Table Of ContentPHYSICS 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 statis-
tical 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
