Scalable simulation of cellular signaling networks

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Scalable simulation of cellular signaling networks Vincent Danos1,4?, Jerome Feret3, Walter Fontana1,2, and Jean Krivine5 1 Plectix Biosystems 2 CNRS, Universite Denis Diderot 3 Harvard Medical School 4 Ecole Normale Superieure 5 Ecole Polytechnique Abstract. Given the combinatorial nature of cellular signalling path- ways, where biological agents can bind and modify each other in a large number of ways, concurrent or agent-based languages seem particularly suitable for their representation and simulation [1–4]. Graphical mod- elling languages such as ? [5–8], or the closely related BNG language [9– 14], seem to afford particular ease of expression. It is unclear however how such models can be implemented.6 Even a simple model of the EGF receptor signalling network can generate more than ???? non-isomorphic species [5], and therefore no approach to simulation based on enumerating species (beforehand, or even on-the-fly) can handle such models without sampling down the number of potential generated species. We present in this paper a radically different method which does not at- tempt to count species. The proposed algorothm uses a representation of the system together with a super-approximation of its ‘event horizon' (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enu- meration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite),

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Publié par

chaeh

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English

Poids de l'ouvrage

1 Mo

ScalablesimulationofcellularsignalingnetworksVincentDanos1,4?,Je´roˆmeFeret3,WalterFontana1,2,andJeanKrivine51PlectixBiosystems2CNRS,Universite´DenisDiderot3HarvardMedicalSchool4E´coleNormaleSupe´rieure5E´colePolytechniqueAbstract.Giventhecombinatorialnatureofcellularsignallingpath-ways,wherebiologicalagentscanbindandmodifyeachotherinalargenumberofways,concurrentoragent-basedlanguagesseemparticularlysuitablefortheirrepresentationandsimulation[1–4].Graphicalmod-ellinglanguagessuchasκ[5–8],orthecloselyrelatedBNGlanguage[9–14],seemtoaﬀordparticulareaseofexpression.Itisunclearhoweverhowsuchmodelscanbeimplemented.6EvenasimplemodeloftheEGFreceptorsignallingnetworkcangeneratemorethannon-isomorphicspecies[5],andthereforenoapproachtosimulationbasedonenumeratingspecies(beforehand,orevenon-the-ﬂy)canhandlesuchmodelswithoutsamplingdownthenumberofpotentialgeneratedspecies.Wepresentinthispaperaradicallydiﬀerentmethodwhichdoesnotat-tempttocountspecies.Theproposedalgorothmusesarepresentationofthesystemtogetherwithasuper-approximationofits‘eventhorizon’(alleventsthatmayhappennext),andaspeciﬁccorrectionschemetoobtainexacttimings.Beingcompletelylocalandnotbasedonanykindofenu-meration,thisalgorithmhasapereventtimecostwhichisindependentof(i)thesizeofthesetofgenerablespecies(whichcanevenbeinﬁnite),and(ii)independentofthesizeofthesystem(ie,thenumberofagentinstances).Weshowhowtoreﬁnethisalgorithm,usingconceptsderivedfromtheclassicalnotionofcausality,sothatinadditiontotheaboveonealsohasthattheevencostisdepending(iii)onlylogarithmicallyonthesizeofthemodel(ie,thenumberofrules).Suchcomplexitypropertiesreﬂectinourimplementationwhich,onacurrentcomputer,generatesabouteventsperminuteinthecaseofthesimpleEGFreceptormodelmentionedabove,usingasystemwithagents.1IntroductionAnimportantthreadofworkinsystemsbiologyconcernsthemodellingoftheintra-cellularsignallingnetworkstriggeredbyextra-cellularstimuli(suchashor-monesandgrowthfactors).Suchnetworksdeterminegrowth,diﬀerentiation,and?ThisresearchwaspartlysupportedbytheNIH/NIGMSgrantR43GM81319-01.6Eg,fromRef.[15,p.4]:“programsimplementingthesemethodsincludeStochSim,BioNetGen,andMoleculizer.However,atthepresenttimeonlyapartoftheentireEGFRnetworkcanbeanalyzedusingtheseprograms”.

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