http://www.cambridge.org/9780521815246

This page intentionally left blank

Methods in Molecular BiophysicsStructure, Dynamics, Function

Our knowledge of biological macromolecules and their interactions is based onthe application of physical methods, ranging from classical thermodynamics torecently developed techniques for the detection and manipulation of singlemolecules. These methods, which include mass spectrometry, hydrodynamics,microscopy, diffraction and spectroscopy, electron microscopy, moleculardynamics simulations and nuclear magnetic resonance, are complementary; eachhas its specific advantages and limitations.

Organised by method, this textbook provides descriptions and examples ofapplications for the key physical methods in modern biology. It is an invaluableresource for undergraduate and graduate students of molecular biophysics inscience and medical schools, as well as research scientists looking for anintroduction to techniques beyond their speciality. As appropriate for thisinterdisciplinary field, the book includes short asides to explain physics aspects tobiologists and biology aspects to physicists.

IGOR N. SERDYUK was born in Odessa, Ukraine, and studied physics at OdessaState University. Following research as a postgraduate student at the Departmentof Polymer Physics, Institute of High Molecular Weight Compounds, Leningrad,he obtained his Ph.D. in 1969. He then studied the physics of proteins as a juniorresearcher at the Laboratory of Protein Physics, Institute of Protein Research,USSR Academy of Sciences, Pushchino, rising to lead his own research groupthere and gaining his D.Sc. (Physics and Mathematics) from Moscow StateUniversity (1981). Since then he has been head of the Laboratory ofNucleoprotein Physics at the Institute of Protein Research, Pushchino. In 1985 hewas awarded the USSR State Prize for Science and Technology and wasappointed Full Professor of Molecular Biology in 1993. He has many years ofexperience teaching molecular biophysics in Moscow University.

NATHAN R. ZACCAI was educated in the French school system and attendedEdinburgh University, where he gained a B.Sc. (Physics, 1997) and subsequentlycompleted his D.Phil. at the University of Oxford (Biochemistry, 2001). He hasundertaken research in immunology, virology and structural biology, specialisingin X-ray crystallography. His initial work was on the structural biology of cellsurface receptors involved in the immune system. He is currently based in thedepartment of pharmacology, at the University of Bristol, where he is developinga research programme on the molecular basis of ion-receptor activation.

ii

JOSEPH (GIUSEPPE) ZACCAI was born in Alexandria, Egypt, and educated inEnglish language schools there and in Rome, and at the University of Edinburgh,where he obtained his B.Sc. (1968) and Ph.D. (1972) in Physics. A postdoctoralfellowship at the Brookhaven National Laboratory, New York, allowed him topursue new interests in the biophysics of biological membranes and theapplication of neutron scattering methods in biology. He continued to developthese interests upon returning to Europe, first at the Institut Laue Langevin (ILL)in Grenoble, widely recognised as the foremost neutron scattering institute in theworld. He holds the position of Directeur de Recherche with the Centre Nationalde la Recherche Scientifique (CNRS) of France, and has been head of theLaboratory of Molecular Biophysics of the Institut de Biologie Structurale (IBS)in Grenoble since it was founded in 1992. Joe Zaccais current research interestsinclude the exploration of the physical chemical limits for life, especially inrelation to the role of water and salt, molecular adaptation, protein dynamics,structure and stabilisation in organisms that live under extreme conditions ofsalinity, temperature, pressure, and exobiology. He has many years of experienceteaching biology to physicists and physics to biologists, and was the first tointroduce these courses at the undergraduate and graduate level at the Universityof Grenoble in the 1980s.

I first asked what methods in molecular biophysics I would expect to use as abiochemist and structural biologist. This text book provides an introduction to thephysics of each of [the techniques used by my own group] as well as a review of theapplications. . . . [It] will be in demand by third year undergraduates in the manycourses run by physicists to introduce them to biological themes. It would also be usedby the many post-graduate students doing . . . research degrees as well aspost-doctorals in chemical biology, biochemistry, cell biology and structural biologyresearch groups. . . . In summary, this is a valuable contribution to the field. . . . this isan area which has advanced tremendously and the major texts in biophysical methodsare now simply out of date. The text covers the methods that young researchers andsome undergraduates will wish to learn. I am sure that it will find itself on the shelvesof many laboratories throughout the world. There is nothing quite like it at the moment.

Sir Tom Blundell FRS, FMedSci,Professor and Head, Department of Biochemistry, University of Cambridge

Thank you very much for giving me the opportunity to preview this wonderful textbook. It has outstanding breadth while maintaining sufficient depth to follow modernexperiments or initiate a deeper understanding of a new subject area. I love thePhysicists and Biologists Boxes to address specific subjects for researchers withdifferent backgrounds. This is one of the most comprehensive and highly relevanttexts on biophysics that I have encountered in the last 10 years, clearly written andup-to-date. It is a must-have for biophysicists working in all lines of research, andcertainly for me.

Nikolaus Grigorieff, Professor of Biochemistry, Brandeis University

[This is] a wonderful up-to-date treatise on the many and diverse methods used . . . inthe fields of molecular biophysics, physical biochemistry, molecular biology,biological physics and the new and emerging field of quantum nanobiology. The widerange of methods available . . . in these multidisciplinary fields has been overwhelmingfor most researchers, students and scientists [who fail] to fully appreciate the utilityand usefulness of the methods [other than their own]. [In many cases, this has] createddisagreements and . . . controversy. The only way to understand and appreciate fullythe problems in quantum nanobiology and their complexity is to utilize and fullyunderstand the many diverse methods covered by the authors in this very finetreatise . . . [It] should be in the library of any serious researcher in the many diversemultidisciplinary fields working on problems in quantum nanobiology. . . . They willbe greatly rewarded by an ability to see and view the problems and their complexitythrough different perspectives, aspects and points of view, . . .

Karl J. Jalkanen, Associate Professor of Biophysics,Quantum Protein Centre, Technological University of Denmark

This most welcome text provides an up-to-date introduction to the vast field ofbiophysical methods. Written in an accessible style with an eye to a broad audience, itwill appeal to biologists who wish to understand how to determine howmacromolecules function and to scientists with a physics or physical chemistrybackground who wish to know how measurement of the physical world can impact ourunderstanding of biological problems. The book succeeds in unifying disparateapproaches under the aegis of developing an understanding of how macromoleculeswork. Importantly, the text also provides the relevant historical background, aninvaluable guide that will aid in the appreciation of what has gone

before and should serve to orient them towards the future and what may be possible. Itis a valuable resource for novice and seasoned biophysicists alike.

Dan Minor, California Institute for QuantitativeBiomedical Research University of California, San Francisco

Methods in Molecular Biophysics is now the book I consult first when faced with anunfamiliar experimental technique. Both classic analytical techniques and the latestsingle-molecule methods appear in this single comprehensive reference.

Philip Nelson, Department of Physics,University of Pennsylvania, and author of Biological Physics (2004)

The authors provide an overview of many of the major recent accomplishments in theuse of physical tools to investigate biological structure. There are interesting historicaland biographical comments that lead the reader into understanding contemporaryconcepts and results. The book will be valuable both for students and researchscientists.

Michael G. Rossmann,Hanley Professor of Biological Sciences, Purdue University

The melding of physics, chemistry and biology in modern science has changed ourview of the natural world and opened avenues for detailed understanding of the originof biological regulation. Methods in Molecular Biophysics provides an up-to-dateview of classical biophysics, theory and practice of modern chemical biology andrepresents an essential text for the interdisciplinary scientist of the 21st Century. Agreat achievement and presentation awaits the student who reads this book, along withan excellent reference for the seasoned practitioner of biophysical chemistry.

Milton H Werner,Laboratory of Molecular Biophysics, The Rockefeller University

The methods, concepts, and discoveries of molecular biophysics have penetrateddeeply into the fabric of modern biology. Physical methods that were once seeminglyarcane are now commonplace in modern cell biology laboratories. This well written,thorough, and elegantly illustrated book provides the connections between molecularbiophysics and biology that every aspiring young biologist needs. At the same time, itwill serve physical scientists as a guide to the key ideas of modern biology.

Stephen H. White, Professor, Department ofPhysiology and Biophysics, University of California at Irvine

Methods in Molecular Biophysics offers a well-written, modern and comprehensivecoverage of the properties of biological macromolecules and the techniques used toelucidate these properties. The authors have done a great service to the biophysicscommunity in providing a long-needed update and expansion of previous texts onanalysis of biological macromolecules. The choice and organization of material isespecially well done. This book will be of considerable value not only to students, butalso, due to the scope and breadth of coverage, to experienced researchers. Ienthusiastically recommend Methods in Molecular Biophysics to anyone who wishesto know more about the techniques by which the properties of biologicalmacromolecules are determined.

David Worcester,Department of Biological Sciences, University of Missouri Columbia

Methods inMolecular BiophysicsStructure, Dynamics, Function

Igor N. SerdyukInstitute of Protein Research, Pushchino,Moscow Region

Nathan R. ZaccaiUniversity of Bristol

Joseph ZaccaiInstitut de Biologie Structurale and Institut LaueLangevin, Grenoble

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So Paulo

Cambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UK

First published in print format

ISBN-13 978-0-521-81524-6

ISBN-13 978-0-511-27792-4

Cambridge University Press 2007

2007

Information on this title: www.cambridge.org/9780521815246

This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

ISBN-10 0-511-27792-X

ISBN-10 0-521-81524-X

Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

hardback

eBook (EBL)

eBook (EBL)

hardback

http://www.cambridge.org/9780521815246http://www.cambridge.org

To Olga, Brinda, Missy.

vii

Contents

Foreword by D. M. Engelman page xiForeword by Pierre Joliot xiiiPreface xv

Introduction Molecular biophysics at the beginning of thetwenty-first century: from ensemble measurements tosingle-molecule detection 1

Part A Biological macromolecules and physical tools 19Chapter A1 Macromolecules in their environment 21Chapter A2 Macromolecules as physical particles 38Chapter A3 Understanding macromolecular structures 65

Part B Mass spectrometry 109Chapter B1 Mass and charge 111Chapter B2 Structure function studies 136

Part C Thermodynamics 171Chapter C1 Thermodynamic stability and interactions 173Chapter C2 Differential scanning calorimetry 194Chapter C3 Isothermal titration calorimetry 221Chapter C4 Surface plasmon resonance and interferometry-based

biosensors 234

Part D Hydrodynamics 247Chapter D1 Biological macromolecules as hydrodynamic particles 249Chapter D2 Fundamental theory 268Chapter D3 Macromolecular diffusion 318Chapter D4 Analytical ultracentrifugation 339Chapter D5 Electrophoresis 388Chapter D6 Electric birefringence 414Chapter D7 Flow birefringence 435Chapter D8 Fluorescence depolarisation 446Chapter D9 Viscosity 466

ix

x Contents

Chapter D10 Dynamic light scattering 481Chapter D11 Fluorescence correlation spectroscopy 505

Part E Optical spectroscopy 517Chapter E1 Visible and IR absorption spectroscopy 519Chapter E2 Two-dimensional IR spectroscopy 562Chapter E3 Raman scattering spectroscopy 573Chapter E4 Optical activity 601

Part F Optical microscopy 625Chapter F1 Light microscopy 627Chapter F2 Atomic force microscopy 641Chapter F3 Fluorescence microscopy 658Chapter F4 Single-molecule detection 683Chapter F5 Single-molecule manipulation 709

Part G X-ray and neutron diffraction 765Chapter G1 The macromolecule as a radiation scattering particle 767Chapter G2 Small-angle scattering 794Chapter G3 X-ray and neutron macromolecular crystallography 838

Part H Electron diffraction 883Chapter H1 Electron microscopy 885Chapter H2 Three-dimensional reconstruction from

two-dimensional images 904

Part I Molecular dynamics 929Chapter I1 Energy and time calculations 931Chapter I2 Neutron spectroscopy 948

Part J Nuclear magnetic resonance 969Chapter J1 Frequencies and distances 971Chapter J2 Experimental techniques 1000Chapter J3 Structure and dynamics studies 1039

References 1076Index of eminent scientists 1103Subject index 1108

Foreword

D. M. ENGELMAN

It might be thought that this book is about methods, and, as is often supposed,that the field of biophysics is defined as a collection of such methods. But, as iscarefully developed in the text, there is a deeper significance -- methods definewhat we (provisionally) know about the world of biological molecules, and bio-physics is a field that integrates pieces of information to give substance to ourexplanations of biology in terms of macromolecular space and time: structure,interactions and dynamics. Two interrelated ideas that biophysicists employ arethe structure--function hypothesis and evolution.

The structure--function hypothesis is crisply discussed in the lucid introductionto the book: the idea is that each macromolecule coded by the genome has afunction, and that the function can be understood using the chemical structure,interactions and dynamics of the macromolecule. Evolution forms the foundationof this reductionist view, since functionality is the basis of natural selection. Thus,biophysical methods teach us, within the limits of the information they give, aboutfunction and evolution. A particular hope, which has been rewarded with a greatdeal of success, is that understanding particular cases will lead to generalisingideas -- base pairing in nucleic acids, oxygen binding by haem, self-associationof lipids to create bounded compartments, for example.

A book that teaches the methods well creates the intellectual framework ofour understanding, and can guide the field. Earlier efforts by Cohn and Edsall,Tanford, Edsall and Wyman, and Cantor and Schimmel have served this importantpurpose in the past, but the advance of time and technology has diluted the forceof these classic works in contemporary biophysics, both in the teaching andthe practice of the field. How welcome, then, a clearly written, thoughtful andmodern text that will serve well, both in formal courses and as a reference. Theauthors have built each method from its fundamental premises and principles,have successfully covered an impressive span of topics, and will be rewarded byattention from an audience that hungers for the next defining text in molecularbiophysics.

New Haven

xi

Foreword

PIERRE JOLIOT

As the authors of this book have written in the Introduction the ideal biophys-ical method would have the capability of observing atomic level structures anddynamics of biological molecules in their physiological environment, i.e. in vivo.Such a method does not exist, of course, and it will probably never exist becauseof insurmountable technical constraints. Characterisation of structural and func-tional properties of biological molecules requires the concerted application of anarsenal of complementary techniques. We note that in practice, however, manyhighly productive molecular biophysics groups are concerned by a single tech-nique that they push to its extreme limits. Such groups develop an essentiallymethodological approach, in which they seek to characterise by their techniqueas many biological molecules as they can. High-throughput crystallography orstructural genomics is an example of this type of biophysics. Its aim is to pro-vide a precious data base of information on three-dimensional protein structures,analogous to that on primary structures from genome sequence -- a data base thatwill be used intensively by all biologists.

A different approach consists in tackling a biological problem with a multi-disciplinary approach, in which molecular biophysics plays a dominant role. Theaim of this approach is to define as finely as possible the functional, structural,and dynamic properties of the molecules implicated in the physiological pro-cess as well as their interactions. It is this type of approach that is implicitlydefended by the book, which provides an important and exhaustive overviewof biophysical techniques currently available, and discusses their strengths andlimitations. The usual first step is to study each molecule in purified form. Mostbiophysical techniques require ordered or disordered samples made up of largenumbers of identical molecules (there are 1016 molecules in 1 mg of a 60 000molecular-weight protein!). The large number of molecules makes it possible toattain the required measurement sensitivity while minimising the damage inducedby the experiment itself (the probing radiation, for example). These molecules are,therefore, studied in conditions that are quite different from their physiologicalenvironment. The next step is to look at associations between the molecules, and,in particular, at the complex supramolecular structures that are now believed to bepresent in the cell. Where it is not possible to organise these complexes in orderedtwo- or three-dimensional structures, their structures can only be observed tolow resolution. Higher-resolution models can be obtained, however, from a

xiii

xiv Foreword

theoretical approach based on the ensemble of structural and dynamics data, onthe complexes themselves and their components. This book also provides chapterson promising new developments, for example in single-molecule detection andmanipulation. The final step, which is still difficult to climb, concerns the study ofmolecules and complexes in vivo. In this context, new technical approaches butalso new ways of thinking must be explored, even if a few biophysical methods arealready able to provide information on molecules in their cellular environment.By applying a function-to-structure approach in addition to the more traditionalstructure-to-function approach, it is possible to explore what are the structuralorganization models compatible with the function properties of an ensemble ofmolecules. For example, it was possible to demonstrate that diffusion of mobilecarriers belonging to the photosynthetic electron transfer chain is restricted tosmall domains, on the basis of a thermodynamic and kinetics analysis of electrontransfer reactions in the photosynthetic apparatus. These domains could be smallmembrane compartments isolated from one another or super complexes formedby the association of several large membrane proteins in which mobile carriersare trapped. In many cases, membranes as well as the cytosol appear to be highlycompartmentalised systems. The determination of supramolecular organisationwithin these compartments will certainly be one of the major goals in modernbiophysics.

Preface

Andre Guinier, whose fundamental discoveries contributed to the X-ray diffrac-tion methods that are the basis of modern structural molecular biology, died inParis at the beginning of July 2000, only a few weeks after it was announced inthe press that a human genome had been sequenced. The sad coincidence servesas a reminder of the intimate connection between physical methods and progressin biology. Not long after, Max Perutz, Francis Crick and then David Blow, theyoungest of the early protein crystallographers, passed away. The period markedthe gradual closing of the era in which molecular biology was born and theopening of a new era. In what has been called the post-genome sequencing era,physical methods are now increasingly being called upon to play an essential rolein the understanding of biological function at the molecular and cellular levels.

Classical molecular biophysics textbooks published in the previous decadeshave been overtaken not only by significant developments in existing methodssuch as those brought about by the advent of synchrotrons for X-ray crystallog-raphy or higher magnetic fields in NMR, but also by totally new methods withrespect to biological applications, such as mass spectrometry and single-moleculedetection and manipulation. Our ambition in this book was to be as up-to-dateand exhaustive as possible. In their respective parts, we covered classical andadvanced methods based on mass spectrometry, thermodynamics, hydrodynam-ics, spectroscopy, microscopy, radiation scattering, electron microscopy, molec-ular dynamics and NMR. But rapid progress in the field (we couldnt very wellask the biophysics community to stop working during the few years it takes towrite and prepare a book!) and the requirement to keep the book to a manageablesize meant that certain methods are either omitted or not perfectly up-to-date.

The key-word in molecular biophysics is complementarity. The Indian story ofthe six blind men and the elephant is an appropriate metaphor for the field. Eachof the blind men touched a different part of the elephant, and concluded on itsnature: a big snake said the man who touched the trunk, the tusks were spears, itsside a great wall, the tail a paint brush, the ears huge fans, the legs were tree trunks.We could add a seventh very short-sighted man to the story who can see the wholeelephant but as a blurred grey cloud to illustrate diffraction methods. As we wrotein the Introduction, the ideal molecular biophysics method does not exist. It wouldbe capable of observing not only the positions of atoms in molecules in vivo, butalso the atomic motions and conformational changes that occur as the molecules

xv

xvi Preface

are involved in the chemical and physical reactions associated with their biologicalfunction, regardless of the time scale involved. No single experimental techniqueis capable of yielding this information. Each provides us with a partial field ofview with its clear regions and areas in deep shadow. In the twenty-first century,physical methods have to cope with very complicated biological problems, whosesolution will depend, on the ability to transfer structural and functional knowledgefrom the operation of a single molecule to the cellular level, and then to the wholeorganism. The splendour and complexity of the task is humbling, but the challengewill be met.

We are deeply obliged to Professor Don Engelman of Yale University, USA,and Professor Pierre Joliot of the Institut de Biologie Physico Chimique, France,who agreed to write forewords for the book. Outstanding scientists and teachers,each is both major actor and observer in biophysical research and the develop-ment of modern biology. Grateful thanks also to expert colleagues for criticaldiscussions on the different methods: Martin Blackledge and the members ofthe NMR laboratory, Christine Ebel, Dick Wade, Hugues Lortat-Jacob, PatriciaAmara, Jean Vicat the members of the laboratory of mass spectrometry, all ofthe Institut de Biologie Structurale, Ingrid Parrot and Trevor Forsyth of the Insti-tut Laue Langevin, France, Regine Willumeit of the GKSS, ForschungszentrumGeesthacht, Germany, Victor Aksenov of the Joint Institute of Nuclear Research,Russia, Lesley Greene, Christina Redfield, Guillaume Stewart-Jones, YvonneJones and David Stuart of the University of Oxford, UK, Jonathan Ruprechtand Richard Henderson of the Laboratory of Molecular Biology, UK, SimonHanslip and Robert Falconer of Cambridge University, UK. Hugh Montgomery ofEdinburgh University, Rebecca Sitsapesan, Bristol University, David Worcester,University of Missouri, Philip Nelson, University of Pennsylvania, Georg Bueldtand Joachim Heberle of the Juelich Research Centre. We gratefully acknowledgesupport from the Radulf Oberthuer Foundation, Germany, the Institut de Biolo-gie Structurale and the Institut Laue Langevin, France, and the Cyril SerdyukCompany, Ukraine. We are indebted to Gennadiy Yenin of the Institute of ProteinResearch, Russia for drawing figures and scientific illustrations, and to AleksandrTimchenko, Margarita Shelestova, Margarita Ivanova, Tatyana Kuvshinkina, andAlbina Ovchinnikova (Institute of Protein Research, Russia) for technical assis-tance. And finally, we would like to thank all our colleagues, friends and fami-lies, and the staff of Cambridge University Press, who supported us with muchpatience, understanding and encouragement.

IntroductionMolecular biophysics at the beginning ofthe twenty-first century: from ensemblemeasurements to single-moleculedetection

The ideal biophysical method would be capable of measuring atomic positionsin molecules in vivo. It would also permit visualisation of the structures thatform throughout the course of conformational changes or chemical reactions,regardless of the time scale involved. At present there is no single experimentaltechnique that can yield this information.

A brief history and perspectives

Molecular biology was born with the double-helix model for DNA, which pro-vided a superbly elegant explanation for the storage and transmission mechanismsof genetic information (Fig. 1). The model by J. D. Watson and F. H. C. Crickand supporting fibre diffraction studies by M. H. F Wilkins, A. R. Stokes, andH. R Wilson, and R. Franklin and R. G. Gosling, published in a series of papersin the 25 April, 1953 issue of Nature, marked a major triumph of the physicalapproach to biology.

The Watson and Crick model was based only in part on data from X-ray fibrediffraction diagrams. The patterns, which demonstrated the presence of a helicalstructure of constant pitch and diameter, could not provide unequivocal proof fora more precise structural model. One of the genius aspects of the discovery wasthe realisation that A--T and G--C base pairs have identical dimensions; as therungs of the double-helix ladder, they give rise to a constant diameter and pitch.From a purely diffraction physics point of view, a variety of helical modelswas compatible with the fibre diffraction diagram, and other authors proposedan alternative model for DNA, the so-called side-by-side model, coupling twosingle DNA helices. This shows that if molecular biology were to be established,it was important to obtain the structure of biological molecules in more detail thanwas possible from fibre diffraction. Considering the dimensions involved, about1 (0.1 nm) for the distance between atoms, X-ray crystallography appearedto be the only suitable method. Major obstacles remained to be overcome suchas obtaining suitable crystals, coping with the large quantity of data required todescribe the positions of all the atoms in a macromolecule, and solving the phaseproblem.

1

2 Introduction

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

DNA (a) (b)BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE SUGAR

PHOSPHATE

BASE

BASE

BASE

BASE

BASE

SUGAR

SUGAR

SUGAR

SUGAR

SUGAR

PHOSPHATE

PHOSPHATE

PHOSPHATE

PHOSPHATE

PHOSPHATE

(c) (d)

Fig. 1 (a) Chemicalorganisation of a singlechain of DNA. (b) Thisfigure is purelydiagrammatic. The tworibbons symbolise thetwo phosphate--sugarchains, and the horizontalrods the pairs of basesholding the chainstogether. The vertical linemarks the helix axis.(c) Chemical organisationof a pair of DNA chains.The hydrogen bonding issymbolised by dottedlines. (d) X-ray fibrediffraction of the B-formof DNA. The figures arefacsimiles from theoriginal papers of Watsonand Crick (1953) andFranklin and Gosling(1953).

Protein crystals had already been obtained in the 1930s. It was not until 1957,however, that Max Perutz and John Kendrew found a way to solve the crystallo-graphic phase problem by isomorphic substitution using heavy-atom derivatives.This permitted the structure of myoglobin to be solved in sufficient detail todescribe how the molecule was folded. The difficulties encountered with proteincrystallisation, and the labour intensive nature of the crystallographic study itself(this was before powerful computers and long calculations were essentially per-formed by post-doctoral hands) appeared to doom protein crystallography toproviding rare, unique information on the three-dimensional structure of a veryfew biological macromolecules. Structural molecular biologists, therefore, con-tinued the development and improvement of methods that do not provide atomicresolution but have complementary advantages for the study of macromolec-ular structures. These methods, at the boundary between thermodynamics andstructure, had already played crucial roles in the century before the discoveryof the double helix. The discovery of biological macromolecules is itself tightlyinterwoven with the application of physical concepts and methods to biology(biophysics).

The application of physics to tackle problems in biology is certainly older thanits definition as biophysics. The Encyclopdia Britannica suggests that the studyof bioluminescence by Athanasius Kircher in the seventeenth century might beconsidered as one of the first biophysical investigations. Kircher showed that anextract made from fireflies could not be used to light houses. The relation betweenbiology and what would become known as electricity has preoccupied physicistsfor centuries. Isaac Newton, in the concluding paragraph of his Principia (1687),reflected that . . . all sensation is excited, and the members of animal bodiesmove at the command of the will, namely, by the vibrations of this Spirit, mutuallypropagated along the solid filaments of the nerves, from the outer organs ofsense to the brain, and from the brain into the muscles. But these are things thatcannot be explained in few words, nor are we furnished with that sufficiency ofexperiments which is required to an accurate determination and demonstrationof the laws by which this electric and elastic Spirit operates. One hundred yearslater, Luigi Galvani and Alessandro Volta performed the experiments on frogs

Introduction 3

legs that would lead to the invention of the electric battery. They also laid thefoundations of the science of electrophysiology, even though, because of theexcitement caused by the electric battery it was well into the nineteenth centurybefore the study of animal electricity was developed further, notably by EmilHeinrich Du Bois-Reymond. Another nineteenth century branch of biophysics,however, that dealing with diffusion and osmotic pressure in solutions, would lateroverlap with physical chemistry, and is more directly relevant to the discovery andstudy of biological macromolecules. The first papers published in Zeitschrift furPhysikalische Chemie (1887) were concerned with reactions in solution, becausebiological processes essentially take place in the aqueous environment insideliving cells.

The thermal motion of particles in solution (Brownian motion) was discov-ered by Robert Brown (1827). The Abbe Nollet, a professor of experimentalphysics, first described osmotic pressure in the early nineteenth century fromexperiments using animal bladder membranes to separate alcohol and water. Thefurther study and naming of the phenomenon is credited to the medical doctorand physiologist Rene J. H. Dutrochet (1828), who recognised the importantimplication of osmotic phenomena in living systems and firmly believed thatbasic biological processes could be explained in terms of physics and chemistry.The theory of osmotic pressure was developed by J. Vant Hoff (1880). GeorgeGabriel Stokes (middle of the nineteenth century) is best known for his funda-mental contributions to the understanding of the laws governing particle motionin a viscous medium, but he also named and worked on the phenomenon offluorescence. The laws of diffusion under concentration gradients were writtendown by Adolf Fick (1856), by analogy with the laws governing heat flow. Thesecond half of the nineteenth century also saw the discoveries of flow birefrin-gence by James Clerk Maxwell and of electric birefringence in solutions byJohn Kerr. Both phenomena depend on the existence of large asymmetric soluteparticles.

Macromolecules, although large as molecules, are still much smaller than thewavelength of light. They could not be seen through direct observation by usingmicroscopes, which had already shown the existence of cells in biological tissueand of structures within the cells such as the chromosomes (from the Greek,meaning coloured bodies). From the knowledge gained from experiments onsolutions it gradually became apparent that the biochemical activity of proteins,studied by Emil Fischer (1882), is due to discrete macromolecules. In 1908,Jean Perrin applied a theory proposed by Albert Einstein (1905) to determineAvogadros number from Brownian motion. The theory of macromolecules is dueto Werner Kuhn (1930) after Hermann Staudinger (1920) proposed the con-cept of macromolecules as discrete entities, rather than colloidal structures madeup of smaller molecules. The discovery of X-rays by Wilhelm Conrad Rontgen(1895), and its application to atomic crystallography in the 1910s through thework of Peter Ewald, Max von Laue and William H. and W. Laurence Bragg

4 Introduction

laid the ground work for the observation of atomic structural organisation withinmacromolecules almost half a century later. Theodor Svedberg (1925) made thefirst direct observation of a protein as a macromolecule of well-defined molarmass by using the analytical centrifuge he had invented. In parallel, the atomictheory of matter became accepted as fact. There was rapid progress in X-raydiffraction and crystallography, electron microscopy and atomic spectroscopy.The novel experimental tools, provided by the new understanding of the interac-tions between radiation and matter, were carefully honed to meet the challengeof biological structure at the molecular and atomic levels. Physicists, encour-aged by the example of Max Delbruck, who chose to study the genetics of abacteriophage (a bacterial virus) as a tractable model in the 1940s, and ErwinSchrodingers influential book What is Life? (1944), which discussed whetheror not biological processes could be accounted for by the known laws of physics,turned to biological problems in a strongly active way.

At the beginning of the twenty-first century, biophysics is dominated bytwo methods, X-ray crystallography and NMR, which play the key role in deter-mining three-dimensional structures of biological macromolecules to high res-olution. But even if all the protein structures in different genomes were solved,crucial questions would still remain. What is the structure and dynamics of eachmacromolecule in the crowded environment of a living cell? How does macro-molecular structure change during biological activity? How do macromoleculesinteract with each other in space and time? These questions can be addressedonly by the combined and complementary use of practically all biophysical meth-ods. Mass spectrometry can determine macromolecular masses with astonishingaccuracy. Highly sensitive scanning and titration microcalorimetry are applied todetermine the thermodynamics of macromolecular folding and stability, and arejoined by biosensor techniques in the study of binding interactions. There has beena rebirth of analytical ultracentrifugation, with the advent of new, highly preciseand automated instrumentation, and it has joined small-angle X-ray and neutronscattering in the study of macromolecular structure and interactions in solutionand the role of hydration. A femtosecond time resolution has been achieved forthe probing of fast kinetics by optical spectroscopy. Light microscopy combinedwith fluorescence probes can locate single molecules inside cells. Scanning forcemicroscopy is determining the profile of macromolecular surfaces and their time-resolved changes. Electron microscopy is approaching close to atomic resolutionand is most likely to bridge the gap between single-macromolecule and cellularstudies. Neutron spectroscopy is providing information on functional dynam-ics of proteins within living cells. Synchrotron radiation circular dichrosm canaccess a wider wavelength range vacuum ultraviolet for the study of electronictransitions in the polypeptide backbone.

Up to the late 1970s, biophysics and biochemistry had only dealt with largemolecular ensembles for which the laws of thermodynamics are readily applica-ble. One hundred microlitres of a 1 mg/ml solution of haemoglobin, for example,

Introduction 5

contains 1018 protein molecules; a typical protein crystal contains of the order of1015 macromolecules. In their natural environment, however, far fewer moleculesare involved in any interaction and exciting new methods have been devel-oped that allow the study of single molecules. Single molecules can now bedetected and manipulated with hypersensitive spectroscopic and even mechani-cal probes such as atomic force microscopy, with which a single macromoleculecan even be stretched into novel conformations. Conformational dynamics canbe measured by single-molecule fluorescence spectroscopy. Fluorescence res-onance energy transfer can measure distances between donor and acceptor pairs insingle molecules, in vitro or in living cells. Near-field scanning optical microscopycan identify and provide dynamics information on single molecules in the con-densed phase.

The historical development of each of the biophysical methods outlined aboveis discussed in more detail in the corresponding section of the book.

Languages and tools

Physike in Greek is the feminine of physikos meaning natural. Physics is thescience of observing and describing Nature. When one of the authors (J. Z.)was a student at Edinburgh University, physics was taught in the department ofNatural Philosophy. The word philosophy, love of wisdom, conveyed quite accu-rately how the wisdom of the observer is brought to bear in science. The observerplays his role through the tools he uses in his experiments and the language heuses to describe his results. Modern science covers so many diverse areas that itis impossible to master an understanding of all the tools and languages involved.Biophysics students are familiar with the language difficulties of trying to com-municate with pure physicists, on the one hand, and pure biologists, on theother, despite decades of interdisciplinary teaching and research in universities.Rather than bemoaning this fact, we should recognise that it reflects the richnessand depth of each discipline, expressed in its own sophisticated language, anddeveloped in its own set of observational tools. Clearly, physics and biology havedifferent languages, but it is important to appreciate that within each disciplinealso there are different languages. Language influences tool development, whichin turn contributes to refine the concepts described by language. Biophysicistshave to be fluent in the various languages of physics and biology and be able totranslate between them accurately. This is a very difficult and sometimes impos-sible task, as any good language interpreter can testify, each language having itsown specificity and view point.

Biophysics deals, to a large extent, with the structure, dynamics and interac-tions of biological macromolecules. What are biological macromolecules? Theirbiological activity is described in the language of biochemistry and molecularspectroscopy; they were discovered through their hydrodynamic and thermo-dynamic properties; they are visualised by their radiation scattering properties,

6 Introduction

and their pictures are drawn in beautiful colour as physical particles. To eachlanguage there corresponds a set of tools, the instruments and methods of exper-imental observation. Progress in probing and understanding biological macro-molecules has undoubtedly been based on advances in the methods used. Phys-ical tools capable of ever increasing accuracy and precision require a paralleldevelopment in biochemical tools (often themselves of physical basis, like elec-trophoresis or chromatography, for example) to provide meaningful samples forstudy. The word meaningful is a key word in the previous sentence. It refers to therelevance of the study with respect to biology (from the Greek bios, life, and logos,word or reason), i.e. biophysics has the goal of increasing our understanding oflife processes. It should be distinguished from biological physics, which dealswith the properties of biological matter, for example to design nanomachinesbased on DNA.

Length and time scales in biology

Biological events occur on a wide range of length and time scales -- from the dis-tance between atoms on the angstrom scale to the size of the earth as an ecosys-tem, from the femtosecond of electronic rearrangements when retinal absorbsa photon in the first step of vision to the 109 years of evolution. Observationtools have been developed that are adapted to the different parts of the lengthand time scales. The cell represents a central threshold for biological studies(Fig. 2). With a usual size of the order of 1--10 m, cells can be seen in the lightFig. 2 A realistic

drawing of the bacteriumEscherichia coli, based onavailable experimentaldata. A flagellum, thedouble cell membraneand its associatedproteins andglycoproteins are shownin hues of green;ribosomes and otherprotein and nucleic acidcytoplasmic componentsare in violet and blue;nascent polypeptidechains are in white; DNAand its associatedproteins are in yellow andorange. The scale is givenby the size of thebacterium of about 1 m,or the double membranethickness of about 10 nm.(http://www.scripps.edu/mb/goodsell/)

Introduction 7

microscope. Also, the durations of cellular processes, which are of the order ofseconds to minutes can be observed and measured with relative ease. If we imag-ined diving into a eukaryotic cell through its plasma membrane, we would seeother membrane structures that separate distinct compartments like the nucleus ormitochondria, large macromolecular assemblies such as chromatin, ribosomes,chaperone molecular machines or multienzyme complexes. Looking for progres-sively smaller structures we would find RNA and protein molecules, then peptidesand other small molecules, water molecules and ions, and finally the atoms thatmake them up (Fig. 3).

102

102

104

106

104

106

108

1010

1.0

The earth as an ecosystem

Whale

Length of DNA inhuman genome

Nematode

Plant cell

Bacterial cell

Virus

Ribosome

Protein

Atom

Animal cell

Human being

Metr

es

Fig. 3 Length scales inbiology.

103

1016

106

109

1012

1015

1.0

Molecular evolution

Protein synthesis

Enzyme catalysis

DNA unfolding

Macromolecular thermalmotions

Bond vibrations

Electronic rearrangementsin vision

Sec

on

ds

Fig. 4 Time scales inbiology.

The smaller the length, the shorter the time, the heavier is the implicationof sophisticated physical instrumentation and methods for their experimentalobservation.

The femtosecond (1015 s) is the shortest time of interest in molecular biology;it corresponds to the time taken by electronic reorganization in the light sensitivemolecule, retinal, upon absorption of a photon, in the first step in vision. Timeintervals of this order can be measured by laser spectroscopy (the distance coveredby light in 1 fs is 3 107 m, or 300 nm, about one half the wavelength of visiblelight). Thermal fluctuations are in the picosecond (1012 s) range; DNA unfoldsin microseconds; enzyme catalysis rates are of the order of 1000 reactions persecond; protein synthesis takes place in seconds etc. The longest time of interestin molecular biology is, in fact, geological time, corresponding to the more thanone thousand million years of molecular evolution (Fig. 4).

The structure--function hypothesis

This book describes the application of classical and advanced physical methodsto observe biological structure, dynamics and interactions at the molecular level.Intensive research since the 1950s has emphasized the fundamental importanceof biological activity at this level. The structure--function hypothesis is the foun-dation of molecular biology. One of its implications is that if a protein existstoday in an organism it is because it fulfils a certain biological function and itsstructure has been selected by evolution. The discovery and study of nucleicacids and proteins as macromolecules with well-defined structures has allowedan unprecedented understanding of processes such as the storage and transmis-sion of genetic information, the regulation of gene expression, enzyme catalysis,immune response or signal transduction. In parallel, it became apparent that wecould act on biological processes by acting on macromolecular structures andpowerful tools were developed not only to further fundamental scientific under-standing but also to apply this knowledge in biotechnology or in drug designpharmacology.

The concept of structure should be understood in the broadest sense. Thethree-dimensional organisation of a protein is not rigid but can adapt to its ligandsaccording to the hypothesis of configurational adaptivity or induced fit. Also,

8 Introduction

many proteins have been found that display a highly flexible random-coil confor-mation under physiological conditions. An intrinsically disordered protein couldadopt a permanent structure through binding, but there are cases of proteins withintrinsic disorder that are biologically active while remaining disordered. A largeproportion of gene sequences appear to code for long amino acid stretches thatare likely either to be unfolded in solution or to adopt non-globular structures ofunknown conformation.

Events taking place on the angstrom and picosecond scales have profoundconsequences for life processes over the entire range of length and time scales --from the length and time associated with a cell, via those associated with anorganism to those associated with the relation between an organism and its envi-ronment. The development of high-throughput techniques for whole genomesequencing, for the analysis of genomic information (bioinformatics), for theidentification of all the proteins present in a cell (functional proteomics), fordetermining how this population responds to external conditions (dynamic pro-teomics) and for protein structure determination (structural genomics) has openedup a new era in molecular biology whose revolutionary impact still remains to beassessed.

Biological macromolecule structures usually appear in pictures as static struc-tures. A more precise definition would be ensemble and time-averaged struc-tures. The atoms in a macromolecular structure are maintained at their averagepositions by a balance of forces. Under the influence of thermal energy, the atomsmove about these positions. Dynamics, from the Greek dynamis meaning strength,pertains to forces. Structure and motions result from forces. It is common usagein biophysics, however, to separate structure from dynamics, considering the firstas referring to the length scale (i.e. to the time-averaged configuration) and thesecond as referring to the time scale (i.e. to energy and fluctuations). The separa-tion into two separate concepts is validated by the fact that the methods used tostudy structure and dynamics are usually quite separate and specialised. Modernexperiments, however, often address both an average structure and how it changeswith time.

Complementarity of physical methods

We know of the existence of macromolecules only through the methods withwhich they are observed. No single method, however, provides all the informationrequired on a macromolecule and its interactions. Each method gives a differentview of the system in space and time: the methods are complementary.

Biological macromolecules take up their active structures only in a suitablesolvent environment. The forces that stabilise them are weak forces (of the order ofkT, where k is Boltzmanns constant and T is absolute temperature), which arise inpart from interactions with the solvent. The study of biological macromolecules,therefore, cannot be separated from the study of their aqueous solutions. The

Introduction 9

103

106 107 108 109 1010

106

109

1012

1015

1015

1012

109

106

103

1018 1

10 000 1000 100 10 1

LS, HD SAXS,SANS NMR

N-cryst

X-cryst

EM

SMD

(m)

( )A

(g) (N )

Mate

rial

Length scale Fig. 5 Length resolutionachieved and amount ofmaterial required for thesample for experimentsusing different physicalmethods to determinestructure. Abbrevations:g, grams; N, number ofmolecules (assuming amolecular weight of theorder of 100 000); LS, lightscattering; HD,hydrodynamics; SAXS,SANS, X-ray and neutronsmall-angle scattering,respectively; NMR,neutron magneticresonance in solution;N-cryst, neutroncrystallography; X-cryst,X-ray crystallography; EMis electron microscopy;SMD is single-moleculedetection methods.

macromolecules are usually studied in dilute or concentrated solutions, in thelipid environment of membranes, or in crystals. Protein molecules or nucleicacid molecules in the unit cell of a crystal are themselves surrounded by anappreciable number of solvent molecules, and there are aqueous layers on eitherside of membranes. According to the experimental method used, we shall considerbiological macromolecules in solution as physical particles (mass spectrometry,single-molecule detection . . .), thermodynamics particles (osmotic pressuremeasurements, calorimetry . . .), hydrodynamics particles (viscosity, diffusion,sedimentation . . .) or radiation interaction particles (spectroscopy, diffractionand microscopy).

The length resolution scale achieved, the techniques involved and the samplemass required for some biophysical methods are illustrated in Fig. 5.

Thermodynamics

It is a result of classical thermodynamics that many properties of solutions, suchas an increase in boiling point, freezing point depression, and osmotic pressure,depend on the number concentration of the solute. At constant mass concentration,therefore, these thermodynamics parameters vary sensitively with the molecularmass of the solute. Thus, for example, macromolecular masses and interactionshave been determined from osmotic pressure measurements.

Macromolecular folding itself and the stabilisation of active biological struc-tures follow strict thermodynamics rules in which interactions with solvent playa determinant role. Sensitive calorimetric measurements of heat capacity as a

10 Introduction

function of temperature showed very clearly that stabilisation free energy presentsa maximum at a temperature close to the physiological temperature, the stabilityof the folded particle decreasing at lower as well as higher temperatures. Theinterpretation is the following. The behaviour of the chain surrounded by solventis much more complex than if it were in a vacuum. Enthalpy may rise, decreaseor even not change upon folding, because bonds can be made equally well withinthe macromolecule and between the chain and solvent components. Similarly forentropy, the loss of chain configuration freedom upon folding may be more thancompensated for by a loss of degrees of freedom for the solvent molecules aroundthe unfolded chain, for example through the exposure of apolar groups to watermolecules. A water molecule in bulk has the freedom to form hydrogen bondswith partners in all directions. Apolar groups cannot form hydrogen bonds, sothat water molecules in their vicinity lose some of their bonding possibilities;their entropy is decreased.

In a protein solution, the heat capacity is strongly dominated by the water, andthat of the macromolecules represents a very small part of the measured total.High-precision microcalorimeters were built to allow experiments on proteinsolutions to be performed. Nevertheless, early calorimetric studies on biologicalmacromolecules concentrated on relatively large effects such as sharp transitionsas a function of temperature. They led to a fundamental understanding of theenergetics of protein folding. There are now important modern developments inthe field. Very sensitive nanocalorimeters have been developed as well as analysisprograms to treat the thermodynamics information and relate it to structural data.The energetics of intramolecular conformational changes, of complex formationand of interactions between partner molecules can now be explored in detail forproteins and nucleic acids. We should recall, however, that calorimetry (like allthermodynamics-based methods) provides measurements of an ensemble averageover a very large number of particles (typically of the order of 1015), even ifresults are usually illustrated in a simple way in terms of changes occurring inone particle.

Hydrodynamics

The first hints of the existence of biological macromolecules as discrete par-ticles came from observations of their hydrodynamic behaviour. The language ofmacromolecular hydrodynamics is the language of fluid dynamics in the specialregime of low Reynolds numbers. The Reynolds number in hydrodynamics isa dimensionless parameter that expresses the relative magnitudes of inertial andviscous forces on a body moving through a fluid. Bodies with the same Reynolds,number display the same hydrodynamics behaviour. Because of this, it is possible,for example, to determine the behaviour of an airplane wing from wind-tunnelstudies on a small-scale model. The Reynolds numbers of a small fish and awhale are 105 and 109, respectively.

Introduction 11

Reynolds numbers in aqueous solutions for biological macromolecules andtheir complexes, from small proteins to large virus particles and even bacteria,are very small. For example, it is 105 for a bacterium swimming with a velocityof about 103 cm/s. Inertial forces are negligible under such conditions, so thatthe motion of a particle through the fluid depends only on the forces acting uponit at the given instant; it has no inertial memory. Particle diffusion through a fluidunder the effects of thermal or electrical energy, and sedimentation behaviour in acentrifugal field can be predicted by relatively simple equations in terms of macro-molecular mass and frictional coefficients that depend on shape. The resolutiondefines the detail with which a particle structure is described. Hydrodynamicsprovides a low-resolution view of a biological macromolecule, for example asa two- or three-axis ellipsoid, but it is also very sensitive to particle flexibilityand particle--particle interactions. Modern hydrodynamics includes a number ofnovel experimental methods. In addition to the classical approaches of analyti-cal ultracentrifugation to measure sedimentation coefficients and dynamic lightscattering to measure diffusion coefficients, we now have free electrophoresis tomeasure transport properties in solution, fluorescence photobleaching recovery tomonitor the mobility of individual molecules within living cells, time-dependentfluorescence polarisation anisotropy and electric birefringence to calculate rota-tional diffusion coefficients, fluorescent correlation spectroscopy and localiseddynamic light scattering to measure macromolecular dynamics.

Radiation scattering

We see the world around us because it scatters light, which is detected by oureyes and analysed in our brains. In a diffraction experiment, waves of radiationscattered by different objects interfere to give rise to an observable pattern, fromwhich the relative arrangement (or structure) of the objects can be deduced. Theinterference pattern arises when the wavelength of the radiation is similar toor smaller than the distances separating the objects. In some cases, the wavesforming the pattern can be recombined by a lens to provide a direct image of theobject. Atomic bond lengths are close to one angstrom unit (1010 m or 0.1 nm),and three types of radiation are used, in practice, to probe the atomic structureof macromolecules by diffraction experiments: X-rays of wavelength about 1 ,electrons of wavelength about 0.01 , and neutrons of wavelength about 0.5--10. Visible light scattering, with wavelengths in the 400--800 nm range, providesinformation on large macromolecular assemblies and their dynamics. X-rays,however, because they permit studies to atomic detail, provided the foundationon which structural biology has been built and is developing.

Neutron diffraction studies of biological membranes, fibres and macro-molecules and their complexes in crystals and in solution became possible inthe 1970s with the development of methods that make full use of the specialproperties of the neutron.

12 Introduction

Following the limitations of staining techniques, cryoelectron microscopy wasdeveloped to visualise subcellular and macromolecular structures to increasingresolution.

In the last decade of the twentieth century, the availability of intense syn-chrotron sources caused a revolution in macromolecular crystallography bygreatly increasing the rate at which structures could be solved. Efficient proteinmodification, crystallisation, data collection and analysis approaches were devel-oped for macromolecular crystallography. Extremely fast data-collection timesmade it possible to use time-resolved crystallography to study kinetic intermedi-ates in enzymes. In parallel, field emission gun electron microscopes were appliedand new methods developed to solve single-particle structures. Spallation sourcesfor neutron scattering promise highly improved data-collection rates.

Light, X-rays and neutrons are scattered weakly by matter and require samplescontaining very large numbers of particles in order to obtain good signal-to-noise ratios. Experiments provide ensemble-averaged structures. Modern electronmicroscopy methods, on the other hand, allow single macromolecular particlesto be visualised.

Spectroscopy

In spectroscopy, the radiation has exchanged part of its energy with the sample,through absorption effects or excitations due to particle internal or global dynam-ics, resulting in a change in the wavelength (frequency or colour) of the outgoingbeam with respect to the incident beam. Since absorption depends on the loca-tion of an atom in a structure, certain types of spectroscopic experiment may alsobe used to study structure. Nuclear magnetic resonance (NMR) spectroscopyis sensitive to close to atomic resolution. The frequency of absorbed radiationcan be measured as a function of time with an accuracy better than one partin a million. The precise nature of the signal depends on the chemical envi-ronment of the nucleus; hence structural information is obtained. In magneticresonance imaging (MRI), millimetre resolution is obtained with metre wave-length probes by placing the body to be observed in magnetic field gradientsand by focusing on nuclei in a given chemical environment; an absorption res-onance then corresponds to a given field value and therefore to a precise location.As with diffraction, for which the wavelength matches the structural resolutionrequired, the beam energy in spectroscopy is chosen so that differences due tosample excitations or absorption can be measured readily. In general, therefore,radiation of different wavelengths is used for diffraction and for spectroscopicexperiments.

Coherent spectroscopy, in which radiation fields of well-defined phase areused, created unprecedented opportunities to study dynamics and time-evolvingstructures. The spin echo method, applied to NMR and neutron spectroscopy,was extended by the photon echo method when coherent lasers became avail-able. Two-dimensional spectroscopy, first developed for NMR, measures the

Introduction 13

1015

(s1)

(m s1)

1024

109

1013 1010 107 104 102 10510

106 103 103

1010 109

3102 3104

106 1091

1021 1018 1015 1012 109 106

1012 109 106 103 1031

Fig. 6 Wavelength,energy and frequency forelectromagnetic andneutron radiation. Thescales in the figure giveapproximate orders ofmagnitude. The precisevalues for the constantsare obtained from: = cwhere are thefrequency andwavelength, respectively,of electromagneticradiation and c is thespeed of light (3 108m/s); E = h (where E isenergy and h is Plancksconstant (6.626 = 1034 Js= 4.136 1015 eV s);the temperatureequivalent of energy,1 eV/k = 11604.5 K, wherek is Boltzmanns constant.In the neutron case, =h/mv (where m/s isneutron speed), and E =12 mv

2, where m isneutron mass (1.67261027 kg).coupling within networks of vibrational modes. It has been applied to the infrared

region to determine the structure of small molecules. The most exciting aspect oftwo-dimensional infrared spectroscopy is the combination of its sensitivity tostructure and time resolution down to the femtosecond.

Taking electromagnetic radiation as an example, atomic diffraction requiresX-ray wavelengths, while intramolecular vibrations correspond to infrared ener-gies (Fig. 6). In NMR spectroscopy, the probing electromagnetic radiation isin the radio-frequency range, corresponding to metre wavelengths. Note thatwith neutron radiation, wavelengths of about 1 (corresponding to interatomicdistances and fluctuation amplitudes) have associated energies of about 1 meV(corresponding to the energies of atomic fluctuations), so that diffraction andspectroscopy experiments can be performed simultaneously to measure atomicamplitudes and frequencies of motion in macromolecules. Molecular time scales,corresponding energies and temperatures are shown in Fig. 7 for different bio-physical methods.

Single-molecule detection

Until the 1980s, biochemical and biophysical studies of biological macro-molecules suffered the fundamental disadvantage of always having to deal with

14 Introduction

1015

105 102 104

1012 109 106 103 1

10

s

Temperature ( K )

NMR NS, FTIR

Energy

ms

s

ns

ps

fs

DLS EBFB

FD

LS, 2-D IR

Tim

e(s

)

(electron volts)

Fig. 7 Molecular timescales, associatedenergies andtemperatures of variousbiophysical methods. Therange follows the dashedblack diagonal but thearrows have beendisplaced horizontally forclarity. Abbreviations:DLS, dynamic lightscattering; NMR, nuclearmagnetic resonance; EB,electric birefringence; NS,neutron spectroscopy;FTIR, Fourier transforminfrared spectroscopy; LS,laser spectroscopy; 2D-IR,two-dimensional infraredspectroscopy; FB, flowbirefringence; FD,fluorescencedepolarisation.

very large numbers of particles, whereas under in-vivo conditions they functionas single particles in a dynamic heterogeneous environment. Structures, dynam-ics and interactions were (and predominantly still are) observed and measuredas ensemble averages. Furthermore, enzymatic, binding or signalling reactionsare in general stochastic, so that the kinetics of a protein activity measurement,for example, is also hidden in an ensemble average when measured in a largemolecular population, even if the reaction is triggered contemporaneously for theentire sample.

Single macromolecules had been visualised by electron microscopy, but onlyin the last decade have methods become available to observe them while they wereactive. The development of single-molecule detection (SMD) techniques now per-mits allows the observation as well as the manipulation of single macromoleculesin action. SMD is based on the two key technologies of single-molecule imagingunder active conditions and nanomanipulation. Single-molecule signals that aredetectable with good signal-to-noise ratios are given by fluorescent labels, whichare observed using fluorescent optical microscopy. Applying total reflection andevanescent field techniques, the resolution of the method is several fold better thanthe diffraction limit given by the wavelength of light. Single-molecule nanoma-nipulation techniques include capturing biomolecules using a glass needle orbeads trapped by the force exerted by a focused laser beam (optical tweezers),and probing molecular forces with atomic force or scanning probe near-fieldmicroscopy. The forces involved are in the piconewton range, comparable to thethermal forces stabilising the active macromolecular structures.

Introduction 15

Table 1. The range of forces in macromolecules

Tensile strength of a covalent bond 1000--2000 pNDeformation of a sugar ring 700 pNBreaking of double-stranded DNA 400--580 pNUnfolding the -fold immunoglobulin domain of the

muscle protein titin180--320 pN

Adhesive force between avidin and biotin 140--180 pNStructural transition of uncoiling double-stranded DNA

upon stretching60--80 pN

Structural transition of double-stranded DNA upontorsional stress

20 pN

Individual nucleosome disruption 20--40 pNUnfolding triple helical coiled-coil repeating units in

spectrin25--35 pN

RNA--polymerase motor 14--27 pNStructural transition of RNA hairpin in ribozyme under

stretching (folding--unfolding)14 pN

Separation of complementary DNA strands (roomtemperature, 150 mM NaCl, sequence-specific)

10--15 pN

Stall force of the myosin motor 3--6 pNForce generated by protein polymerisation in growing

microtubules3--4 pN

Comment 1Entropic force

The typical energy

scale for a

macromolecule is

thermal energy: kBT =4 1021 J. Since thelength scale of

biomacromolecules is

of order of 1 nm, the

force scale is on the

order of the

piconewton (1012 N).Therefore an entropic

force can be calculated

as kBT/(1 nm), which is

equal to 4 pN at 300 K.

Erwin Schrodinger wrote in 1952 that we would never be able to perform experi-ments on just one electron, one atom, or one molecule. In the early 1980s, however,scanning tunnelling microscopy was invented by G. Binning and H. Rohrer andradically changed the ways scientists view matter. Mechanical experiments tomeasure the piconewton forces that structure a single macromolecule becamepossible (Comment 1).

In optical tweezer instruments (Fig. 8(a)) one or two laser beams are focusedto a small spot, creating an optical trap for polystyrene beads. One end of asingle molecule (DNA, for example) is attached to a bead, while the other endis attached to a moveable surface, which, in this example, is another bead on aglass micropipette. The opposing force is measured, as the molecule is stretchedby moving the micropipette.

In magnetic tweezer instruments (Fig. 8(b)), one end of the single moleculeis attached to a glass fibre, while the other end is attached to a magnetic bead. Amagnetic field exerts a constant force on the bead. The extension and rotation ofthe molecule as a function of the applied force is then measured.

In an atomic force microscopy experiment (Fig. 8(c)), one end of the moleculeis attached to a surface, and the other to a cantilever. As the surface is pulled away,the deflection of the cantilever is monitored from the position of a reflected laserbeam.

16 Introduction

Laser BeamMicroscopeobjectives

Laser Beam

DNA molecule

Polystyrenebead

Glass micropipette

SNS

N

F

Bead

DNA

Glass substrate

(a)

(b)

(c)

DNA

Laser

Cantilever

Detector

St ag e

Fig. 8 A schematic viewof three main techniquesused in single-moleculeforce studies: (a) opticaltweezer, (b) magnetictweezer and (c) atomicforce microscopy(Carrion-Vazquez et al.,2000).

The experiments allow a new structural parameter to be accessed within asingle molecule: force (Table 1). The upper boundary for force measurementsin micromanipulation experiments is the tensile strength of a covalent bond (inthe eV/ range or about 1000--2000 pN). The smallest measurable force limit isset by the Langevin force (about 1 fN), which is responsible for the Brownianmotion of the sensor (size of the order of 1 m).

Introduction 17

Note that the total range of forces in Table 1 covers only three orders ofmagnitude. Until single-molecule techniques became available, information onprotein stability could only be obtained by measuring the loss of structure underdenaturing conditions (by using temperature, chemical agents or pH) from whichfolding free energy could be calculated for an ensemble average of molecules.Free energy, however, does not provide direct information on mechanical stability.For mechanical stability, it is important to know how the total energy varies as afunction of spatial coordinates. Several proteins were studied to measure the forcerequired to unfold a single molecule. These studies revealed very large differencesin magnitude (which can reach the order of a factor of 10) between the unfoldingforces for different protein domains whose melting temperatures are very similar.These results demonstrated that the mechanical stability of a protein fold is notdirectly correlated with its thermodynamic stability. We expect the analysis ofthe mechanical properties of macromolecules to set the foundation of a new fieldof study, mechanochemical biochemistry.

Part ABiological macromolecules andphysical tools

Chapter A1 Macromolecules in their environment page 21A1.1 Historical review 21A1.2 Macromolecular solutions 22A1.3 Macromolecules, water and salt 28A1.4 Checklist of key ideas 35Suggestions for further reading 37

Chapter A2 Macromolecules as physical particles 38A2.1 Historical review and biological applications 38A2.2 Biological molecules and the flow of

genetic information 40A2.3 Proteins 43A2.4 Nucleic acids 50A2.5 Carbohydrates 54A2.6 Lipids 58A2.7 Checklist of key ideas 61Suggestions for further reading 63

Chapter A3 Understanding macromolecular structures 65A3.1 Historical review 65A3.2 Basic physics and mathematical tools 67A3.3 Dynamics and structure, kinetics, kinematics,

relaxation 92A3.4 Checklist of key ideas 105

Chapter A1Macromolecules in their environment

A1.1 Historical review

The discovery of biological macromolecules is tightly interwoven with the historyof physical chemistry, which formally emerged as a discipline in 1887, when thejournal founded by Jacobus Vant Hoff and Wilhelm Ostwald, Zeitschrift furPhysikalische Chemie, was first published. Interestingly, the first papers wereconcerned with reactions in solution, because biological processes essentiallytake place in the aqueous environment inside living cells.

The nineteenth century discoveries of solution properties that led to ourknowledge about biological macromolecules are described briefly in the Intro-duction. We must also mention the Grenoble chemist Francois-Marie Raoult(1886), who formulated the freezing-point depression law that made it possibleto determine the molecular weight of dissolved substances, and Hans Hofmeis-ter (1895), a medical doctor and physiologist, who was interested in the diureticand laxative effects of salts, and classified them according to how they modifiedthe solubility of protein in aqueous solutions. The Hofmeister series was laterestablished as a ranking order of the salting-out, or precipitating, efficiency ofions. Gilbert Newton Lewis introduced the concepts of activity in 1908, and ofionic strength, with Merle Randall in 1921. In 1911, Frederick George Don-nan published a paper on the membrane potential developed during dialysis ofa non-permeating electrolyte. Peter Debye and Erich Huckel (1923) proposeda theory for electrolyte solutions. In recent decades, modern methods, such asdynamic light scattering and small-angle neutron scattering, developed for thecharacterisation of polymers, and especially polyelectrolytes, have contributedsignificantly to our current understanding of biological macromolecules insolution.

There is now a growing interest in the behaviour of proteins in non-aqueoussolvents and even in vacuum, mainly in the context of biotechnology, but also withrespect to whether or not water is essential to life. Proteins, as active biologicalparticles, have evolved in the presence of water, however, and, to a large extent,cannot be considered separately from their aqueous environment. We recall thateven crystals of biological macromolecules contain an appreciable amount ofsolvent and should be considered as organised macromolecular solutions.

21

22 A Biological macromolecules and physical tools

Comment A1.1Biologists box:Molecular massunits

Molar mass is in

g mol1 or SI units ofkg mol1.

Relative molecular

mass or molecular

weight is a

dimensionless

quantity, defined as the

ratio of the mass of a

molecule relative to

1/12 the mass of the

carbon isotope 12C.

The molar mass of 12C

is very close to

12 g mol1. Molarmass (in kg mol1)can, therefore, be

converted to molecular

weight by dividing by

103 g mol1 (theequivalent of

multiplying by 1000

and cancelling units).

Biochemists use

molecular mass

expressed in daltons

(Da) (1 Da = 1 atomicmass unit = 1/12 of themass of 1 atom of 12C).

A1.2 Macromolecular solutions

A solution is a homogenous mixture at the molecular level of two or more com-ponents. The majority component is the solvent; the others are the solutes. Weshall deal mainly with macromolecular aqueous solutions, in which the solventis water, and the solutes are macromolecules and other small molecules, such assimple salts.

A1.2.1 Concentration

The solute concentration can be defined in various ways.

The weight or mass fraction is the mass of solute per unit weight of solution (or per

100 weight units of solution if it is expressed as a weight or mass percentage).

The usual unit of molecular mass in biochemistry is the dalton (Comment A1.1).

The molarity is the number of moles of solute per litre of solution. Expressing

a concentration in molar terms has the advantage of being more relevant than

using weight fraction with respect to the colligative properties of the solution (i.e.

properties that depend only on the number of solute particles rather than on the

mass of solute or its specific properties; see also Section A1.2.3).

The molality is the number of moles of solute per kilogram of solvent. Expressing

solute concentration in these terms has the advantage that molality is obtained

by weighing masses of solute and solvent, whereas molarity depends also on

measuring a solution volume. Masses are invariant, while the volume of the sol-

ution is a function of temperature and pressure.

The mole fraction and volume fraction definitions are similar to that of weight

fraction but refer to moles or volume of solute per total moles or total volume,

respectively.

The usual ways of measuring concentrations in protein and nucleic acid solutionsare discussed in Comment A1.2.

A1.2.2 Partial volume

The partial volume of a solute is equal to the volume change of the solutionupon addition of the solute, under given conditions. The partial volume is notsimply the volume occupied by the added solute, because its presence may leadto a volume change in the solvent. The partial volumes of charged moleculesin aqueous solution are an interesting illustration of solvent effects. The watermolecule can be represented by a small electric dipole. Liquid water has a ratherloose hydrogen bonded structure (see Section A1.3.4); when in the presence ofions, water molecules orient around the charges effectively taking up a smallervolume than in the bulk liquid. The effect is called electrostriction. The partialvolume of a charged ionic solute may be negative, therefore, as is the case for the

A1 Macromolecules in their environment 23

Comment A1.2 Physicists box: Measuring protein and nucleic acidconcentrations (see also Section E1.1, Comment E1.3)

The concentration of protein or nucleic acid solutions cannot be measured simply by

weighing an amount of material into the solvent. Protein and nucleic acid powders

obtained from lyophilisation or precipitation always contain an unknown quantity of

hydration water and salt ions, which are necessary for the maintenance of an active

conformation. Furthermore, extremely low protein and nucleic acid concentrations

are sufficient for many experimental methods, and it is not possible to weigh

micrograms or less of material with precision. Protein concentrations are measured

by colorimetric assays (e.g. the Bradford assay), in which an indicator interacts

chemically with the polypeptide, or by spectrophotometry, in which the absorption

of light at a given wavelength is proportional to the amount of material present. The

absorbance at 280 nm is particularly sensitive to the presence of tryptophan,

tyrosine and cysteine amino acid residues, and for most proteins it is of the order of

1 for a 1 mg ml1 solution and a path length of 1.0 cm. The exact value, however,varies with the number of sensitive residues in the protein. Nucleic acids show a

strong absorbance at 260 nm (1 absorbance unit corresponds to about 40

micrograms per millilitre), which is used to measure their concentration in solution.

The colorimetric and spectrophotometric measurements yield relative values with

respect to a calibration series. When absolute concentration values are required, e.g.

as they are for the interpretation of small-angle scattering data (Chapter G2), the

colorimetric or spectrophotometric values have to be calibrated on an absolute scale

for the specific macromolecule, e.g. by precise amino acid analysis of the sample.

Na+ and Mg2+ ions, for example. The decrease in volume due to electrostrictionfor these ions is greater than the volume they effectively occupy in the solution.The partial volume of the K+ ion is slightly positive; electrostriction does notquite compensate for the volume occupied by the ion. Note that ions cannot beadded separately to a solution, so that partial ionic volumes were obtained byinterpolation from data on different neutral salts. It is also a consequence of elec-trostriction that ionic partial volume values are solvent composition-dependent;in general they increase with salt concentration, for example, because the waterhas already suffered some electrostriction.

The partial specific volume of a solute is the volume change of the solutionper gram of added solute.

The partial molal volume of a solute is the volume change of the solution permole of added solute.

The partial volumes of ions and biological macromolecules, in usual units,are given in Comment A1.3. Nucleic acids and to some extent carbohydrates,depending on their specific chemical natures, are polyelectrolytes and their partialvolume values are strongly solvent salt-concentration-dependent. Interestingly,

24 A Biological macromolecules and physical tools

Comment A1.3 Partial molal volumes of ions and partial specificvolumes of biological macromolecules (see also Section D4.8)

Ion Partial molal volume(ml mole1)

Na+ in water 5.7Na+ in sea-water (0.725 molal NaCl) 4.4K+ in water 4.5K+ in sea-water (0.725 molal NaCl) 5.9Mg2+ in water 30.1Mg2+ in sea-water (0.725 molal NaCl) 27.0Cl in water 22.3Cl in sea-water (0.725 molal NaCl) 23.3

From Millero F. J. (1969) Limnol. Oceanogr. 14, 376--385.

Macromolecule Partial specific volume (ml g1)

Proteins 0.73 (0.70--0.75)Carbohydrates 0.61 (0.59--0.65)RNA 0.54 (0.47--0.55)DNA 0.57 (0.55--0.59)

Note that the spread in values for proteins corresponds to different protein

molecules, while that for the other macromolecules also takes into account variations

with solvent salt concentration. For example, a given RNA molecule has a partial

specific volume of 0.50 ml g1 in water and 0.55 ml g1 in high salt concentration.

the partial volumes of proteins correspond well to the sum of their amino acidcomponent volumes and they are not salt-concentration-dependent despite thefact that protein surfaces may show significant charge. This is because thereare compensating effects on the volume from electrostrictive protein--solventinteractions on the one hand, and a looser surface packing of amino acid residueson the other (see also Chapter D4).

A1.2.3 Colligative properties

Colligative properties of solutions (from the Latin ligare, to bind) are propertiesthat depend only on the number of solute molecules per volume and not on themass or the nature of the molecules. The discovery of the colligative properties ofsolutions played an essential role in early physical chemistry, by allowing accuratemeasurements of molecular weight, which in turn provided evidence for the very

A1 Macromolecules in their environment 25

existence of atoms and molecules. Raoults law states that in an ideal solutionat constant temperature the partial pressure of a component in a liquid mixtureis proportional to its mole fraction. Colligative properties related to Raoults lawand applicable to dilute solutions of non-volatile molecules are the rise in boilingpoint and decrease in freezing point that result when a solute is dissolved in asolvent. The temperature differences between the values for the ideal solutionand those for the pure solvent are proportional in each case to the number ofsolute molecules present. These laws can still be applied to non-ideal solutionsby applying the concepts of chemical potential and activity.

Fig. A1.1 Chemicalpotential (see text).

A1.2.4 Chemical potential and activity

Consider the box shown in Fig. A1.1, with a barrier separating solutions ofdifferent molar concentration, CA, CB, on either side, respectively. If we opena breach in the barrier, there is a net flow of solute molecules from the high-to the low-concentration side, similar to water flowing down a gravity potentialgradient. A potential can, therefore, be associated with the solute concentration.The chemical potential, , of a solute is the free energy gain upon addition ofone mole into the solution (see also Chapter C1).

= G/C

In solution thermodynamics, the free energy difference between two solu-tions of concentrations CA, CB, (in number of moles per volume of solution),respectively, is given by:

GA GB = G = RT ln CACB

(A1.1)

where R and T are the gas constant and absolute temperature, respectively. Theexpression results from integration of the Boltzmann equation, which describeshow molecules in a perfect gas at constant temperature distribute according totheir free energy:

pApB

= exp(

GA GBRT

)(A1.2)

where pA, pB are pressures at constant volume (proportional to molar concen-tration) associated with states of free energy GA, GB, respectively. In a trivialrewriting Eq. (A1.1) becomes

G = (CA CB) = RT ln CACB

(A1.3)

Expressing the relation in terms of free energy or chemical potential differ-ences, rather than absolute values, avoids having to define a standard free energyor chemical potential (e.g. that associated with an ideal solution at a given con-centration, temperature and pressure). The equations apply to ideal solutions,

mCA > mCB

26 A Biological macromolecules and physical tools

i.e. solutions in which the solute molecules behave as point particles and do notinteract in any way with each other (or with the vessel).Comment A1.4

Mole fraction andmolarity values ofusual solutions ofbiologicalmacromolecules

The mole fraction in a

300 g l1 aqueoussolution of 30 kD

macromolecules is

1/4000; the molarity of

the solution is 10 mM.

Corresponding to a

high concentration for

most biophysical

experiments, this is

similar to the protein

concentration in

cytoplasm. The mole

fraction in a 3 mg ml1

solution, which is

usual for many types

of biophysics

experiment, is

1/400 000; the

molarity of the

solution is 100 M.

G. Lewis introduced the concept of activity in 1908 to account for deviationsfrom ideal behaviour in solutions. Writing Eq. (A1.3) in terms of activity, ratherthan concentration:

G = RT ln aAaB

(A1.4)

The activity of solute A is given by aA = ACA and A is an activity coefficientin the appropriate units and is equal to 1 for an ideal solution. Activity coefficientsare obtained experimentally, for example, from deviations from Raoults law. Byreplacing concentration with activity, equations that were derived in the idealcase could be applied in practice to real solutions.

A1.2.5 Temperature

The rise in boiling point and decrease in freezing point of solutions due to thepresence of solute are not very useful properties when dealing with biologicalmacromolecules such as proteins or nucleic acids -- firstly, because the molefraction of macromolecule in even highly concentrated solutions is very low(Comment A1.4); secondly, because biological macromolecules are usually notstable in pure water solvent and the molar concentration of buffer solutes and ionsstrongly dominates the effect; and, finally, because proteins and nucleic acids areusually not stable at the boiling and freezing points of water. Proteins and nucleicacids have evolved to be able to fold into their stable and active conformationsin limited solvent conditions, and in limited ranges of the thermodynamic par-ameters of temperature and pressure (see Part C). It is interesting to note, how-ever, that there exist organisms, called extremophiles (lovers of the extreme),which have adapted to various extreme environmental conditions, including tem-perature (Comment A1.5).

CA