may be noted:

CELL MEMBRANE AND SOLUTE TRANSPORT l

l

l

l

l

5.4

The favoured structure from glycolipids and phospholipids in water is a two dimensional bimolecular sheet or lipid bilayers (Scheme 5.6). The lipid bilayers where the phospholipid molecules are orientated with their hydrophobic chains in the interior of the structure and their hydrophilic head groups on the surfaces, can have macroscopic dimensions and can have structures of up to about 1 mm2 in area. The formation of lipid bilayers in aqueous solution is due to hydrophobic interactions (see, Chapter 4). Recall that hydrophobic interactions also play a major role during protein folding in aqueous solution. (Chapter 4) After the formation of bilayer structure, the stability is conferred on it by multiple non-covalent interactions e.g., van der Waals forces between the hydrocarbon chains, electrostatic interactions and hydrogen bonding attractions between the polar head groups and molecules of water. In the open bilayer arrangement, all the acyl side chains except for those at the edges are protected from interaction with aqueous environment.

FLUID MOSAIC MODEL OF MEMBRANE STRUCTURE

Singer and Nicholson (1972) proposed the fluid mosaic model for the overall structure of biological membranes, in which the membranes can be viewed as two-dimensional solutions of oriented lipids and are composed of essentially a lipid bilayer (Scheme 5.7). The fatty acyl chains in the interior of the membrane generate a fluid, hydrophobic region. The integral membrane proteins may be thought as floating in the two dimensional sea of lipids. Both proteins and lipids are free to move laterally in the plane of the bilayer. The lipid bilayer has a dual role, it acts both as a solvent for integral membrane proteins and as well as a permeability barrier. The carbohydrate chains attached to some proteins and lipids of the plasma membrane are exposed to the outside but never inside of the cell.

141

Structure of a micelle

The fatty acid salts which contain only one fatty acid chain (such as sodium palmitate, a constituent of soap), the molecules form a spherical micellar structure when the hydrophobic fatty acid chains are hidden inside the micelle and the hydrophilic headgroups interact with the surrounding water molecules. As the two fatty acid chains of phospholipids are too space demanding and bulky to fit into the interior of a micelle, the favoured structure for most phospholipids in aqueous solution is a bilayer structure.

142

BIOPHYSICAL CHEMISTRY

Integral proteins are those membrane proteins which are firmly embedded in the bilayer. The peripheral proteins are loosely attached to the outer or inner surface.

Peripheral protein

Oligosaccharides

Glycolipids

Hydrophobic core Hydrophobic fatty acid chains Integral protein

Hydrophilic polar head

Peripheral protein

The fluid mosaic model of membrane structure SCHEME 5.7

5.5 A typical solute e.g., glucose enters the cells along the downhill gradient (from high to low concentration) via facilitated diffusion involving a transporter protein.

Like any other cell, the interior of a neuron has a high concentration of K+ ion and a low concentration of Na+ ion. The membrane of an axon in the resting state has membrane potential of – 60 mV. When in the resting state the membrane of an axon is far more permeable to K+ than to Na+ and consequently the membrane potential largely depends on the ratio of the internal to external concentration of K+.

TRANSPORT ACROSS MEMBRANES

(A) MECHANISM AND SCHEMATIC REPRESENTATION TRANSPORT SYSTEM

OF

The biological membranes are relatively impermeable and therefore, provide a barrier for the free passage of substances across these. Some nonpolar compounds are capable of dissolving in the lipid bilayer and cross the membrane unassisted, however in the case of polar or charged compounds or ions, a membrane protein is needed to assist the transmembrane movement. A phospholipid bilayer with its hydrophobic interior is permeable e.g., to water and gases O2, CO2, N2 and is also permeable to small uncharged polar molecules like urea and ethanol. This bilayer is however, impermeable to ions Na+, K+, Cl–, 2+ Ca ; to uncharged polar molecules like glucose and charged polar molecules e.g., amino acids, ATP and glucose 6phosphate transport (Scheme 5.8). One may consider two major factors which affect solute transport across membranes: l Concentration gradient across the membrane: The solute moves through the membrane from the region of higher concentration to the region of lower concentration, until the two regions have equal solute concentrations. In short the diffusion depends on chemical gradient. l The electrical potential across the membrane: The solutes move toward the solution which has the

CELL MEMBRANE AND SOLUTE TRANSPORT

143

opposite charge. Together the concentration gradient and electrical potential across the membrane are referred to as electrochemical gradient.
Normally inside of the cell has a negative charge. Often molecules can passively traverse a membrane down electrochemical gradients by simple diffusion (process 1, Scheme 5.8) or a membrane protein simply facilitates the diffusion of a solute down its electrochemical gradient (process 3, Scheme 5.8). This simple or facilitated diffusion represents a spontaneous movement toward equilibrium contrasts with active transport (process 4, Scheme 5.8) against electrochemical gradient that requires energy. There are several sources of this energy. It may directly come from the hydrolysis of ATP. This energy is also made available when another solute moves down its electrochemical gradient with sufficient energy to carry another molecule up its gradient (e.g., accumulation of glucose by symport with Na+). The movement of ions across membranes occurs via ion channels. The ion channels are transmembrane proteins which allow only selective entry of various ions (process 2, Scheme 5.8). The transmembrane channels are pore like structures of proteins and open transiently and are therefore gated. The gates are controllable via opening or closing. In a ligand gated channel a specific molecule binds to a receptor and opens the channel (see, Scheme 5.15c). In a voltage gated channel the opening or closing depends to changes in membrane potential (as in the axon of a nerve cell). Transported substance

1

3 2 Channel protein

Carrier protein

Electrochemical gradient En

Lipid bilayer

4

Simple (passive) diffusion

er

gy

Facilitated diffusion

Passive transport

Active transport

Mechanism of transport across a biological membrane SCHEME 5.8

144

BIOPHYSICAL CHEMISTRY

Several non-lipid soluble (lipophobic) small molecules like monosaccharides e.g., D-glucose can pass through the plasma membrane via facilitated diffusion (a uniport). This transport which is brought about by the carriers may also involve more than one molecule simultaneously and may function in more than one direction(s). The transport system may be divided into three categories and the relevant nomenclature is: l Uniport system: This system transports a single molecule in one direction through the membrane e.g., transport of glucose to the erythrocytes (Scheme 5.9). l Symport system: This system may carry two different substances in the same direction e.g., transport of Na+ and glucose to the intestinal mucosal cells from the gut.

Schematic representation of transport systems SCHEME 5.9

Antiport system: Antiport systems move two substances in opposite directions e.g., Na+ in and Ca2+ out. This is an example of exchange of one molecule (or ion by another molecule or ion). This classification of transport system i.e., uniport, symport or antiport, however does not specify whether these three general classes of transport system represent energyindependent (passive transport) or energy requiring (active transport) processes. One may consider the transport of e.g., charged solute Na+ or K+ through a lipid bilayer. Since one is dealing with an aqueous environment the ions are solvated. Potassium channels are about 100-fold more permeable to K+ than to Na+. The ionic radius of Na+ is much smaller than that of K+ so that a bare Na+ could pass easily through the pore of K+ channel. However, Na+ a smaller ion compared with K+ has a greater localization of charge and thus binds to the solvating water molecules very strongly. To pass through a lipid bilayer the ion is required to first get dehydrated by giving up its water coat (Scheme 5.9a). The free energy cost l

The transporters (carrier proteins) have some properties which are similar to enzymes. Thus the glucose transporter (a protein) is highly specific for only glucose. Thus glucose but not fructose may enter the erythrocyte by facilitated diffusion. Carrier proteins (transporter protein) further display certain properties similar to enzymes. In addition to being specific for a particular substance a transport protein is saturable, displays binding kinetics, is pH and temperature dependent and is influenced by inhibitors.

CELL MEMBRANE AND SOLUTE TRANSPORT

of dehydrating Na+ is much higher than for K+. Moreover, the channels of the transporter proteins not only bind their substrates with stereochemical specificity but also pay for the cost of dehydration via weak non-covalent interactions. The negative free-energy change of binding through these weak interactions compensates the positive free-energy change which arises due to dehydration of an ion. The K+ channel thus compensates the energy used to strip away its hydration shell and consequently K+ flows through the K+ channel. If however, Na+ ion was to pass a K+ channel, the higher cost of dehydrating Na+ would be unrecovered and the Na+ ion is thus rejected.

Potassium channels select K+ over Na+ due to higher cost of dehydrating Na+. Binding of solvating water by Na+ is much stronger than K+. SCHEME 5.9(a)

(B) PASSIVE

AND

FACILITATED DIFFUSION

The following points may be noted: l No input of metabolic energy is needed for the passive transport of substances across a biological membrane. l The rate of diffusion (transport) is proportional to the concentration gradient of the substance across the membrane during passive diffusion. l There are two types of passive transport, simple and facilitated diffusion. During facilitated diffusion again no energy is required. The distinguishing feature from simple diffusion is that facilitated diffusion is dependent on specific carrier proteins (transport proteins). The specific carrier proteins which are needed when molecules like glucose, galactose, leucine, phenylalanine etc., are transported have been isolated and characterized. Kinetics of Simple and Facilitated Diffusion The rate of movement of a solute in simple passive diffusion is directly proportional to the concentration of the solute and the process is not saturable (Scheme 5.9b). The substances

145

In the case of simple diffusion removal of shell of hydration is highly endergonic consequently energy of activation (∆G‡) for diffusion across membrane is very high. The role of a transporter protein is to reduce the ∆G‡ for transmembrane diffusion. As an example potassium channels select K+ over Na+ by taking advantage of higher cost to strip away the hydration shell of Na+. The role of a transporter protein is to reduce. The ∆G‡ by forming multiple weaker noncovalent interactions with the dehydrated species.

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Kinetics of simple (passive) diffusion SCHEME 5.9(b)

transported across membrane via carrier mediated (facilitated) diffusion are saturable. This process of transport is closely similar to an enzymatic reaction in which the substrate is solute outside the cell (Sout). The product is the solute itself inside the cell (Sin) while the enzyme is the transporter (a protein). On measuring the rate of glucose uptake as a function of external solute concentration one obtains a hyperbolic plot (Scheme 5.10). At high external solute concentrations the rate of uptake approaches Vmax. One can Vmax

Rate

Facilitated diffusion 1/2 Vmax Kt

Like simple diffusion, facilitated diffusion also involves the movement of substances from a region of higher concentration to the region of lower concentration, unlike simple diffusion, a facilitated diffusion is a carrier assisted transport process where a substance binds to the carrier and is then dissociated.

Solute concentration Kinetics of carrier mediated (facilitated) diffusion SCHEME 5.10

derive the rate equations for this process in a similar manner to enzyme-catalysed reactions (see Scheme 1.31) which leads to an expression (Scheme 5.11) which is closely similar to MichaelisMenten equation. Note from (Scheme 5.10) that concentration at half-maximal velocity equals the binding constant Kt of the carrier for the solute while Vmax is the maximal rate. Vmax [S ]out K t + [S ]out = The initial velocity of accumulation of solute inside the cell when its concentration around the surrounding medium is [S]out

V0 =

where

V0

Kt = A constant (Ktransport), which is analogous to Michaelis constant Km SCHEME 5.11

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147

A good example of facilitated diffusion is found in the uptake of glucose in erythrocytes by the glucose transporter and the following points may be considered: l Supply of glucose from the blood plasma forms the basis of energy yielding metabolism in erythrocytes. l In erythrocytes glucose transporter is an integral membrane protein which carries glucose into cells by facilitated diffusion. Such transporters are uniporters and thus carry only one substrate. The movement of glucose by facilitated diffusion infact involves a family of tissue-specific glucose transporters (GLUT). The glucose transporter of erythrocytes – GLUT-1 is present in most cells but primarily in erythrocytes, placenta and brain. It is called GLUT-1 in order to distinguish it from related glucose transporters GLUT-3, GLUT-4. l The erythrocyte glucose transporter is an integral membrane protein of mass 45 kDa. This protein is asymmetrically oriented in the plasma membrane and it traverses the membrane with 12 α-helices which form a central pore from which glucose can pass after the conformational change in the protein. l The transporter (the carrier protein) shows specificity for ions or sugars and occurs in two principal conformations.

Glucose

Glucose is bound to a stereospecific site on the transporter

Plasma membrane

Outside

Inside

Glucose transporter can exist in two conformations. In this conformation the binding site is exposed to outer surface of plasma membrane with glucose in high concentration

Glucose is released from the transporter to the cytoplasm

SCHEME 5.12 l

The uniporter protein during e.g., the transport of glucose forms a central pore via which the glucose

Facilitated diffusion accelerates the rate at which the equilibrium is established across the membrane. Facilitated diffusion however, does not transport substances against a concentration gradient.

148

In order to maintain a concentration gradient across the membrane, glucose is quickly phosphorylated inside the cell by hexokinase. The glucose 6-phosphate thus formed is no longer a substrate for the glucose transporter. Active transport of a substance across a membrane against its concentration gradient is termed active transport. Active transport requires input of metabolic energy. The energy is derived from the coupled hydrolysis of ATP. The energy is also available in an ion driven active transport. The transport of a molecule (e.g., glucose) across the membrane is coupled to the movement of an ion Na + down its concentration gradient. The movement of glucose which is the major fuel molecule for most cells between cells and the blood circulation is affected by facilitated diffusion by tissue specific glucose transporters (GLUT). These transporters are uniporters carrying only one substance In ion driven active transport symporters e.g., glucose— Na + symport allow simultaneous passage of two substances in the same direction.

BIOPHYSICAL CHEMISTRY

l

molecule passes after conformational changes in the protein. The glucose transport process is freely reversible. The direction of movement of glucose is governed by its relative concentrations on either side of the membrane (Scheme 5.12). After the release of glucose the transporter returns to the original conformation and is then ready to transport another molecule of glucose.

(C) ACTIVE TRANSPORT 1. Introduction Active transport is a result of solute movement against a concentration or electrochemical gradient. During passive transport the transported species always move down its electrochemical gradient and there is no accumulation above the equilibrium concentration. The active transport, on the other hand leads to the accumulation of a solute above the equilibrium point. The following points may be noted: l The active transport of substances is also carrier mediated, but requires an input of metabolic energy. l This energy is derived usually from direct coupling to the hydrolysis of ATP (ATP ADP + Pi). l This energy can also be derived by coupling to the movement of an ion down its concentration gradient. ∆G) and Transport Across 2. Free Energy Change (∆ Membranes—Thermodynamic Treatment of Membrane Transport Change in the free energy of the transported substance determines: l Whether the transport process is passive or l Whether the transport process is active. The free energy change in transporting an uncharged solute molecule (e.g., glucose) from a region where its concentration is C1 to a region where its concentration is C2 is given by equation (Scheme 5.13). C2 C2 ∆G = RT loge C = 2.303 RT log10 C 1 1

The free energy change (∆ ∆G) during the passive transport SCHEME 5.13

In case the substance represents an ion, the electrical potential across the membrane has to be taken into account. The sum of the concentration and electrical terms is called the electrochemical potential. The free-energy change is then given by equation (Scheme 5.14). C2 G = RT loge C + ZF V 1

where

Z = Charge on transported species V = Transmembrane electrical potential (in volts) F = Faraday constant (96,480 C mol–1)

The free energy change during the transport of an ion. SCHEME 5.14

The following points may be considered:  When G is positive, the transport process must be active.  When G is negative the transport process can be passive.  The active transport process requires a coupled input of free energy.  Passive transport can occur spontaneously. Simple and Facilitated Membrane Transport Occur Spontaneously Recall that passive transport (simple) diffusion and facilitated diffusion occurs spontaneously. When one studies the transfer of 1 mole of a solute X from a region of higher concentration () to a lower () then the chemical potential of X is given by (Eqn. I, Scheme 5.14a). X = ºX + RT ln[X]

...(I)

where ºX is the standard chemical potential and one uses concentration instead of activity. The change in Gibbs energy i.e., difference in chemical potential is given by (Eqn. , Scheme 5.14a) G = (X) – (X) = RT ln [X] – RT ln[X]

[ X ] = RT ln [ X ]  SCHEME 5.14(a)

...(II)

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BIOPHYSICAL CHEMISTRY

The following points may be noted: l µºX being a constant cancels during substraction. l As [X]β < [X]α therefore, ∆G < 0. l Consequently the transport will continue till the concentrations in the regions α and β are the same and this leads to ∆G = 0. 3. Ion Driven Active Transport (Accumulation of Glucose by Symport with Na+) Cells maintain a low intracellular Na + concentration and a high intracellular K+ concentration. The Na +/K + ATPase is an integral membrane protein (see Scheme 5.17) which sets and than maintains the intracellular concentrations of Na+ and K+ ions. In the process 3Na+ ions are moved out of the cell for 2K+ ions which move in. Thus as a result of this a potential is also established across the membrane.

In intestinal epithelial cells glucose is accumulated by symport with Na+. Glucose along with other sugars and amino acids gets transported across the apical membrane from a low concentration in the lumen of the intestine to a higher concentration in the cytosol of the epithelial cell by a glucose/ Na+ symport involving a symporter protein. This is a typical example of ion-driven active transport (Scheme 5.15). During this process glucose and Na+ bind to different sites of the glucose transporter. Na + moves into the cell down its electrochemical gradient to provide energy for the movement of glucose against its concentration gradient.

Accumulation of glucose by symport with Na+ involving a symporter protein. A Na+ gradient drives the active transport of glucose SCHEME 5.15

This sodium-glucose symport actually carries 2Na+ for each glucose. The energy needed for Na+-glucose symport is derived from:

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151

Greater concentration of Na+ outside compared to inside (the chemical potential). l Transmembrane potential (the electrical potential) being inside negative tends to draw Na+ inward. For the Na+-glucose symport, the source of energy is from the following: + l The greater concentration of Na outside the cell than inside. This represents the chemical potential. l Moreover, the transmembrane potential which is electrical potential is negative inside and hence draws Na+ inside. The electrochemical potential of Na+ is thus represented (Scheme 5.15a). l

[Na+ ]in ∆G = RT ln [Na + ] + nF ∆E out

where

n = 2 i.e., the number of Na+ during the symport process of glucose SCHEME 5.15(a)

A consideration of typical values gives an estimate of ∆G from (Scheme 5.15a) l membrane potential of –50 mV + l intracellular [Na ] of 12 mM + l an extracellular [Na ] of 145 mM Sufficient Gibbs energy (∆G) ~ 22.5 kJ is made available on re-entry of two Na+ ions inside the cell which is more than enough to pump glucose against the large concentration gradient. 4. Ion Transport Through Cell Membranes—Ion Channel Opening Recall that flow of molecules and ions across a biological membrane is controlled by two classes of membrane proteins: 1. Channels 2. Pumps (e.g., ATPase). Ion channels represent continuous polar pathways across membranes which allow the movement of ions down their electrochemical gradients. Most cells have a variety of Na+, K+, Ca2+ and Cl– channels and their activities are regulated. Ion channels are very selective, and generally allow the passage of only one type of ion (Na+, K+, Ca2+ etc.). Ion

Movement of Na + and K + ions across the membrane is crucial to the function of nerves. Key to nerve transmission lies in the movement of ions across cell membranes. Cells are all individual. In multicellular organisms there is a need for the cells to communicate with one another so that complex biologic processes can be coordinated for growth and metabolism. Communication is essential if e.g., the human body is to operate in a coordinated and controlled fashion. Communication may be thought of as an electrical pulse which travels down the nerve cell towards the target e.g., a muscle cell or another nerve.

152

The maintenance electrochemical gradients in biological systems is of great importance e.g., is nerve conduction. The process consumes around 30% of the total energy expenditure of the cell. Generally cells maintain low Na+ and high K+ intracellular concentration along with a net negative electrical potential inside.

Control and communication come primarily from the brain and spinal column (the central nervous system – CNS) which receives and sends messages via a vast network of nerves. The message as an electrical ‘pulse’ travels down the nerve cell towards the target e.g., a muscle cell or another nerve. Acetylcholine is a neurotransmitter, a compound which transmits nerve impulses across the synapses between nerve cells. (Scheme 5.20). After the transmission of nerve impulse between cells

BIOPHYSICAL CHEMISTRY

channels are protein complexes that traverse the cell membrane and are made up of several protein subunits which come together to form a central pore (hollow area) through which ions pass selectively. The channel is lined with polar amino acids so that the pore is hydrophilic (Scheme 5.15b). The permeability of a channel depends on the size, extent of hydration and the extent of charge density of the ion. For example, Na + has a higher charge density than K + , consequently hydrated Na+ is larger than hydrated K+. Thus sodium channel favours the passage of Na+ over K+, this ionic selectivity partly depends on steric factors. Compared to Na+.H2O, K+.H2O is too large.

SCHEME 5.15(b)

An ion channel has an open and a closed state, thus these channels are gated and these gates can be controlled by opening or closing. The channels may be ligand—gated when a specific molecule binds to the receptor protein to bring a conformational change in the protein which opens the ion channel (Scheme 5.15c). In a voltage gated channel, on the other hand, opening and closing is in response to changes in membrane potential. The Na+/K+ ATPase creates a charge imbalance across the plasma membrane by driving out 3Na+ from the cell for 2K+ pumped in. Thus in summary the ion flux through a channel leads to a redistribution of charge on the two sides of the membrane and this leads to a change in the transmembrane electrical potential Vm. Recall that movement of Na+ and K+ ions across the membrane is key to the function of nerves/nerve transmission. The outlines of the change from the closed to the open conformation of a channel protein in response to a neurotransmitter e.g., acetylcholine

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153

is presented (Scheme 5.15c). The acetylcholine receptor protein has suitable binding sites for the neurotransmitter acetylcholine (only one is shown for simplicity). The receptor protein has several complimentry binding sites for a neurotransmitter only one COO– is shown

Ion channel opened

–

Ion channel closed –

O2C

CH2N

CH2N

+

Na

O2C

+

+

Receptor ion channel protein (I)

(II)

Absence of a neurotransmitter the conformation of the receptor ion channel protein seals the ion channel

–

A neurotransmitter fits into the binding site, the COO is pulled closer to the positively charged nitrogen. Receptor ion protein is forced to change its conformation to open the ion channel. The channel gate keeps open till the neurotransmitter detaches from the binding site.

SCHEME 5.15(c)

5. ATP–Driven Active Transport—Structure and Action of Na+/K+-ATPase Virtually every animal cell type maintains a high internal concentration of K+ while a low internal concentration of Na+, along with a net negative electrical potential inside. This imbalance is maintained by a primary active transport system —the ATPase which is an integral membrane protein. This protein Na+K+ ATPase couples breakdown of ATP to the simultaneous movement of both Na+ and K+ against their electrochemical gradients. The Na+/K+ ATPase is also called the Na+/K+ pump. The Na+ K+ pump (Na+ K+ ATPase) is responsible for the maintenance of high K+ and low Na+ concentrations in the cells. Na+ K+ ATPase pumps 3Na+ ions from inside the cell to outside and brings 2K+ ions from the outside to the inside with a concomitant hydrolysis of intracellular ATP (Scheme 5.16). In the cell membrane this protein (Na+ K+-ATPase) or the + Na K+ pump binds sodium ion in the presence of ATP, producing ADP, a phosphorylated pump, and transported sodium ion (II, Scheme 5.16). In the presence of potassium ion the phosphate is removed from the pump, producing free

acetylcholine must be hydrolyzed very quickly so that the receiving cell can get ready to receive another impulse. Acetylcholine estrase is the enzyme which is responsible for this hydrolytic step and this catalytic activity of the enzyme is due to its —CH2OH group. O CH3C

CH3 OCH2CH2NCH3 + H2O + CH3 Acetylcholine Acetylcholinesterase CH3

O CH3C

–

O

+ HOCH2CH2NCH3 + Choline

CH3

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BIOPHYSICAL CHEMISTRY

SCHEME 5.16

Several arrow poisons and other steroid derivatives like digitoxigenin and ouabain (pronounced wah’-bane) act as potent and specific inhibitors of Na+/K+ ATPase.

phosphate and transported potassium ion. The pump operates only to move potassium ion into the cell and sodium ion out of the cell and is an example of active transport. The overall process is presented (Scheme 5.17). The main portion of the cellular ATP (~ 70%) in nerve cells is used by Na+ K+ pump to maintain the required cytosolic Na+ and K+ levels. The Na+ K+ ATPase exists in different conformations in the presence of Na+ or K+. It is thought there are three binding sites with high Na+ affinity and two with K+ affinity.

SCHEME 5.17

It is suggested that ATPase can exist in two conformations which interchange. The phosphorylated form has a high affinity for K + while a low affinity for Na + . The dephosphorylated form on the other hand has a high affinity for Na+ and low affinity for K +. The splitting of ATP provides the necessary energy required for the active transport of these cations. ATPase is phosphorylated by ATP in the presence of Na+ and Mg2+ ions (I and II, Scheme 5.16). The phosphorylated form is hydrolyzed if K+ is present. In summary during phosphorylation K + is not required while dephosphorylation does not require Na + or Mg2+. Glucose transport is of key importance in energy utilisation. It may occur via facilitated diffusion (see, Scheme 5.12) from the blood plasma using a specific glucose transporter protein (GLUT 1) or via active transport by symport with Na+. Apart from these two mechanisms glucose transport may involve other mechanisms as well. In glucose–Na+ symport, Na+ moves into the cell down its electrochemical gradient thereby dragging glucose with it, thus with greater Na+ gradient more glucose will enter the cell. Glucose transport stops with a low Na+ in the extracellular fluid. In order to have a steep Na+ gradient this Na+-glucose symport is dependent on Na+K+ ATPase. Thus Na+K+ ATPase both sets as well as maintains the intracellular concentrations of Na + and K + thereby generating a transmembrane electrical potential.

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BIOPHYSICAL CHEMISTRY

5.6

NERVE CONDUCTION—PROPAGATION OF IMPULSE ALONG A NERVE

(A) INTRODUCTION The transmembrane electrical potential V m of –60 mV (negative inside the cell) is created by Na+K+ ATPase by carrying 3Na+ out of the cell for every 2K+ brought in. The membrane is then said to be polarized.

Neurons (nerve cells) change their electric potential by controlling the changes of flux of Na + and K + ions through channels. When the membrane potential of a neuron rises (very rapidly) beyond the resting potential of about –60 mV to about +30 mV, the membrane is then said to be depolarised and consequently an action potential (nerve impulse) is generated.

Recall that cells are all individual, however in a complex organism e.g., human body for proper coordination for growth and metabolism these must communicate. The nervous system in eukaryotes is a highly rapid but complex signaling system which is mediated by nerve impulses. The major function of nerve cells (neurons) is to receive, conduct and transmit the signals of the excited-state sensory cells. The generation and transmission of nerve impulses is controlled by neuronal apparatus. The membrane which forms the surface of neuronal cells maintains an asymmetry of inside-outside voltage i.e., electrochemical potential and is electrically excitable (a symmetric distribution of ions across the cell membrane leads to this transmembrane potential). On stimulation the ion channels in the proteins (embedded in the lipid bilayer) which provide selective conductance are opened to allow a rapid influx Na+ or Ca2+ (with or without the efflux of K+). This process leads to a collapse of the voltage difference in a segment of the membrane and that segment is said to be depolarised (see, Scheme 5.20). However this gradient is quickly restored with the help of pumps in the membrane e.g., Na+K+/ATPase. When large segment of the membrane are depolarised in this way the electrochemical disturbance which result leads to the propagation of a wave-like form down the membrane thus generating a nerve impulse.

(B) NERVE IMPULSE GENERATION

AND

TRANSMISSION

Recall that in almost every animal cell type the concentration of Na+ is lower in the cell and the concentration of K+ is higher. This leads to a transmembrane electrical potential Vm of –60 mV (inside negative) to exist (Scheme 5.18). The enzyme Na+K+ ATPase maintains this balance by moving three Na+ out of the cell for every two K+ which are moved in. Na + K + ATPase not only maintains the intracellular concentrations of Na + and K + to generate a membrane electrical potential but also maintains it. Considering a typical animal cell, a transmembrane electrical potential Vm of – 60 mV (inside negative) exists and the membrane is then said

CELL MEMBRANE AND SOLUTE TRANSPORT

157

Na+ Na+ Na+ + +

Na K ATPase

+

+ –

+

–

+

–

+

–

+

–

+ –

+ –

–

ATP

+

+

–

A nerve cell

–

– ADP + Pi

+

–

+

–

+

–

+

K+ K+ –

–

–

–

–

–

–

+

+

+

+

+

+

+

Dendrites Plasma membrane. Membrane potential Vm = –60 mV

Cell body Nucleus

Axon

In a cell a transmembrane electrical potential of –60 mV (inside negative,

Myelin sheath

+ +

resting state) is generated and maintained by the enzyme Na K ATPase

SCHEME 5.18

to be polarized. With ion flux through a channel (Scheme 5.18) a redistribution of the charge on the two sides of the membrane takes place and with it Vm also changes and the membrane is then said to be depolarised. When the membrane potential is depolarized beyond a critical threshold value (i.e., from –60 to – 40 mV) a nerve impulse or action potential is generated. This membrane potential attains a positive value within about a millisecond to about +30 mV before becoming negative again and this amplified depolarisation is propagated along the nerve terminal. The following points may be noted: l Neurons and muscle cells are electrically active since their membrane potential can change with time. l In cells the membrane potential –60 mV (inside negative) is generated by the enzyme Na+K+ ATPase. In this state, the membrane is said to be polarized and transmembrane electrical potential Vm of –60 mV is the resting potential. l A neuron can change its electric potential by controlling the changes in the permeability of the plasma membrane to Na+ and K+ ions, changing Vm. + l For example, the influx of Na ion brings about a depolarization of the membrane by bringing Vm closer to zero. [Recall such an ion influx of e.g., Na+ through the channel is passive when compared to the active transport by the Na+K+ ATPase.] l The electrochemical potential of the ion across the membrane determines the direction of spontaneous

Synaptic cleft Secretory vesicles containing neurotrarnsmitters l

l

l

l

Nerve cells have a nerve body with projections of plasma membrane (dendrites). Dendrites receive messages from other nerves in the form of nerve impulses which may stimulate the nerve. The cell body collects the sum total of these messages and passes these on as another nerve impulse down the length of the nerve (axon). The axon is padded with sheaths of mylein made up mainly of the lipid shingomylein which act to insulate the signal as it passes down the axon. The axon end has synaptic vesicles to store the chemical neurotransmitters e.g., acetylcholine.

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BIOPHYSICAL CHEMISTRY

The Na+ K+ ATPase generates the Na+, K+ gradients which are a key to the excitability of nerve and muscle.

flow of this ion across the polarised membrane. The force (∆G) that is required for the spontaneous flow of Na+ into the cell through an ion channel is given by the relationship (Scheme 5.19). ∆G = RT ln  Cin  + ZFVm  Cout  where Cin/Cout is the ratio of concentrations of Na+ on the two sides of the membrane Vm (or ∆ψ) difference in electrical potential R is the gas constant T is the absolute temperature Z is the charge on the ion and

The cell membrane of axon has also sodium potassium ion channels but these are voltage gated in contrast with acetylcholine receptor (protein) channel which is ligand gated.

In the resting state the membrane of an axon is much more permeable to K+ than to Na +, consequently membrane potential is largely dependent on the ratio of internal to the external concentration of K+. A few K+ ions may escape down the ion channels out of the cell. This situation will tend to build up instead an electric potential such that the inside of the cell membrane is more negative than the outside which is in opposition to the resting potential and consequently flow of K+ ions is arrested. Recall that these ion fluxes are passive (see, Scheme 5.8) as compared to the active transport by the Na+K+ ATPase. With large transient changes in the permeability of Na+ and K + ions in the axon membrane, action potentials are generated. Recall a nerve impulse is an electrical signal generated by the flow of ions across the plasma membrane of a neuron.

F is the Faraday constant SCHEME 5.19 l

l

l

l

Recall that in a neurocell or a myocyte the concentration of Na+, K+, Ca2+ and Cl– differs largely in cytosol and extracellular fluid, the resting Vm is of –60 mV. These facts along with a consideration of (equation, Scheme 5.19) reflect that the opening of a Na + (or Ca 2+ ) channel will be attended with a spontaneous inward flow of Na + resulting in depolarisation of the membrane. A given ionic species will keep flowing through the channel till the combination of concentration gradient and electrical potential provides a driving force (Scheme 5.19). With the flow of Na+ down its concentration gradient the membrane is depolarized (Scheme 5.20). Thus on stimulation of a neuron, its membrane potential rises quickly from the resting position of –60 mV to around + 30 mV in a millisecond, as a consequence one says that membrane is depolarised to generate an action potential. At this stage Na+ channels close immediately and instead K+ channels open leading to the flow of K+ out of the cell and the negative resting potential is restored again within about a millisecond. When the action potential is generated it reverses the polarity of membrane at that point. This in turn effects the neighbouring area of the axon and depolarizes it beyond the critical threshold level and the process continues along the whole length of the

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159

axon (Scheme 5.20). Thus in summary the voltage gated Na+K+ channels of neuronal membranes propagate the action potential as a wave of depolarization via inward flow of Na+ followed by polarization (turning negative again) by the outflow of K+. Membrane

On stimulation, the membrane potential of a nerve cell rises within a millisecond from its resting potential of –60 mV to around +30 mV to result in depolarization of an axon membrane and an action potential is generated. +40

Membrane potential (mV)

+ + + + + + ++ + + + – – – – – – –– – – – – – – – – – –– – – – + + + + + + ++ + + + Resting state of an axon (of a nerve cell)—K + ion

Action potential

+20 0

Resting potential

–20 –40 –60 –80

channels open Na+ ion channels shut

1 Stimulus

Ion permeabilities

Nerve terminal end

Na+

30 20 10

K+

0

+ + + – – – + + + + ++ ––– +++ ––– –– – ––– +++ ––– –– – +++ – – – +++ +++

Direction of impulse movement

+++ ++ + – –– +++ – –– – – – +++ – – – – –– – – – +++ – – – +++ ++ + – –– ++ + Area of depolarization moves down the axon—the message (nerve conduction) Generation of an action potential in a nerve cell.

SCHEME 5.20 l

3

The nerve cells vary their electric potential by the by mediating transient changes in Na+ and K+ permeability.

Region of depolarization

– – – + + + ++ + + + + + + – – – –– – – – + + + – – – –– – – – – – – + + + ++ + + +

2 Time (msec)

When the action potential reaches the nerve terminal, it leads to the release of a chemical neurotransmitter e.g., acetylcholine (see, Scheme 5.15c) from the synaptic vesicles. This neurotransmitter then diffuses to bind with specific receptors (proteins) in the plasma membrane to trigger a change in Vm for nerve conduction.

1

2 Time (msec)

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5.7

MORE ON TRANSPORT OF IONS THROUGH MEMBRANES

(A) INTRODUCTION In earlier sections an account of cell membranes has been presented regarding transport of solutes/ions across them. Membrane potential and nerve conduction has been discussed in detail. Mathematical treatment of the following aspects have been presented: l Energy of activation during simple diffusion of ions through membrane channel proteins (Scheme 5.9a). l Kinetics of simple and facilitated diffusion (Scheme 5.9b and 5.10). l Free energy change – Thermodynamic treatment of membrane transport (Scheme 5.13, 5.14, 5.14a and 5.15a). l Flow of ions (spontaneous) across a polarized membrane as determined by the electrochemical potential of that ion across the membrane (Scheme 5.19). Recall that the following forces are responsible for transport across cell membranes: l Concentration gradient l Pressure/temperature gradient and electrical potential gradient. The following discussion further adds to the concepts of membrane transport.

(B) DONNAN EFFECT

AND

MEMBRANE EQUILIBRIUM

The Donnan Effect (after the British Chemist Frederick George Donnan, 1870–1956) deals with the important effect of charged macromolecules on the distribution of small ions across the membrane. The macromolecules are limited to one side of a semipermeable membrane. The Donnan effect describes the uneven distribution at equilibrium of small diffusible ions on the two sides of a membrane that is freely permeable to these ions but impermeable to macro molecular ions, in the presence of a macromolecular electrolyte on one side of the membrane.

CELL MEMBRANE AND SOLUTE TRANSPORT

PROBLEMS AND EXERCISES 1. What are biological membranes. Describe their chemical composition and draw the structure of their major components? 2. What is the fluid-mosaic model of a biological membrane? Discuss briefly the mechanism of transport across a biological membrane. 3. Draws the equations for free energy change during passive and active transport through a biological membrane. 4. Explain the difference in active and passive transport across a membrane. 5. What is ion driven active transport? Explain glucose transport driven by a Na+ gradient (glucose–Na+ symport). 6. What is Na+/K+ ATPase? Write the mechanism by which it works. 7. What is an ion channel protein? How it works to attain an open and closed conformation? 8. Write short notes on (a) Transmembrane electrical potential (b) Working of enzyme Na+K+ ATPase (c) Action potential. 9. Describe the generation of a nerve impulse. What is the role of neurotransmitters and ion channel proteins for the generation of nerve impulse? 10. Draw the resting state of nerve cell. How a nerve impulse gets initiated and conducted? 11. Draw a relationship which controls the flow of an ion through an ion channel? How long an species can go on flowing through the channel? [Hint see Scheme 5.19] 12. Draw a mathematical relationship for simple (passive) or facilitated transport which occurs spontaneously during the transfer of 1 mole of a solute X from a higher region of concentration to a lower region. [Hint see Scheme 6.14a] How this transport has a significance during nerve conduction? 13. Discuss the kinetics of simple and facilitated diffusion [Hint see Scheme 5.9–5.11]. 14. Why Na+ ions are unable to flow through K+ channels? What role the transporter protein of the biological membrane plays during such a flow? [Hint see Scheme 5.9a]

161

162

BIOPHYSICAL CHEMISTRY

C H A P T E R

6 Sizes of the polymer chains reflet strongly on its properties. Measurement of the molar mass (M) of a polymer characterises their dimensions. The molar mass of a polymer is the mass of 1 mole of the polymer and is reported in units of g mol–1 or kg mol–1. Thus the multiplication of the numerical value of molecular weight by the specific units g mol–1 it can be converted into the equivalent value of molar mass (a molecular weight of 100000 is equivalent to a molar mass of 100000 g mol –1 which in turn is equivalent to a molar mass of 100 kg mol–1).

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

6.1

INTRODUCTION

The major problems regarding a large biological molecule are to know its size and shape and molar mass. Macromolecules have high molar mass (104 to 1010 g mol–1). These special situations faced from a macromolecule require their study by special techniques unlike the small ordinary molecules. Here one is concerned with natural macromolecules like proteins, nucleic acids, polysaccharides (cellulose), and polyisoprene (rubber).

6.2

MOLECULAR WEIGHT OF MACROMOLECULES

Recall that a macromolecule is composed of a large number of monomers which are joined together. As the polymer chains are broken at different stages the final product may contain the macromolecules with different sizes and weights. Because of this non-uniform nature among the polymer molecules regarding molecular sizes and individual characteristics of varying lengths in solution, the masses of polymer molecules display a range. It is therefore, necessary to take the average molar mass of a given sample of a polymer.

MOLAR MASS

OF

MACROMOLECULES

From the above discussion it is clear that molar mass has a special meaning when applied to a macromolecule. Two most important definitions to define the molar mass of a macromolecule are:

162

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

163 Molecular Weight/Molar Mass

1. Number-Average Molar Mass ( M n ) One defines the number-average molar mass ( M n ) as ‘the sum of the products of the molar mass of each fraction multiplied by its mole fraction’ (Eqn. I, Scheme 6.1). From this equation one arrives at (Eqn. II, Scheme 6.2) where the average is the arithmetic mean of the molar mass distribution. Generally it is easier to use weight fractions instead of numbers of molecules. This leads to an expression (Eqn. III, Scheme 6.3). From this expression one can deduce the expression of ( M n ) in terms of weight fraction when one combines (Eqn. II, Scheme 6.2 and Eqn. IV, Scheme 6.4) to give (Eqn. V, Scheme 6.5). Mn =

∑

X i Mi

...(I)

Xi = the mole fraction of molecules of molar mass Mi which is given by the ratio of Ni to the total number of molecules. SCHEME 6.1

Mn =

∑N M ∑N i

i

i

...(II)

SCHEME 6.2

∑N M

wi = Ni Mi

i

...(III)

i

The weight fraction wi is the mass of molecules of molar mass Mi divided by the total mass of all the molecules. SCHEME 6.3 (Equation IV, Scheme 6.4). The value from which it can be deduced that

∑ (w

i

/ Mi ) =

∑N ∑N M i

i

i

...(IV)

SCHEME 6.4

Mn = 1

∑ (w / M ) i

i

...(V)

SCHEME 6.5

2. The weight-average Molar Mass ( M w ) One defines the weight-average molar mass ( M w ) as ‘the sum of the products of the molar mass of each fraction multiplied by its weight fraction’ (Eqn. VI, Scheme 6.6). When this equation is combined with (Eqn. III, Scheme 6.3) M w can be expressed in terms of the numbers of molecules (Eqn. VII, Scheme 6.7)

The term “molecular weight which is commonly used particularly in the older biochemical literature is not preferred since it is somewhat misleading. It is a dimensionless quantity. The more correct terms are relative molecular mass” (RMM) without units or “molar mass” (kg mol–1 or g mol–1) one dalton (1 Da) is equal to 1 amu (atomic mass unit).

164

BIOPHYSICAL CHEMISTRY

Mw =

∑w M i

...(VI)

i

SCHEME 6.6

Mw

=

∑N M ∑N M i

2 i

i

i

...(VII)

SCHEME 6.7

Monodisperse and Polydisperse Polymers

Consider a polymer mixture having three chains with MW = 1000, two chains with MW = 1200, and five chains with MW = 1400, the values of amd Mw calculated: Mn

Mn

=

Mw

=

are then

3(1000) + 2(1200) + 5(1400) 3+2+5 = 1240 3(1000)2 + 2(1200)2 + 5(1400)2 3(1000) + 2(1200) + 5(1400) = 1265

The value of Mw is greater than that of Mn . This is the usual case because of the greater contribution, in the calculation, by polymers with larger molecular weights. The ratio Mw / Mn is a useful quantity called the polydispersity index. Its value is a measure of how broad the range of molecular weights is. If Mw/Mn = 1.0, then the polymer is monodisperse, i.e., all its chains have the same molecular weight as is so in the protein myoglobin.

A polymeric system whose molecules all have the same molar mass is said to be monodisperse, if the molecules do not have identical molar masses, the polymer is said to be polydisperse. Biopolymers e.g., proteins and nucleic acids which occur in living organisms are often monodisperse (e.g., all polypeptide chains of the protein myoglobin have the same composition, length and mass). Synthetic polymers are not monodisperse unless extra steps are taken to separate the product into its constituents. From a consideration of the equations developed for M n and M w , the following points become clear: l

The weight average molar mass is always greater than the number average molar mass, thus M w > M n .

l

In monodisperse polymers (when all particles are identical in mass) then M w = M n .

l

The measure of polydispersity for any polymer is nothing but the measure of size dispersion only.

l

By definition the ratio M w / M n must be greater than 1 for a polydisperse polymer which is known as the polydispersity or heterogeneity index. This value is often used as a measure of the breadth of the molar mass distribution. Normally M w / M n is in the range 1.5– 2.0, though there are many polymers which have smaller or much larger values of polydispersity index.

A perfectly monodisperse polymer will show M w / M n = 1.00. l The presence of molecules of higher molar mass makes the value of M w very sensitive, on the other hand, however, with the presence of lower molar mass molecules the value of M n become sensitive.

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

165

Often higher molar mass averages are observed. This is so with certain methods of molar mass measurement (e.g., sedimentation equilibrium) yield the z-average molar mass ( M z ) . M z is derived from (Eqn. VIII, Scheme 6.8). Mz =

∑ N M ∑ N M = ∑w M ∑w M i

3 i

i

2 i

i

2 i

i

i

...(VIII)

SCHEME 6.8

6.3

METHODS OF DETERMINATION OF MOLAR MASSES OF MACROMOLECULES

The way in which macromolecules move in solution, and the way in which they change the way the solution flows, gives rise to a range of hydrodynamic techniques that can be used to study their structure and properties, e.g., molar masses of macromolecules. Some of these hydrodynamic techniques explain: l The movement of macromolecules during analytical ultracentrifugation and the differences between sedimentation equilibrium and sedimentation velocity experiments. l Describe how viscosity experiments might give information about molecular size.

(A) SEDIMENTATION METHOD: ULTRACENTRIFUGATION (MOLAR MASS FROM SEDIMENTATION VELOCITY METHOD) Centrifuge methods as applied for the separation and analysis of biomolecules depend on the centrifugal forces which are analogous to gravitational forces (generally much larger) which can be imposed on solutions rotated at high speed. This is the basis of analytical ultracentrifugation (AUC). A centrifuge is a device comprising a rotor in which samples are spun at high speed about a vertical axis. The samples may be enclosed in special wedge-shaped cells for analytical methods (Scheme 6.8a). The (outward) force exerted on an object of mass m, rotating at a distance r from the axis with angular velocity ω, is equal to mrω2. This is equivalent to an acceleration of rω2. Sedimentation velocity method to determine molar mass involves rotating the solution cell at very high speeds typically 60,000–70,000 rpm. In a sedimentation equilibrium experiment

Molar Mass Distribution Normally, polymers consist of macromolecules with a range of molar masses. As the molar mass changes at intervals of M0, the distribution of molar mass is not continuous. Generally for most polymers these intervals are very small in comparison to the total range of molar mass and the distribution can be assumed to be continuous as shown in the curve below. — Mn = 100 000

4.0

–1

g mol — Mw = 199 900 3.0

g mol

–1

4

10 wi

— Mz = 299 850

2.0

g mol

–1

1.0

0

0

200 000

400 000

Mi /gmol

–1

A molar mass distribution curve

166

BIOPHYSICAL CHEMISTRY

the cell is rotated at a relatively low speed (typically 5000 to 10,000 rpm.) The rate of sedimentation of a particle is a function of molecular mass, shape and size of the particle. The rate at which a particle sediments in a centrifuge in a centrifugal field is related to the net force acting on it. The centrifugal force, Fc, acting on a particle is given by the relationship (Eqn. I, Scheme 6.9). The (outward) force exerted on an object of mass m, rotating at a distance r from the axis with angular velocity ω, is equal to mrω2. This is equivalent to an acceleration of rω2.



Photomultiplier tube

Rotor Sample cell

Counterbalancing cell r

Sedimentation involves the fall of the particles in a viscous medium under the gravitational force. Sedimentation rate can be used to know the size of the particles. However, a sedimenting particle is influenced by two forces: l The force of the gravity field l The resistance of the medium i.e., the force of internal friction. The otherwise small rate of sedimentation of suspended particles under the influence of gravity is enhanced by the application of ultracentrifuge technique by T. Svedberg (Nobel Prize in 1926).

Light from monochromator Analytical centrifuge rotor. The angular velocity  is the rate of rotation in radians per second. One complete rotation (360°) is equal to 2 radians. SCHEME 6.8(a)

Fc = mω2r

...(I)

where: m = mass of the particle r = distance of the particle from the revolving axis ω = angular velocity SCHEME 6.9

In addition to Fc (Centrifugal force), the buoyancy of the particle has also to be considered. This buoyancy is due to the displacement of the solvent molecules by the particle. This buoyancy force (Fb) leads to a reduction of the force on the particle by rω2 times the mass of the displaced solvent. Thus the net force which acts on the particle is given by (Eqn. (II) Scheme 6.10). Net force = Fc – Fb

= ω2rm – ω2rms = ω2rm – ω2rvρ

where: Fc = centrifugal force

...(II)

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

167

The centrifugal force on a sedimenting macromolecule

Fb = buoyancy force ms = mass of displaced solvent v = volume of the particle

Velocity v

ρ = density of the solution SCHEME 6.10

The following points may be considered: l The net force acting on a particle accelerates it (Newton’s second law of motion). l A frictional force is exerted alongside by the medium on the particle. l This frictional force is proportional to the

Frictional drag

Centrifugal force

Opposing frictional and centrifugal forces

sedimentation velocity, dr . dt l The frictional force is equal to the product of the frictional coefficient f (in units Nm–1 s) as well as the sedimentation velocity, however, it operates in the direction opposite to the net force. l At steady state, therefore, the frictional force equals the net force, with the subsequent movement of the molecule to the bottom of the cell with a velocity dr/ dt (Eqn. III, Scheme 6.11) f

dr dt

= ω2rm – ω2rvρ

...(III)

SCHEME 6.11

The equation (III, Scheme 6.11) depicted as equation (IV), Scheme 6.12) and rearranging it leads to equation (V, Scheme 6.13. f

dr dt

= ω2rm – ω2rm v ρ

...(IV)

where: = ω2rm(1 – v ρ) v = partial specific volume

mv

= incremental volume increase SCHEME 6.12

s =

dr / dt m(1 − v ρ) = f ω2r

s =

M 1− vρ NA f

...(V)

Sedimentation Coefficient(s) is expressed in Svedberg units (S), in honour of the Swedish scientist T. Svedberg (Nobel Prize 1926) who pioneered much of the early work in this field (1S =10–13 s).

168

BIOPHYSICAL CHEMISTRY

where: M = molar mass of the solute NA = Avogadro’s number s = sedimentation coefficient SCHEME 6.13

Remarks on (Schemes 6.12 and 6.13) l Measurement of the volume (v) of the particle is difficult. Instead, therefore, one introduces the term partial specific volume v which is defined as the increase in volume on dissolving 1 g of dry solute in a large volume of the solvent. The quantity mv represents the incremental volume increase on adding to the solvent one molecule of mass m. (Thus mv = volume v of the particle). l One can therefore, determine molar mass M of the solute provided sedimentation coefficient (s) and frictional coefficient (f) are known. The following points may be considered: l The sedimentation coefficient (s) is conventionally expressed in Svedberg units (s). l The frictional coefficient of a spherical solute particle is given by (Eqn. VI, Scheme 6.14) l

f = 6πηrs where: rs = radius of a spherical solute

...(I)

η = viscosity of the medium SCHEME 6.14

l

Consideration of equation (V, Scheme 6.13) gives the relationship equation (VII, Scheme 6.15. sN A (6πηrs ) sN Af M = 1− vρ = 1− vρ

...(VII)

SCHEME 6.15

l

Now, the diffusion coefficient D is given by the relation equation (VIII, Scheme 6.16). D =

kBT f

where: kB = Boltzmann constant T = absolute temperature SCHEME 6.16

...(VIII)

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

169

The ease with which a solute molecule moves depends on its thermal energy. The thermal energy is shown by kBT (where kB is the Boltzmann constant and T is the absolute temperature), and its frictional coefficient f. l With the larger value of kBT, the particle becomes more energetic in its motion and with the larger f, the greater the frictional force the medium exerts on the solute. According to Einstein, the ratio of these two opposing factors gives the diffusion coefficient, D, of the solute. (Eqn. IX, Scheme 6.17). l

f =

kBT D

...(IX)

SCHEME 6.17

l

The value of D (in units m2 s–1 or cm2 s–2) reflects on the ease with which the solute molecules diffuse in solution. Rearranging (Eqn. VIII, Scheme 6.16) gives (Eqn. IX, Scheme 6.17) and finally the substitution of (Eqn. IX, Scheme 6.17) into (Eqn. VIII, Scheme 6.16) gives (Eqn. X, Scheme 6.18). sN AkBT sRT M = D(1 − v ρ) = D(1 − v ρ)

...(X)

where: NAkB = R, the gas constant. SCHEME 6.18

l

In (Eqn. X, Scheme 6.18), the sedimentation coefficient comes from (Eqn. XI, Scheme 6.19). The values of D and v are found from separate experiments. s =

dr / dt ω2r

or

sdt =

1 dt ω2 r

...(XI)

SCHEME 6.19

l

Integration over the distance traveled by the particle from r = r0 (t = 0) to r = r(t = t) gives the value of (s) sedimentation coefficient (Eqn. XII, Scheme 6.20)

∫

t 0

1 r dr ω2 r0 r 1 r s = t ω2 ln r 0

sdt =

∫

or ln(r/r0) = sω2t

...(XII)

SCHEME 6.20

When ln r is plotted versus t the result is a straight line with the slope sω2, from which one can calculate the value of s (Scheme 6.21).

One can calculate the molecular mass of a biopolymer e.g., a protein from ultracentrifugation studies. This is based on the principle that a high molecular mass molecule sediments faster and diffuses slower than a lower molecular weight molecule of the same density. This is given by Svedberg equation (Scheme 6.18)

170

BIOPHYSICAL CHEMISTRY

A straight line with a slope equal to sω2 when ln r is plotted against t (ref. to Eqn. 12, Scheme 6.20) SCHEME 6.21

(B) MOLECULAR

MASS FROM SEDIMENTATION EQUILIBRIUM

This is an accurate method for molar mass determination which does not require the data of shape of the diffusion coefficient of a molecule under study. Sedimentation equilibrium methods measure the concentration gradients of molecules in solution when spun at 10,000 rpm, instead of the 60,000 rpm or so required for a sedimentation velocity experiment. A perfect balance between sedimentation and diffusion is then achieved. In diffusion, solute molecules move from a higher concentration to a lower one, while sedimentation reverses this process. When an equilibrium is established, no net flow takes place. In current instruments, several samples (including controls) can be run simultaneously. The concentration gradient, as a function of radius (r), is measured using UV/visible absorbance, fluorescence or refractive index methods, using optical systems which are mounted outside the rotor. During a normal diffusion process, the flux (J) (the net amount of solute which diffuses through a unit area per unit time is proportional to the concentration gradient (Eqn. I, Scheme 6.22). J ∝ –

dc dr

= –D

dc dr

where: dc/dr = the concentration gradient (change concentration c along direction r)

...(I) of

D = the diffusion coefficient SCHEME 6.22

As concentration gradient is negative in the direction of diffusion thus a negative sign is required to make the value of flux J a positive quantity. However, in the sedimentation

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

171

equilibrium experiment, the concentration gradient infact increases with increasing r value. Thus from (Eqn. I, Scheme 6.22) one arrives at the expression (Scheme 6.23). From consideration of (Scheme 6.12), the sedimentation rate for solute molecules in a solution (concentration c) is given by expression (Eqn. II, Scheme 6.24). Since at equilibrium the diffusion rate becomes equal to the sedimentation rate which reflects to (Eqn. III, Scheme 6.25). dc dr kBT dc RT dc = f dr = f N dr A

J = D

...(I)

SCHEME 6.23

dr dt

= or

c

dr dt

=

ω2rm (1 − v ρ) f

...(II)

2

c ω rm (1 − v ρ) f

SCHEME 6.24

RT = fN A or RT c ω2rm(1 − v ρ) = N A c

dr dt

dc dr ...(III)

dc dr

SCHEME 6.25

On rearranging one gets an expression (Scheme 6.26). dc c where:

=

M ω2r (1 − v ρ) dr RT

M = molar mass (given by mNA) SCHEME 6.26

If one integrates between r1(c1) and r2(c2) the expression (Scheme 6.27) is reached. Thus one can calculate the molar mass M from the measurement of concentrations of the solute i.e., c1 and c2 at r1 and r2 (optical techniques) and when v , ρ and ω are known.

∫

M ω2 (1 − v ρ) r2 dc r dr = c1 c RT r1 2 c ln 2 = M ω (1 − v ρ) (r 2 − r 2 ) 2 1 c1 2RT c2

∫

SCHEME 6.27

172

BIOPHYSICAL CHEMISTRY

The viscosity of a fluid is an index of its resistance to flow. A common device to measure viscosity is the Ostwald viscometer. It consists of a bulb (A) with markings x and y, attached to a capillary tube B and a reservoir bulb C. A known volume of the liquid to be studied is introduced into C, sucked into A, and the time taken for the liquid to flow between x and y is noted. In practice, the viscosity of a solution is determined by comparison with a standard which normally represents the pure solvent.

x

A

y

C B

(C) MOLAR MASS

FROM

VISCOSITY MEASUREMENTS

Viscosity measurements give information regarding the overall shape of a macromolecule. Viscosity of the solution, can be measured quickly, easily and with inexpensive equipment. In some situations, moreover, the results can be used to estimate the molecular mass of the dissolved material. As a result, it is a commonly used technique in studies of both natural and synthetic macromolecular materials. Solutions of macromolecules are more viscous than the pure solvent. This is the basis for one of the earliest experimental methods to determine the shape and properties of biomolecules. There are several ways to measure solution viscosities, however the Ostwald viscometer is commonly used. Viscosities are generally expressed relative to the viscosity of the pure solvent by using the terms relative viscosity (ηr), specific viscosity (ηsp) and intrinsic viscosity ([η]) which are defined (Scheme 6.28) where c is the concentration of macromolecules. Due to molecular interactions and other nonideality effects in solution, [η] is normally determined by extrapolation to zero concentration from a range of measurements (Scheme 6.29) which gives information regarding variation of intrinsic viscosity η sp /c, with concentration. Relative viscosity: ηr = η/η0 Specific viscosity: ηsp = (η – η0)/ηr = ηr – 1 Intrinsic viscosity: [η] = ηsp/c (as c

0)

SCHEME 6.28

An Ostwald viscometer. The time a liquid takes to move between markings x and y is measured and compared with that of a reference liquid. A: bulb; B: capillary tube; and C: reservoir bulb.

sp/c [ ]

Concentration (c) SCHEME 6.29

The molar mass of a polymer depends upon the intrinsic viscosity and is represented for a given molecular type in a given solvent by an empirical equation (Scheme 6.30)

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

Molecule

Shape

[η] mL/g

M g/mol

Ribonuclease

Globular

3.4

13,680

Hemoglobin

Globular

3.6

64,450

Hemoglobin (Denatured)

Random Coil

19

64,450

Collagen

Rod

1150

350,000

Denaturation of Proteins A change in the shape of a protein molecule leads to its denaturation as e.g., from a globular form to a random coil form. Under such circumstances one expects the

6.1 16.6 18.8 92.6 26 124 144 1790

TABLE 6.1: Intrinsic viscosities of some biologically active biopolymers

Several solvent systems open up the proteins and polypeptides to give random coils such a solvent system can be made by adding high concentrations of polar species e.g., detergents, urea, or guanidine hydrochloride to an aqueous solution of a protein or a polypeptide. The disulphide cross links present in proteins can be ruptured by the addition of a reducing agent like β-mercaptoethanol. An empirical correlation exists for polypeptide and proteins where by in such solvents the number of amino acid residues can be known from [η] = 0.732 n0.656 (n = no. of amino acid residues)

2,970 13,680 15,500 197,000

where M is the molecular mass and K and α are empirical constants. If these parameters have been measured for polymer fractions with known molecular masses, the equation (Scheme 6.30) can be used to obtain such mass data from the easily obtained intrinsic–viscosity results. l Shape of a Molecule The value of α (Scheme 6.30) depends on the shape, or geometry, of the macromolecule: α = 0 for a sphere, α = 0.5 for a random coil, and α ≈ 1.8 for a long rigid rod. When for a macromolecule the values of K and α are known, the relationship (Scheme 6.30) leads to a quick estimate of its molar mass from the intrinsic viscosity measurement. However, if the molar mass of the macromolecule is known, then (Scheme 6.30) can be used to determine the shape of the molecule. l Conformational Changes in Biopolymers Intrinsic viscosity throws light on the conformational changes of proteins. When a globular protein unfolds to form a random coil, its intrinsic viscosity increases, but when a rod-shaped protein such as collagen or myosin unfolds, the intrinsic viscosity decreases because of a decrease in the asymmetry of the molecule (Table 6.1).

Insulin Ribonuclease Hemoglobin Myosin

SCHEME 6.30

[η] mL/g

(K and α = empirical constants)

Residues/ chain

M = the molar mass of the polymer

Sometimes viscosities are still given in non-SI units called “poise P” named after a French physician. Jean Poiseuille (1797–1869), who developed a method for measuring blood pressure and who was responsible for fundamental studies of liquid flow 1 P = 0.1 N s m–2.

Molecular mass

[η] = KM α

Biopolymer

where:

173

174

BIOPHYSICAL CHEMISTRY

intrinsic viscosity to change from small to a larger value. Thus viscosity measurement provides an easy way to study protein denaturation. Ribonuclease undergoes an abrupt viscosity change around 40ºC, to show the uncoiling of the otherwise compact globular form at lower temperatures. This process is reversible and when the temperature is lowered the viscosity curve is retraced with the reformation of globular form.

[ ] mL/g

6 The change in intrinsic viscosity of protein ribonuclease at pH 2.8 (thermal denaturation). The value at low temperature is typical for a compact globular protein. The increase reflects the partial uncoiling of the molecule at high temperatures.

5

4

3

20 30 40 50 60 T (°C)

(D) OSMOTIC PRESSURE AND MOLAR MASSES OF MACROMOLECULES Membrane Osmometry When a solution is separated from the solvent by a semipermeable membrane, the excess hydrostatic pressure which must be applied to the solution to check inflow of solvent and establish an equilibrium is termed the osmotic pressure of the solution.

When a solution is separated from the pure solvent by a semi-permeable membrane (e.g., a cellophane membrane) i.e., a membrane that permits the solvent molecules to pass but not of solute molecules, the solvent molecules always tend to pass through the membrane into the solution. This general phenomenon is termed osmosis, and the flow of solvent molecules generates an osmotic pressure which at equilibrium just prevents further flow. The equilibrium osmotic pressure, π, can be measured using a capillary osmometer (Scheme 6.31). l Molecular mass from osmotic-pressure measurements The Van’t Hoff equation for osmotic pressure is π = RTc . Van’t Hoff derived this equation by considering the analogy with the state equation for an ideal gas. He assumed that 1 mol of an ideal gas, when confined to a volume of 1 liter, would exert a pressure of 2.27 MPa on the walls of the vessel. He reasoned that the molecules of a solute, when dissolved at a concentration of 1 mol/l should behave in the same way as the particles of the gas. This pressure he called “osmotic”.

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

175

Applied pressure

h Pure solvent

Solute

Pure solvent

Polymer solution

Semi-permeable membrane

Schematic representation of an osmotic pressure apparatus SCHEME 6.31

The equation of state for an ideal gas is (I, Scheme 6.32) which can be rewritten as (II, Scheme 6.32). The Van’t Hoff relation (π = cRT) is only applicable for ideal solutions, or with some approximation for very dilute solutions. This restriction can be overcome using a correction factor. This is the socalled osmotic coefficient (g). Thus Van’t Hoff equation becomes π = gcRT. n RT V n RT = cRT π = V

P =

...(I) ...(II)

SCHEME 6.32

Alternatively, one can rewrite (Eqn. II, Scheme 6.32) as (Eqn. III, Scheme 6.33). Molar masses of compounds thus can π =

c RT M

or

π c where

=

...(III)

RT M

M = molar mass of the solute in g/mol c = concentration of the solute in g L–1 of the solution SCHEME 6.33

The following relation is identical to PVT relationship of gases. πV = nRT where: π = osmotic pressure in atm V = volume of the solution in liters n = number of moles of solute R = gas constant, 0.0821 liter-atm/mole-ºK T = the absolute temperature π =

n RT V



RT  (1 + Bc + Cc2 + Dc3 + ...) = c M

...(IV)

where: B, C, and D are called the second, third and fourth virial coefficients, respectively. SCHEME 6.34



 RT + RTBc = c M

...(V)

SCHEME 6.35

A graph of /c versus c (Scheme 6.36) (a straight-line plot), extrapolated to c = 0, gives the intercept on the ordinate (  / c) = RT/M. as RT/M, i.e., clim 0

The intercept on the y-axis (as c2 value for the molar mass, (M).

0) gives the correct

Nonideal behaviour

 c

Ideal behaviour RT M

c Extrapolation of the osmotic pressure—concentration ratio to infinite dilution for determination of molar mass for an ideal and a non-ideal solution. SCHEME 6.36

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

6.4

177

ELECTROPHORESIS

(A) INTRODUCTION Charged molecules under the influence of an electric field will tend to move towards the positive or negative electrode, depending on the sign of the molecular charge and not on the molecular mass. For molecules in solution, this motion is opposed by viscous drag from the surrounding environment, so the resulting electrophoretic mobility will depend on a number of factors, including the overall charge, size and shape of the molecule. This is the principle of electrophoresis (Scheme 6.37). Electric field E Electrophoresis velocity v

+

Frictional drag F = fv –

– –

–

–

q+

+

Electrostatic force qE + + + +

–

++ –

– Starting point

Electrophoresis. Molecules move in an electric field E depending on their net charge molecular mass and shape. SCHEME 6.37

In the steady state for a particle with charge q in an electric field E, the electrostatic force on the particle will be exactly balanced by the viscous drag (Eqn. I, Scheme 6.38) to give the electrophoretic velocity of the particle. fv = qE or v = qE/f

...(I)

where: f = frictional resistance of the solvent v = velocity of the molecule q = charge on the molecule E = Applied electric field SCHEME 6.38

The frictional drag is given approximately for a spherical molecule by Stoke’s law and a relation (Eqn. II, Scheme 6.39) is reached.

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BIOPHYSICAL CHEMISTRY

f = 6πηr

...(II)

where: r = radius of the spherical molecule η = viscosity of the medium SCHEME 6.39

On equating (Eqns. I, Scheme 6.38 and II, Scheme 6.39) one obtains the relation (Eqn. III, Scheme 6.40) and the electrophoretic mobility, µ of a molecule is defined as the migration per unit field strength from (Eqn. IV, Scheme 6.40). Eq = 6πηrv µ =

q ν = E 6πηr

...(III) ...(IV)

or µ =

q f

SCHEME 6.40

Thus biomolecules migrate depending on the ratio of net charge to frictional coefficient. Since f is strongly massdependent for classes of biopolymers of similar shape (e.g., globular proteins and linear DNA), differences in µ approximate closely to differences in charge/mass ratio. This description is sufficient to know as to how net charge, mass and shape underlie the separation of molecules in electrophoresis. SDS = sodium dodecyl sulfate [Me(CH2)10CH2OSO2O–Na+], also known as sodium lauryl sulfate, is a common component of household detergents and shampoos; PAGE = polyacryl-amide gel electrophoresis. Hydrophobic

SDS

SO4– Na+ Hydrophilic

(B) GEL ELECTROPHORESIS Most electrophoresis of biological molecules is done in gels rather than using the solution. This avoids diffusion and convection that would interfere with sharp separations in liquids. It also makes it easier to stain and detect the samples at the end of the experiment. The gels in common use in electrophoresis of proteins and nucleic acids are polyacrylamide and agarose.

(C) SDS–PAGE

AND

MOLAR MASS

A variation of the gel electrophoresis technique known as sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS-PAGE) allows to determine the molar mass of proteins under denaturing conditions. In this technique a protein is treated with the denaturing agent sodium dodecyl sulfate

BIOPOLYMERS AND THEIR MOLECULAR WEIGHTS

179

Sodium dodecyl sulfate (SDS)

HSCH2(CHOH)2CH2SH

β-mercaptoethanol

Dithiothreitol

SCHEME 6.41

The denaturing agent SDS binds strongly to most proteins (Scheme 6.42) and β-mercaptoethanol ruptures disulfide linkages in proteins. The surface charge on the SDS-protein complex is because of the exposed sulfate ions. The complex assumes the shape of a long rod of constant width. Its length is a function of the protein’s molar mass.

Denatured protein –

– – – – – – – – – – – –

CH3–(CH2)10–CH2OSO3–Na+ HOCH2CH2SH

The detergent sodium dodecyl sulphate (SDS) consists of a hydrophobic 12carbon chain and a polar sulphated head. The hydrophobic chain can intercalate into hydrophobic parts of the protein by detergent action, disrupting its compact folded structure.

– – – – –

– – – – – – – – – – – –

SDS

–

– – – – –

(SDS) and β-mercaptoethanol or dithiothreitol, both of which act to reduce the number of disulphide bonds in proteins (Scheme 6.41)

Unfolded protein

Folded protein

A somewhat idealized view of the clustering of SDS molecules around a denatured protein molecule

SCHEME 6.42

A plot of the logarithm of the molar mass of the proteins versus the electrophoretic mobility of their SDS complexes generates a straight line with a negative slope (Scheme 6.43). The molar mass of an unknown protein can be easily found from the electrophoretic mobility of its SDS complex and the standard calibration curve.

Protein RRM

70,000 50,000 30,000 20,000 10,000 0.2

0.3 0.4 0.5 0.6 0.7 0.8 Relative electrophoretic mobility

Relative mobility of proteins of different molar masses on SDS-PAGE SCHEME 6.43

PROBLEMS AND EXERCISES 1. Discuss the terms molecular mass and molecular weight as applied to biopolymers. 2. What is weight-average molar mass? Describe in detail polydispersity and heterogeneity index.

The information which cannot be obtained regarding protein size in normal (nondenaturing) electrophoresis can be obtained by denaturing (unfolding) the protein in a strong detergent solution. Sodium dodecyl sulphate is a strong detergent that disrupts the native structure of proteins in solution and forms a micelle encapsulating the unfolded polypeptide chain.

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BIOPHYSICAL CHEMISTRY

3. Describe an analytical centrifuge rotor and its utility in determining the molar mass of biopolymers. 4. Describe the method of molar mass determination by sedimentation velocity method. 5. How can you determine the molecular mass of a biopolymer from sedimentation equilibrium method? 6. Compare and contrasts the sedimentation velocity method with sedimentation equilibrium method for determining the molar mass of a biopolymer. 7. What is osmotic pressure? How one can determine the molecular mass of a biopolymer from it? 8. What is electrophoretic mobility? Describe the factors which effect this mobility. 9. Write a short note on SDS-PAGE and molecular mass determination.

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

181

C H A P T E R

% 7.1

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

INTRODUCTION AND GENERAL PRINCIPLES

Low molecular weight substances can readily undergo dissolution, however, biopolymers take considerable time to do so. At fairly low concentrations, polymer solutions are highly viscous while low molecular weight substances are far less viscous even at high concentrations. In the case of low molecular weight solutes the individual molecules (mostly the ions) are discrete and separate from one another which are held together within the solid matrix by van der Waal’s or electrostatic forces of attraction. When such a solute and a solvent solute are brought together, the solvent molecules surround the solute molecules at the surfaces to establish solvent-solute interaction and break the solute-solute attraction. Consequently the solute molecules (which are discrete) are isolated from the solid phase. Since their size is comparable to that of the solvent molecules, they diffuse fast into the solvent phase and the dissolution process is thus fast. Biopolymers, however, are very large molecules as compared to the solvent molecules. These are made up of tightly folded random coils. These molecular coils also do not represent discrete and separate entities but are interpenetrating and entangled with one another. There are also varying degrees of cohesive and attractive forces between different segments of the same molecular coil as well as neighbouring coils. Thus, solvent molecules take time to establish interactions with polymer molecules, to overcome the forces of attraction, to release individual molecules out of 181

182

When a polymer fragment interacts with a solvent, forces of attraction or dispersion start acting between them. When the solvent-solute interaction becomes more powerful than the solutesolute interaction, the forces holding the polymer segments together are weakened and the solvent molecules force their way between the segments. The overall process thus leads to the solvation of segments. Overall this is a slow process.

BIOPHYSICAL CHEMISTRY

the chain entanglement and get them out of the polymer phase. This is the difference in the dissolution process of low and high molecular weight substances.

7.2

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

Thermodynamic principles which govern the dissolution of low molecular weight solutes and biopolymers (high molecular weight-solutes) are the same. A change of state of a system from e.g., solid to solution in Thermodynamic terms is related to changes in the entropy (∆ S) and the enthalpy (∆ H) of the system. The following points may be noted: l Any given system tries to shift in the direction of a state in which the enthalpy or the heat content (H) is minimum, and/or the entropy or degree of disorderliness or randomness (S) is maximum. A system can spontaneously shift from one state to another state provided in the process, there is a loss in the enthalpy (– ∆ H) and/or a gain in the entropy (+ ∆ S). When the system changes from one state to another, the associated entropy and enthalpy changes are independent of each other. During a change the enthalpy can increase (+ ∆ H), decrease (– ∆ H) or remain unchanged (∆ H = 0). Moreover, during the same process, there can be either an increase or a decrease in the entropy factor. l If during a process, there is a decrease in the enthalpy with a simultaneous increase in the entropy (– ∆ H and + ∆ S), both of them support the change of state and the process is spontaneous. l When there is an increase in the enthalpy along with a decrease in the entropy (+ ∆ H and – ∆ S), both the parameters are unfavourable and the change of state (e.g., solid to solution) does not occur. l In a situation when both the entropy as well as enthalpy either increase or decrease i.e., one entity supports the process, while the other opposes it, the feasibility of such a process then depends on the sign of the Gibbs free energy change (∆ G), which is a manifestation of two different entities (∆ H) and (∆ S) as show in (Scheme 7.1).

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

183

∆G = ∆ H – T ∆S SCHEME 7.1

This concept of Gibbs free energy change is central to different energy-related areas in chemical, biochemical and biological reactions and the relative predominance of the entities ∆ H and ∆ S will influence the course of the reaction e.g., dissolution which is a process being discussed.

(A) DISSOLUTION

OF A

LOW MOLECULAR WEIGHT SOLUTE

The following points may be considered: l Dissolution of a substance leads to increase in entropy. (The solute particles become more disordered in the dissolved state compared to that in the bound state of the solute). Thus the only other parameter which will decide the feasibility of the process of dissolution is change in enthalpy. l When there is decrease in enthalpy (– ∆ H) i.e., the dissolution process is exothermic, the resultant free energy change (∆G) becomes negative and dissolution becomes a spontaneous process (Scheme 7.1). l The process of dissolution also becomes spontaneous when the process is neither exothermic nor endothermic. The entropy gain alone is then sufficient to bring about a decrease in the free energy of the system. l With an increase in enthalpy (+ ∆ H), the dissolution process is endothermic. In this case, the process of dissolution will be opposed by the + ∆ H factor, while it will be favoured by the + ∆ S, and the process is feasible as long as + ∆ H is less than T∆S. When + ∆ H becomes equal to or greater than T∆S, the dissolution process cannot take place. l When the dissolution process is exothermic, the solute is soluble in the solvent in all proportions. l During an endothermic dissolution, in the initial stages of the dissolution process (the + ∆ H value) is less than the T∆S value and that is why dissolution occurs in the first place. With the progress of the dissolution process, the entropy gain (T∆S) progressively decreases because the concentration of the solute phase is decreasing while that of the solution phase is

Under the usual conditions of constant temperature and pressure, the thermodynamic condition to form a twocomponent solution is that the Gibbs free energy G12 of the mixture must be less than the sum of the Gibbs free energies G1 and G2 of the pure individual components. This requirement is defined in terms of the Gibbs free energy of mixing. ∆Gm = G12 – (G1 + G2) which must be negative (i.e., ∆Gm < 0) for the formation of a solution. Gibbs free energy is related to enthalpy H and entropy S by the standard thermodynamic equation, therefore, a useful relation for ∆Gm is (∆Gm = ∆Hm – T∆Sm).

184

BIOPHYSICAL CHEMISTRY

increasing. When the T∆S value decreases and becomes equal to + ∆ H, ∆ G = 0, consequently no further dissolution is possible. At this stage an equilibrium is established between the gain both in entropy as well as enthalpy. The number of solute molecules going into solution equals those precipitating out. The solution at this point of equilibrium is called ‘saturated’.

(B) DISSOLUTION

OF A

MACROMOLECULE

The thermodynamic principles regarding dissolution of macromolecules are the same. The following points may be noted: l When strong attraction forces operate between the polymer segments and solvent molecules, the heat of dissolution becomes negative (– ∆ H), and this makes the process of dissolution favourable. The macromolecule is then completely soluble in the solvent in all proportions. l When these strong forces are absent, and only weak dispersion forces are operative between the polymer and the solvent, the ∆ H becomes positive. Dissolution can still occur even when ∆ H is positive as long as its value is less than T∆S. Fortunately, in the case of macromolecules also, the magnitude of entropy gain in the dissolution process is high. l When a macromolecule undergoes changes in its state from solid to solution, both the molecular mobility as well as the segmental mobility is generated. Macromolecules are made up of hundreds of segments rotating freely around fixed angles (independent of each other, in a limited sense, at least), they assume innumerable ‘conformations’ in the dissolved state. This freedom of molecular mobility and the segmental mobility lead to an increase in entropy in the dissolved polymer. This increased entropy factor can accommodate + ∆ H, leading to negative ∆ G, thus making dissolution possible. l Initially the dissolution process is highly favourable. With the increase in the concentration of the solution, the T∆S value becomes progressively lower as observed during the dissolution of a low molecular weight-

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

l

l

l

185

polymer. An equilibrium is finally attained when + ∆ H becomes equal to T∆S. In the case of macromolecules the solvation occurs at random i.e., segment after segment, until all segments in the molecular coil are fully solvated. The process of solvation of macromolecules and their subsequent diffusion into the solvent phase is slow. Since the polymer molecules are much larger compared to the solvent molecules, the latter penetrate deep into the polymer segments and the polymer is in a swollen state. In reality, in each polymer molecule some segments are solvated (unfolded) whereas some others remain unsolvated (aggregated). There is a constant diffusion of the solvent molecules between the solvated and the aggregated segments. Consequently some of the solvated segments get aggregated, while some of the aggregated ones are solvated. As a result, a dynamic equilibrium is set up between the solvated and the aggregated segments within the swollen mass. As a result of this polymer molecules do not move out of the polymer phase and no separate solution phase is formed. On adding more quantity of the polymer to this swollen mass, the solvent molecules start penetrating into the newly added polymer to make it swell. The attack on the freshly added polymer sample by the solvent molecules and the polymer swelling continues till a fresh equilibrium is attained between the solvated and the aggregated chain segments. The newly added polymer therefore, loses its identity and becomes a part of already existing swollen mass. Thus the volume of the swollen mass increases. With an increase in the polymer-to-solvent ratio, the ratio of the aggregated to the solvated chain segments in the swollen mass also increases. A ‘saturation’ point, when the unswollen solid polymer existing in equilibrium with the solution, is never attained.

(C) MOLECULAR WEIGHT

OF A

POLYMER

AND

DISSOLUTION

The above discussion describes the dissolution of a monodispersed polymer system. While dealing with a

Dissolution of a biopolymer is a slow process and involves two stages. In the first stage, the solvent molecules penetrate deep into the polymer to generate a swollen gel. In the second stage, when the strong polymer-solvent interactions overweigh the polymerpolymer intermolecular forces the swollen gel becomes a true solution.

In a polymer-solvent system when + ∆ H is very high and exceeds the T ∆ S value, the dissolution cannot take place and the polymer is not affected by the solvent.

186

BIOPHYSICAL CHEMISTRY

polydispersed system (having both low and high molecular weight components) initially the low molecular weight components get fully solvated. These diffuse out to give a solution. The higher molecular weight components are still in the process of progressive solvation. The following points may be considered: l When ∆H is negative, the high molecular weight components also get fully solvated with time and go into solution. When however, ∆H is positive, the point of equilibrium may be reached before the high molecular weight components also get fully solvated. At the state of equilibrium + ∆H equals T∆S. Thus molecules with a molecular weight below a certain critical value will be in solution and those above it will be in a swollen state. Such a system, where equilibrium exists between the solution phase and the swollen solute phase, is called sol-gel system. The critical molecular weight value, which is a measure of the solubility in such an equilibrium system, can be shifted by using binary solvent mixtures in varying proportions. Such binary solvent systems usually comprise a ‘good solvent’ (with – ∆H value) and a ‘poor’ solvent or a ‘non-solvent’ (with + ∆H values). All components of the polymer sample go into solution in a good solvent. When a poor solvent is added, due to its + ∆H factor the equilibrium is shifted in a direction that some of the segments in the molecular coils of the highest molecular weight components are brought into aggregation (they are desolvated) and therefore, these molecules form the gel phase (the highest molecular weight fraction of the polymer sample now precipitates out of the solution phase). By adding more of the poor solvent, the equilibrium is further shifted in such a way that the biggest molecules among the remaining molecules in solution precipitate out. This principle is involved in the fractional precipitation method for the separation of a polymer in to different fractions.

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

7.3

THERMODYNAMIC PRINCIPLES AND DISSOLUTION OF CRYSTALLINE AND AMORPHOUS POLYMERS

The crystalline and amorphous polymers differ from each other in their phase state and are therefore, expected to display different behaviour during dissolution in a solvent. However, as far as thermodynamic principles are concerned, these are true for both these types, i.e., whether ∆ H is negative or positive its magnitude should be less than T∆S. When it is so dissolution of polymer whether amorphous or crystalline will occur. The dissolution of an amorphous polymer is comparable to mixing of two liquids. Two liquids being of the same phase state will mix readily provided ∆ G of mixing is negative. Unlike this, the crystalline polymer is in the crystalline phase state, while the solvent is in the liquid phase state. Since the two different phases cannot mix to form a single homogeneous system, mixing or dissolution is impossible unless both of them are brought into the same phase state. The first step involved in dissolving a crystalline polymer is thus to bring it to the liquid phase. A crystalline polymer can be brought into liquid phase state either by heating to its melting point or under conditions which lead to cleavage of long range order present in crystalline state. The free energy relation governing the solubility of crystalline polymers near their melting point is in (Scheme 7.2). where,

∆G = (∆ Hm + ∆ Hf) – T · (∆Sm + ∆Sf) m and f = Mixing and fusion, respectively. SCHEME 7.2

7.4

HEAT OF DISSOLUTION AND THE SOLUBILITY PARAMETER

As already discussed the amorphous and crystalline polymers differ in their phase state. Their behaviour is different when they are dissolved in a solvent. Dissolution of an amorphous polymer is like the mixing of two liquids, as an amorphous polymer is considered to exist in the liquid phase state. The dissolution of a crystalline polymer involves the mixing of two substances existing in two different phase states (the crystalline phase polymer, and the liquid phase solvent). The heat of mixing (∆ Hm) of two liquids, whose dissolution involves

187

188

BIOPHYSICAL CHEMISTRY

only dispersion forces (endothermic mixing, is in Scheme (7.3) given by Hildebrand and Scott). 2

 ∆E 1/2  ∆E 1/2  2  φφ ∆ H m = Vm   1  −  V2   1 2  V1     where, Hm = heat of mixing Vm = total volume of the two liquids ∆E1 and ∆E2 = energy of vaporisation of liquids 1 and 2 V1 and V2 = the molar volumes of the two liquids φ1 and φ2 = volume fractions of liquids 1 and 2. (∆E/V) = the amount of energy required to vaporise a unit volume of the liquid SCHEME 7.3

During vaporisation, energy is spent to overcome the cohesive force holding the molecules together and to allow the molecules completely separate out into the gaseous state. The term (∆ E/V), refers to a measure of the cohesive force that holds molecules in the liquid together and is designated as the ‘cohesive energy density’ (CED). The term ‘solubility parameter’ (δ), for the square root of the CED is given in (Eqn. I, Scheme 7.4). One can now relate the heat of mixing of two liquids (∆ Hm) to the solubility parameter of two liquids (Eqn. II, Scheme 7.4), and the following points may be noted: 1/2

 ∆E  δ =    V  where, δ = solubility parameter ∆H m Vmφ1φ2

= (δ1 – δ2)2

...(I)

...(II)

SCHEME 7.4

The magnitude of the heat of mixing is based on the square of the difference between the solubility parameters of two liquids. l For mixing to take place, the positive heat of mixing is to be at a minimum. This requires the difference between the solubility parameters (δ1 and δ2) to be as low as possible. When δ1 = δ2, then ∆ Hm becomes zero and mixing will occur readily as a result of entropy factor. The polymer dissolution can thus be predicted when (Eqn. II, Scheme 7.4) is simplified to (Eqn. III, Scheme 7.5). l

 H = (p – s)2 ps where, the subscripts p and s denotes polymer and solvent respectively. SCHEME 7.5

The following predictions may be made from (Eqn. III, Scheme 7.5).  The polymer will dissolve only in a solvent with  values very close to that of the polymer.  When p and s values are different, dissolution will not occur.  The above observations hold good in the case of amorphous polymers.  The theory does not hold when applied to crystalline polymers as well as to solvents with strong polar groups and hydrogen bonding. The solubility parameter theory is based on dispersion forces and, hence, does not apply to polymer-solvent systems with positive interaction where  H is negative. Dissolution does take place in such cases even when p and s are very different.

The heat of dissolution of a polymer as related to the solubility parameters of the components has been discussed. Polymer solutions generally display considerable deviations from Raoults law, and the law is obeyed only at extreme dilutions. Apart from deviations at higher concentrations, small entropies of mixing is another reason. The effect of small entropies of mixing may be due to large difference in molecular size between polymer and solvent molecules. The molecular size difference may be explained by considering the structure of polymer and polymer solutions based on the quasicrystalline lattice model for solutions. An assumption is made that the molecules of a solution of polymer and solvent can be arranged in different ways (W). The Boltzmann relation (Scheme 7.5a) defines W and entropy of mixing. Sm = k ln W where,

Sm = the entropy of mixing k = the Boltzmann constant. SCHEME 7.5(a)



190

BIOPHYSICAL CHEMISTRY

The following points may be noted regarding lattice model concept: l It is assumed that the polymer molecule is made up of a large number of chain segments of equal length which are joined flexibly together. l The sizes of the polymer chain segments are comparable with that of the solvent molecules, and the lattice sites. l The polymer segments can occupy the lattice sites as shown in (Scheme 7.5b).

(I)

(II)

A liquid lattice. (I) represents mixture of molecules of equal size, (II) polymer molecules located at the lattice sites, (The mixture of solvent molecules with a polymer molecule showing the connectivity of polymer segments.) SCHEME 7.5(b) l

l

Due to the large size of the polymer molecule, the number of ways of arranging the polymer segments will be relatively small, thus the entropy of mixing for polymer dissolution is much less as compared with low molecular weight solutes. Flory and Huggins showed that the entropy of mixing for polymer solutions can be given by relation (Eqn. I, Scheme 7.6). ∆Sm where, the subscript s p φs and φp (given by Eqns. II and

= – k(Ns ln φs + Np ln φp) = the solvent and = the polymer = volume fractions III) N φs = (Ns + nN p )

φp =

nN p (Ns + nN p )

...(I)

...(II) ...(III)

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

where

191

Ns = the number of solvent molecules Np = number of polymer molecules n = the number of segments in a polymer molecule SCHEME 7.6

The heat of mixing is expressed by the relation given in (Scheme 7.7). The Flory-Huggins interaction parameter measures where,

∆ Hm = kT χNsφp χ = the Flory-Huggins interaction parameter. SCHEME 7.7

the solvent power of the system and distinguishes between a good and a poor solvent. (The lower value for the FloryHuggins parameter indicates a good solvent, while a high value shows a poor solvent). The free-energy of mixing of polymer solutions in terms of χ is in (Scheme 7.8). ∆Gm = kT(χNsφp + Ns ln φs + Np ln φp) SCHEME 7.8

Two entropy factors contribute to the free energy of dilution. One of these involves contact between polymer segments and solvent molecules, while the other is conformational entropy. The overall free energy of dilution is the sum of these two (Scheme 7.9). ∆Gm = ∆Gconform + ∆Gcontact

(I)

NOW ∆Gconform = RT ln (1 − φ p ) +  1 − 1  φ p  n   

(II)

AND ∆Gcontact = RT [χφ2p] Therefore,

  1 ∆Gm = RT ln (1 − φ p ) +  1 −  φ p + χφ2p  n    

(III) (IV)

SCHEME 7.9

The relation (Eqn. IV, Scheme 7.9) is derived for a monodisperse polymer, when dealing with a polydisperse system the n factor in this relation is to be replaced by (n ) where n represents the average value of the number of segments in a polymer. Thus for a polydisperse polymer (Eqn. IV, Scheme 7.9) can be written as (Eqn. V, Scheme 7.10).

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BIOPHYSICAL CHEMISTRY

  1 ∆Gm = RT ln(1 − φ p ) +  1 −  φ p + χφ2p  n    

(V)

SCHEME 7.10

MEASUREMENT

OF

OSMOTIC PRESSURE

Significantly one can determine the osmotic pressure of the polymer solution from the relation (Eqn. V, Scheme 7.10). The osmotic pressure (π) is related to the partial molar free energy of mixing by relation (Scheme 7.11). On substituting ∆ Gm from (Scheme 7.11 in Eqn. V, Scheme 7.10) one gets the relations (Scheme 7.11a). πVs = –∆Gm where,

Vs = the partial molar volume of the solvent π = osmotic pressure SCHEME 7.11

− πVs = RT ln (1 − φ p ) +  1 − 1  φ p + χφ2p  n    π =

−RT Vs

 1  2 ln (1 − φp ) +  1 − n  φp + χφp 

SCHEME 7.11(a)

While dealing with dilute solutions the value of φp 0, one may choose the solution giving positive values of rD to obtain the familiar quadratic formula (Eqn. XI, Scheme 7.21). One takes only positive values of rD since these are physically significant. (A+)(1)/rD + z(M) – rD(B–)(1) = 0

(IX)

SCHEME 7.19

rD2 = z(M)rD/(s) – 1 = 0

(X)

SCHEME 7.20

rD = z(M)/2(s) + {1 + [z(M)/2(s)]2}1/2

(XI)

SCHEME 7.21

Now (Eqn. XI, Scheme 7.21) indicates clearly that, in general, rD ≠ 1, so that A+ and B– do not equally distribute themselves across the membrane. This unequal distribution happens even though the system is at equilibrium, and even though one has assumed no binding of A+ or B– to M.

7.7

MUSCULAR CONTRACTION AND ENERGY GENERATION IN MECHANOCHEMICAL SYSTEM

(A) INTRODUCTION Muscle is the main biochemical transducer (machine) which converts potential (chemical) energy into kinetic (mechanical) energy. Muscle is the largest single tissue in the human body. Three types of muscles are found in vertebrates: skeletal, cardiac and smooth.

On introduction of the macromolecule into the system, it is in a neutral form, so that it brings counterions with it. For example, if the charge z on M is positive, then the macromolecule could be added to the solution in the form of a salt with B– counterions.

(B) ACTIN AND MYOSIN ARE THE MAJOR PROTEINS OF MUSCLE The mass of a muscle is made up of 75% water and more than 20% protein. The two major proteins are actin and myosin. Myofibril is a unit which contains thick and thin filaments of muscle fibers. The thick filaments contain myosin. The thin filaments contain actin, tropomyosin, and the troponin complex (troponins T, I and C). When muscle contracts, the thick and thin filaments slide over one another, shortening the length of the sarcomere. (Sarcomere is a functional as well as a structural unit of the muscle contractile system).

(C) THICK AND THIN FILAMENTS SLIDE PAST ONE ANOTHER IN MUSCLE CONTRACTION Muscle shortens by as much as a third of its original length on contraction. A sliding-filament model is the basis of muscle contraction. The following points may be noted about this model:  The lengths of thick and thin filaments do not change on muscle contraction.  However, the length of the sarcomere undergoes a decrease since the overlap between the two types of filaments increases. Thick and thin filaments slide past each other during contraction.

Sarcomere Thin filaments

Thick filaments

Extended

Sarcomere Contracted Overlapping arrays of thick and thin filaments of a muscle SCHEME 7.22



A force of contraction is generated by a process that actively moves one type of filament past neighbouring filaments of the other type (Scheme 7.22).

(D) ROLE OF MYOSIN AND ACTIN-CONVERSION ENERGY INTO MECHANICAL ENERGY

OF

CHEMICAL BOND

Myosin has three biological activities. First, myosin molecules spontaneously assemble into filaments in solutions of physiologic ionic strength and pH. The thick filament consists mainly of myosin molecules. Second, myosin is an enzyme (myosin is an ATPase). Thirdly, myosin binds the polymerised form of actin which is the major constituent of the thin filament. The hydrolysis of ATP is used to drive movement of the filaments. ATP binds to myosin heads and is hydrolyzed to ADP and P i by the ATPase activity of the actomyosin complex. (Scheme 7.23) ATP + H2O

ADP + Pi + H+

SCHEME 7.23

The binding of myosin with the polymerised form of actin (F-actin) is key to the generation of the force which slides the thick and thin filaments past each other. Myosin therefore, can be regarded as a mechanoenzyme since it catalyzes the conversion of chemical-bond energy into mechanical energy.

(E) Ca2+ PLAYS A CENTRAL ROLE CONTRACTION

IN

REGULATION

OF

MUSCLE

The contraction of all muscles occurs from by the general mechanism described above. Muscles from different organisms and from different cells and tissues within the same organism may involve different molecular mechanisms for the initiation of their contraction and relaxation. In all systems, Ca 2+ plays a key regulatory role. There are two general mechanisms of regulation of muscle contraction: actin-based and myosinbased. The former operates in skeletal and cardiac muscle, the latter in smooth muscle.

(F) THE HIGH ENERGY PHOSPHATES

IN

FORMATION

OF

ATP

In the contractile system of skeletal muscle cells, the proteins myosin and actin act to transduce the chemical energy of ATP into motion. ATP binds tightly to one conformation of myosin which catalyzes the hydrolysis of its bound ATP, the

ADP and Pi dissociate from the protein which then attains another conformation till another molecule of ATP binds and the cycle continues. ATP as such is present only in small amounts in muscles to sustain contraction only for fraction of a second. To continue the contraction, muscles require a quick synthesis of ATP from ADP which involves the consumption of creatine phosphate which is a high energy phosphate compound. Creatine phosphate is present in the skeletal muscle and the enzyme creatine kinase catalysis the reversible reaction (Scheme 7.24). ADP + Phosphocreatine

Creatine kinase

ATP + Creatine G10 = –12.5 kJ/mol

SCHEME 7.24

When a sudden demand for energy consumes ATP, the phosphocreatine reservoir is used to replenish ATP. When the demand for energy slows down ATP produced by catabolism is used to replenish the phosphocreatine reservoir by reversal of the creatine kinase reaction. High energy phosphate compounds e.g., phosphocreatine are collectively called phosphagens. These compounds are stored in vertebrate muscle.

Osmotic pressure has been described in detail in Chapter 6 (See, Schemes 6.31–6.36). The determination of molecular mass using this technique has been discussed in detail. The determination of osmotic pressure of polymer solutions can also be made (See, Scheme 7.11). PROBLEMS AND EXERCISES 1. Why the dissolution of a polymer in a solvent is a slow process? How this dissolution differs from a low molecular weight compound? 2. How thermodynamic functions explain the dissolution of a biopolymer? 3. During the dissolution of a polymer in a solvent a saturation point is not reached. Explain. 4. Discuss the thermodynamics of dissolution of crystalline and amorphous polymers.

THERMODYNAMICS OF BIOPOLYMER SOLUTIONS

5. Discuss the relation between molecular weight of a polymer and its dissolution. 6. Discuss the heat of mixing of polymer solutions based on Flory-Huggins theory. 7. How one can determine osmotic pressure of the polymer solution from partial molar free energy of mixing? 8. What are the muscle proteins? How these are involved in the muscle contraction by sliding filament theory? 9. How myosin and actin are involved to convert chemical bond energy into mechanical energy? 10. Discuss sliding filament model in muscle contraction. Discuss the energy requirements needed for the process. 11. What is the source of energy in muscle contraction? Explain in detail.

199

200

BIOPHYSICAL CHEMISTRY

C H A P T E R

8

DIFFRACTION METHODS

8.1

Light Scattering Large particles scatter light very efficiently. A well known example is the light scattered by specks of dust in a sunbeam. Thus, light scattering provides a convenient method for the characterization of polymers, large aggregates (such as colloids), and biological systems from proteins to viruses.

INTRODUCTION—GENERAL PRINCIPLES OF LIGHT SCATTERING

The physical properties of a macromolecule e.g., a biopolymer can be determined by light scattering and X-ray diffraction methods. Scattering of light takes place when light beam encounters matter. The medium may be transparent or opaque (or turbid). The light scattering occurs due to turbidity of medium. On interaction of the oscillating electric field of electromagnetic radiation with the electrons in a particle, an oscillating dipole moment is generated with a magnitude proportional to the polarizability of the particle and the strength of the field. Elastic light scattering is observed when the oscillating dipoles in the particle radiate at the same frequency as the frequency of the exciting electromagnetic radiation. The term elastic refers to the fact that the incident and scattered photons have similar frequency and consequently the same energy. When the medium is perfectly homogeneous (a perfect crystal) the scattered waves interfere destructively in all directions except in the direction of propagation of the exciting radiation. In the case of a medium which is inhomogeneous (an imperfect crystal or a solution of macromolecules) radiation is scattered into other directions as well. Scattering of light by particles with diameters much smaller than the wavelength of the incident radiation is called Rayleigh scattering (Scheme 8.1) which has several characteristic features:

200

DIFFRACTION METHODS

201 Detector

Sample q

Generally, the passage of radiation through a material is reduced. This is not due to absorbance but by scattering of the radiation (light) by suspended particles or other inhomogeneities. This is called Rayleigh Scattering.

Incident ray Io Monochromatic source Scattering intensity, I

Rayleigh scattering from a sample of point-like particles. The intensity of scattered light is dependent on the angle θ between the incident and scattered beams. SCHEME 8.1 l

l l

l

8.2

The intensity of scattered light is proportional to λ–4, therefore, shorter wavelength radiation is scattered more intensely compared to longer wavelengths. The intensity of scattered light is proportional to the molar mass of the particle. The intensity of scattered light depends on the scattering angle θ (Scheme 8.1). In practice, data are collected at several angles to the incident beam. For very dilute solutions excited by plane-polarized light, the Rayleigh ratio, Rθ is the measure of the intensity of scattered light at a given scattering angle θ which is defined as in (Scheme 8.2).

LIGHT SCATTERING BY MACROMOLECULES AND MEASUREMENT OF AVERAGE MOLAR MASS

The phenomenon of light scattering is employed to determine the average molecular mass ( M w ) of polymers. This determination is possible since it is not only a suspended particulate matter which scatters a light beam, however, solute molecules in a solution can also do so. In fact, it has been established that in solutions and liquid mixtures, scattering of light occurs due to changes in density or refractive index within the system arising from compositional variations. During scattering of light, the amplitude of scattering is

In case of polymer solutions in which the solute molecules are larger in size compared to the wavelength of light, modified version of relation (Scheme 8.1a) is employed.

202

BIOPHYSICAL CHEMISTRY

found to be proportional to the mass, M, of the particle which scatters the beam of light. In practice however, it is the intensity of the scattered light which is found experimentally (the square of the amplitude). Debye (1944) gave an expression (Scheme 8.1a) which relates the M w of the solute particle to the intensity of scattered light. This expression (Debye equation) holds only for particles which are smaller than the wavelength of light used for the scattering experiment. KC R90

=

HC 1 = + 2BC τ M

SCHEME 8.1(a)

Definition of Mathematical Symbols (Scheme 8.1a) l

R90 (Rθ) – B and C B represents the second virial coefficient. C is the concentration of the solution while R90 is called the Rayleigh ratio at 90º observation angle. This ratio in a generalised case is represented as Rθ. The Rayleigh ratio is determined at an observation angle of 90º. Hence Rθ = R90, and Rayleigh expression can be rewritten (Scheme 8.2). Rθ =

i θr 2 I0V

where, iθ is the intensity of the scattered light per unit volume V of scattering material observed at a distance r and at an angle of θ with reference to the incident beam, and I0 is the intensity of the incident beam. SCHEME 8.2 l

τ = turbidity of the medium A medium can be transparent or opaque (or turbid). The turbidity of a medium results from scattering of light. When the intensity of incident beam of light is I0, and on passing the light through a medium of thickness, x, the incident intensity is reduced to I due to scattering (the absorption of light by the medium is excluded), the turbidity, τ of the medium is given by (Scheme 8.3). The turbidity of a medium characterises I I0

= exp (– τx) SCHEME 8.3

DIFFRACTION METHODS

l

203

the fraction of the incident light beam scattered in all directions on passing through some medium with thickness of 1 cm. K and H light-scattering calibration constants These are defined by (Eqs. I and II, Scheme 8.4) K =

2π2n 2(dn / dC )2 λ 4N A

...(I)

H =

32π3n 2 (dn / dC )2 3λ 4N A

...(II)

where π = the mathematical symbol with a numerical value of 3.14 n = the refractive index of the solution (dn/dC) = the specific refractive index increment, i.e., the change of refractive index with concentration λ = the wavelength of the incident light NA = Avogadro’s number SCHEME 8.4

The polymer molecules e.g., biopolymers in solution exist as randomly coiled swollen chains and different regions of the macromolecular coil (A and B, Scheme 8.5) simultaneously scatter the incident light beam. Thus, different regions of the same particle get exposed to incident light with a different phase. The end result is that the scattered beam consisting of light waves emerging from different regions of the same particle interfere with one another and, therefore, the intensity of the scattered light diminishes when observed at an angle θ. Put differently the value of R θ varies with θ, and consequently Debye equation (See, Scheme 8.1a) can now be written in modified form (Eqn. I, Scheme 8.6).

Io

A

B 



I

Scattering of light by a polymer molecule SCHEME 8.5

I

The light-scattering technique provides an easy method for determining the molecular masses of polymers in the range of 10,000 to 10,000,000. This technique requires the experimental determination of either Rθ or τ using a light-scattering photometer, and of n and dn/dC using a differential refractometer.

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BIOPHYSICAL CHEMISTRY

KC Rθ where,

=

HC 1 = + 2BC τ Mw P(θ)

(I)

P(θ θ) = the particle-scattering factor describing the angular dependence of the scattered light according to the relationship (Eqn. II, Scheme 8.6)

1 16π2 2 θ 1+ 〈S 〉 sin2   P(θ) = 2 3λ 2 where,

(II)

〈S 2 〉 = the mean square radius of gyration of the polymer random coil.

SCHEME 8.6

When one substitutes the value of P(θ) in (Eqn. I, Scheme 8.6) a relation (Scheme 8.7) is obtained. P(θ) is considered as a correction factor to the scattered intensity at different values of θ, so that P(θ) = 1 at θ = 0. Similarly, BC = 0 at C = 0. Thus, the relationship (Scheme 8.7) can take the forms (Eqns. III–V, Scheme 8.8). KC Rθ

=

HC 1 16π2 θ = + 2 〈S 2 〉 sin2   + 2BC 2 τ   Mw 3λ Mw SCHEME 8.7

 KC  θ 1 16π2 + 〈S 2〉 sin2   R  = 2 Mw 3λ Mw  θ C →0

(III)

1  KC  + 2BC R  = M  θ θ→0 w

(IV)

 KC  1 R  = M  θ C, θ→0 w

(V)

SCHEME 8.8

One may use two methods, the Debye method and the Zimm method by which one can determine the molecular mass of a polymer using the relationships (Schemes 8.1a–8.8). The Debye method involves the determination of the particlescattering factor P(θ) and requires a prior knowledge of the exact shape of the biopolymer in solution. The Zimm method on the other hand eliminates this requirement by adopting a double extrapolation of the plots of C/Rθ versus sin2 (θ/2) + kC (where k is an arbitrary constant) to both zero angle of scattering (θ = 0) and zero concentration (C = 0), when P(θ)

DIFFRACTION METHODS

205

= 1 and BC = 0. The ordinate intercept leads to the value of 1/( KM w ) . From the Zimm plot (Scheme 8.9), the molecular

mass, the second virial coefficient and the meansquare radius of gyration can be calculated using relations (Eqns. V, IV and III, Scheme 8.8) respectively.

A typical Zimm Plot of light scattering. l

Experimental Points.

⊗ Extrapolated Points. Zero angle, θ = 0 (X-axis). Zero concn. C = 0 (Y-axis). SCHEME 8.9

8.3

X-RAY DIFFRACTION AND THREE DIMENSIONAL STRUCTURES OF MACROMOLECULES

INTRODUCTION One can reveal the precise three-dimensional positions of most atoms e.g., in a protein molecule by X-ray crystallography. The three-dimensional structures thus found reflects on understanding the protein structure and function. Proteins are the most abundant macromolecules found within cells and are unique polymers of amino acids. Proteins are highly organized structures with defined shapes. The conformation of a protein can be found out by X-ray diffraction which is carried out on the crystals of proteins (X-ray crystallography). This early technique provides a view of the relative position of atoms within a structure subsequently lHNMR spectroscopy

206

BIOPHYSICAL CHEMISTRY

Crystallization of Myoglobin

Myoglobin in dilute buffer (NH4)2SO4

has provided a useful development. The X-ray diffraction provides a static view as if each atom in the molecule of protein is firmly fixed in position. However, this view has been subsequently modified and now it is appreciated that the atoms of a protein are in state of constant motion and thus reflect on the dynamic nature of the molecule. X-ray diffraction studies on a protein (a macromolecule) generate an average position around which every atom moves. One may consider O2-binding protein myoglobin that stores oxygen in the tissues of the body ready for use when the cells require it. X-ray crystallography showed that the single polypeptide chain of this typical globular protein is made of α-helical secondary structure. There are eight αhelices in myoglobin (Scheme 8.10).

SCHEME 8.10

Myoglobin in 3M (NH4)2SO4 pH = 7 Some days after

Myoglobin crystal

The technique of X-ray crystallography requires the crystals of a protein since the technique requires that all molecules should be precisely oriented. A protein can be obtained in its crystalline form by the addition of ammonium sulphate to the concentrated solution of protein as the added salt reduces its solubility. Thus following this technique crystals of myoglobin can be obtained. The X-ray crystallographic studies need a protein crystal, a detector and a source of X-rays. A beam of X-rays strikes the protein crystal, most of the X-rays pass through the crystal while a small amount of the radiation is diffracted by the crystal. The diffracted beams are detected by X-ray films and the image recorded on the detector is called the diffraction pattern. This pattern represents a collection of spots of varying intensity (Scheme 8.11). The blackening is proportional to the intensity of the scattered X-ray beam. The intensities of the diffraction maxima i.e., the darkness of the spots on the photographic film are then used by applying a mathematical relation (Fourier transform to construct the three dimensional image of the protein crystal.)

X-ray source

Protein crystal

X-ray beam

Diffracted beams

Detector (e.g., film)

(a) When a narrow beam of X-rays strikes a crystal, part of it passes through it straight while the rest is scattered (diffracted) in different directions and these diffracted beams are detected by X-ray film. The diffraction data leads to the threedimensional structure of a protein. (b) Photograph of a myoglobin crystal.

(a)

(b) X-ray diffraction pattern seen on the screen

Outlines of crystallographic experiment SCHEME 8.11

The following points may be noted: The electrons scatter X-rays: The amplitude of the wave scattered by an atom is proportional to its number of electrons. Thus compared to a hydrogen atom, a carbon atom scatters six times more strongly. There is recombination of scattered waves depending on the atomic arrangement. Every atom has a contribution to every scattered beam. The scattered waves reinforce one another (on the film) if in phase, while these cancel one another if these are out of phase. X-ray diffraction patterns give information if a macromolecule is a crystalline polymer. A crystalline polymer will diffract X-rays like crystalline substances. In such a

208

Unlike simple inorganic compound e.g., NaCl polymers do not have a perfectly ordered crystal lattice formation and are not completely crystalline. They contain both crystalline and amorphous regions. Consequently, the X-ray diffractions from them are found to be a mixture of sharp as well as diffused patterns.

BIOPHYSICAL CHEMISTRY

situation sharp and well defined X-ray diffraction patterns are obtained. When however, the polymer is amorphous, the X-ray patterns are broad and diffused (Scheme 8.12). Recall that several macromolecules may have both crystalline and amorphous regions. Thus X-ray diffraction patterns reflect on the structural feature of a polymer. One example is of X-ray diffraction pattern from a melt-crystallized polymer which displays rings superimposed on a diffuse background, the diffuse background shows the presence of amorphous phase while the rings show the presence of a second phase as randomly oriented crystallites (a, Scheme 8.12). In the case of an amorphous polymer there is only a diffuse ring (b, Scheme 8.12) and there are no well defined rings. The presence of rings on X-ray diffraction pattern correspond to Bragg reflections from crystallographic planes within the crystals. Only a diffuse ring, no separate well defined rings on this diffuse ring

Rings superimposed on a diffuse background

(a) Crystalline polymer

(b) Amorphous polymer

SCHEME 8.12

X-RAY DIFFRACTION PATTERNS One has learnt that X-ray diffraction pattern from a crystal is a collection of spots of different intensities. The following discussion is aimed to know the position as well as intensities of the diffraction spots as determined by the spacing between the different sets of parallel planes of the crystal lattice. Recall that macromolecules may be either crystalline or amorphous. Macromolecules in solid state tend to form crystalline regions within the larger mass of material, especially when the chains can form regular, ordered structures or where intermolecular forces such as hydrogen bonds can form (Scheme 8.13). Crystalline domains differ from those regions with no ordered structure, the amorphous

DIFFRACTION METHODS

209

The generalized structure of a solid polymer displaying amorphous and crystalline regions. SCHEME 8.13

domains. Crystallinity tends to increase the strength and stiffness of a polymer. Macromolecules therefore, behave differently on exposure to X-rays. Since the polymers (macromolecules) contain both crystalline and amorphous regions, the X-ray diffractions from them consist of a mixture of sharp as well as broad and diffused patterns. X-rays, like visible light, exhibit a wave nature and the wavelength of light can be measured using a diffraction grating. A diffraction grating consists of a series of lines separated by a distance of roughly one wavelength (λ) of the monochromatic light. When a monochromatic beam of light falls on the grating, the light waves emerging from the grating interfere with one another, to either amplify or eliminate the light in a particular direction and, finally, display alternately dark and bright bands on the screen. (See, Scheme 8.12) In a crystal lattice, the molecules are placed as a welldefined and repetitive pattern and can behave as a diffraction grating. A crystalline substance, therefore, diffracts X-rays and gives patterns which are, indeed, the ‘fingerprints’ of the substance. In the Bragg’s-law description of diffraction, an X-ray beam which impinges on a lattice plane at an angle θ is described as being reflected from that plane at an equal angle (Scheme 8.14). This corresponds to a scattering angle 2θ. The Bragg conditions for observing diffraction require that the path difference between reflected beams from adjacent lattice planes be an integral number of wavelengths. This condition clearly is met from Bragg’s equation (Scheme 8.15). Consider the Bragg law (Scheme 8.15).

210

Diffraction of X-rays by Crystals of Proteins/DNA For the determination of molecular structure, X-rays are used because the wavelength of this radiation is of the same order of magnitude as atoms and covalent bond-lengths. The diffraction pattern obtained yields the information which one can use to calculate the molecular structure. However, the diffraction pattern is a two-dimensional array of ‘spots’ of particular position and intensity. To detect diffracted X-rays with high enough sensitivity, it is necessary that many atoms contribute to the diffraction pattern. Thus the molecule under investigation must be present in the ordered threedimensional array of a crystal so that many equivalent atoms in different molecules contribute to the diffraction pattern. Often in the case of biomacromolecules, it is difficult to obtain crystals of good quality and this is a major limitation of this approach.

BIOPHYSICAL CHEMISTRY

SCHEME 8.14

2d sin θ = nλ where,

n is any integer. d is the distance between two adjacent lattice planes. SCHEME 8.15

The reflections with n = 2, 3, ... are called second-order, third-order, and so on. These correspond to path-length differences of 2, 3, ... wavelengths. In modern work it is normal to absorb the n into d and to rewrite the Bragg law (Scheme 8.16). λ = 2d sin θ SCHEME 8.16

The nth-order reflection arises from the {nh, nk, nl} planes. The primary use of Bragg’s law is in the determination of the spacing between the layers in the lattice. Once the angle θ corresponding to a reflection has been determined, d may readily be calculated.

8.4

PHOTON CORRELATION SPECTROSCOPY (PCS) ALSO CALLED THE DYNAMIC LIGHT SCATTERING (DLS)

(A) INTRODUCTION

The diffusional or Brownian motion of molecules in a liquid or gas gives rise to fluctuations in density or concentration which can be observed by using optical methods.

Particles, emulsions and molecules in suspension display Brownian motion. This is the motion induced by the bombardment by solvent molecules that themselves are moving due to their thermal energy. When the particles or molecules are illuminated with a laser, the intensity of the scattered light fluctuates at a rate that is dependent upon the size of the particles as smaller particles are ‘kicked’ further by the solvent molecules and move more rapidly. Analysis of these intensity fluctuations yields the velocity of the Brownian motion and hence the particle size using the Stokes-Einstein relationship.

DIFFRACTION METHODS

(B) FLUCTUATIONS DIFFUSION

IN

211

LIGHT SCATTERING

ARE USED TO

MEASURE

One may imagine a small volume element in a solution of macromolecules. At any given moment in time, some molecules will be diffusing into this volume, while others will diffuse out (Scheme 8.17). If the volume is large enough, or the observation period is long enough, then these numbers moving in or out will cancel. In the case of small volumes over short time intervals this will not always be the case and fluctuations in density of concentration will take place. For a beam of light passing through the sample, these fluctuations will be observed as fluctuations in refractive index and some of the light will be scattered. This scattered light will appear to ‘twinkle’ as the number of molecules in the volume element fluctuates up or down. The rate at which this twinkling occurs is dependant (amongst other things) on the rate at which the molecules are diffusing in solution. This forms the basis of the technique known as ‘dynamic light scattering’ (DLS). When a laser beam is passed through the solution of macromolecules, and the time dependence of the light scattered from a small volume within the sample is recorded (Scheme 8.17).

A small element of volume from which scattering is being recorded, where diffusion in and out is occurring.

A recording of fluctuating intensity of scattered light in a (DLS) experiment. SCHEME

8.17

The rate of random motion of solute molecules, as a consequence of their thermal energy is measured by the diffusion coefficient, D which is given by the simple relationship (Scheme 8.18).

Most measurements of D are now made by dynamic lightscattering methods. This technique has the advantage over earlier methods because only small amounts of solution are required and rapid measurement is possible.

212

BIOPHYSICAL CHEMISTRY

kT RT = f Nf k = the Boltzmann constant, N = Avogadro’s number, and f = a quantity called the frictional coefficient. D =

where,

SCHEME 8.18

The shape and frequency of this flickering pattern on analysis gives the ‘autocorrelation time’ (τ), which is related to the diffusion constant (D) of the molecules. This information is used to know the relative molecular masses and heterogeneities of macromolecular samples.

(C) OPTICAL ROTATORY DISPERSION (ORD) DICHROISM (CD)

AND

C IRCULAR

Introduction Light is electromagnetic radiation, which is associated with two wave motions (electric and magnetic) propagated in time and generated by oscillating electric and magnetic dipoles. The energies associated with electric and magnetic waves are equal however, most optical measurements (UV-vis and chiroptical) are concerned only with the electric field.

The following points may be noted: l The light beam used in UV-vis spectroscopy is essentially unpolarized. Use of linearly polarized (plane-polarized light) to investigate optically active (chiral) molecules is a powerful method to get structural and stereochemical information. l Plane polarized light is electromagnetic radiation in which the electric vector (E) oscillates in a single plane (Scheme 8.19).

In ordinary radiation (I), the electric field associated with the light waves oscillates in all directions perpendicular to the direction of propagation. In plane polarized light (II), light has vibration in only one direction. This direction is the plane of polarization e.g., the xz plane as shown. SCHEME 8.19 l

Plane polarized light may be resolved into a pair of orthogonal polarization states which are left and right circularly polarized light. In the case of circularly polarized light, the transverse vibrations trace out a helix as a function of time. (Scheme 8.20)

DIFFRACTION METHODS

213

SCHEME 8.20 l

l

Linearly polarized light can be well represented as a combination of two oppositely rotating coherent beams of circularly polarized light. The linearly polarized light is then the vector sum of the left and right circularly rotating components. When the circularly polarized light passes through an optically active medium, which may be a solid, liquid, or gas, the refractive index (n) for one circularly polarized component is different from that for the other. Thus the chiral molecules have the ability to rotate the plane of plane polarized light, a phenomenon called optical activity. The medium is then said to be circularly birefringent and to have the property given by (Scheme 8.21). ∆n =nL – nR ≠ 0 where, nL and nR are the refractive indices for left and right circularly polarized light, respectively. SCHEME 8.21

The left and right circularly polarized light beams pass through an achiral sample or racemic mixture and travel with the same velocity and thus enter and exit the medium in phase. No rotation of the plane of linearly polarized light as it passes through and exists the medium is therefore, observed.

The refractive index (n) reflects the ratio of the speed of light in vacuum to the speed of light in the medium.

214

The quantity called the specific rotation [α] was introduced by Biot (1835), and defined [α]Tλ = α lc where, α = observed angle of rotation of the plane of polarisation l = is the pathlength in dm and c is the concentration of the optically active substance in g cm–3. As specific rotation is a function of the wavelength of light and temperature, both must be specified (T is in degrees Celsius). The units of specific rotation are deg dm –1 cm3 g–1.

Optical activity results from the refraction of right and left circularly polarized light (cpl) to different extents by chiral molecules. The refractive index of a medium is not constant but depends on the wavelength of light used. Thus the optical rotation, which depends on the refractive index, also varies with wavelength.

BIOPHYSICAL CHEMISTRY

l

l

The difference in the refractive indices of left and rightcircularly polarised components nL and nR is termed optical rotation or circular birefringence. Optical rotation varies with wavelength of the radiation. The change in optical rotation with wavelength is termed optical rotatory dispersion (ORD). Thus the source of the rotation, and ORD is birefringence, that is, unequal slowing down of right (R) and left (L) circularly polarized light (nR ≠ nL, where n is the index of refraction) as the light passes through the sample. Differences in refractive indices correspond to differences in light velocities. As a result, one of the two circularly polarized components of the linearly polarized light gets retarded after emerging from the optically active medium, left circularly polarized component (EL) lags behind the right (ER). The two components thus do not remain in phase and the resultant (linear polarization) vectors (in plane x′z) get rotated by the angle α to the original plane of polarization (Scheme 8.22). Optical rotations at a single wavelength, such as 589 nm (sodium D-line), are used to detect and quantitate optical activity. Optical rotations measured over a range of wavelengths, as in ORD spectroscopy, have been used to determine absolute configuration. X

X E

EL 

ER

X

E X 

X

Z

Rotation of E (measured by α) when EL and ER make different angles with the X-axis. SCHEME 8.22

DIFFRACTION METHODS l

215

Recall the Biot equation for specific rotation [α]. Modified Biot equation and terms like molar optical rotatory power, molar rotation are now in use. The angle of rotation α of the plane of linearly polarised light and the specific rotation αm are related (Scheme 8.23) (other expressions with different dimension of α are also in use). αm =

where,

α V m l

= = = =

αV ml

angle in radians volume (m3) mass (kg) length (m) SCHEME 8.23

Molar optical rotatory power, [α]m is defined by the expression (Scheme 8.24). [α]m = αm M where,

M = molecular mass (kg mol–1) SCHEME 8.24

(D) OPTICAL ROTATORY DISPERSION (ORD) Biot discovered that some naturally occurring (chiral) organic compounds possess the unusual property of rotating the plane of polarization of a linearly polarized incident light beam. In 1817, Biot and Fresnel found that the extent of optical rotation of a compound increases on using light of increasingly shorter wavelength for the measurement. The change in optical rotation with wavelength is called optical rotatory dispersion (ORD). In ORD one normally measures the sign and magnitude of rotation of plane polarized light vs. wavelength of incident light. The S-shaped ORD curve (Scheme 8.25) is known as a Cotton effect, in honor of the French physicist Aimé Cotton, who observed both ORD and CD phenomena, in 1896. With measurements of optical rotation (Scheme 8.25) at shorter wavelengths, the rotation increases. It increases rapidly as the absorption maximum is approached. Somewhat before this maximum, rotational values reach a maximum (termed a peak), then drop drastically, going through zero rotation, until another inflection point (termed a trough) is reached. The rotation then tends to increase again. When the

Apart from optical rotation, the combination of circular birefringence and circular dichroism gives rise to another important chiroptical phenomenon the Cotton effect which usually becomes manifest when one observes the change of optical rotation with wavelength (ORD).

Circular birefringence and CD occur simultaneously. ORD involves measurement of a rotation, while CD involves measurement of an absorption, namely the differential absorption of leftand right-handed circularly polarized radiation. Thus CD occurs only in the vicinity of an absorption band, whereas ORD is theoretically finite everywhere.

216

Since both CD and ORD involve optical measurements on chiral molecules these are thus termed chiroptical techniques.

BIOPHYSICAL CHEMISTRY

peak precedes the trough on measuring from longer to shorter wavelength, the Cotton effect is called positive, if however, the trough precedes the peak, it is negative Cotton effect (not shown here). Peak Cotton effect region

Specific rotation

(+)

Plain ORD region

0 = 295 O

(–)

Trough 200

300

400 500 , nm ORD curve of a saturated chiral ketone the crossover point from positive to negative rotational values, λ0 = 295 nm, is close to the UV absorption maximum of the ketone. SCHEME 8.25

The absorption band which corresponds to zero rotation is conventionally called the optically active absorption band. Outside the region of this band, the relationship between optically activity and wavelength i.e., ORD of a chromophore is given by the Drude equation (Scheme 8.26). In other words, a plain curve can be described mathematically by Drude equation. αm = where,

λ02

(λ 2 − λ 02 )

λ0 = a constant representing the wavelength of the nearest optically-active absorption band SCHEME 8.26

(E) CIRCULAR DICHROISM (CD) In contrast to ORD, CD is due to the difference in absorption of right and left cpl (εR ≠ εL, where ε is the molar absorption coefficient).

The optically active medium has an unequal molar absorptivity coefficient ε for left and right circularly polarized light. This difference in molar absorptivity (Scheme 8.27) is termed circular dichroism. ∆ε = εL – εR ≠ 0 SCHEME 8.27

DIFFRACTION METHODS

217

Circular dichroism changes linearly-polarised light into ellipticallypolarised light, i.e., the resultant electric field vector traces an elliptical path (Scheme 8.28)

SCHEME 8.28

When a linearly polarised light beam passes through a chiral medium, its two circularly polarised components show different refractive indices and different absorption coefficients which give rise to two chiroptical properties. These are circular birefringence and circular dichroism respectively. Although these two properties are interrelated their effects are best treated separately.

The shape and appearance of a CD curve has close similarity with that of an ordinary (UV–vis) absorption curve of the electronic transition to which it corresponds. CD curves may however, be positive or negative. CD curves plot ∆ε (or [θ]) vs. wavelength. They are difference spectra representing the difference in absorption of left and right circularly polarized light, hence the signed nature of the curve. Each CD curve for each electronic transition also displays a positive or negative Cotton effect. For every CD Cotton effect there exists a corresponding ORD Cotton effect of similar sign to show their apparent similarity in pattern (Scheme 8.29)

Both CD and ORD phenomena are linked to chiral substances and is not observed for achiral compounds or racemic mixtures.

Positive (I) and negative (II) CD Cotton effects of an isolated absorption band with their respective ORD curves superimposed along with their UV electronic absorption. The wavelength (λ0) at the sign change crossover point of the ORD curve corresponds to λmax of the CD curve. SCHEME 8.29

As εL is not equal to εR (See, Scheme 8.27) ε will no longer oscillate along a single line but will trace out the ellipse

In the relationship εL – εR = ∆ε, εL and εR are the molar absorption coefficients for left and right cpl, respectively, at the absorption wavelength. The sign of ∆ε defines the sign of the CD. The signs of the CD curve and that of the corresponding ORD curve in the region of an anomaly are the same. At a given wavelength, both phenomena, ORD and CD, reflect the interaction of polarized light with the same chirotopic chromophore.

218

Generally, the CD peaks are several orders of magnitude smaller than absorption peaks. In contrast to an UV absorption band, a CD band is signed as the difference (εL – εR) can be either positive or negative.

BIOPHYSICAL CHEMISTRY

shown as in (Scheme 8.30). The difference in ε values is measured according to this equation. [θ] = 3300(εL – εR) where,

[θ] = the molar ellipticity (deg cm2 dmol–1) of the optically active compound SCHEME 8.30

On passage through the sample in a region where absorption occurs, the incident linearly polarized light is converted into elliptically polarized light, that is, the resultant electric field vector traces an elliptical path (Scheme 8.31). Elliptically polarized light is the most general form of polarized light; linear and circular polarization are special cases of elliptical polarization.

Variation of E incident circularly polarised light for circular dichroism. The E vector traces out an ellipse. The major axis of the ellipse lies along the x′-axis and forms the angle of rotation, α, to the original plane of polarization, the xz plane. SCHEME 8.31

(F) STRUCTURE OF BIOPOLYMERS (PROTEINS) CD SPECTRA

FROM

ORD

AND

The following points may be noted: l Both ordinary absorption (UV–vis) spectroscopy and chiroptical (ORD and CD) spectroscopy are based on

DIFFRACTION METHODS

l

l

l

219

the same photophysical process (the promotion of an electron from a ground state orbital to an excited state orbital). These differ in that the (UV–vis) measures the absorption of ordinary light associated with the promotion of an electron, while the chiroptical spectroscopy ORD and CD measures the absorption of left and right circularly polarized light and displays the difference in their absorption. ORD is observed at wavelengths far removed from absorption bands whereas CD is encountered in the region of absorption bands. The CD peaks are discrete and have higher resolution. Thus, CD studies have advantages over ORD studies. Generally speaking it seems reasonable to state that if a choice must be made, then CD is preferred over ORD, as the inherent simplicity of CD spectra recommends them over ORD for most of applications. Both ORD and CD are important tools for studying the conformation of biomolecules in solution. The use of CD spectroscopy, and to a somewhat lesser extent ORD, is especially important in the study of macromolecules because it is one of the few spectroscopic techniques that is able to study the helical secondary structure that characterizes such molecules. In contrast to X-ray diffraction techniques, CD and ORD provide information about the conformations of biopolymers in solution. The secondary structure content (helix, sheet and coil) in macromolecules can be studied by the mean residue rotation, according to the Moffit-Yang equation (Scheme 8.32). The value of b0 is used to study the secondary structure, e.g., at λ0 = 212 nm: [m′] λ = a0

where,

2

λ02

λ −

λ02

+ b0

2

λ04

(λ − λ02 )2

[m′] = the mean residue rotation a0 = an environment-dependent coefficient b0 = solvent-independent coefficient SCHEME 8.32

220

BIOPHYSICAL CHEMISTRY l l l l

Polypeptides get organised into their principal conformational forms. The atoms within the box constitute a rigid planar unit.

Recall that CD is highly sensitive to the interaction between neighbouring chromophores. In polypeptides and in polynucleotides e.g., interaction between adjacent amide groups and adjacent aromatic nuclei, respectively, during light absorption accounts for most of the intensity of the CD bands.

b0 = 0 for random coil b0 = – 630 for 100% right-handed helix. Left-handed helix and β-sheet have + b0 values. Recall that the optical activity of chiral molecules increases towards shorter wavelengths due to π – π* and σ – σ* transitions. The π – π* and n – π* transitions of amino acids are at 195 and 225 nm, respectively. The Cotton effect around 220 nm is used for the detection and estimation of α-helices in proteins. The α-helical and β-pleated forms of proteins display different and fairly large CD extrema around 220 nm while the random coil has still different and much weaker Cotton effect. The formation of an α-helix is a cooperative phenomenon when a large number of weak H-bonds are involved. It does not form if the polypeptide chain is too short (less than a heptamer) and the transition of a random coil to an α-helix with increase of the chain length is shown by CD and ORD spectra. Thus when intramolecular hydrogen bonding prevails, the polymer chain coils into an α-helix. There is a dramatic increase in the intensity of the Cotton effect in the vicinity of 220 nm under such circumstances. Formation of α-helical structure allows absorption of radiation by numerous properly oriented like chromophores. This leads to large CEs (Cotton effect) by the interaction of the chromophores with near neighbours. The CD spectroscopy allows the presence of the α-helices in proteins to be inferred with greater certainty compared to any other secondary structural features (Scheme 8.33). The peptides organise to attain stereoregular forms with the number of peptide units in the polymer reaching a range of 5–12. The polypeptide molecules organize themselves by extending the chains and by hydrogen bonding intermolecularly (between NH and C = O groups) with like chains. This arrangements either in parallel or anti-parallel ways will give βpleated forms. The CD bands then increase in intensity and change in sign, the CD spectrum becoming virtually enantiomeric with that of the random coil form (Scheme 8.33).

DIFFRACTION METHODS

221

-Helical form of a biopolymer, with typical increase in the intensity of cotton effect

70 -pleated sheet

50 40 30

[] x10

–3

2

Degree cm /Decimole

60

20 10 0 –10 –20 –30 –40 190

200

210

220

230

240

250

 (nm) Random coil alsomost enantiomeric with the CD spectrum of -pleated sheet

SCHEME 8.33 l

A study of the secondary structural feature of proteins, is generally studied by the treatment of the CD spectrum as a linear combination of ellipticities at specified wavelengths contributed by every conformational form. Such analyses have been refined to include additional conformations which may be present in proteins e.g., β turns. The relation (Scheme 8.34) for such studies is now available in the data handling software of contemporary CD spectrometers. Solution of equation (Scheme 8.34) with ellipticity data determined at different wavelengths provides the f values. [θ]λ = fH[θ]H + fβ[θ]β + ft[θ]t + fR[θ]R

where,

[θ]λ = the mean residue ellipticity at a given wavelength (the ellipticity of the macromolecule per peptide unit)

222

BIOPHYSICAL CHEMISTRY

f = fraction of each conformational form present in the protein other [θ] terms = the corresponding ellipticities for the α-helical H, β-form β, β-turn t, and unordered R forms, respectively. SCHEME 8.34 l

Variations in secondary structures in proteins with change in pH and the solvents different H-bond forming ability can also be studied from CD or ORD. The CD and ORD curve of a protein being studied is compared with reference curves and are thus calibrated regarding percentage of secondary structures. PROBLEMS AND EXERCISES

1. Describe the Zimm’s method for determining the molecular mass of a biopolymer. How this method differs from Debyemethod? 2. Discuss as to how the molecular mass of a compound can be determined using the concept of light scattering. 3. What is turbidity? Online the details of its relation with molecular mass of a biopolymer. 4. What is the relation between scattered light and molecular mass? 5. Write short notes on: (a) Bragg equation and X-ray diffraction (b) X-ray diffraction and macromolecules 6. Discuss briefly optical properties in relation to structure of biopolymers. 7. Discuss small angle and large angle X-ray scattering in relation to structure of biopolymers. 8. Write short notes on: (a) Cotton effect (b) ORD curves (c) ORD and biopolymers 9. What is CD? How it is better than ORD to determine the shape of proteins? 10. Discuss X-ray diffraction and structure of a macromolecule. 11. How Bragg equation when applied in X-ray diffraction can give information about the nature of a macromolecule? 12. What is Brownian motion? Discuss PSC. 13. What is photon correlation spectroscopy? Discuss its used in the study of macromolecules.

INDEX

223

INDEX

5-fluorouracil 38 5-Fu 38 5–methyluracil 40 δ-guanidino group 112 α helical 80 α-helical structure 16, 85 α-helix 15, 17, 18, 86, 90, 206 α-helix formation 19 α-Keratin 23 β-sheet 90 2D NMR 93

A A digestive enzyme 32 Acelylcholine 152, 157, 159 Acid base catalysis 27 Actin 23, 196 Action potentials 158 Activated amino acid 47 Activation barrier 56 Activation energy 56 Active transport 4, 51, 148 Adenine 39 Adenosine triphosphate (ATP) 5 ADP 7, 51, 62, 66 Air oxidation 22 Alanine 13 Albumin 20 Alcohol dehydrogenase 36, 54 Amide bond 15 Amino acids 12, 13

Amorphous domain 209 Amorphous polymer 187 AMP 47 Amphipathic 116 Anabolic processes 57 Anabolism 51, 68 Animal glues 90 Anomeric carbon 29 Antibodies 23 Anticodon 46 Anticodon triplet 46 Anticondon arm 46 Antiparallel β sheet 20, 83 Antiport system 144 Aqueous environment 118 Arginine 15, 112 Ascorbate 11 Asparagine 14 Aspartic acid 15 ATP 4, 7, 47, 51, 52, 62, 64, 66, 76 Average molecular mass 201 Axon 157

B β sheet 19, 90 Bacterial cell wall 29 Bases in nucleaic acids 39 Bilayer lipid aggregates 140 Biochemical reactions 56 Biochemical reactions in a cell 66 Bioenergetic reactions 72

223

Bioenergetics 51 Biological cell 1 Biological oxidation 53 Biological oxidation–reduction 69 Biological phosphate compounds 67 Biological significance (pKa and pH) 127 Biologically important reactions 73 Biomolecules 105 Biopolymers 52 Biosynthesis of macromolecules 52 β-oxidation of fatty acids 7 β-pleated sheet 15 β-pleated structure 20, 86 Bragg’s-law 209 Brownian motion 210 β-turn 88 Buffers 130

C Cage structure 119 Carbocation 29 Carboxypeptidase A 113 Cardiac muscle 197 Carrier proteins 4, 144 Catabolic 52 Catabolism 51, 57, 68 Catalase 10 Catalysis by proximity 27 Catalysis by strain 28 CD 212, 215

224

CD spectra 90 Cell membrane 1, 136 Cell wall 1 Cellular metabolic activity 53 Cellular metabolism 52 Central dogma 44 Centrifugal force 167 Chain dimensions 95 Chain end 98 Chaperone proteins 94 Chaperones 94 Characterization of polymers 200 Chemical energy 52 Chemical potential 151 Cholesterol 137, 139 Choline 139 Chromosomes 2, 40 Chymotrypsin 27 Circular dichroism 216 Citric acid cycle 7, 8, 11 Clausius-Mossotti equation 110 Codon 47 Coenzymes 24 Cofactors 24 Cohesive energy density 188 Cohesive force 188 Collagen 23 Collagen helix 83 Competitive inhibitor 35 Concentration gradient 4, 160 Configuration 79 Configurational statistics 95 Conformation 79-80 Conformational changes in biopolymers 173 Conjugate acid 127 Conjugated base 127 Controlled switches 87 Cotton effect 216 Coulomb’s law 111 Coupled reactions 56 Covalent bond 105 Covalent catalysis 28, 30 Covalent disulphide bonds 21 Creatine phosphate 68, 198 Cristae 6

BIOPHYSICAL CHEMISTRY

Crystalline domain 209 Crystalline polymer 187 C-terminal 16 C-terminal peptide 113 C-terminus 86 Cyanogen bromide 85 Cysteine 14 Cytochrome 11 Cytochrome c 23 Cytochrome oxidase 9 Cytochrome reductase 9 Cytoplasm 10, 136 Cytosine 39 Cytoskeletol proteins 11 Cytoskeleton 11, 12 Cytosol 1, 2, 11, 88 Cytosolic NADH 11

D D-Amino acids 80 Debye method 204 Degree of dissociation 126 Denaturation 31 Denaturation of proteins 173 Denatured enzyme 31 Dendrites 157 Deoxyribonucleotides 13 Diffusing-gas 101 Diffusion coefficient 211 Digitoxigenin 155 Dihedral angles 81 Dihydroxyacetone phosphate 11 Dipole induced dipole 107 Dipole/Induced-dipole Interaction 109 Dipole-dipole interactions 21, 106, 108 Disordered H2O molecules 115 Dissociation of – H2O 126 – a biopolymer 185 – a low molecular weight solute 183 – a macromolecule 184 Disulphide bonds 20, 90, 118 Disulphide bridges 22 Disulphide cross links 173

DNA 12, 13, 40, 43, 52 DNA double helix 41 DNA polymerases 45 DNA strands 123 Domain 86 Donnan effect 160, 194 Donnan equilibrium 194 Donnan membrane equilibrium 193 Donnan ratio 194 Driven active transport 150 Drug discovery 36

E E. coli 1 Eclipsed 80 Edman’s degradation 85 E-FAD 12 E-FADH2 12 Effect of pH 31 Effect of temperature 30 Electric potential 151, 156 Electrical gradients 5 Electrical potential across the membrane 142 Electrical potential gradient 160 Electrical signal 158 Electrochemical gradients 4, 152 Electrochemical potential 5, 160 Electrochemical potential of Na+ 151 Electron carriers 8, 9, 72, 75 Electron transfer 70 Electron transfer chain (ETC) 6, 8, 75 Electron transport 71-72 Electrostatic interactions 21, 108, 111, 114, 118, 125 Electrostatic repulsion 19 Elliptically polarized light 217-218 Enantiotopic faces 26 Enantiotopic ligands 26 Endergonic 9 Endergonic reactions 57, 59 Endoplasmic reticulum 1 Endoplasmic reticulum (ER) 9 Endothermic 183 Endothermic mixing 188 Endothermic reaction 59

INDEX

225

End-to-end distance 97, 104 Energetically favourable reaction 62 Energy changes during a reaction 55 Energy for life 75 Enthalpy 58, 182, 183 Enthalpy change 125 Entropy 58, 116, 117, 182, 183 Entropy change 121 Entropy of mixing 189, 190 Enzyme activity 30 Enzyme alcohol dehydrogenase 36 Enzyme inhibition 35 Enzyme inhibitors 35 Enzyme-catalyzed reaction 55 Enzymes 13 Enzymes as catalysts 25 Enzyme-substrate complex 115 Equilibrium constant 60 Esterification of tRNA 48 ETC 70, 75 Ethanolamine 139 Eukaryotes 1 Exergonic 9 Exergonic reactions 57-58 Exothermic 183 Exothermic reactions 59

F Facilitated diffusion 146, 155, 160 Facilitated transport 4 F-actin 197 FADH 69 Fatty acids 13 Ferric ion 54 Ferrous ion 54 Fibrinogen and thrombin 23 Flavin 70 Flavorproteins 9 Flory-huggins theory 189 Flow of genetic information 44 Fluid mosaic model 141 Folding of proteins 105 Food energy 8 Forbidden conformations 83 Force of muscle contraction 197 Formaldehyde 36

Formation of – activated tRNA 48 – of ATP 197 Fractional precipitation 186 Free energy 52, 55, 58 Free energy change 5, 54, 56, 58, 115 Freely-Jointed chains 96 Frictional drag 167 From ORD and CD 218 Fumarate 34 Function of nucleic acids 44 Function of proteins and enzymes 22

G Gaussian chains 100 Gaussian distribution function 98 Gel electrophoresis 178 Gene 2 Genetic information 13, 24, 42 Gibbs energy 151 Gibbs free energy 183 Gibbs free energy change 55 Globular proteins 19, 20, 88 Gluconeogenesis 11 Glucose 53, 145 Glucose 6-phosphate 57, 63 Glucose transport 155 Glucose transporter 147 Glucose uptake 146 Glucose—Na+ symport 148 Glue 90 Glutamic acid 15, 19 Glutamine 15 Glyceraldehyde 3-phosphate 11 Glycerol 137-138 Glycerol 3-phosphate dehydrogenase 11 Glycine 15, 79 Glycogen 13 Glycolipids 139 Glycolysis 7, 11, 12, 52 Glycospingolipids 137 Golgi apparatus 10 Golgi complexes 1 Good solvent 186

Guanidine group 112 Guanidinium ion 112 Guanine 39

H Heat of dissolution 187 Helical strands in DNA 120 Helical structure 17 Heme enzymes 11 Heme prosthetic group 206 Hemoglobin 23 Henderson-Hasselbalch equation 129 Hereditary information 40 Hexokinase 148 High energy phosphate 67 High energy phosphate bonds 69 Histidine 15 Human erythrocytes 66 Hydrodynamic length 104 Hydrogen acceptor 122 Hydrogen bonding 121 Hydrogen bonds 17, 21, 41, 111, 118 Hydrogen donor 122 Hydrogen ion titration curves 125 Hydrogen-bond acceptor 18 Hydrogen-bond donor 18 Hydrolases 24 Hydrolysis of ATP 63 Hydrophobic bonds 117 Hdrophobic environment 121 Hydrophobic interactions 21, 116, 118, 119 Hydrophobic interactions and membranes 118

I Increase in entropy 115, 120 Inhibitors of Na+/K+ ATPase 154 Inosile 139 Insulin 23 Integral protein 3 Interactions of biological molecules 124 Intermolecular interactions 105

226

BIOPHYSICAL CHEMISTRY

Intracellular concentrations of Na+ and K+ ions 150 Intrinsic viscosity 95, 172 Ion channel opening 151, 153 Ion channel protein 152 Ion-dipole interactions 106, 111 Ionic bond 111 Isoleucine 14, 19, 80 Isomerases 24, 94

K Ka 128 Keratin 18 Kinetics of enzymes 30 Kinetics of simple and facilitated diffusion 145 Koshlands induced fit model 28 Krebs cycle 7 Kuhn segment 104

L Laws of thermodynamics 52 Left handed α-helices 87 Left-handed α-helix 83 Lennard–Jones expression 108 Leucine 14 Ligases 24 Light scattering by macromolecules 201 Light scattering 200, 203 Light scattering calibration constants 203 Lineweaver and Burk method 34 Lineweaver-Burk plot 33 Lipids 13, 52 London equation 107 London forces 106-107 London or dispersion forces 106 Loss of electrons 71 Loss or gain of free energy 57 Lyases 24 Lysine 15 Lysosomes 1, 10 Lysozyme 24, 29, 132

M ‘M’ compartment 6 Mechanical work 51 Mechano-chemical system 195 Mechanoenzyme 197 Membrane channel 88 Membrane electrical potential 156 Membrane osmometry 174 Membrane potential 151 Membrane potential (Em) 71 Messenger RNA 44, 46 Metabolic energy 52 Metabolic enzymes 11 Metabolic oxidative reactions 72 Metabolism 57 Methane 117 Methanol 36 Methanol poisoning 36 Methionine 14 Micelle 141 Michaelis constant (KM) 33 Michaelis-Menten equation 32, 146 Mitochondria 1, 136 Mitochondrion 5, 8 Mitrochondrial matrix 7 Moffit-Yang equation 219 Molar mass 163, 172 – from sedimentation velocity method 165 – of a polymer 162 – of macromolecules 162 Molecular polarization 110 Molecular refractive index 111 Molecular weight 162 – of a polymer and dissolution 185 Molten globule 92 Monodisperse and polydisperse polymers 164 Monosaccharides (glucose) 13 Motif 86 Movement of glucose 148 mRNA 2, 43 mRNA template 44 Muscle contraction 196 Muscular contraction 57, 195 Mylein 157

Myoglobin 23, 164, 206 Myoglobin crystal 206 Myosin 23, 196

N Na+/K+ ATPase 150, 152 NAD+ 26 NADH 7, 8, 9, 12, 26, 69 NADH-Q reductase 9 Native (active) conformation 31 Native conformation 22, 88 Native state 22 Nature of active site 35 Negative DG 57 Nernst equation 76 Nerve conduction 156 Nerve impulse 156, 158 Nerve impulse conduction 57 Nerve impulses 152 Neurons 156, 158 Neuro-transmitter 152, 159 Newly synthesized DNA 45 Nicotinamide 69 Non-competitive inhibitors 36-37 Noncovalent forces 105 Non-enzymecatalyzed reaction 55 Non-solvent 186 N-terminal 15 N-terminus 86 Nucleic acids 38, 52, 120 Nucleoid 2 Nucleolus 3 Nucleoside 39 Nucleotides 39 Nucleus 2 Number average molar mass 163

O ‘O’ compartment 6 Optical activity 80 Optical rotatory dispersion 215 Optimum pH 31 ORD 90, 212, 215 Ordered water molecules 117, 120 Organelles 1, 136 Osmotic pressure 192, 198



P





S Q

R



228

Serum albumin 23 Shape of a molecule 173 Silk 20 Simple and facilitated membrane transport 149 Simple diffusion 160 Single electron 70 Sites of potential hydrogen bonding 124 Smooth endoplasmic reticulum 10 Smooth muscle 197 Solubility parameter 188 Solute transport 136 Specific transport proteins 3 Specific viscosity 172 Sphingomyelin 138 Sphingosine 138, 139 Spiral protein secondary structure 17 Stable conformations of biopolymers 124 Staggered 80 Standard free changes in biochemical reactions 61 Standard free energy change 5, 58 Statistical calculations 101 Statistical mechanics 95, 97 Statistical mechanics in biopolymers 95 Stereo-selectivity 25 Stereo-specificity 25 Steric crowding 19 Steric hindrance 20 Steric match 113 s-trans configuration 81 Structure of a solid polymer 209 Structure of biopolymers 218 Structure of nucleic acids 38 Succinate 34 Supersecondary structure 86 Svedberg units 168

BIOPHYSICAL CHEMISTRY

Swollen gel 185 Swollen mass 185 Symport system 144 Symporters 148 Synaptic vesicles 157 Synthesis of ATP 71 Synthetic reactions 57

T Tertiary conformation of a protein 21 Tertiary structure of proteins 118 Thermal motion 110 Thermodynamic driving force 17 Thermodynamic segment 96, 104 Thermodynamic stability 125 Thermodynamic treatment of membrane transport 160 Thermodynamics of biopolymer solutions 181 Threonine 14, 19, 80 Thymene 38 Thymine 39 Titration curves 130 – of amino acids 131 Torsion angles 81 Transfer RNA 44, 46 Transferases 24 Transition state 55 Translation 46 Transmembrane electrical potential 156 Transmembrane potential 151 Transport across membranes 142, 148 Transport of – a protein 88 – glucose 3 – ions 3 – ions through membranes 160 Transporters 144

True solution 185 Trypsin 85 Tryptophan 14 Turbidity 202 Tyrosine 14

U Ultracentrifugation 165 Unfolding of proteins 88 Uniport system 144 Uracil 38, 40

V Valine 14, 19 Van der Waals – contact distance 124 – forces 106, 107, 111, 124 – interactions 17, 120 – radii 19 Vertebrate muscle 68 Viruses 12 Viscosity 172 Viscosity measurements 172

W Watson and Crick 42 Weight-average molar mass 163

X X-ray – crystallography 205 – diffraction 205 – diffraction patterns 208 – pattern 18

Z Zimm method 204 Zwitter ion 15