系統(tǒng)生物學IV－細胞仿真學習資料

劉筆鋒教授華中科技大學生命科學與技術學院系統(tǒng)生物學IV------細胞仿真1Content1.VirtualBiologicalLaboratory2.ComputationalCellBiology—TheStochasticApproach計算細胞生物學——隨機法3.AWhole-CellComputationalModel計算模型PredictsPhenotypefromGenotype2VirtualBiologicalLaboratoryOutlineForasystem-levelunderstandingoflivingcells,aquantitativerepresentationofthesesystemsinvolvingmathematicalmodelsandcorrespondingcomputertoolsisrequired.

Modelingconceptwhichreliesuponmodularstructuringofcellularsystemsfocusingstronglyonthebiomolecularstructureofthesesystems.IntheVirtualBiologicalLaboratory,theprocessmodelingtoolPROMOTcontainsanobject-orientedknowledgebasewithreusablemodelingentitiesandenablesapurelysymbolicalmodeldevelopmentprocessviaagraphicaluserinterface.ThesimulationenvironmentDIVAthenusesthemodellibraryfordynamicsimulation,parameterestimationandmodelanalysis.

TwoexamplesofmodelsofcomplexregulatorynetworksinEscherichiacoliandinSaccharomycescerevisiaearegiven.3VirtualBiologicalLaboratoryIntroductionCurrentstatusSystem-levelunderstandingofhowcellsandorganismsfunctionisactuallyveryrudimentary,duetotworeasons:系統(tǒng)水平上理解細胞和生物體的功能處于非常初級的階段。主要原因：1.Theoverwhelmingpartofexperimentalinvestigationscanbecharacterizedasqualitativeanddescriptive.2.duetothecomplexityofcellularsystemseventhe(nearly)completemeasurementofthesystems’stateswillnotenableanintegratedunderstandingofallrelevantfunctionalconnectionsandtheirinfluenceontheobservablebehavior.系統(tǒng)水平上理解細胞和生物體的功能處于非常初級的階段。主要原因：其一，對于生物分子細節(jié)的理解，目前絕大部分的實驗是定性的和描述性的；其二，由于細胞系統(tǒng)的復雜性，即使是對系統(tǒng)狀態(tài)本身完全（或接近完全）的測量也無法獲得所有相關功能聯(lián)系的整體性認識，以及它們對于可觀察行為的影響。4VirtualBiologicalLaboratoryIntroductionApproach:mathematicalmodelsExamples:E-Cell(Tomitaetal.,1999),VirtualCell(Schaffetal.,1997)twomajorchallengesfortheapplicationofmathematicalconceptsinthelifesciencesstillhavetoberesolved:1.Aconceptionalframeworkpromotinginterdisciplinaryresearchinthisdirectionbyfindinga”common”,non-mathematicallanguage.2.Aclearlydefinedmodelingconceptadaptedtocellularsystemsthatallowsforeasymodeldevelopmentandinterpretation.systemsarecomposedof’functionalunitsormodules.system-andsignal-orientatedmodelingconceptforcellularsystems.5VirtualBiologicalLaboratoryModularModelingConceptWhyandHowitcouldbepossible?Livingcellbeingcomposedofsubunitsoflimitedautonomy(functionalunits).Submodelsasentitiesinthe”modelworld”correspondtofunctionalunitsinthe”realworld”.Identificationandrepresentationoffunctionalunits,thatis,howtodemarcatetheseunits,i.e.howtodecomposeacomplexcellularbiochemicalnetworkintosmallerunits.6VirtualBiologicalLaboratory1.GeneralreflectionsonmetabolismandcellularregulationAtaveryabstractlevel,acellcanbedividedintotwogeneralsub-networks,aregulatorynetwork(informationflow)andametabolicnetwork(massflow).ModularModelingConcept7VirtualBiologicalLaboratory1.GeneralreflectionsonmetabolismandcellularregulationForasystem-wideunderstandinganddescriptionofcellularfunction,theserelationsbetweenmetabolismandregulationimplytwomajorconsequences:Firstly,duetotheirprominentroleinbringingaboutthesystems’behaviour,cellularregulationhastobedescribedinamorecoherent(anddetailed)waythanin”traditional”approachestomathematicalmodeling.Secondly,moreattentionhastobegiventoasignal-orientedviewofthesesystems,whichuntilnowhavemainlybeenconsideredfromamass-floworientedpointofview.ModularModelingConcept8VirtualBiologicalLaboratory1.Generalreflectionsonmetabolismandcellularregulation一般的在新陳代謝和細胞調控反映Ascellularregulationisestablishedbyespeciallycomplexgeneandproteinnetworks,acloserlookattheoverallstructureofcellularregulationmayhelptodealwiththiskindofcomplexity.Inthisrespect,oneimportantfeatureoftheregulatorynetworkisitshierarchicalstructure.分級結構ModularModelingConcept9VirtualBiologicalLaboratoryModularModelingConcept1.GeneralreflectionsonmetabolismandcellularregulationForthesystem-widedescriptionofacell,capturingtheseconstitutive基本的principlesinthemodelingprocesshasfirstofallthenegativeconsequenceofresultingindetailedandthusseemingly表面上似乎morecomplexmathematicalmodels.Thisiscompensated不常forbyseveraladvantagesasthedetaileddescriptionenables:(i)toconsidersystem-wide全系統(tǒng)的coupling耦合ofcellularregulationandhencetodescribetheinterplay相互影響ofglobalandlocalcontrol.(ii)tointegrate整合knowledgeonwell-characterizedgeneralcomponentsinordertogreatlyfacilitate幫助parameterdeterminationforspecialsubsystems子系統(tǒng).(iii)

toexploit開發(fā)hierarchicalnetwork分級網(wǎng)絡structuresformodelreduction.10VirtualBiologicalLaboratoryModularModelingConcept2.Identificationandrepresentationoffunctionalunits功能單位Asweaimatintegratingcellularmass-andsignalprocessingfunctions,eachofthesefunctionalunitshastobecomposedofapartofthemetabolicnetworkandacorresponding相應的partoftheregulatorynetwork.Forthisdemarcation劃分,weuseapreliminary初步的setofthreebiologicallymotivatedcriteria動機標準.Tobe(relatively)self-contained獨立的,themoduleshave:

(i)toperform執(zhí)行acommonphysiologicaltasksuchasrepresentalinearpathwayforaminoacidsynthesis.(ii)tobecontrolledatthegeneticlevelbycommonregulatorsi.e.identical同一的transcriptionfactors/theorganizationinoneoperon.(iii)

topossess擁有acommoninformationprocessing(signaltransduction)network.Essentialfeature基本特征isthecombinationofclassicalconceptsintheanalysisofmetabolicsystemswithasignal-oriented面向信號perspective觀點，透視圖tocellularregulation.11VirtualBiologicalLaboratorye.g.12VirtualBiologicalLaboratoryModularModelingConcept2.IdentificationandrepresentationoffunctionalunitsAtthemostfundamentallevel,afinite有限的anddisjunct分離的setof”elementarymodelingobjects”hasbeendefined.13VirtualBiologicalLaboratoryModularModelingConcept2.IdentificationandrepresentationoffunctionalunitsPropertiesofelementarymodelingobjects:(i)Theyhavestructuralpropertiesrepresentingthenumberandtypesofinputsandoutputs.Asimplesubmodelforanenzymatic酶的reaction,forinstance,needsatleasttwoinputs/outputsconnectedwithmassflowofsubstrate/productandonecontrolsignalforenzymeconcentration.(ii)Themodelingobjectsareassignedbehaviouralproperties行為道具,i.e.mathematicalequationsdescribingthedynamicbehaviour.(iii)Furthermore,eachmodelingobjectisassignedaspecificsymbolicrepresentation.象征符號14VirtualBiologicalLaboratoryModularModelingConcept2.IdentificationandrepresentationoffunctionalunitsElementarymodelingobjectscansubsequently隨后beinterconnected聯(lián)系的toformhigheraggregatedstructures.15ModularModelingConceptSummaryThemodularmodelingapproachenablesonetoprogressivelyobtainaholisticdescriptionofmorecomplexfunctionalunits.Theorganizationofthesemodelingobjectsinanobject-orientedclasshierarchyalsolaysthebasisforcomputer-aidedmodeldevelopment.VirtualBiologicalLaboratory16VirtualBiologicalLaboratoryVirtualBiologicalLaboratory(VBL):OutlinePurpose:toenablecomputerexperimentswithcellularsystemsinanalogytoexperimentscarriedoutwithrealbiologicalsystemsinthelaboratory.Application:quantitativeandqualitativeanalysisofoverallbehaviour,systematicdesignoffunctionalunitsbygeneticmodificationsandthesystematicplanningofreallaboratoryexperiments.Structure:integratingmathematicalmodelswithasound健全的biologicalbackgroundandmethodsfordatastorage數(shù)據(jù)儲存,computer-aidedmodeling,simulationandmodelanalysisinasoftwaretool.Accordingly,thedevelopmentofsuchatoolrequirestheclosecooperationofbiologists,informationscientistsandsystemscientists.17amaximalconvergenceof”modelworld”and”realworld”VirtualBiologicalLaboratory18Theprocessmodelingtool:PROMOT,originallydesignedforapplicationinchemicalengineering.Thesimulationenvironment:DIVA,forthenumericalanalysisoftheresultingmodels.PROMOT

distinguishes

structural,behaviouralandobject-orientedmodeling.

VirtualBiologicalLaboratory19Duringstructuralmodeling,modulesandtheirinterfaces,thesocalledterminals,areidentifiedaccordingtothebiologicalmodelingconceptandaggregated聚集inanaggregationhierarchyofmodules.Oneverylevelofthishierarchythemodulesarelinkedtogetherusingtheirterminals.Theselinksrepresenttheexchangeofmaterial,momentum動量,energyorinformationbetweenthemodules.

Modulescontainbehaviouralmodelingentities實體,i.e.variablesandequations.Theyformadifferentialalgebraic微分方程equationsystem(DAE),thatisusedduringthesimulation.

PROMOTnotonlyallowsforthedevelopmentofseparatemodelsbut,italsoenablestheimplementationanduseofflexible,object-orientedknowledgebasescontainingreusablemodelingentities.Thestructuralandbehaviouralmodelingentitiesarerepresentedasmodelingclasses.Userscannotonlyaggregatemodelingentitieswhicharealreadycontainedintheknowledgebasebuttheyarealsoabletoextendmodelingclassesbyaspecialsubclass(e.g.touseaspecialenzymekinetic)withoutre-implementingthecommonparts.VirtualBiologicalLaboratory20e.g.VirtualBiologicalLaboratory21Usingknowledgebases,modelformulationmeanstheselectionandlinkingofpre-definedmodelingobjectsviatheGUIandparametrizingtheresultingmodel.

Usingflexibleandseparatelytestedmodulesitshouldbepossibletobuildupverylargeandcomplexcellularmodelsinasimilarway,e.g.amodelofawholecell.(unliketheE-Cell)MathematicalmodelsgeneratedusingPROMOTcanbeanalyzedwithinthesimulationenvironmentDIVAThissimulationtoolhasbeendesignedespeciallyfordealingwithlarge-scaledynamical(differential-algebraic)systems,whichariseinchemicalprocessengineering,butalsointhemathematicalmodelingofcomplexcellularnetworks.ModelsinDIVAarehandledbysparse-matrixnumericswhichmakesthesimulatorcapabletoworkonmodelswithupto5000differentialequations.InsideDIVAmanydifferentnumericalcomputationscanbeperformedbasedonthesamemodel.VirtualBiologicalLaboratory22Therearecurrentlyfourmethodsforcellularmodels:(i)Dynamicsimulationofthemodelwithdifferentintegrationalgorithms集成算法;(ii)Sensitivityanalysisforparameterswithrespecttoexperimentaldata;(iii)Parameteridentificationaccordingtoexperimentaldata;(iv)Model-basedexperimentaldesign.Thevisualization形象化andpost-processing后處理ofthesimulationresultsaredonewithinthestandardnumericsoftwareMATLAB.ForaConclusionThecombinationofPROMOTandDIVAiswellsuitedtoformthecoreofthe”electronicinfrastructure”ofaVBL.VirtualBiologicalLaboratory23EXAMPLE1:CataboliterepressioninE.coli

Lactosetransportandmetabolism:Theregulatoryproteinsinvolvedinglucose-lactosediauxieinE.coliinfluencetheexpressionofthelactosemetabolizingenzymes.Thelactoserepressor,LacI,isabletobindtoacontrolsequenceinfrontofthelacoperonintheabsenceoflactose,therebyinhibitingtranscriptionfromlacZp.Thisrepressionisrelievedinthepresenceofallolactose,thenaturalmolecularinducerofthelacoperon.Globalsignaltransduction:AdditionalcontrolisexertedbytheCrpprotein.Thisproteinisactiveintheregulationofanumberofoperons,mostinvolvedincarbohydrateuptake.TheCrpproteinisabletoformacomplexwithcAMP,thatactsasatranscriptionalactivatorforthelacoperonaswellasfortheothermembersofthecrpmodulon.TheconcentrationofthealarmonecAMPinsidethecellisregulatedbycomplexmechanisms.VirtualBiologicalLaboratory24Themodelshowsahierarchicalstructure:Thepathwaysforglucoseandlactoseareunderthecontrolofasuperimposedsignaltransductionpathway.25AmathematicalmodelCataboliterepressioninE.coli:

SimulationandexperimentalresultsforE.coliK-12wildtype.26Tosummarizetheresultsofthismodel:(i)themodelquantitativelydescribesexperimentalresultsobtainedwithanumberofmutantstrains;(ii)themodelallowsthepredictionofthetimecourseofnotyetmeasurablevariableslikecAMP;(iii)themodelcanbeusedasabasisforfurtheranalysis.Itisnowusedtotesthypothesisesaboutregulatoryphenomenainfluencingthegrowthofsomemutantstrains.VirtualBiologicalLaboratory27G1checkpointG1G2G2checkpointMcheckpointMSControl

systemEXAMPLE2:CellcycleregulationinBuddingyeastG1checkpointG028VirtualBiologicalLaboratory2930Tosummarizetheresultsofthismodel:(i)biologicalknowledgeontheregulatorynetworkunderconsiderationissufficienttoexplaintheobservedbehaviour;(ii)theseeminglycomplexbehaviourresultsfromtheinterplayofregulatorycircuits,whichhavetobeviewedinaquantitativewaytogetaclueontheentirenetwork’sfunction;(iii)mathematicalmodelinggiveshintsthatthisnetworkconstitutesarelativelyrobustregulatorymodule.VirtualBiologicalLaboratory31VirtualBiologicalLaboratoryConclusion(i)Findingconceptstodealwiththecomplexityoflivingsystemsrepresentsthemajorchallengeonthewaytoasystem-levelunderstandingofcellsandorganisms;(ii)Itessentiallyreliesuponthemodularmathematicalmodelingoftheoverallbehaviourofcellularfunctionalunits.Thedecomposition分解ofcellsintosuchunitsisoriented定向atthemodularbiomolecularstructureofcellularsystems;(iii)Thisdemarcation劃分alsorepresentsthemostcrucial重要的aspectofthemodelingconceptasmainlyheuristiccriteria啟發(fā)式標準areappliedatthemoment.32ComputationalCellBiologyTheStochasticApproachOutlineAlthoughtheneedforcomputationalmodelingandsimulationincellbiologyisnowwidelyappreciated,theconventionalapproach

常規(guī)方法ofrepresentingbiochemicalreactionsbycontinuous,deterministicrateequations,cannoteasilybeappliedtointracellularprocessesbasedonmulti-proteincomplexes,orthosethatdependontheindividualbehaviourofsmallnumbersofmolecules.

Stochasticmodeling隨機模型hasemerged出現(xiàn)asanalternative,andphysicallymorerealistic,approachtophenomenasuchasintracellularsignalingandgeneexpression.HereweintroducetheSTOCHSIMalgorithm算法andprovideacomparisonofwithanotherpopularstochasticapproachdevelopedbyGillespie.33Chemicalsignalingcascadeisthemostfundamentalinformationprocessingunitinbiologicalsystems.Photoreceptor Vertebratephotoreceptorconvertsexternalenergy(lightquanta)intoachangeinconcentrationintracellularsignalingproteins(Ca2+??Vesicalrelease??).Chemotaxis

E.colichemotaxisnetworkconvertsexternalchangeofstimulusintoachangeinconcentrationofsignalingproteinCheYp,whichcontrolscellmotilebehavior.UseE.colichemotaxisnetworkasaprototypetoexplorethegeneralinformationprocessingprincipleinbiologicalsystems.InformationProcessinginBiologicalSystemsComputationalCellBiologyTheStochasticApproach34Background:IntroductiontoChemotaxisinE.coliFluorescentlylabeledE.coliDimensions: Bodysize:1μminlength 0.4μminradius Flagellum:10μmlong

45nmindiameterPhysicalconstants: Cellspeed:20-30μm/sec Meanruntime:1sec Meantumbletime:0.1secOneofthekeyfeaturesofE.colichemotaxisnetwork:Adaptation.ComputationalCellBiologyTheStochasticApproach35Adaptationistherestorationofpre-stimulusbehaviorfollowingachangeinexternalstimulus.Fig.1Adaptationtoaddition/removalofstimuli.Attractant:30μMMeAsp.Repellent:100μMNiCl2YFP/CFP~[CheYp]Whyresponsevary?Fig.2TheleftmostcurveistherelationbetweentheadaptationtimeofE.coliandstep-wisechangeof[MeAsp](1e-2~1e+4μM).ComputationalCellBiologyTheStochasticApproach36SignalTransductionPathwayMotorResponseStimulusFlagellarResponse(?)MotionComputationalCellBiologyTheStochasticApproach37SignalTransductionNetworkComputationalCellBiologyTheStochasticApproach38WithStochsim,ageneralplatformforsimulatingreactionsusingastochasticmethod,tosimulatereactions.Reactionshaveaprobabilitiesptooccur.Unimolecularreaction單分子反應n:Numberofmoleculesfromreactionsystemn0:Numberofpseudo-moleculesNA:Avogadroconstantp:Probabilityforareactiontohappen

Δt:SimulationtimestepV:SimulationvolumeBimolecularreaction雙分子反應ComputationalCellBiologyTheStochasticApproach39ParametersValuesforReceptorActivationEn:methylatedreceptorcomplex;activationprobability,P1(n)Ena:ligand-boundreceptorcomplex;activationprobability,P2(n)En*:activeformofEn

En*a:activeformofEnaActivationProbabilitiesnP1(n)P2(n)00.020.0029110.10.0220.3120.130.940.34540.9970.98ComputationalCellBiologyTheStochasticApproach40ParametersValuesforProteinsReactionVolume:1.41x10-15literRateconstantsgivenabove.InitialNumbersofMoleculesMoleculeNumberConcentration(μM)Y1568418Yp00R2500.29E6276-B19282.27Bp00ComputationalCellBiologyTheStochasticApproach41ParameterValueforMotorResponse運動反應ParametersvaluesParameterValueLiteraturevalueKR5.9μM3~12μMKT1.7μM1~7μMKf(0)1.0E-5μM3.35E-4μMKb(0)1.5E+4μM2.2E+4μMμ2.211.61ComputationalCellBiologyTheStochasticApproach42Outputofthechemotaxisnetworkisthemotorstatewhichdeterminesthemotilebehavior.

Rrun TtumbleRun

Tumble

tt+Δtv=20μm/sDr=0.06205s-1

αγ=4μ=-4.6β=18.32FromMotorResponsetoCellMotion細胞運動ComputationalCellBiologyTheStochasticApproach43ModelValidation:

StepResponseandAdaptationTime適應時間

E.colimotorresponseto10μMstep-wisechangeofAspatt=5sec.ThemotorCCWbiasisplottedasafunctionoftime. Adaptationtimeundervariousstep-wisechangeof[Asp]from0to0.1,1,10,100,respectively.AdaptationtimeisdefinedasthemotorCCWbiasreturnstoitspre-stimulusvalue.(1000isrunning)ComputationalCellBiologyTheStochasticApproach44Impulseresponseofwild-typecell，impulseduration0.2sec.Left:ExperimentalresultfromStevenM.Blocketall,Cell(1982)Right:Simulationresult(datasmoothed)ModelValidation:

ImpulseResponseofWild-typeCell脈沖響應ComputationalCellBiologyTheStochasticApproach45ModelValidation:校驗

Running&TumblingIntervals翻滾的間隔ThedistributionofmotorCCWandCWevents.Left:korobkovaetal.,2004Right:Simulationresults.(Red:CCWevents;Black:CWevents)ComputationalCellBiologyTheStochasticApproach46Comparison:(i)TheGillespiealgorithmmakestimestepsofvariablelength,basedonthereactionrateconstants反應速率常數(shù)andpopulationsize群體大小ofeachchemicalspecies;(ii)TheGillespiecannoteasilyhandlethereactionsofmultistatemolecules;(iii)TheSTOCHSIMislikelytobeslowerthantheGillespiealgorithmincalculatingtheeventualoutcomeofasmallsetofsimplebiochemicalreactions,especiallywhenthenumbersofmoleculesislargeifwithoutthereactionsofmultistatemolecules;(iv)Spatialstructures空間結構canbeincorporatedinto成為一部分theSTOCHSIMframeworkwithrelativeease,asonecandirectlydefinethespatiallocation空間位置ofindividualmolecules—somethingthatwouldbedifficulttodowiththeGillespiealgorithm.47AWhole-CellComputationalModelOutline

Awhole-cellcomputationalmodelofthelifecycleofthehumanpathogen病原體

Mycoplasmagenitalium生殖支原體thatincludesallofitsmolecularcomponentsandtheirinteractions.Anintegrativeapproach積分方法tomodelingthatcombinesdiversemathematicsenabledthesimultaneousinclusion同時包含offundamentallydifferentcellularprocessesandexperimentalmeasurements.Thewhole-cellmodelaccountsforallannotated有注釋genefunctionsandwasvalidated確認againstabroadrangeofdata.Themodelprovidesinsightsintomanypreviouslyunobserved

未被遵守的cellularb