Table Of Content“main” pagei
Physical Models of Living Systems
Philip Nelson
UniversityofPennsylvania
withtheassistanceofSarinaBromberg,
Ann Hermundstad, and Jason Prentice
W. H. Freeman and Company
NewYork
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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
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FormyclassmatesJaniceEnagonio,FengShechao,andAndrewLange.
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Whosedwellingisthelightofsettingsuns,
Andtheroundoceanandthelivingair,
Andthebluesky,andinthemindofman:
Amotionandaspirit,thatimpels
Allthinkingthings,allobjectsofallthought,
Androllsthroughallthings.
–WilliamWordsworth
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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
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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
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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
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1.2.6a Informalcriterionforafalsifiableprediction 21
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viii DetailedContents
1.2.6b Morerealisticviraldynamicsmodels 21
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1.2.6c EradicationofHIV 22
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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
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DetailedContents ix
3.4.1a Extendednegationrule 60
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3.4.1b Extendedproductrule 60
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3.4.1c Extendedindependenceproperty 60
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3.4.4 GeneralizedBayesformula 60
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3.5.2a Skewnessandkurtosis 60
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3.5.2b Correlationandcovariance 61
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3.5.2c Limitationsofthecorrelationcoefficient 62
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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
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4.4.3 MoreabouttheLuria-Delbrückexperiment 89
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4.4.5a AnalyticalapproachestotheLuria-Delbrück
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calculation 89
4.4.5b Othergeneticmechanisms 89
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4.4.5c Non-geneticmechanisms 90
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4.4.5d DirectconfirmationoftheLuria-Delbrückhypothesis 90
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Problems 91
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