Table Of Content

PHYSICS OF LIFE The Physicist’s Road to Biology This page intentionally left blank PHYSICS OF LIFE The Physicist’s Road to Biology by Clas Blomberg Theoretical Biological Physics Group (KTH) Royal Institute of Technology Stockholm, Sweden Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Linacre House, Jordan Hill, Oxford OX2 8DP, UK First edition 2007 Copyright © 2007 Elsevier B.V. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone ((cid:2)44) (0) 1865 843830; fax ((cid:2)44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://www.elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging in Publication Data A catalog record is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record is available from the British Library ISBN: 978-0-444-52798-1 For information on all Elsevier publications visit our website at books.elsevier.com Printed and bound in The Netherlands 07 08 09 10 11 10 9 8 7 6 5 4 3 2 1 Contents Preface ix Part I General introduction 1 Introduction: the aim and the scope of the book 1 2 The physics of life: physics at several levels 5 Part II The physics basis 3 Concepts and numerical reference 17 3A Numerical values 18 4 Basics of classical (Newtonian) dynamics 19 5 Electricity: the core of reductionism basis 26 5A General electrostatics 26 5B Formalism of electrostatics* 29 5C Magnetism 37 5D Relations between electric and magnetic fields: Maxwell’s equations* 40 5E Radiation 42 6 Quantum mechanics 44 6A The thermodynamic path to quantum mechanics 45 6B Basic principles of quantum mechanics 48 6C The hydrogen atom* 53 6D The strange features of quantum mechanics 58 7 Basic thermodynamics: introduction 63 7A Thermodynamic concepts 63 7B Energy and entropy 64 7C The second law of thermodynamics 67 7D Free energies and chemical potential 68 8 Statistical thermodynamics 71 8A Basic assumption and statistical entropy 71 8B Energy distribution* 76 8C More on micro- and macrostates 78 Part III The general trends and objects 9 Some trends in 20th century physics 81 10 From the simple equilibrium to the complex 85 11 Theoretical physics models: important analogies 92 vi Contents 12 The biological molecules 96 12A General properties of proteins and amino acids 96 12B Sugars 104 12C Nucleic acids 105 12D The genetic code 108 12E Energy-storing substances 111 12F Lipids: membranes 112 13 What is life? 113 Part IV Going further with thermodynamics 14 Thermodynamics formalism and examples: Combinatorial expressions and Stirling’s formula 117 14A General formalism: energy concepts 118 14B Mixing entropy 123 14C Water: solubility 125 14D Formalism of mixing and solutions* 126 14E Chemical thermodynamics* 129 14F Non-equilibrium thermodynamics* 132 15 Examples of entropy and order/disorder 138 15A Shuffling cards 139 15B The monkey library and DNA 140 15C Order and disorder 142 15D The relation to the second law 144 16 Statistical thermodynamics models 146 16A Magnetic analogies and molecule conformations 146 16B Ising-type models of 1D systems* 156 16C Renormalisation methods* 163 16D Spin glass 169 Part V Stochastic dynamics 17 Probability concepts 173 17A Examples 174 17B Normal distribution: approximation of binomial distribution 177 18 Stochastic processes 178 18A Introduction: general account 178 18B Terminology and formal basis 180 18C Ergodicity in biology 181 19 Random walk* 182 19A Formalism 183 19B Absorbing and reflecting boundaries 186 19C First passage time 188 19D Non-intersecting random walk 190 20 Step processes: master equations* 191 20A Poisson process 193 20B Processes with a small number of states and constant transition probabilities 194 20C Formalism: matrix method 195 20D A process with constant average and extinction possibility 201 Contents vii 20E Birth–death process with extinction 203 20F Reaction kinetics as step processes 206 20G Diffusion-controlled reaction as step process 209 20H Barrier passage as step process 212 20I When an average picture goes wrong: mutations and exponential growth 214 21 Brownian motion: first description* 216 21A Introduction 216 21B Formalism 217 21C Brownian motion in linear force fields: fluctuation–dissipation theorem 220 22 Diffusion and continuous stochastic processes* 221 22A Diffusion 221 22B Diffusion-controlled reactions 224 22C Gaussian processes 225 22D Fokker–Planck equations 226 22E Examples: comparisons between master equations and Fokker–Planck equations 230 23 Brownian motion and continuation* 234 23A Fokker–Planck equations for Brownian motion 235 23B Brownian motion in potentials 238 23C Brownian motion description of the passage over a potential barrier 239 23D Low-friction situation 243 23E Brownian motion description of stochastic resonance 245 Part VI Macromolecular applications 24 Protein folding and structure dynamics 249 24A General discussion 249 24B Protein folding as stochastic process 252 24C Stretched kinetics* 253 25 Enzyme kinetics 255 25A Enzyme actions: organisation 255 25B Formalism: basic enzyme kinetics 259 25C Allosteric action* 261 Part VII Non-linearity 26 What does non-linearity do? 267 26A Non-linearity in cells: oscillations, pulses and waves 271 27 Oscillations and space variation* 273 27A Electric circuit 273 27B Chemical oscillating systems 275 27C Neural signal generation 278 27D Diffusion–reaction equations and spatial structures 281 27E Non-linear waves 284 28 Deterministic chaos 288 28A General features of irregular sequences 289 28B Chaotic differential equations* 295 28C Characteristics of chaos* 298 28D Unstable orbits: control of chaos* 307 viii Contents 29 Noise and non-linear phenomena 310 29A General remarks 310 29B Stochastic resonance 311 29C Non-linear stochastic equations 312 Part VIII Applications 30 Recognition and selection in biological synthesis 321 30A Introduction: recognition 321 30B Selection in nucleic acid synthesis 323 30C Selection in protein synthesis 326 30D Formalism in non-branched processes without proofreading* 329 30E Formalism of proofreading kinetics* 332 30F Further features of selection: error propagation 338 31 Brownian ratchet: unidirectional processes 340 32 The neural system 343 32A General discussion 343 32B Spin-glass analogy 346 32C More on network features 348 32D Noise in the neural system 349 33 Origin of life 350 33A Ideas about early molecular evolution 350 33B Thoughts on stability of co-operative systems 362 33C The dynamics of replicating objects in the origin of life* 364 33D Errors and mutations* 367 33E Autocatalytic growth: hypercycles* 371 Part IX Going further 34 Physics aspects of evolution 377 35 Determinism and randomness 383 35A General discussion 384 35B Game of life 387 35C Laplace’s formula 389 35D Macroscopic world 390 35E Final words 392 36 Higher functions of life 392 36A Thinking, memory and the mind 392 36B The free will and determinism 396 37 About the direction of time 401 38 We live in the best of worlds: the anthropic principle 406 References 411 Index 421 * Sections marked by an asterisk are mainly of a mathematical-formula character. Other sections are more or less descriptive. Preface For me, the journey to the physics of life began in the sixties when I was a theoretical physics student searching for a proper subject for a continued carrier. I started with statistical thermodynamics and with lattice models. A great challenge at that time was to provide a proper theory of phase transitions. At the same time I enjoyed reading about the progress and development of molecular biology, in particular, through articles in Scientific American. I read these articles with a physicist’s mind and thought I saw a lot of physics aspects. This was exciting. I had and still have a great interest in Nature and biology, a form of which can be seen on the cover of this book. Then, from some different directions I found that statistical thermodynamics and the models I had started to work with had potential applications in polymer science and in molecular biology. With a support from the growing discipline of biophysics and Rudolf Rigler, Anders Ehrenberg and Måns Ehrenberg, I dared to take the step to begin research in “theoretical biological physics” as it is called nowadays. I got resources to form a small group, which I think became quite successful. This book can be characterised as a mixture of my experience with the field, influences from all co-workers at The Royal Institute of Technology in Stockholm and elsewhere at different times, teaching at different levels and inspirations from numerous discussions on deep ques- tions from those on organisation and the second law of thermodynamics to the esoteric ones about consciousness, determinism and free will. Important inspiration sources for the book are the activities in Agora of biosystems together with Peter Århem and Hans Liljenström as well as the recent discussion group at the Karolinska Institue around Ingemar Ernberg. I want to mention two prominent physicists, whose works are of significant importance to biology. One is Edmé Mariotte, a 17th century French scientist. He among other things, studied pressure and is often mentioned together with the British scientist Robert Boyle for the relation between pressure and volume, often called the Boyle–Mariotte’s law. His physics activities comprised studies in hydrodynamics with applications on the importance of pressure for raising the sap in trees. He also considered vision, found the blind spot in our eyes, and had ideas on colours and paintings, ideas that are still applicable and are referred to at the internet. The other person, Albert Einstein, is maybe the best-known physicist of all times besides Newton. He is famous for the relativity theories, which do not play much role in biological physics. However, he did much more than this, in particular, he made important progress in statistical thermodynamics. In his remarkable year 1905, he had two papers, which were as pioneering as relativity theory. He gave a basis for Brownian motion, and by that could show how the irregular movements of atoms provide observable effects, a very important finding at that time. This is still an important theme that takes a prominent part in my book. He also laid the foundation of quantum mechanics, probably the greatest achievement of the 20th century. By this, he solved some severe dilemmas of light effects and of statistical thermodynamics, which I discuss here as a particular path to quantum mechanics, maybe not the commonest one. He gave the relation between radiation ix