Physical Models of Living Systems PDF
Preview Physical Models of Living Systems
“main” pagei Physical Models of Living Systems Philip Nelson UniversityofPennsylvania withtheassistanceofSarinaBromberg, Ann Hermundstad, and Jason Prentice W. H. Freeman and Company NewYork “main” pageii Publisher:KateParker AcquisitionsEditor:AliciaBrady SeniorDevelopmentEditor:BlytheRobbins AssistantEditor:CourtneyLyons EditorialAssistant:NandiniAhuja MarketingManager:TarynBurns SeniorMediaandSupplementsEditor:AmyThorne DirectorofEditing,Design,andMediaProduction:TraceyKuehn ManagingEditor:LisaKinne ProjectEditor:KerryO’Shaughnessy ProductionManager:SusanWein DesignManagerandCoverDesigner:VickiTomaselli IllustrationCoordinator:MattMcAdams PhotoEditors:ChristineBuese,RichardFox Composition:codeMantra PrintingandBinding:RRDonnelley Cover:[Two-color,superresolutionopticalmicrograph.]Twospecificstructuresinamammaliancell havebeentaggedwithfluorescentmoleculesviaimmunostaining:microtubules(false-coloredgreen) and clathrin-coated pits, cellular structures used for receptor-mediated endocytosis (false-colored red). See also Figure 6.5 (page 138). The magnification is such that the height of the letter“o”in thetitlecorrespondstoabout1.4µm.[ImagecourtesyMarkBates,Dept.ofNanoBiophotonics,Max PlanckInstituteforBiophysicalChemistry,publishedinBatesetal.,2007.Reprintedwithpermission fromAAAS.]Inset:Theequationknowntodayasthe“Bayesformula”firstappearedinrecognizable formaround1812,intheworkofPierreSimondeLaplace.Inournotation,theformulaappearsas Equation3.17(page52)withEquation3.18.(Theletter“S”inLaplace’soriginalformulationisan obsoletenotationforsum,nowwrittenas .)Thisformulaformsthebasisofstatisticalinference, includingthatusedinsuperresolutionmicroscopy. P Titlepage:IllustrationfromJamesWatt’spatentapplication.Thegreenboxenclosesacentrifugal governor.[FromAtreatiseonthesteamengine:Historical,practical,anddescriptive (1827)byJohn Farey.] LibraryofCongressPreassignedControlNumber:2014949574 ISBN-13:978-1-4641-4029-7 ISBN-10:1-4641-4029-4 ©2015byPhilipC.Nelson Allrightsreserved PrintedintheUnitedStatesofAmerica Firstprinting W.H.FreemanandCompany,41MadisonAvenue,NewYork,NY10010 Houndmills,BasingstokeRG216XS,England www.whfreeman.com “main” pageiii FormyclassmatesJaniceEnagonio,FengShechao,andAndrewLange. “main” pageiv Whosedwellingisthelightofsettingsuns, Andtheroundoceanandthelivingair, Andthebluesky,andinthemindofman: Amotionandaspirit,thatimpels Allthinkingthings,allobjectsofallthought, Androllsthroughallthings. –WilliamWordsworth “main” pagev Brief Contents Prolog:A breakthrough on HIV 1 PART I First Steps Chapter 1 Virus Dynamics 9 Chapter 2 Physics and Biology 27 PART II Randomness in Biology Chapter 3 Discrete Randomness 35 Chapter 4 Some Useful Discrete Distributions 69 Chapter 5 Continuous Distributions 97 Chapter 6 Model Selection and Parameter Estimation 123 Chapter 7 Poisson Processes 153 JumptoContents JumptoIndex v “main” pagevi vi BriefContents PART III Control in Cells Chapter 8 Randomness in Cellular Processes 179 Chapter 9 Negative Feedback Control 203 Chapter 10 Genetic Switches in Cells 241 Chapter 11 Cellular Oscillators 277 Epilog 299 AppendixA Global List of Symbols 303 Appendix B Units and DimensionalAnalysis 309 Appendix C NumericalValues 315 Acknowledgments 317 Credits 321 Bibliography 323 Index 333 JumptoContents JumptoIndex “main” pagevii Detailed Contents WebResources xvii TotheStudent xix TotheInstructor xxiii Prolog:A breakthrough on HIV 1 PART I First Steps Chapter 1 Virus Dynamics 9 1.1 FirstSignpost 9 1.2 ModelingtheCourseofHIVInfection 10 1.2.1 Biologicalbackground 10 1.2.2 Anappropriategraphicalrepresentationcanbring outkeyfeaturesofdata 12 1.2.3 Physicalmodelingbeginsbyidentifyingthekeyactorsand theirmaininteractions 12 1.2.4 Mathematicalanalysisyieldsafamilyofpredicted behaviors 14 1.2.5 Mostmodelsmustbefittedtodata 15 1.2.6 Overconstraintversusoverfitting 17 1.3 JustaFewWordsAboutModeling 17 KeyFormulas 19 Track2 21 1.2.4 Exitfromthelatencyperiod 21 ′ 1.2.6a Informalcriterionforafalsifiableprediction 21 ′ JumptoContents JumptoIndex vii “main” pageviii viii DetailedContents 1.2.6b Morerealisticviraldynamicsmodels 21 ′ 1.2.6c EradicationofHIV 22 ′ Problems 23 Chapter 2 Physics and Biology 27 2.1 Signpost 27 2.2 TheIntersection 28 2.3 DimensionalAnalysis 29 KeyFormulas 30 Problems 31 PART II Randomness in Biology Chapter 3 Discrete Randomness 35 3.1 Signpost 35 3.2 AvatarsofRandomness 36 3.2.1 Fiveiconicexamplesillustratetheconceptofrandomness 36 3.2.2 Computersimulationofarandomsystem 40 3.2.3 Biologicalandbiochemicalexamples 40 3.2.4 Falsepatterns:Clustersinepidemiology 41 3.3 ProbabilityDistributionofaDiscreteRandomSystem 41 3.3.1 Aprobabilitydistributiondescribestowhatextentarandom systemis,andisnot,predictable 41 3.3.2 Arandomvariablehasasamplespacewithnumerical meaning 43 3.3.3 Theadditionrule 44 3.3.4 Thenegationrule 44 3.4 ConditionalProbability 45 3.4.1 Independenteventsandtheproductrule 45 3.4.1.1 Cribdeathandtheprosecutor’sfallacy 47 3.4.1.2 TheGeometricdistributiondescribesthewaiting timesforsuccessinaseriesofindependenttrials 47 3.4.2 Jointdistributions 48 3.4.3 Theproperinterpretationofmedicaltestsrequiresan understandingofconditionalprobability 50 3.4.4 TheBayesformulastreamlinescalculationsinvolving conditionalprobability 52 3.5 ExpectationsandMoments 53 3.5.1 Theexpectationexpressestheaverageofarandomvariable overmanytrials 53 3.5.2 Thevarianceofarandomvariableisonemeasureofits fluctuation 54 3.5.3 Thestandarderrorofthemeanimproveswithincreasing samplesize 57 KeyFormulas 58 Track2 60 JumptoContents JumptoIndex ‘‘main’’ page ix DetailedContents ix 3.4.1a Extendednegationrule 60 ′ 3.4.1b Extendedproductrule 60 ′ 3.4.1c Extendedindependenceproperty 60 ′ 3.4.4 GeneralizedBayesformula 60 ′ 3.5.2a Skewnessandkurtosis 60 ′ 3.5.2b Correlationandcovariance 61 ′ 3.5.2c Limitationsofthecorrelationcoefficient 62 ′ Problems 63 Chapter 4 Some Useful Discrete Distributions 69 4.1 Signpost 69 4.2 BinomialDistribution 70 4.2.1 Drawingasamplefromsolutioncanbemodeledintermsof Bernoullitrials 70 4.2.2 ThesumofseveralBernoullitrialsfollowsaBinomial distribution 71 4.2.3 Expectationandvariance 72 4.2.4 Howtocountthenumberoffluorescentmoleculesina cell 72 4.2.5 Computersimulation 73 4.3 PoissonDistribution 74 4.3.1 TheBinomialdistributionbecomessimplerinthelimitof samplingfromaninfinitereservoir 74 4.3.2 ThesumofmanyBernoullitrials,eachwithlowprobability, followsaPoissondistribution 75 4.3.3 Computersimulation 78 4.3.4 Determinationofsingleion-channelconductance 78 4.3.5 ThePoissondistributionbehavessimplyunder convolution 79 4.4 TheJackpotDistributionandBacterialGenetics 81 4.4.1 Itmatters 81 4.4.2 Unreproducibleexperimentaldatamayneverthelesscontainan importantmessage 81 4.4.3 Twomodelsfortheemergenceofresistance 83 4.4.4 TheLuria-Delbrückhypothesismakestestablepredictionsfor thedistributionofsurvivorcounts 84 4.4.5 Perspective 86 KeyFormulas 87 Track2 89 4.4.2 Onresistance 89 ′ 4.4.3 MoreabouttheLuria-Delbrückexperiment 89 ′ 4.4.5a AnalyticalapproachestotheLuria-Delbrück ′ calculation 89 4.4.5b Othergeneticmechanisms 89 ′ 4.4.5c Non-geneticmechanisms 90 ′ 4.4.5d DirectconfirmationoftheLuria-Delbrückhypothesis 90 ′ Problems 91 JumptoContents JumptoIndex
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