Modeling and simulation of genetic regulatory syst

JOURNALOFCOMPUTATIONALBIOLOGYVolume9,Number1,2002MaryAnnLiebert,Inc.Pp.67–103ModelingandSimulationofGeneticRegulatorySystems:ALiteratureReviewHIDDEDEJONGABSTRACTInordertounderstandthefunctioningoforganismsonthemolecularlevel,weneedtoknowwhichgenesareexpressed,whenandwhereintheorganism,andtowhichextent.Theregulationofgeneexpressionisachievedthroughgeneticregulatorysystemsstruc-turedbynetworksofinteractionsbetweenDNA,RNA,proteins,andsmallmolecules.Asmostgeneticregulatorynetworksofinterestinvolvemanycomponentsconnectedthroughinterlockingpositiveandnegativefeedbackloops,anintuitiveunderstandingoftheirdy-namicsishardtoobtain.Asaconsequence,formalmethodsandcomputertoolsforthemodelingandsimulationofgeneticregulatorynetworkswillbeindispensable.Thispaperreviewsformalismsthathavebeenemployedinmathematicalbiologyandbioinformaticstodescribegeneticregulatorysystems,inparticulardirectedgraphs,Bayesiannetworks,Booleannetworksandtheirgeneralizations,ordinaryandpartialdifferentialequations,qualitativedifferentialequations,stochasticequations,andrule-basedformalisms.Inad-dition,thepaperdiscusseshowtheseformalismshavebeenusedinthesimulationofthebehaviorofactualregulatorysystems.Keywords:geneticregulatorynetworks,mathematicalmodeling,simulation,computationalbiology.1.INTRODUCTIONThegenomeofanorganismplaysacentralroleinthecontrolofcellularprocesses,suchastheresponseofacelltoenvironmentalsignals,thedifferentiationofcellsandgroupsofcellsintheunfoldingofdevelopmentalprograms,andthereplicationoftheDNAprecedingcelldivision.Proteinssynthesizedfromgenesmayfunctionastranscriptionfactorsbindingtoregulatorysitesofothergenes,asenzymescatalyzingmetabolicreactions,orascomponentsofsignaltransductionpathways.Withfewexceptions,allcellsinanorganismcontainthesamegeneticmaterial.Thisimpliesthat,inordertounderstandhowgenesareimplicatedinthecontrolofintracellularandintercellularprocesses,thescopeshouldbebroadenedfromsequencesofnucleotidescodingforproteinstoregulatorysystemsdeterminingwhichgenesareexpressed,whenandwhereintheorganism,andtowhichextent.Geneexpressionisacomplexprocessregulatedatseveralstagesinthesynthesisofproteins(Lewin,1999).ApartfromtheregulationofDNAtranscription,thebest-studiedformofregulation,theexpressionInstitutNationaldeRechercheenInformatiqueetenAutomatique(INRIA),UnitédeRechercheRhône-Alpes,655avenuedel’Europe,Montbonnot,38334SaintIsmierCEDEX,France.6768DEJONGFIG.1.Exampleofageneticregulatorysystem,consistingofanetworkofthreegenesa,b,andc,repressorproteinsA,B,C,andD,andtheirmutualinteractions.Theguredistinguishesseveraltypesofinteraction.MorecomplexgraphicalconventionstorepresentcellularnetworksareproposedbyKohn(1999,2000).ofagenemaybecontrolledduringRNAprocessingandtransport(ineukaryotes),RNAtranslation,andtheposttranslationalmodicationofproteins.ThedegradationofproteinsandintermediateRNAproductscanalsoberegulatedinthecell.Theproteinsfulllingtheaboveregulatoryfunctionsareproducedbyothergenes.ThisgivesrisetogeneticregulatorysystemsstructuredbynetworksofregulatoryinteractionsbetweenDNA,RNA,proteins,andsmallmolecules.Anexampleofasimpleregulatorynetwork,involvingthreegenesthatcodeforproteinsinhibitingtheexpressionofothergenes,isshowninFig.1.ProteinsBandCindependentlyrepressgeneabybindingtodifferentregulatorysitesofthegene,whileAandDinteracttoformaheterodimerthatbindstoaregulatorysiteofgeneb.1BindingoftherepressorproteinspreventsRNApolymerasefromtranscribingthegenesdownstream.Analysesofthehugeamountsofdatamadeavailablebysequencingprojectshavecontributedtothediscoveryofalargenumberofgenesandtheirregulatorysites.TheKEGGdatabase,forinstance,containsinformationonthestructureandfunctionofabout110,000genesfor29species(KanehisaandGoto,2000).Insomecases,theproteinsinvolvedinthecontroloftheexpressionofthesegenes,aswellasthemolecularmechanismsthroughwhichregulationisachieved,havebeenidentied.Muchlessisknown,however,aboutthefunctioningoftheregulatorysystemsofwhichtheindividualgenesandinteractionsformapart(Brownsteinetal.,1998;Collado-Videsetal.,1996;Fieldsetal.,1999;Kanehisa,2000;Lander,1996;LoomisandSternberg,1995;Nowak,1995;Palsson,1997;Strohman,1997;Thieffry,1999).Gaininganunderstandingoftheemergenceofcomplexpatternsofbehaviorfromtheinteractionsbetweengenesinaregulatorynetworkposesahugescienticchallengewithpotentiallyhighindustrialpay-offs.ThestudyofgeneticregulatorysystemshasreceivedamajorimpetusfromtherecentdevelopmentofexperimentaltechniqueslikecDNAmicroarraysandoligonucleotidechips,whichpermitthespatiotemporalexpressionlevelsofgenestoberapidlymeasuredinamassivelyparallelway(BrownandBotstein,1999;Lipschutzetal.,1999;LockhartandWinzeler,2000).Othertechniques,suchasthemassspectrometricidenticationofgel-separatedproteins,allowthestateofacelltobecharacterizedontheproteomiclevelaswell(Kahn,1995;Mann,1999;PandeyandMann,2000;ZhuandSnyder,2001).Althoughstillintheirinfancy,thesetechniqueshavebecomeprominentexperimentaltools,byopeningupawindowonthedynamicsofgeneexpression.Inadditiontoexperimentaltools,formalmethodsforthemodelingandsimulat