Rule based modelling of cellular signalling

Vincent Danos1

Description

Niveau: Supérieur
Rule-based modelling of cellular signalling Vincent Danos1,3,4, Jerome Feret2, Walter Fontana3, Russell Harmer3,4, and Jean Krivine5 1 Plectix Biosystems 2 Ecole Normale Superieure 3 Harvard Medical School 4 CNRS, Universite Denis Diderot 5 Ecole Polytechnique Abstract. Modelling is becoming a necessity in studying biological sig- nalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agent- based or concurrent languages, such as ? [1–3] or the closely related BioNetGen language [4–10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that trans- parently represents biological knowledge. In this way, rules become a nat- ural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11, 12]. An exciting aspect of the agent-based approach is that it naturally lends it- self to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to ?, our representation language of choice.

• combinatorics can


• throughout cellular


• agent-based approach


• cellular signalling


• rules provide


• rule applies


• partial order


• rules

Sujets

• Denis Diderot
• École polytechnique
• Cellular Signalling

Informations

• Publié par: chaeh
• Nombre de lectures: 37
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Rule-basedmodellingofcellularsignalling VincentDanos 1,3,4 ,Je´roˆmeFeret 2 ,WalterFontana 3 ,RussellHarmer 3,4 ,and JeanKrivine 5 1 PlectixBiosystems 2 E ´ coleNormaleSupe´rieure 3 HarvardMedicalSchool 4 CNRS,Universite´DenisDiderot 5 E ´ colePolytechnique Abstract.Modellingisbecominganecessityinstudyingbiologicalsig- nallingpathways,becausethecombinatorialcomplexityofsuchsystems rapidlyoverwhelmsintuitiveandqualitativeformsofreasoning.Yet,this samecombinatorialexplosionmakesthetraditionalmodellingparadigm basedonsystemsofdifferentialequationsimpractical.Incontrast,agent- basedorconcurrentlanguages,suchasκ[1–3]orthecloselyrelated BioNetGenlanguage[4–10],describebiologicalinteractionsintermsof rules,therebyavoidingthecombinatorialexplosionbesettingdifferential equations.Rulesareexpressedinanintuitivegraphicalformthattrans- parentlyrepresentsbiologicalknowledge.Inthisway,rulesbecomeanat- uralunitofmodelbuilding,modification,anddiscussion.Weillustrate thiswithasizeableexampleobtainedfromrefactoringtwomodelsofEGF receptorsignallingthatarebasedondifferentialequations[11,12].An excitingaspectoftheagent-basedapproachisthatitnaturallylendsit- selftotheidentificationandanalysisofthecausalstructuresthatdeeply shapethedynamical,andperhapsevenevolutionary,characteristicsof complexdistributedbiologicalsystems.Inparticular,onecanadaptthe notionsofcausalityandconflict,familiarfromconcurrencytheory,to κ,ourrepresentationlanguageofchoice.UsingtheEGFreceptormodel asanexample,weshowhowcausalityenablestheformalizationofthe colloquialconceptofpathwayand,perhapsmoresurprisingly,howcon- flictcanbeusedtodissectthesignallingdynamicstoobtainaqualitative handleontherangeofsystembehaviours.Bytamingthecombinatorial explosion,andexposingthecausalstructuresandkeykineticjunctures inamodel,agent-andrule-basedrepresentationsholdpromiseformak- ingmodellingmorepowerful,moreperspicuous,andofappealtoawider audience. 1Background Alargemajorityofmodelsaimedatinvestigatingthebehaviorofbiologicalpath- waysarecastintermsofsystemsofdifferentialequations[11–16].Thechoice seemsnatural.Thetheoryofdynamicalsystemsoffersanextensiverepertoireof mathematicaltechniquesforreasoningaboutsuchnetworks.Itprovides,atleast inthelimitoflongtimes,awell-understoodontologyofbehaviors,likesteady

states,oscillations,andchaos,alongwiththeir(linear)stabilityproperties.The readyavailabilityofnumericalproceduresforintegratingsystemsofequations, whilevaryingoverparametersandinitialconditions,completesapowerfulwork- benchthathassuccessfullycarriedmuchofphysicsandchemicalkinetics.Yet, thisworkbenchisshowingclearsignsofcrackingundertheponderouscombina- torialcomplexityofmolecularsignallingprocesses,whichinvolveproteinsthat interactthroughmultiplepost-translationalmodificationsandphysicalassocia- tionswithinanintricatetopologyoflocales[17]. Representationsofchemicalreactionnetworksintermsofdifferentialequa- tionsareaboutchemicalkinetics,nottheunfoldingofchemistry.Infact,all molecularspeciesmadepossiblebyasetofchemicaltransformationsmustbe explicitlyknowninadvanceforsettingupthecorrespondingsystemofkinetic equations.Everymolecularspecieshasitsownconcentrationvariableandan equationdescribingitsrateofchangeasimpartedbyallreactionsthatpro- duceorconsumethatspecies.Thesereactions,too,mustbeknowninadvance. Manyionchannels,kinases,phosphatases,andreceptors–tomentionjusta few–areproteinsthatpossessmultiplesitesatwhichtheycanbemodified byphosphorylation,ubiquitination,methylation,glycosidilation,andaplethora ofotherchemicaltaggingprocesses.Aboutoneinahundredproteinshaveat least8modifiablesites,whichmeans256states.Asimpleheterodimeroftwo distinctproteins,eachwiththatmuchstate,wouldweighinatmorethan65,000 equations.Itiseasilyseenthatthiscombinatoricscanrapidlyamounttomore possiblechemicalspeciesthancanberealizedbytheactualnumberofmolecules involvedinacellularprocessofthiskind.Theproblemisnotsomuchthata deterministicdescriptionisnolongerwarranted,butratherthattheequations, whetherdeterministicorstochastic,cannolongerbewrittendown—andifthey could,whatwouldonelearnfromthem? Thisdifficultyiswellrecognized.Onewayoutistouseaggregatevariables describingsetsofmodificationforms.Forexample,onemightbundletogetherall phosphoformsofareceptor,regardlessofwhichsitesarephosphorylated.This, however,isproblematic.First,thechoiceofwhattoaggregateandnotisunprin- cipled.Second,theappropriatelevelofaggregationmaychangeovertimeasthe systemdynamicsunfolds.Third,theaggregationiserrorprone,sinceithastobe donewithoutapriormicroscopicdescription.Afurther,moresubtle,difficulty isthatanextensionalsystemofdifferentialequationsdescribestheconstituent moleculesonlyintermsofinteractionsthatarerelevantinagivencontextof othermolecules.Itdoesnotcharacterizemolecularcomponentsintermsoftheir potentialinteractionsthatcouldbecomerelevantifthecompositionofthesys- temweretochange.Asaconsequence,“compositionalperturbations”,suchas addinganovelmolecularcomponent(adrug)ormodifyinganextantone(to modeltheeffectsofknockingoutasiteoraddinganewdomain)arevirtu- allyimpossibletocarryoutbyhand,sincetheyrequire,again,enumeratingall chemicalconsequencesinadvanceandthenrewritingallaffectedequations. Theseproblemshaveledtorecentattemptsatdescribingmolecularreaction networksintermsofmoleculesas“agents”,whosepossibleinteractionsarede- 2