Computational Cell Biology

Computational cell biology by FallInterdisciplinary Applied mathematicsVolumes published are listed at the end of this bookSpringerNew yorkBerlinHeidelbergbarcelonaHong KongLondonMilanSingaporeTokyoChristopher P. Fall Eric s. Marland John M. WagnerJohn j. TysonEditorsComputational cell BiologyWith 210 lllustrationsSpringerChristopher P. FallEric s marlandJohn M. WagnerCenter for Neural Science Department of Mathematical Sciences Center for Biomedical ImagingNew York UniversityAppalachian State UniversityTechnologyNew York. NY 10003Boone. nc 28608University of Connecticut HealthUSAUSACenterfall@cns. nyu.edumarlandes@ apostate. eduFarmington. CT 06030USAWagner(@ nsouchc.eduJohn j. TysonDepartment of BiologyVirginia polytechnic InstituteBlacksburg, VA 24061USAtyson@vt.edueditorsS.S. AntmanJE. MarsdenDepartment of mathematicsControl and Dynamical SystemsMail code 10-81Institute for Physical Science and TechnologyCalifornia Institute of TechnologyUniversity of marylandPasadena CA 91125College park, MD 20742USAUSAL. SirovichS. WigginsDivision ofControl and Dynamical SystemsBr.pplied MathematicsMail code 10-81Brown UniversityCalifornia Institute of TechnologProvidence ri 12Pasadena ca 91125USAUSAMathematics Subject Classification(2000): 92-01, 92BXX, 92C30, 92C20Library of Congress Cataloging-in-Publication DataComputational cell biology /editors, Christopher P. Fall... [et al.p cm-(Interdisciplinary applied mathematics)Includes bibliographical references and indexIsBN 0-387-95369-8(alk. paper1. Cytology--Computer simulation. 2. Cytology--Mathematical models. I Fall, Christopher PI. SeriesQH585.5D38C65200571.60113-dc212001054912ISBN0-387-95369-8Printed on acid-free papero 2002 Springer-Verlag New York, IncAll rights reserved. This work may not be translated or copied in whole or in part without the written permission of thepublisher(Springer-Verlag New York, Inc, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts inconnection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval,electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed isforbiddenThe use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified assuch, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rightsPrinted in the united states of america987654321SPIN10853277Springer-Verlag New York Berlin HeidelbergA member of Bertelsmann Springer Science+Business Media gmbHPREFACESoftware: We designed the text to be independent of any particular software, but haveincluded appendices in support of the XPPaut package. XPPAUT has been developedby Bard ermentrout at the University of Pittsburgh, and it is currently available freeof charge. XPPAUT numerically solves and plots the solutions of ordinary differentialequations. It also incorporates a numerical bifurcation software and some methods forstochastic equations. Versions are currently available for Windows, Linux, and Unixsystems. Recent changes in the Macintosh platform(oSX)make it possible to use XPPthere as well. ermentrout has recently published an excellent users manual availablethrough SIAM (Ermentrout 2002)There are a large number of other software packages available that can accomplishmany of the same things as XPPaUt can, such as matlaB, maple v, Mathematica, andBerkeley Madonna. Programming in C or Fortran is also possible. However XPPAUTis easy to use, requires minimal programming skills, has an excellent online tutorialand is distributed without charge. The aspect of Xppaut which is available in veryfew other places is the bifurcation software AUTO, originally developed by e.j. DoedelThe bifurcation tools in XPPAUT are necessary only for selected problems, so manyof the other packages will suffice for most of the book. The the book and web sitecontain code that will reproduce many of the figures in the book as students solve theexercises and replicate the simulations using other packages, we would encourage thesubmission of the code to the editors We will incorporate this code into the web siteand possibly into future editions of the bookThere are many people to thank for their help with this project. Of course, weare deeply indebted to the contributors, who first completed or wrote from scratch thechapters and then dealt with the numerous revisions necessary to homogenize the bookto a reasonable level. Carla Wofsy and Byron Goldstein, as well as albert Goldbeterencouraged us to go forward with the project and provided valuable suggestions. Wethank Chris Dugaw and david Quinonez for their assistance with typesetting severalof the chapters and randy szeto for his work with the graphic design of the book Wethank james Sneyd for many helpful comments on the manuscript, and also Tim Lewisfor commenting on several of the chapters. Carol Lucas generously provided manycorrections for the first half of the text. C.F., .W, and e.M. were supported in part bythe Institute of Theoretical dynamics at UC Davis during some of the preparation ofthe manuscript.We suspect that Joel, for a start, would have thanked Lee Segel, Jim MurrayLeah Edelstein-Keshet and others whose pioneering textbooks in mathematical biol-ogy certainly informed this one. We know that Joel would have thanked many friendsand colleagues for contributing to the true excitement he felt in his "second careerstudying biology. while we have dedicated this work to the memory of joel, Joelsdedication might well have been to his wife, Susan; his daughter, Sarah; his son anddaughter-in-law, Sidney and Noelle; and his grandson, Justin JoelWe hope you enjoy this text, and we look forward to your comments and sugges-tions. We strongly believe that a textbook such as this might serve to help to develop thefield of computational cell biology by introducing students to the subject. This textbookJoel edward Keizer 1942-1999Joel Keizers thirty years of scientific work set a standard for collaborative research intheoretical chemistry and biology. Joel served the University of california at Davis for 28years, as a Professor in the departments of Chemistry and of Neurobiology, Physiologyand Behavior, and as founder and Director of the Institute for Theoretical dynamicsWorking at the boundary between experiment and theory Joel built networks of collab-orations and friendships that continue to grow and produce results. This book evolvedfrom a textbook that Joel began but was not able to finish The general outline andgoals of the book were laid out by joel, on the basis of his many years of teaching andresearch in computational cell biology. Those of us who helped to finish the project-asauthors and editors--are happy to dedicate our labors to the memory of our friend andcolleague, Joel Edward Keizer. All royalties from this book are to be directed to theJoel E. Keizer Memorial Fund for collaborative interdisciplinary research in the lifeSciencesThis page intentionally left blankPrefaceThis text is an introduction to dynamical modeling in cell biology. It is not meantas a complete overview of modeling or of particular models in cell biology. Rather,we use selected biological examples to motivate the concepts and techniques used incomputational cell biology. This is done through a progression of increasingly morecomplex cellular functions modeled with increasingly complex mathematical and computational techniques. There are other excellent sources for material on mathematicalcell biology, and so the focus here truly is computer modeling. This does not mean thatthere are no mathematical techniques introduced because some of them are absolutelyvital, but it does mean that much of the mathematics is explained in a more intuitivefashion, while we allow the computer to do most of the workThe target audience for this text is mathematically sophisticated cell biology orneuroscience students or mathematics students who wish to learn about modeling incell biology. The ideal class would comprise both biology and applied math studentswho might be encouraged to collaborate on exercises or class projects. We assumeas little mathematical and biological background as we feel we can get away withand we proceed fairly slowly. The techniques and approaches covered in the first halfof the book will form a basis for some elementary modeling or as a lead in to moreadvanced topics covered in the second half of the book Our goal for this text is toencourage mathematics students to consider collaboration with experimentalists andto provide students in cell biology and neuroscience with the tools necessary to accessthe modeling literature and appreciate the value of theoretical approachesThe core of this book is a set of notes for a textbook written by joel Keizer before hisdeath in 1999. In addition to many other accomplishments as a scientist, Joel foundedand directed the Institute of Theoretical dynamics at the university of california, DavisIt is currently the home of a training program for young scientists studying nonlinearVIIIPREFACEdynamics in biology. As a part of this training program Joel taught a course entitledComputational Models of Cellular Signaling, " which covered much of the material inthe first half of this bookJoel took palpable joy from interaction with his colleagues, and in addition to histruly notable accomplishments as a theorist in both chemistry and biology, perhaps hisgreatest skill was his ability to bring diverse people together in successful collaborationIt is in recognition of this gift that Joels friends and colleagues have brought this text tocompletion We have expanded the scope but at the core you will still find Joels hand inthe approach, methodology, and commitment to the interdisciplinary and collaborativenature of the field. The royalties from the book will be donated to the joel E. Keizerfoundation at the University of California at Davis, which promotes interdisciplinarycollaboration between mathematics, the physical sciences, and biologyAudience: We have aimed this text at an advanced undergraduate or beginning graduateaudience in either mathematics or biology.Prerequisites: We assume that students have taken full-year courses in calculus andbiology. Introductory courses in differential equations and molecular cell biology aredesirable but not absolutely necessary. Students with more substantial background ineither biology or mathematics will benefit all the more from this text, especially thesecond half. No former programming experience is needed, but a working knowledge ofusing computers will make the learning curve much more pleasant. Note that we oftenpoint students to other textbooks and monographs, both because they are importantreferences for later use and because they might be a better source for the materialInstructors may want to have these sources available for students to borrow or consultOrganization: We consider the first six chapters, through intercellular communicationto be the core of the text. They cover the basic elements of compartmental modelingand they should be accessible to anyone with a minimum background in cell biologyand calculus. The remainder of the chapters cover more specialized topics that can beselected from, based on the focus of the course. Chapters 7 and 8 introduce spatialmodeling, Chapters 9 and 10 discuss biochemical oscillations and the cell cycle, andChapters 11-13 cover stochastic methods and models. These chapters are of varyingdegrees of difficultyFinally, in the first appendix, some of the mathematical and computational con-cepts brought up throughout the book are covered in more detail. This appendix ismeant to be a reference and a learning tool Sections of it may be integrated into thechapters as the topics are introduced The second appendix contains an introduction tothe XPPAUT ODE package discussed below. The final appendix contains psuedocodeversions of the code used to create some of the data figures in the textnternet Resources: This book will have its own web page which will contain a variety of resources. We will maintain a list of the inevitable mistakes and typos andwill make available actual code for the figures in the book. The web address ishttp://www.compcell.appstate.edu