Chapman & Hall/CRC Computational biology has developed rapidly during the last two C Mathematical and Computational Biology Series decades following the genomic revolution which culminated in the o sequencing of the human genome. More than ever it has developed m into a field which embraces computational methods from different p branches of the exact sciences: pure and applied mathematics, u computer science, theoretical physics. This Second Edition provides t a solid introduction to the techniques of statistical mechanics for a graduate students and researchers in computational biology and t i biophysics. o n • Material has been reorganized to clarify equilibrium and a nonequilibrium aspects of biomolecular systems l • Content has been expanded, in particular in the treatment of the B electrostatic interactions of biomolecules and the application of i non-equilibrium statistical mechanics to biomolecules o • New network-based approaches for the study of proteins are l o presented. g All treated topics are put firmly in the context of the current research y literature, allowing the reader to easily follow an individual path S into a specific research field. Exercises and Tasks accompany the e presentations of the topics with the intention of enabling the readers c o to test their comprehension of the developed basic concepts. n d Ralf Blossey is a Research Director at the French National Center E d for Scientific Research, the CNRS, and is based in Lille, in the North i t i of France. His work during the last fifteen years has focused on the o n Computational Biology application of statistical mechanics methods to DNA, proteins, gene regulatory networks and chromatin. He has collaborated with many scientists from computer science, mathematics, computational A Statistical Mechanics Perspective B biology, molecular and cellular biology, as well as colleagues from l his original field of training, statistical physics. o s Second Edition s e y COMPUTER SCIENCE & ENGINEERING Ralf Blossey CRC Press titles are available as eBook editions in a range of digital formats K377353_cover.indd All Pages 5/13/19 10:21 AM Computational Biology A Statistical Mechanics Perspective Second Edition Computational Biology A Statistical Mechanics Perspective Second Edition Ralf Blossey CRCPress Taylor&FrancisGroup 6000BrokenSoundParkwayNW,Suite300 BocaRaton,FL33487-2742 (cid:13)c 2019byTaylor&FrancisGroup,LLC CRCPressisanimprintofTaylor&FrancisGroup,anInformabusiness NoclaimtooriginalU.S.Governmentworks Printedonacid-freepaper InternationalStandardBookNumber-13:978-1-138-58786-1(Hardback) Thisbookcontainsinformationobtainedfromauthenticandhighlyregardedsources.Rea- sonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the conse- quences of their use. The authors and publishers have attempted to trace the copyright holdersofallmaterialreproducedinthispublicationandapologizetocopyrightholdersif permissiontopublishinthisformhasnotbeenobtained.Ifanycopyrightmaterialhasnot beenacknowledgedpleasewriteandletusknowsowemayrectifyinanyfuturereprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means,nowknownorhereafterinvented,includingphotocopying,microfilming,andrecord- ing,orinanyinformationstorageorretrievalsystem,withoutwrittenpermissionfromthe publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com(http://www.copyright.com/)orcontacttheCopyrightClearanceCen- ter, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not- for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system ofpaymenthasbeenarranged. Trademark Notice:Productorcorporatenamesmaybetrademarksorregisteredtrade- marks,andareusedonlyforidentificationandexplanationwithoutintenttoinfringe. Library of Congress Cataloging-in-Publication Data Names:Blossey,Ralf,author. Title:Computationalbiology:astatisticalmechanicsperspective/ RalfBlossey. Description:Secondedition.|BocaRaton,Florida:CRCPress,[2020]| Series:Chapman&Hall/CRCmathematicalandcomputationalbiology| Includesbibliographicalreferencesandindex. Identifiers:LCCN2019011496|ISBN9781138587861(hbk:alk.paper)| ISBN9780429503672(ebk) Subjects:LCSH:Biomolecules--Mechanicalproperties.|Statistical mechanics.|Computationalbiology. Classification:LCCQH506.B572020|DDC572.80285--dc23 LCrecordavailableathttps://lccn.loc.gov/2019011496 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To SyMaNi and Mum Contents PREFACE TO THE SECOND EDITION ix PREFACE TO THE FIRST EDITION xi Part I Equilibrium Statistical Mechanics Chapter 1(cid:4) Equilibrium Statistical Mechanics 3 1.1 Z: THE PARTITION FUNCTION 3 1.2 RELATION TO THERMODYNAMICS 7 1.3 COMPUTING Z 13 1.4 THE ISING MODEL 15 Chapter 2(cid:4) Biomolecular Structure: DNA, RNA, Proteins 39 2.1 DNA, RNA AND PROTEINS: THE BUILDING BLOCKS 39 2.2 REPRESENTING RNA STRUCTURE 47 2.3 COMPUTING RNA SECONDARY STRUCTURE: COMBINATORICS 51 2.4 THE RNA PARTITION FUNCTION 55 2.5 PROTEIN FOLDING AND DOCKING 61 2.6 PULLING DNA 68 Chapter 3(cid:4) Phase Transitions in RNA and DNA 83 3.1 RNA PHASE BEHAVIOUR 83 3.2 THE DNA MELTING TRANSITION 86 3.3 THE MELTING PROFILES OF GENOMIC DNA AND CDNA 98 vii viii (cid:4) Contents Chapter 4(cid:4) Soft Matter Electrostatics 119 4.1 THE FREE ENERGY OF ELECTROSTATIC SYSTEMS 119 4.2 THE POISSON-BOLTZMANN EQUATION 122 4.3 PROTEIN ELECTROSTATICS 126 4.4 CHROMATIN ELECTROSTATICS 131 Part II Non-equilibrium Statistical Mechanics Chapter 5(cid:4) Back to P: Probabilities over Time 151 5.1 STOCHASTIC PROCESSES 152 5.2 THE MASTER EQUATION 155 5.3 THE FOKKER-PLANCK AND LANGEVIN EQUATIONS 163 5.4 SEQUENCEALIGNMENT:ANON-EQUILIBRIUMPHASE TRANSITION 176 Chapter 6(cid:4) Fluctuation Theorems 191 6.1 THE FLUCTUATION-DISSIPATION THEOREM 191 6.2 THE JARZYNSKI EQUALITY AND CROOKS’ THEOREM 193 6.3 APPLICATIONS OF THE FLUCTUATION THEOREMS 195 Chapter 7(cid:4) Dynamics of Biological Networks 207 7.1 THE λ-REPRESSOR 208 7.2 DYNAMICS OF GENE REGULATORY NETWORKS 216 7.3 INTRINSIC NOISE 226 Chapter 8(cid:4) Biological Networks: Space 245 8.1 EXTRINSIC VS. INTRINSIC NOISE 245 8.2 THE TURING INSIGHT 249 8.3 NETWORKS AS GRAPHS 256 8.4 STATISTICAL MECHANICS OF NETWORKS 263 8.5 SMALL WORLDS 267 Index 281 Preface to the Second Edition I am grateful to the publisher who asked me to renew my book as a second edition. Indeed, after more than ten years, the field of computational biol- ogy/statistical physics—the particular interface of two fields I am interested in—has matured in many ways. Going through the first edition again was a great pleasure when comparing past views to current insights. As a consequence, the book has substantially changed while maintaining its corecontents.Newmaterialhasbeenadded,butinparticularIhavereworked its whole architecture. In the second edition, there are only two parts: one on equilibrium statistical physics and one on non-equilibrium statistical physics. Thetheoreticaltoolsinthesefieldsthatthebookintroducesareplacedatthe beginning of each part, and then the applications follow. I hope that this new structure will help the readers to master the material. As a side effect of following the now classic dichotomy of statistical physics— equilibrium and non-equilibrium—the focus on universal aspects, those that statistical physics is most attuned to, has been sharpened. Even more than before, this makes the book not a biophysics book. Since 2006, when the first edition went into print, new books on biophysics have appeared, especially bioinformatics books. I hope that with its modifications, including updated additional notes to the literature and references, this book will continue to find its readership and help to introduce its readers to this exciting field of research. Lille, February 2019 Ralf Blossey ix