A framework for mapping

´r3,EddaKlipp2,StefanHohmann1,HiroakiKitano3,5,6,7Carl-FredrikTiger1,2,8,FalkoKrause2,8,GunnarCedersund1,3,4,RobertPalme

andMarcusKrantz1,2,5,*

¨teborg,Sweden,2TheoreticalBiophysics,Humboldt-Universita¨tzuBerlin,Berlin,Germany,DepartmentofCellandMolecularBiology,UniversityofGothenburg,Go

¨pingUniversity,Linko¨ping,Sweden,4FreiburgInstituteofDepartmentofClinicalandExperimentalMedicine,DiabetesandIntegrativeSystemsBiology,Linko

AdvancedSciences,SchoolofLifeSciences,Freiburg,Germany,5TheSystemsBiologyInstitute,Tokyo,Japan,6SonyComputerScienceLaboratories,Inc.,Tokyo,Japanand7OkinawaInstituteofScienceandTechnology,Okinawa,Japan8Theseauthorscontributedequallytothiswork

¨tzuBerlin,Invalidenstr.42,Berlin10115,Germany.Tel.:þ493020938389;*Correspondingauthor.TheoreticalBiophysics,Humboldt-Universita

Fax:þ493020938813;E-mail:marcus.krantz@biologie.hu-berlin.de

31Received8.7.11;accepted16.3.12

Intracellularsignallingsystemsarehighlycomplex.Thiscomplexitymakeshandling,analysisandvisualisationofavailableknowledgeamajorchallengeincurrentsignallingresearch.Here,wepresentanovelframeworkformappingsignal-transductionnetworksthatavoidsthecombinatorialexplosionbybreakingdownthenetworkinreactionandcontingencyinformation.Itprovidestwonewvisualisationmethodsandautomaticexporttomathematicalmodels.WeusethisframeworktocompilethepresentlymostcomprehensivemapoftheyeastMAPkinasenetwork.Ourmethodimprovespreviousstrategiesbycombining(I)moreconcisemappingadaptedtoempiricaldata,(II)individualreferencingforeachpieceofinformation,(III)visualisationwithoutsimplificationsoraddeduncertainty,(IV)automaticvisualisationinmultipleformats,(V)automaticexporttomathematicalmodelsand(VI)compatibilitywithestablishedformats.Theframeworkissupportedbyanopensourcesoftwaretoolthatfacilitatesintegrationofthethreelevelsofnetworkanalysis:definition,visualisationandmathematicalmodelling.Theframeworkisspeciesindependentandweexpectthatitwillhavewiderimpactinsignallingresearchonanysystem.

MolecularSystemsBiology8:578;publishedonline24April2012;doi:10.1038/msb.2012.12

SubjectCategories:metabolicandregulatorynetworks;computationalmethods;simulationanddataanalysis

Keywords:combinatorialcomplexity;mathematicalmodelling;networkmapping;signaltransduction;visualisation

Introduction

Alllivingcellsinteractwithandrespondtotheirenvironmentviathecellularsignal-transductionnetwork.Thisnetworkencompassesallcellularcomponentsandprocessesthatarerequiredtoreceive,transmitandinterpretinformation.Duetoitskeyroleincellularphysiology,thesignallingnetwork,andseveralofitssubnetworks,havebeenintenselystudiedinarangeoforganisms.However,suchnetworksarehighlycomplexanddifficulttoanalyseduetotheso-calledcombinatorialexplosion(Hlavaceketal,2003).Thisexplosionreferstothefactthatthespecificstateofeachcomponentisdeterminedbymultiplecovalentmodificationsorinteractionpartners,andthatthesepossibilitiesrapidlycombinetoaverylargenumberofpossiblespecificstates.Experimentaldatadonotgenerallydistinguishbetweenallthesespecificstates,butinsteadfocusmostlyonreactionsbetweenpairsofcompo-nents,usuallygivingnoorlimitedinformationonothermodificationsorinteractionpartnersofthereactants.Hence,&2012EMBOandMacmillanPublishersLimitedthereisadiscrepancybetweenthegranularityoftheempiricaldataandthehighlydefinedspecificstatesusedinmostmathematicalmodels.Thismakestheinterpretationanduseofempiricaldatainthecontextofsuchmodelstatesambiguousandoftenarbitrary.Theseproblemsposemajorchallengesforsystemsbiology,astheypreventusfrom(i)unambiguouslydescribinganetwork,(ii)visualisingitwith-outsimplificationsorunsupportedassumptionsand(iii)automaticallygeneratingmathematicalmodelsfromknowl-edgeindatarepositories.

Largeeffortshavebeeninvestedinaddressingtheseissues.Signallingsystemsarecommonlyvisualisedthroughtheinformal‘biologist’sgraph’thatissimpleandintuitive,butlacksthestringentformalismandprecisionrequiredtomeetthethreecriteriaabove(exemplifiedbyThorneretal,2005).Thelackofstandardisedglyphs(defininge.g.,mechanismofinformationtransferandhowedgescombinestoregulatetargetnodes)makestheinformationinthe‘biologist’sgraph’ambiguousanddifficulttoreuse.Toaddressthis,the

MolecularSystemsBiology20121Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalcommunityhasdevelopedtheSystemsBiologyGraphicalNotation,SBGN(LeNovereetal,2009).Thisincludesthreevisualformats;theactivityflowdiagram,theentityrelation-shipdiagramandtheprocessdescription(orprocessdiagram).Theactivityflowdiagramsharesmanypropertieswiththe‘biologist’sgraph’,buttheentityrelationshipdiagramandprocessdescriptionallowpreciserepresentations.Theprocessdescriptioncorrespondstothestatetransitionreactionformatusedinmostmodelsdevelopedbythesystemsbiologycommunity,andwhichhavebeenstandardisedintheSystemsBiologyMarkupLanguage(SBML;Huckaetal,2003).Theprocessdescriptioncouldmeeteachofthethreecriteriaabovebutitsutilityisseverelyaffectedbythecombinatorialexplosion.Itisbasedonaspecificstatedescription,whichmeansthat,foreachcomponent,eachpossiblecombinationofmodificationsandinteractionpartnersmustbeaccountedforexplicitly.Hence,onlyverysimplesystemscanbedescribedcompletelyandonlyveryfewmodelsincludetheentirestatespace(Kiselyovetal,2009)whilethevastmajorityincludesimplifyingomissions.Whilesimplificationsareoftenneces-sary,thelackofdiscriminationbetweenarbitraryomissionsandexclusionsbasedonexperimentalevidenceisasignificantshortcoming.Theseissuesarepartiallyaddressedintheentityrelationshipdiagram,ormolecularinteractionmap,whichcomesintwoflavours;explicitandimplicit(calledheuristicandcombinatorialbytheauthor(Kohnetal,2006)).Theexplicitversionrequiresallspecificstatestobedisplayedandhencesharethelimitationsoftheprocessdescription.Incontrast,theimplicitversiondisplaysonlythepossiblereactiontypes(orelementalreactions,aswewillcallthembelow)andhencelargelyavoidsthecombinatorialexplosion.Theentityrelationshipdiagramrepresentseachcomponentasasinglenodeandreactionsinacondensedformat.WhilenotasintuitiveastheotherSBGNformats,ithastheadvantageofconcentratingallinformationonagivenproteinandworksespeciallywellforsimpleregulatorycircuits,astheconcen-tratedinformationmakesitdifficulttotracetheorderofeventsinmorecomplexnetworks.ThethreeSBGNformathascomplementarystrengths,butthereiscurrentlynosoftwareavailableforconversionbetweenthethreedifferentvisualisa-tionformats.However,theSBGNstandardsareundercontinuousdevelopmentandtheseissueswilllikelybeaddressedinthefuturethroughtheSBGNmarkuplanguage,SBGN-ML.

Similareffortsonthemodellingsidehaveresultedinrule-basedmodellingandassociatedvisualisationformats(Faederetal,2005).Briefly,rulesaredefinedasreactionsthatarevalidunderaparticularsetofcontingencies,andeachreactionisspecifiedforeachsuchcontingencyset.Thismeansthatwhenareaction’srateisincreasedbyphosphorylationofonecomponentitwillbedefinedbytworules;onewherethatcomponentisphosphorylatedandonewhereitisnot.Whiletheserulesdefinetheentirestatespaceandthesystemstayssubjecttothefullcombinatorialexplosion,theruledescriptionhasalleviatedthecombinatorialproblemintworespects:(1)thesystemhasbeendescribedmorecompactlyand(2)theactualisedstatespacemightbesignificantlyreducedbyintroducingonlythosestatesthatareactuallypopulated(LokandBrent,2005),orbyusingagent-basedstochasticmodelling(Sneddonetal,2011).Theruledefinitionformatis

2MolecularSystemsBiology2012alsoasignificantsteptowardsthegranularityofempiricaldata,ascomparedwiththeabstract-specificstates.Theseadvantagesaremirroredonthevisualisationsidebygraphicalreactionrules,whichusetheprocessdescriptionformattodisplayindividualrules(Blinovetal,2006).Networklevelvisualisationhasusedeithertopologicalcontactmaps(Danos,2007)orentityrelationshipdiagrams(LeNovereetal,2009),andthesecomplementaryvisualisationformatshaverecentlybeencombinedintheextendedcontactmap(Chyleketal,2011).Contactmapshavesoftwaresupport,butneitherentityrelationshipdiagramsnorextendedcontactmapscanbegeneratedautomaticallyfromtherule-basedmodels.Hence,therule-basedformatpartiallyaddressestheautomaticcreationofmodelsfromdatarepositories(iii),asitprovidesthetoolstogeneratemathematicalmodelsautomaticallyoncetheknowledgehasbeenreformulatedasrules.However,therule-basedsystemprovidesacumbersomeformatfor(i)unambiguousnetworkdescriptionandisnotdevelopedfor(ii)comprehensivevisualisations.Takentogether,thisraisesthequestionwhethergraphical-andmodel-basedformatsarethemostappropriateforstringentnetworkdefinition,orwhethertherearemoresuitablenetworkdefinitionformatsthatallowbothvisualisationandautomaticmodelgeneration.

Here,wepresentanewframeworktodescribecellularsignal-transductionnetworks.Ournetworkdefinitionhasthesamegranularityasexperimentaldata,avoidsthecombina-torialcomplexity,canbeautomaticallyvisualisedincomple-mentarygraphicalformatsincludingallthreeSBGNformatsandunambiguouslydefinesmathematicalmodels.Therxnconsoftwaretoolcomplementstheframeworkbyautomatingvisualisationandmodelcreation.Thekeyfeatureofourframeworkisthestrictseparationofelementalreactions(andtheircorrespondingstates);whichdefinesthepossiblesignallingeventsinthenetwork,fromcontingencies;whichdescribesthecontextualconstrainsonthesereactions.Importantly,eachelementalreactioncorrespondsdirectlytoasingleempiricalobservation,suchasaprotein–proteininteractionoraspecificphosphorylation.Thecontingenciesdefinetheconstraintsontheseelementalreactionsintermsofoneormoreelementalstates,forexample,bydefiningtheactivestateofaproteinkinaseorthecompositionofafunctionalproteincomplex.Hence,theformatdirectlylinkmodelstatestoempiricalobservationsatthesamelevelofgranularity,whichpre-emptstheneedforadditionalassump-tionsorextrapolations.Moreover,theseparationbetweenreactionsandcontingencieslargelyavoidsthecombinatorialexplosionasonlycombinatorialstateswithknownfunctionalinfluenceareconsidered.Therxncontoolprovidesautomaticexporttoestablishedvisualformatsandtotwonewvisualisa-tionmethods,whichallowcompactcomprehensiverepresen-tation.Finally,theframeworkisstringentandunambiguouslydefinesamathematicalmodel,andtherxncontoolsupportexporttoSBMLandrule-oragent-basedmodels.Thisallowscodingofmodelsinaformatthatmirrorsempiricaldata,whichcanbeautomaticallyvisualisedandwhichishighlysuitableforiterativemodelbuilding.WeillustrateournewapproachbyconductingthemostcomprehensiveliteraturesurveytodateofthecompleteMAPkinasesignallingnetworkofSaccharomycescerevisiae.Takentogether,weprovideaframeworkthatintegratesthethreelevelsofnetworkanalysis;

&2012EMBOandMacmillanPublishersLimiteddefinition,visualisationandmathematicalmodellingandasupportingsoftwaretoolforautomaticvisualisationandexporttomathematicalmodels.Weexpectthistobehighlyusefulforthecommunityandenvisionacommonframeworktobridgedifferentstandardsaswellasexperimentalandtheoreticalsystemsbiologyefforts.

Results

Thissectiondescribesthearchitectureoftheframework,includingitsdatastructure,thedifferentmethodsofvisualisa-tionandhowitrelatestoamathematicalmodel(Figure1A).Inthefirstpart,wepresenttheresultsofthemethodsdevelopmentanddescribethesystemindetail.Inthesecondpart,wepresentourresultsusingtheMAPkinasenetwork.TheframeworkhasbeenimplementedintherxnconsoftwaretoolthatisdistributedfreelyundertheopensourceLGPLlicenceandcanbedownloadedfromwww.rxncon.org.

Thedatastructure

Theeventsinasignal-transductionnetworkcanbecategorisedinfourtypes:(1)catalyticmodifications,(2)bindingsandinteractions,(3)degradationandsynthesisand(4)changesinlocalisation.Duetothelimitedinformationonspatial(re)distributionofcomponents,wehavefocusedontypes1–3here(TableI).However,theframeworkisfullycapabletoincludelocalisationreactionsandtherxncontoolwillbeupgradedtoencompasstheseinthefuture.Thefirststepofthenetworkdefinitionistodistiltheavailableknowledgeintotwodistinctcategoriesofinformation:whatcanhappen,andwhenitcanhappen.Thewhat-aspect(referredtoasC1,orelementalreactions)specifiesthepossibleevents,includingtheeventtype(1–3above),andwhichcomponentsandsitesthatareinvolved.Thewhen-aspect(referredtoasC2,orcontingencies)specifieshowthereactionrateisaffectedbythestateoftheinvolvedcomponents.Forinstance,theMAPkinaseHog1phosphorylateitstargetHot1(C1—‘what’;Figure1B),andthisreactiononlyoccurswhenHog1isphosphorylatedonbothThr174andTyr176(C2—‘when’).Thissecondcategoryofknowledgethereforerepresentsthecausalrelationships,orcontingencies,betweenthereactionscharacterisedinthefirstclassofknowledge.TheseparationofC1fromC2allowsustodefineevenlargecomplexnetworksstringentlyinaconciseformat,asexemplifiedwiththeyeastMAPkinasenetworkbelow.

Thewhat-aspectsoftheknowledgearerepresentedinthereactionlist(Figure1C;simplifiedexample).Importantly,wehavebrokendownthereactionnetworkinelementalreactions,whichchangeelementalstates.Anelementalstateissimilartoanempiricalobservation,suchasaninteractionbetweentwoproteinsoraspecificmodificationataspecificsiteonaspecificprotein.Ifaproteinhasbeenphosphorylatedontwosites,thiscorrespondstotwodifferentelementalstates.Inotherwords,theelementalstatescorrespondtooverlapping(non-disjoint)sets.Thisisdifferentfromthespecificstatesinordinarystatetransitionmodels,butanalogoustothemacroscopicstatesusedintheworksbyConzelmannetal(2008)(Borisovetal,2008).Anelementalreactionissimilarly&2012EMBOandMacmillanPublishersLimitedAframeworkformapping,visualisationandautomaticmodelcreation

C-FTigeretaldefinedasatwo-componentreactionthatmodifiesasingleelementalstate.Notethatthisprecludeslumpedreactionsandthat,forexample,akinase–substrateinteractionandphos-phorylationmustbedescribedbytwodifferentelementalreactions.Hence,thereactionlisthasthesamegranularityastypicalempiricaldata,whichpre-emptstheneedforassump-tionsinthemappingprocess.Italsoallowsustousetheestablishedformatforhigh-throughputdata(Starketal,2006),includingspecificreferencingofeachreactionwithPubMedidentifiersandcomplementedwithadditionaldetailssuchasactivedomains,subdomainsandresidues(SupplementaryTablesS1andS2).

Thewhen-aspectoftheknowledgeisdescribedinthecontingencylist(Figure1D;simplifiedexample).Thislistdefinesthecontextualconstraintsonallelementalreactions.Mostcontingencieswillcorrespondtothedirecteffectofsingleelementalstatesofthecomponentsinvolvedintheparticularelementalreaction,butBooleanstatesallowforcombinatorialeffectsandindirecteffectsin,forexample,scaffoldsthatcannotbedirectlyattributedtoasingleelementalstateinoneofthereactants.Therearesixdistinctreactioncontingencies;theEffectorcanbeabsolutelyrequired(!),positive(Kþ),completelyneutral(0),negative(KÀ),absolutelyinhibitory(x)orofunknowneffect(?).Theseoverlappartiallywiththeinfluencesofentityrelationshipdiagrams(LeNovereetal,2011),butdistinguishbetweennoeffect(0)andnoknowneffect(?).TheBooleanstatesprovideamiddlelayerbetweenreactioncontingenciesandacombinationofelementalstatesand/orinputs,usingeither‘AND’or‘OR’todefine,forexample,largecomplexesoralternativemechanisms.Inaddition,inputsandoutputsfunctionaselementalstatesandreactions,respectively,attheinterfacebetweenthenetworkandtheexternalenvironment.EachrowinthecontingencylistcontainsaTarget(elementalreaction,outputorBooleanstate),anEffector(elementalstate,inputorBooleanstate)andasymboldescribinghowtheEffectorinfluencestheTarget(Contingency)thatisacontingencysymbol(!,Kþ,0,KÀ,x,?)whentheTargetisanelementalreactionoranoutputandaBooleanoperator(AND,OR)whentheTargetisaBooleanstate.ThedatastructureisillustratedwithasimplifiedversionoftheShobranchoftheHOGpathway(Figure1B).Thereactionliststatethat,forexample,Hog1phosphorylates(‘Pþ’)Hot1(Figure1C;eighthreaction;onthelastrow),andthecontingencyliststatethatthisreactionrequires(‘!’)thatHog1isphosphorylatedonbothThr174andTyr176(Figure1D,lasttworows).Thesestatesinturncorrespondtothereactionssixandseven,respectively(Figure1C).Hence,thereactionandcontingencyinformationsufficetodescribethenetworkandtheirseparationkeepsthedescriptionconciseandatthegranularityofempiricaldata.Consequently,thedatastructureaddressesthefirstissue;unambiguousnetworkdefinition.

Visualisingthesignal-transductionnetwork

Weaddressthesecondissue;comprehensivevisualisation,withtwonovelformsofvisualisation;thecontingencymatrixandtheregulatorygraph.Thesealsokeepreactionsandcontingenciesseparateandhenceavoidthecombinatorial

MolecularSystemsBiology20123Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalAB

DCEFG

H

I

J

4MolecularSystemsBiology2012&2012EMBOandMacmillanPublishersLimitedAframeworkformapping,visualisationandautomaticmodelcreation

C-FTigeretalexplosionandimplicitassumptions.Bothincludethecom-pleteinformationaboutreactions(C1)andcontingencies(C2).Thisdatastructureisalsowellsuitedforvisualisationinentityrelationshipdiagramsorextendedcontactmaps,andtherxnconsoftwaretoolsupportsexporttotheentityrelationshipformat(Chyleketal,2011;LeNovereetal,2011).Wealsoprovideexporttothereactiongraph/activityflowdiagramandtheprocessdescription,thoughneitherofthesecanfullyandaccuratelyrepresentthenetworkasdiscussedbelow.Never-theless,theyallprovidetheiruniqueadvantagesandcanbeautomaticallygeneratedwiththerxncontoolandtheinformationinthereactionandcontingencylists.

Thecontingencymatrixintegratestheinformationinthereactionandcontingencylists(Figure1E).Thematrixisspannedbythereactionsandtheircorrespondingstates(C1)andpopulatedbythecontingenciesofreactionsonstates(C2).Eachrowcorrespondstooneelementalreactionandeachcolumncorrespondstooneelementalstate.Thesymbolineachreaction–stateintersectionspecifieshowthatspecificreactiondependsonthatspecificstate.Together,onerow

TableIThirteenreactiontypeswereusedtomaptheMAPkinasenetwork

containsthecompletesetofrulesareactionfollows,andhencedescribeshowitworksineveryspecificstate.Thisisrelatedtoadependencymatrix(Yangetal,2010),althoughtheentriesinthecontingencymatrixaremoredetailedandunambiguous.Intheexample(Figure1E),thefirstrowshowsthat(a)thebindingofSho1toSte11cannotoccurifeitherofthecomponentsisalreadypartofsuchadimer(column1),(b)thatwedonotknowwhetherthepriorbindingofSho1toPbs2(column2)orphosphorylationofSte11(column3)effectstheSho1–Ste11bindingand(c)thattheotherstatesappearingintherowareirrelevantforthisspecificbindingreaction—astheydonotdescribepropertiesofSho1orSte11.Theprimaryadvantagesofthecontingencymatrixarethatit(1)allowsacomprehensivedocumentation/visualisa-tionofallreactionsanddependencieswithinthenetwork,(2)thatitdoessowithoutrequiringassumptions,(3)thatitexplicitlydefinesunknownsandhencegapsinourknowledgeand(4)thatthematrixconstitutesatemplatefromwhichmathematicalmodelscanbederivedautomatically(seebelow).

ReactionCategoryCategory

typePþPÀAPPTGEFGAPUbþCUTppiipii

BINDDEG

1111111122223

CovalentmodificationCovalentmodificationCovalentmodificationCovalentmodificationCovalentmodificationaCovalentmodificationaCovalentmodificationCovalentmodificationAssociationAssociationAssociationAssociation

Synthesis/degradation

SubclassSubclassID1.11.11.11.11.21.21.31.42.12.12.22.33.3

(De)Phosphorylation(De)Phosphorylation(De)Phosphorylation(De)PhosphorylationGTP/GDPhydrolysis/exchange

GTP/GDPhydrolysis/exchange

(De)UbiquitinationProteolyticprocessingppiipii

BINDDEG

Modifieror

boundaryPPPPPPUb

TruncatedN/AN/AN/AN/A

ReactionReactionnametypeID1.1.11.1.21.1.31.1.41.2.11.2.21.3.11.42.1.12.1.22.22.33.3

PhosphorylationDephosphorylationAutophosphorylationPhosphotransferGuanineNucleotideExchange

GTPaseActivationUbiquitination

Proteolyticcleaveage

Protein–proteininteractionIntra-proteininteractionInteraction(non-proteins)BindingtoDNADegradation

Thetableindicatesreactiontypeandclassification.Additionaldetailsareprovidedinthe‘ReactionDefinition’sheetofSupplementaryTablesS1andS2.aForconvenience,theG-proteincycleisapproximatedasacovalentmodificationbyaddition/removalofphosphateto/fromabasic,GDP-boundform.

Figure1Schematicrepresentationofthedatastructure.(A)Theinputdataarethereactionandcontingencylists,whichcontainsthe‘what-aspects’and‘when-aspects’ofthereactionnetwork,respectively.Therxnconsoftwareusestheseliststocreatearangeofvisualisationsaswellascomputationalmodels.Theseconversionsrequirenoadditionalinformationandarefullyautomated.(B)AsimplifiedversionoftheSho1branchoftheHogpathwayinS.cerevisiaewillbeusedtoillustratethedatastructure.This‘biologist’sgraph’showstheactivatingphosphorylationcascade(arrows)fromSte20toHot1.ScaffoldingandmembranerecruitmentbySho1facilitatesthefirsttwophosphorylationevents(greylines).(C)The(simplified)reactionlistdefinestheelementalreactionsbetweenpairsofcomponents.Itincludesthetwocomponents(columnsIandIII),reactiontype(columnII;‘ppi’¼protein–proteininteraction,‘Pþ’¼phosphorylation;seeTableIforcompletelistofreactions),reaction(columnIV,aconcatenationofthecomponentsandthereactiontype)andresultantstate(columnV;proteindimersorphosphorylatedstates).Notethateachelementalstateonlydefinesasingleaspectofeachcomponent’sspecificstate.(D)The(simplified)contingencylistdefinestherelationshipbetweenstatesandreactions.Itcontainstheaffectedreaction(Target,columnI),theinfluencingstate(Effector,columnIII),andtheeffectthisparticularstatehasonthatreaction(contingency,columnII).(E)Thereactionandcontingencyinformationissummarisedinthecontingencymatrix.Thematrixisdefinedbyelementalreactions(rows)andstates(columns).Thecellsdefinehow(if)eachreaction(row)isaffectedbyeachstate(column);thatis,thereactions’contingenciesondifferentstates.Notethatonlydirectcontingenciesareconsidered;reaction/stateintersectionswhichdonotsharecomponentsareblackedout.Thegreyfields(‘x’)areautomaticasstatesarebinaryandhenceareactioncannotoccurifthestateisalreadytrue.Thegreenfields(‘!’/‘Kþ’)areimportedfromthecontingencylist,andallotheropenfieldsaredefinedasunknowneffect(‘?’).Thisinformationcanalsobevisualisedinanumberofgraphicalforms:Thereactiongraph(F)displaysnetworktopologywitheithercomponentsortheirdomainsasfunctionalunits.Theregulatorygraph(G)combinesthereactionandcontingencyinformationtodisplaythecausalrelationshipbetweenthereactionsinthenetworkandprovidesacompletegraphicalrepresentationoftheknowledgecompiledinthecontingencymatrix.Thelimitedprocessdescription(H)displaysthecatalyticmodificationsinthesignal-transductionnetworkasstatetransitionswithcatalystsbutwithoutcomplexformation(compareSupplementaryFigureS1).Theinteractionanddistancematrices(I)provideacompactdescriptionofnetworktopologyandallowcalculationofdistancesbetweennodes.Finally,thereactionandcontingencydatacanbevisualisedasanentityrelationshipdiagram(J).Thesevisualisationsandtheequationsystemforthissystem,subsystemoryourownfavouritenetworkdefinedinthesameformatcanbeautomaticallygeneratedusingtherxnconsoftware.

&2012EMBOandMacmillanPublishersLimitedMolecularSystemsBiology20125Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalThereactiongraphdisplaysatopological,directedreactionnetwork(Figure1F).Itrepresentseachentityasasinglenodeandeachrelationshipbetweenapairofentitiesasasingleedge.Edgescanbenon-directional(e.g.,proteinÀproteininteraction),unidirectional(e.g.,phosphorylation)orbidirec-tional(e.g.,phosphotransfer).Thefullreactiongraphdisplaysthedomainsandresiduesinvolvedineachreaction.Theproteinpartsareindependentnodesanddefinedasneigh-bours(proteinscanhavedomainsorresidues,domainscanhavesubdomainsorresidues,subdomainscanhaveresidues).Theinclusionofdomaininformationmakesthereactiongraphsimilartothe(extended)contactmaps(Danos,2007;Chyleketal,2011).Thereactiongraphandcontactmapsarebothpurelytopologicalanddonotincludeanycontextualinformation,incontrasttotheextendedcontactmapwhich,forexample,mayshowthatbindingonlyoccurstophos-phorylatedresidues.Wealsouseacondensedvariantthatdisplaysonlythecentralnodeforeachcomponentandcollapsesmultiplereactionsofthesamekindbetweenapairofcomponentstoasingleedge,andhencecorrespondscloselytotheactivityflowdiagramofSBGN(SupplementaryFigureS1B;LeNovereetal,2009).Theadvantagesofthereactiongraphare(1)therelativesimplicitythatmakesitusefulforvisualisationofevenlargenetworksand(2)thatitissuitedforvisualisationoflarge-scaledatasetswithinthecontextofthatnetwork(seebelow).

Theregulatorygraphshowshowinformationisconveyedthroughthenetwork(Figure1G).Itimprovesonthereactiongraphbyincludinginformationoncausalitybetweenthereactionsinthenetwork(C2data).Theregulatorygraphshowsthenetwork’sregulatorystructure;thatis,whichreactions(viastates)actuallyinfluencetherateofotherreactions.Itisabipartitegraphwiththeelementalreactions(red)andelementalstates(blue)asnodes.Reaction-to-stateedgessimplyshowwhichreactionsproduceorconsumewhichstates.Thestate-to-reactionedgesshowwhichstates(productsofupstreamreactions)affectthedynamicsofwhich(downstream)reactions.Thesestate-to-reactionedgescorre-spondtothesymbolsinthecontingencylist,i.e.,‘!’,‘Kþ’,‘KÀ’or‘x’.Theregulatorygraphcaneasilybetranslatedintoaninfluencegraph,whichcanbeusedforstructuralanalysisofthenetwork(Kaltenbachetal,2011).Incontrasttotheinfluencegraphor‘story’(Danos,2007),theregulatorygraphstrictlyseparatestheeffectsofreactions(productionordestructionofstates)andthemodifiers(increaseordecreaseinreactionrates)viadistinctedgetypes.Furthermore,onlythe(modified)elementalstatesaredisplayedandthe(theunmodified)complementarysource/targetstateisimplicit.Hence,likeinthe‘stories’,cyclicmotifsonlyappearwhenthereisatruefeedbackinthesystem.Thisvisualisesboththe(possible)sequenceofeventsandthefeedbacksclearly.However,incontrasttothe‘story’,theregulatorygraphiscomprehensiveandsimultaneouslyvisualisesallpossiblepathsor‘stories’.Inthisexample(Figure1G),theuppermostnodepaircorrespondstothereactionwhereSho1bindsSte11(Sho_ppi_Ste11)andtheresultingstateSho1–Ste11.Thereaction-to-stateedgelinkingthesetwonodesidentifiesSho1–Ste11astheproductofthisbindingreaction.Notethatthesourcestatesforthisreactionareomitted(i.e.,Sho1notboundtoSte11andSte11notboundtoSho1).The

6MolecularSystemsBiology2012state-to-reactionedgefromSho1–Ste11toSte20_Pþ_Ste11showsthatthephosphorylationofSte11bySte20isenhancedintheSho1–Ste11complex.ThisreactioninturnproducesthestateSte11-{P},whichisrequiredforphosphorylationofPbs2onbothSer514andThr518.Hence,theinformationflowcanbefollowedthroughoutthenetworkasalledgesareunidirectional.Themainadvantagesoftheregulatorygrapharethatit(1)allowsacomprehensivedocumentation/visualisationofallreactionsandcontingencieswithinthenetwork,(2)thatitdoessoinaverycompactformat(3)withoutforcingnon-supportedassumptions,(4)thatitcanbeusedforstructuralanalysisofthenetworkand(5)thatitclearlyshowstheinformationflowthroughthenetwork.

Processdescriptionsarewellestablishedandallowvisuali-sationoftheinformationflowandmechanisticdetailsimultaneously(Kitanoetal,2005).Theyareexcellentforrepresentationofsmallnetworkswhicharecompletelyknown,butlackofdata(oftherightgranularity)invariablyleadtounsupportedassumptions.Inaddition,thesediagramsrapidlybecomeverycomplex,generallyforcingadhocreductionandadditionalimplicitandunsupportedassump-tions.Therefore,processdescriptionsdonotallowacompletedescriptionofthenetworkwiththestringencywerequire.However,theprocessdescriptioncanbeclearandeasytoread,andwegeneratealimitedversionwhichexcludescomplexformationandhenceavoidsmostofthecombinatorialcomplexity.Thedifferenceishighlightedbytheupperthreenodesintheexample(Figure1H),whereSte20phosphorylatesSte11.Incontrasttofullprocessdescription,thebindingofSte11toSho1,andhowthisbindingwouldaffectthephosphorylation,isnotincluded(compareSupplementaryFigureS1).The(limited)processdescriptionhasseveraladvantages:It(1)isintuitivetoreadand(2)definesinwhichinternalstate(s)anenzymeisactive,itssubstrateandtheexacttargetresidue,which(3)conveystheinformationflowthroughthepathway,theenzyme–substraterelationshipsaswellasthegapsinourunderstandingoftheseaspects.

Theinformationcanalsobeusedtogenerateinteractionmatricesthatspecifywhichcomponentsreactwithwhichcomponents.Thesecanberenderedatseverallevelsofdetailrangingfromacompleteinteractionmatrixincludingproteindomainsandtargetresiduesthatdefineseachinteractiontype,viacondensedinteractionmatriceswithonlyonerowandcolumnperproteinthatstillcontainsreactiontypeinforma-tion(Figure1I,uppermatrix),tonumericalmatricesthatonlyincludeinformationonconnectionanddirectionality.Weusedthelattertocalculatethedistanceswithinthenetworktogenerateadistancematrix(Figure1I,lowermatrix).

Finally,therxncontoolprovidesexporttoentityrelationshipdiagrams(Figure1J).Liketheregulatorygraph,theentityrelationshipdiagramdisplaysreactionsandcontingenciesseparatelyandhencelargelyavoidsthecombinatorialcom-plexity.Theentityrelationshipdiagramhastheadvantageofconcentratingallinformationonagivenproteinaroundacentralnode,whichworksespeciallywellforsimpleregula-torycircuits.Thisemphasisestheroleofeachcomponentwithinthenetwork,incontrasttotheregulatorygraphwhichemphasisestheinformationflowthroughthenetwork.Theentityrelationshipdiagramisgeneratedautomaticallybythe

&2012EMBOandMacmillanPublishersLimitedAframeworkformapping,visualisationandautomaticmodelcreation

C-FTigeretalrxnconsoftwareandvisualisedviaBiographer(Biographer).Inthesameway,therxnconsoftwarecanbeusedtogeneratethecontingencymatrix,thereactiongraphs,theregulatorygraph,and,viaBioNetGen(Blinovetal,2004),theSBMLfilethatconstitutethebasisfortheprocessdescription.Thesegenerationsarefullyautomatedandhencetheframeworkaddressestheissueof(ii)automaticnetworkvisualisationwithoutfurtherassumptionsand—inthecaseofthecon-tingencymatrixandregulatorygraph—withoutanysimplifications.

proteinsin,forexample,homodimers,andcanthereforenotdefinestricttrans-reactionswithinsuchdimers.Apartfromtheseissues,wecanreproducethesamemodelwithonlycosmetic/nomenclaturedifferences(seeSupplementaryinformationfordetails).Hence,theframeworkaddressestheissueof(iii)automaticmodelgenerationfromthedatabaseofbiologicalinformation.

MappingtheMAPkinasenetwork

Asabenchmark,wehaveusedthepresentedframeworkandanextensiveliteraturesearchtocreateacomprehensivemapfortheyeastMAPkinasenetwork(SupplementaryTableS1).Reactionshavebeendefinedwithspecificresiduesanddomainswheneverexperimentalsupportwassufficient.Thedegreeofexperimentalevidencehasbeenevaluatedmanuallyandindividuallyforeachentry,andreferencestoprimaryresearchpaperssupportingeachinteractionhavebeenincludedinthereactionandcontingencylists(column‘PubMedIdentifier(s)’).Wehaveusedmechanisticdataonreactions(C1)andacombinationofmechanisticandgeneticdataoncontingencies(C2)betweenreactionsandreactants’statesfromprimaryresearchliterature.Themappingisbasedsolelyonprimaryresearchpapersanddefactoshowndatatoensureahigh-qualitynetworkreconstruction.Wechosetoexcludealmostallgeneticdataasindirecteffectscannotberuledouteveninwell-performedgeneticscreens.Finally,wedecidednottoincludespatialdata,aswefoundinformationespeciallyonregulationof(re)localisationtoosparse.Tothebestofourknowledge,wehaveeliminatedallquestionableinformationfromthecompileddataset,andconvincingreactionslackingsolidmechanisticevidencehavebeenincludedbutclearlyanddistinctlylabelled.

TheMAPkinasenetworkcontains84components,181elementarystatesand222elementaryreactions,correspond-ingtomanyhundredsofthousandsofspecificstates.Thisnetworkislargeenoughtobeaseverechallengetotheestablishedvisualisationandanalysismethods.WedidinfactfailtogeneratethecompletestatespaceandterminatedtheBioNetGenexpansionafterthefirstthreeiterationswhichgenerated207,1524and372097specificstates,respectively.Weusearangeofgraphicalformatstovisualisedifferentaspectsofthishighlycomplexnetwork.First,wedisplaythenetworktopologyinthereactiongraphs(Figure2).These

Generationofmathematicalmodels

Thecontingencymatrixisatemplateforautomaticgenerationofmathematicalmodels.Eachelementalreactioncorrespondstoabasic(context-free)ruleinarule-oragent-basedmodel(TableII),or,inotherwords,asetofrulesthatshareareactioncentre(Chyleketal,2011).Allcontextualconstrainsonanelementalreactionisdefinedinasinglerowinthecontingencymatrix,andthisrowdefinestheelementalreaction’simplementationintherule-basedformat.Thebasicrulesufficesiftherearenoknownmodifiersofaparticularelementalreaction(i.e.,only‘0’and‘?’apartfromtheintersectionwithitsownstate(s)(whichisalways‘x’foraproductstateand‘!’forasourcestate)).Everyothercontingencysplitstheexpressionintworules;onewhenthatelementalstateistrueandonewhenitisfalse.Thenumberofrulesneededonlyincreaseswiththenumberofquantitativemodifiers(‘Kþ’and‘KÀ’)asthequalitativemodifierssetstherateconstanttozeroineitherthe‘true’(for‘x’)orfalse(for‘!’)case(seeSupplementaryinformationfordetails).TheexpansiontorulesisfullydefinedinourdataformatandtherxnconsoftwaretoolautomaticallygeneratestheinputfileforthecomputationaltoolBioNetGen(Blinovetal,2004).Thisfilecanbeusedforrule-basedmodelling,network-freesimulationandcreationofSBMLfiles.Thetranslationtoandfromtherule-basedformatisunambiguousinbothdirections,andweillustratethiswithtranslationofarule-basedmodelofthepheromoneresponsepathway(yeastpheromonemodel.org).Thismodelcontainslumpedreactionswhichwetranslatetocombinationsofelementalreactions,resultinginadifferentequationstructurebutthesamefunctionalitygivenappropriatechoiceofrateconstants(SupplementaryTableS3).Furthermore,wecannotdistinguishdifferentidentical

TableIIImplementationofelementalreactionsintherule-basedformat

Elementalreaction

Interactions(‘‘ppi’’,‘‘i’’or‘‘bind’’)Intra-proteininteractions(ipi)Phosphorylations(Pþ)Autophosphorylations(AP)Phosphotransfers(PT)Dephosphorylations(PÀ)Nucleotideexchanges(GEF)Nucleaseactivations(GAP)Ubiquitination(Ubþ)

Proteolyticcleavages(CUT)Degradations(DEG)

BioNetGenruleimplementation

A(B)þB(A)oÀ4A(B!1).B(A!1)A(A1,A2)oÀ4A(A1!1,A2!1)

AþB(PsiteBU)À4AþB(PsiteBP)A(PsiteBU)À4A(PsiteBP)

A(PsiteBP)þB(PsiteBU)oÀ4A(PsiteBU)þB(PsiteBP)AþB(PsiteBP)À4AþB(PsiteBU)AþB(GnPBU)À4AþB(GnPBP)AþB(GnPBP)À4AþB(GnPBU)

AþB(UBsiteBU)À4AþB(UBsiteBUB)

AþB(DomainBU)À4AþB(DomainBtruncated)AþBÀ4A

kf,krkfkfkfkf,krkfkfkfkfkfkf

ThetabledisplayshowthedifferentelementalreactionsinTableIaretranslatedtotherule-basedformat.SeeSupplementaryinformationforadditionaldetails.

&2012EMBOandMacmillanPublishersLimitedMolecularSystemsBiology20127Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalfiguresshowthatthenumberofcharacterisedphosphoryla-tionreactionsvastlyoutnumbersthatofcharacteriseddephosphorylationreactions(68to16;Figure2A),andthatseveralwell-establishedprocessesareonlysupportedbygeneticdata(includingtheentireMAPkinasecascadebelowPkc1;Figure2B,dashedlines).Thereactiongraphalsoallowscomparisonbetweentheestablishedpathwayarchi-tectureandtheunbiasedglobalproteinÀproteininteractionstudiesandsyntheticlethalnetworks(Figure3AandB,respectively).

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8MolecularSystemsBiology2012&2012EMBOandMacmillanPublishersLimitedAframeworkformapping,visualisationandautomaticmodelcreation

C-FTigeretalInthecontingencymatrix(Figure4),wevisualisethecombinedknowledgewehaveabouttheMAPkinasesystem(C1andC2).Thecorematrix(redblockofrowsandblueblockofcolumns)describealltheelementalreactions,elementalstatesandthe(possible)contingenciesofreactiononstates.Theblackfieldshereshowwhenthereisnooverlapbetweenthecomponentsinthereactionsandthosedefinedinthestates.Therefore,thematrixwillalwaysbesparselypopu-lated.However,wealsoseethatmostoftheremainingfieldsaregrey;thatis,effectnotknown(‘?’).Thismeansthatourknowledgeofreactions(C1;whichdefinesrowsandcolumns)ismuchstrongerthanourknowledgeofthecausalitybetweenthesereactions(C2;thecells).Weonlyhavedataonaminorityofallpossiblecontingencies,andthesegapsareexplicitlyshowninthecontingencymatrix.Itshouldalsobenotedthatnotalleffectscanbeascribedtosingleelementalstates.WehaveaddedanouterlayerofBooleanstates(purplerowsandcolumns)toaccountforthesecases.TheBooleanstatesdescribecomplexmechanismssuchasscaffoldingandcaninprinciplecorrespondtothespecificstatesof,forexample,processdescriptions.However,theyareonlyaddedwhenneededtodescribeempiricalresults.NotethatonlyasmallfractionofthestatesareBoolean,whichreflectsthelowabundanceofempiricaldataonthecombinatorialeffectofelementalstates(i.e.,specificstates).Therefore,webelieveittobebettertousemappingstrategieswhichdonotrequiresuchdata.Finally,thematrixcontainsalayerofinputsandoutputs(grey;columnsandrows,respectively).Theseconstitutethesystem’sinterfacewiththeoutside.

Theregulatorygraph(Figure5)displaystheinformationinthecontingencymatrixgraphically,byshowinghowreactionsproduceorconsumestates,andhowstatesinfluencereactions.ThisgraphcontainsthefullC1andC2information,andwouldfallapartwithouteither.Infact,theisolatedreaction–statepairsthatfalloutsidethegraphdosobecausetheyhavenoknownincomingoroutgoingcontingencies.ThegraphshowsthattheMAPkinasenetworkisratherwellconnected,asmostreactionsareindeedlinkedinasinglegraphbycontingencies.However,therearerelativelyfewinputandoutputpoints;manyreactionsdonothaveknownregulatorsandmanystatesdonothavedefinedregulatoryeffects.Onlyreaction–statepairsthatappearbetweenthesystem’sinputandoutputwouldbeabletotransmitinformation.Thismeanseitherthatallotherpairsareirrelevantforthedynamicsofthesignal-transductionprocess,orthatwearelackinginformationabouttheirroleinthisprocess.Infact,suchloseendsmightbeexcellentcandidatesfortargetedempiricalanalysis.OneexamplewouldbeMsb2’sbindingtoCdc42,whichisreportedtobeimportantforthe

pseudohyphaldifferentiationpathway;raisingthequestionofwhetherthisbindingisregulatedinresponsetothestimulithatactivatethispartoftheMAPkinasenetwork.Anotherpointthatstandsoutisthealmostcompletelackof(documented)informationexchangebetweenpathways.TheexceptionistheShobranchoftheHogpathway,whichiscloselyintertwinedwiththematingpathway,asbothareactivatedbythesharedMAPkinasekinasekinaseSte11andpartsofthecellpolaritymachinery.

Wehavealsogeneratedanetworkmapintheestablishedprocessdescriptionformat,butwithoutcomplexformations(Figure6).Thisdecisioneliminatedmostofthecombinatorialexplosionandtheneedforimplicitassumptions.However,thereisstilluncertaintyinthespecificphosphorylationstateoftheactivestateofcertaincatalysts,suchasSsk2,Ste11andSte7.Likewise,wedonotknowifphosphorylationorderisanissueforproteinswithmultiplephosphorylationsites.Incontrasttotheregulatorygraph(Figure5),theprocessdescriptionbecomesmorecomplicatedthemoreunknownswehaveandFigure6issimplified(compareSupplementaryFigureS2).However,thelimitedprocessdescriptioninFigure6clearlyshowsthecatalyst–targetrelationships,andreinforcestheimpressionthatveryfewoftheknownphosphorylationreactionsarebalancedbyknowndephosphorylationreactions.

Finally,weautomaticallygeneratedamathematicaldescrip-tionoftheentirenetworkasaproofofprinciple.TherxnconsoftwareusedthecontingencymatrixtogeneratetheinputfileforBioNetGen(Blinovetal,2004).Thecorrespondingnetworkistoolargetocreatebutcouldbesimulatedwiththenetwork-freesimulatorNFSim(Sneddonetal,2011).Furtheranalysisofthissystemfallsoutsidethescopeofthispaper,buttheinputfiletoBioNetGenand/orNFSimwithtrivialparametersisincludedasasupplement.Hence,acompletemathematicalmodelcanbeautomaticallygeneratedfromthereactionandcontingencydata,andtoourknowledgethisisthefirstframeworkthatintegratesnetworkdefinitionatthegranularityofempiricaldatawithautomaticvisualisationandautomaticmodelcreation.

Discussion

Itisclearthatthecomplexityofsignal-transductionnetworksisoneofthemajorchallengesinsystemsbiology,impedingourabilitytovisualise,simulateandultimatelyunderstandthesenetworks.Thisissuehasbeenwidelyrecognisedandsubstantialeffortshavebeencommittedtoimproveandstandardiseourtoolsforvisualisationandmodellingof

Figure2ThereactiongraphcompactlydisplaysthetopologyoftheS.cerevisiaeMAPkinasenetwork.(A)ThereactiongraphoftheMAPKnetworkdisplaysthecomponentsasnodesandthereactionsasedges.Eachcomponentisdefinedbyacentralmajornodeandperipheralminornodesindicatingdomains,subdomainsandspecificresidues(blue).Wheninteractingdomainsandtargetresiduesareknown,reactionsaredisplayedasedgesbetweentheseminornodes.Incontrast,thecondensedreactiongraph(B)displayseachcomponentasasinglenode,andeachtypeofreactionbetweentwonodesasasingleedge.Nodesareeitherproteins(circles),smallmolecules(diamonds)orDNA(square).Edgecoloursindicatereactiontype(co-substratesandco-products):Grey;protein–proteininteraction(N/A),red;phosphorylation(ÀATP,þADP),orange;guaninenucleotideexchange(ÀGTP,þGDP),blue;dephosphorylationorGTPaseactivation(þPi),gold;ubiquitination(Àubiquitin,ÀATP,þADP,þPi),black;phosphotransferorproteolyticcleavage(N/A).Thedomainlayoutin(A)prioritisesreadabilityanddomainorganisationdoesnotreflectlinearsequenceorproteinstructure.Arrowheadsindicatedirectionalityforunidirectionalorreciprocalcatalyticmodifications.Reactionsforwhichwefoundnodirectevidencebutwhicharesupportedbyconvincinggeneticdatahasbeenincludedasdashedlines.Notethemuchhigherfrequencyofreportedphosphorylationreactionsascomparedwithdephosphorylationreactions;intotalthenetworkincludes68phosphorylationreactionsbutonly16dephosphorylationreactions(A).

&2012EMBOandMacmillanPublishersLimitedMolecularSystemsBiology20129Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalcellularnetworks(Huckaetal,2003;LeNovereetal,2009).Thesestandardisationeffortsareessentialfordataexchangeandreusability,butmanyoftheexistingtoolsareunsuitablefordefinition,visualisationandmathematicalmodellingoflargenetworks.Thearguablymostimportantproblemsarethecombinatorialcomplexity,thegranularitydifferencebetween

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10MolecularSystemsBiology2012&2012EMBOandMacmillanPublishersLimitedAframeworkformapping,visualisationandautomaticmodelcreation

C-FTigeretalempiricalandtheoreticaldata,andthelackofexchangeformatsbetweendifferenttheoreticaldescriptions.Here,wehaveintroducedanewframeworkfornetworkdefinitionatthesamegranularityasmostempiricaldata.ThisformatwasalreadyavailableforC1(reaction)information,asourlistofelementalreactionsusesthesameformatashigh-throughputdata(PSICQUIC).Wedescribecontextualinformationatthesamegranularityinourcontingencylist(C2),whichnotonlyallowsanintuitiveandaccuratetranslationofempiricaldatabutalsolargelyavoidsthecombinatorialcomplexity.Contrarytostatetransitionbaseddescriptionsbutliketherelatedrule-basedformat,thereactionandcontingencybaseddescriptionbecomessmallerthelessknowledgewehaveasonlyknownreactionsandcontingenciesareconsidered.Thisformatalsoprovidesforhighlydetailedreferencingaseachelementalreactionandcontingencycanandshouldbetiedtoempiricalevidence(i.e.,researchpaper(s)).Furthermore,weshowthatthisformatisstringentandunambiguouslydefinebothrule-basedmodelsandgraphicalformats,suchastheactivityflowdiagram(condensedreactiongraph),entityrelationshipdiagramandprocessdescriptionformatsofSBGN.Ourframeworkalsosupportstwonewvisualisationformatsthatweintroducehereandthatcandisplayourcompleteknowl-edgedatabase(thecompletereactionandcontingencylists).Finally,ourframeworkprovidesaveryhighreusabilityandextendibility,astheunderlyingnetworkdefinition—inlistformat—isveryeasytoextend,mergeandreuseinothercontext,whichisnotthecaseformostgraphicallyormathematicallydefinedsystems.Ofcourse,thislevelofdefinitionstillleavestheissuesofparameterestimationandgraphicallayout,butthesewouldtypicallyneedtoberepeatedevenwhenmerginggraphicalandmathematicalnetworkdefinitions.Hence,weadvocateamorefundamentallevelofnetworkdefinitionthangraphicalormathematicalformalism.Weenvisagethisorasimilarframeworkasastandardtogreatlyfacilitatemodel/networkconstruction,exchangeandreusability.

WehaveappliedthismethodtomapouttheMAPkinasenetworkofS.cerevisiae.Thisnetworkwaschosenasabenchmarksinceitisbothwellcharacterisedandrepresenta-tiveforsignaltransductioningeneral.Itconsistsofthreeclearsubgraphs,whichhavetraditionallybeenconsideredmoreorlessinsulatedpathways;theHighOsmolarityGlycerol(Hog)pathway,theProteinKinaseC(PKC)pathwayandtheMATing(MAT)pathway,whichalmostcompletelyoverlapswiththePseudoHyphalDifferentiation(PHD)pathway.Thesepath-wayshavealsobeenmappedordocumentedinseveralotherefforts.KEGGpresentsacombinedmapofthetraditionalMAPkinasepathwaysinaformatsimilartoitsmetabolicpathways(Kanehisaetal,2006,2010).However,thestringentedgedefinitionsusedforthemetabolicnetworkshavebeenabandonedandthisisa‘biologist’sgraph’.ThepictureissimilarwiththemapsofyeastMAPkinasepathwaysatScienceSTKE(e.g.,Thorneretal,2005).Forexample,thesemapsdisplaySte11withfourupstreamregulators,butitisunclearhowtheyregulateSte11andhowtheircontributionscombine(e.g.,ANDorOR?).Therefore,thesenetworkmapsmayprovideanexcellentintroductiontothenetworksbyprovidingacomponentslistandaroughideaofthecomponents’rolesinthenetwork,buttheyneitherdefinereactions(C1)norcontingencies(C2)unambiguously.Ontheoppositeend,wehavetherecentlypublishedprocessdescriptionofthecellcycleanditssurroundingsignallingnetwork(Kaizuetal,2010).ThiscontainsexplicitdefinitionofbothC1andC2information.However,thetremendousnumberofspecificstatesinsuchanetworkforcessimplifications,whichnotonlyleadstoalossofknowledge,butalsomixesupknowncontingencies(C2)witharbitraryassumptionsmadetosimplifythenetwork.OneexampleinthisparticularcasewouldbetheseparationoftheupstreamactivationofSte11anditsdownstreameffectontheHogandMatingpathways.Theoutputofthismoduleisdefinedbythecontextofitsactivation,andthisinformationislostduetothesearguablynecessarysimplifications.Inaddition,thegranularitydifferencebetweenthehighlyspecificmapstatesandtheunderlyingbiologicaldatamakesthemappingambiguous,leadingtofurtherunsupportedassumptions.Despitetheseshortcomings,theprocessdescriptionisusefulforvisualisationofcertainnetworkpropertiesduetotheexplicitrepresentationofhighlydetailedknowledgesuchastargetresidues.However,westressthatneitheroftheseestablishedandwidelyusedmethodsaresufficienttoaccuratelycapturetheentiresignal-transductionnetwork.Instead,weintroducethecontingencymatrixandthebipartiteregulatorygraphasalternativemethods,whichareabletofullycapturetheentireknowledgedatabasewithoutsimplifi-cationsorassumptions.Togetherwiththeestablishedmeth-ods,thesevisualisationsprovideanunprecedentedviewonthechosenbenchmarksystem,andwetrustthatthiscompletelyreferencedandcomprehensivemapoftheMAPkinasesignallingnetworkinS.cerevisiaewillbeausefulreferencematerialfortheresearchcommunity.

Theseresultshavedirectbearingonthemanyeffortstocreatelargedatarepositories.Purereaction(C1)data,suchasproteinÀproteininteractionnetworks,canberetrievedusingthestandardisedMolecularInteractionQueryLanguage(MIQL;whichourreactionlistisdesignedtobecompatiblewith)andPSICQUIC(PSICQUIC).PSICQUICaccesses,forexample,ChEMBL(Overington,2009),BioGrid(Breitkreutzetal,2010),IntAct(Arandaetal,2010),DIP(Xenariosetal,2002),MatrixDB(Chautardetal,2009)andReactome(Croftetal,2010).Severalofthesedatabaseshaveadditionalinformationincludingcontingency(C2)informationandastandardised(non-graphical)formatfordefinitionand

Figure3Thecondensedreactiongraphisanexcellenttoolforvisualisationofhigh-throughputdata.(A)PhysicalinteractionswithintheMAPKnetwork.Theglobalprotein–proteininteractionnetworkwasretrievedfromBiogrid(Starketal,2006),filteredforphysicalinteractionsexcludingtwohybrid,andvisualisedonthecondensedreactiongraph(Figure2A).Purpleedgesindicateprotein–proteininteractionsandtheirthicknessindicatesthenumberoftimestheywerepickedup,rangingfromasingletime(dashedline)to19times.NodesthatappearfadedhavenointeractionswithanyothercomponentintheMAPKnetworkreportedinthisdataset.NotethatthenodesthatdonotcorrespondtosingleORFswouldbeexcludedautomatically(e.g.,theSCFcomplex,DNA,lipids).Thesmaller,boxednetworkdisplaythecorrespondingtwo-hybridinteractionnetwork.(B)GeneticinteractionswithintheMAPKnetwork.SyntheticlethalinteractionswereretrievedfromBiogridandvisualisedasper(A).Alsoquantitativedata,suchasmutantphenotypesandgeneexpressionlevels,canbedirectlyvisualisedonthenetwork.

&2012EMBOandMacmillanPublishersLimitedMolecularSystemsBiology201211Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalElemental statesBool.InFigure4Thecontingencymatrixprovidesacompletedescriptionofthenetworkornetworkmodule.Thecorecontingencymatrixisspannedbytheelementalreactions(rows,inred)andtheelementalstates(columns,inblue).Theadditionalblocksarederivedfromthecontingencylistandcontaintheformationrules(rows)andeffects(columns)ofBooleanstates(bothpurple)aswellastheoutputof(rows)andinputto(columns)thenetwork(bothgrey).Thecellsinthematrixdefinehoweachreaction(row)dependsoneachstate(column).Theeffectsrangefrombeingabsolutelyrequired(‘!’),viapositiveeffector(‘Kþ’),noeffect(‘0’)andnegativeeffector(‘K–’)toabsolutelyinhibitory(‘x’),oritcanbeunknownorundefined(‘?’).EachBooleanstateisdefinedbyasingleoperator(‘AND’or‘OR’)fortheelementalstates,otherBooleansand/orinputsthatdefinesit.ThecontingencymatrixdisplayedherecontainsthecompleteMAPKnetwork.Notethatthecontingencymatrixissparselypopulated.Thisisbothbecausemostcombinationsofreactionsandstateslackoverlapincomponents(blacksquares)andbecausewehaveverylimitedknowledgeofthepossiblecontingencies(greysquares).Overall,theinformationonwhatreactionscanoccurismuchmoreabundantthanonhowtheyareregulated.

OutBool.Elemental reactionsretrievalwouldfurtherimprovetheusefulnessoftheseresourcesandfacilitatefurtheranalysisofthestoredinforma-tion.Theframeworkweproposehereprovidessuchaformatwiththekeyadvantageofincludingexporttomathematical

12MolecularSystemsBiology2012models.Sincemathematicalmodellingisthemostcentralandnaturalsteptobringtheknowledgeinthesedatabasesintoausefulform,wherequantitativesystemspropertiescanmostexhaustivelybeanalysed,theintroductionofsuchanexportis

&2012EMBOandMacmillanPublishersLimitedAframeworkformapping,visualisationandautomaticmodelcreation

C-FTigeretalFigure5Theregulatorygraphvisualisethecausalitybetweenreactionsandrevealstheregulatorystructureofthenetwork.Thisbipartitegraphillustratestherelationshipsbetweenthereactions(rednodes)andstates(bluenodes)withinthenetwork.Edgesfromreactionstostatesdefinehowstatesareproduced(blue)orconsumed(purple),andeachsuchedgecorrespondstoasingleelementalreaction.Edgesfromstatestoreactionsdefinehowstatesregulateotherreactions,andeachsuchedgecorrespondtoasinglecontingency(Green;absoluterequirement(‘!’)orpositiveeffector(‘Kþ’),red;negativeeffector(‘K–’)orabsolutelyinhibitory(‘x’)).Booleansareusedwhentheeffectonareactioncannotbeattributedtosingleelementalstates(whitediamonds(OR)ortriangles(AND)connectedtothestates/Booleans/inputsthatdefinethemwithblacklines).Inputsaredisplayedingreyandconnectedtotheelementalreaction(s)theyinfluence.Likewise,outputsaredisplayedingreyandconnectedtothestatestheyareinfluencedby.Signalscanbefollowedthroughthenetworkfromexternalcues(grey;top)totranscriptionalresponse(grey;bottom)asalledgesaredirectional.Reactionswithoutinputarenot(knowntobe)regulatedandwouldthereforebeexpectedtohaveconstantrates;likewisestateswithoutoutputhaveno(defined)impactonthesystem.Wehavealsoincludedlikelybutundocumentedrequirementsforenzyme–substratebindingsbeforecatalysisasdashedlines.Theregulatorygraphistheonlygraphicalrepresentationusingthecompleteinformationinthecontingencymatrix,andhencetheonlycompleteandcompletelygraphicalvisualisationofthenetwork.Itisalsothemostpotentvisualisationtoevaluatethedegreeofknowledgeaboutthenetwork.Forexample,visualisationofhigh-throughputdatawouldresultindisconnectedreaction–statepairsonly,duetothelackofregulatoryinformation(noC2data).

animportantstepforward.Thisframeworkisstillnotasflexibleasdirectmodeldefinitionbutitprovidesdistinctadvantages.Formulatingmodelsdirectlyusingclassicalstatetransitionreactionsiseithersubjectiveorverycumbersomeinpracticeduetothecombinatorialexplosion,andstatetransitionbasedmodelsforthenetworksofthesizeweconsiderherearetoolargetobesimulated.Theclosestrelatedmodellingframeworkisrule-basedmodelling,inwhichmodelscanbeformulatedwithoutthesecombinatorialexplosionproblems,anditisalsotoarule-basedformatthatweexportourmodels.However,theclassicalrule-basedmodellingframeworkslackallthedatabasepropertiesofourframework,suchasthecontingencymatrixanditsexporttovariousnovelvisualisationformats.Inshort,onecouldthereforesaythatourframeworkcombinesthebestofexistingknowledgedatabaseswithnewvisualisationtoolsandrule-basedmodelling.

Inconclusion,wepresentamethodtodocumentandvisualisesignal-transductionnetworksthatimprovesonpreviousstrategiesinthefollowingrespects;(I)itallows&2012EMBOandMacmillanPublishersLimitedconcisemappingatthesamegranularityasbiologicaldata,hencepre-emptingtheneedforimplicit,unsupportedassump-tions,(II)itallowsreferencingofeachelementalreactionandcontingencyseparatelyandhandlesunknownsexplicitly,(III)thenetworkcanbevisualisedwithoutanysimplificationsorassumptionsthatincreasetheuncertainty,(IV)thevisualisa-tionscanbeautomaticallygeneratedfromthedatafiles,(V)thenetworkdefinitionisatemplatefromwhichamathema-ticalmodelcanbeautomaticallygenerated(VI)andexportedtoSBMLand(VII)thesuppliedtemplateandrxncontoolmakesthemethodimmediatelyusefulforanyonewithaninterestinsignaltransduction.Hence,ourframeworkbridgethreecriticallevelsofsignal-transductionnetworkanalysis;definition,visualisationandmathematicalmodelling,aswellasempiricaldataandtheoreticalanalysis.

Materialsandmethods

TheMAPkinasenetworkmapisbasedonthepaperslistedbelow.Thespecificreference(s)arelistedforeachreactionandcontingency

MolecularSystemsBiology201213Aframeworkformapping,visualisationandautomaticmodelcreationC-FTigeretalFigure6Thelimitedprocessdescriptiondisplaysallposttranslationalmodificationsandtheircatalysts,butexcludescomplexformation.Eachspecificinternalstateisrepresentedasadistinctnode,althoughsomeintermediatephosphorylationstateshavebeenexcluded.Phosphorylationsareindicatedwithredarrows(ATPasco-substrateandADPasco-product),GEFreactionsasorangearrows(ÀGTP,þGDP),anddephosphorylationorGAPreactionsasbluearrows(þPi).Onlyafractionofthecatalyticmodificationshaveaknowncatalystforbothforwardandreversereactions,andtherequiredstateofthecatalystknownisinevenfewercases.Therefore,eventhishighlysimplifiedprocessdescriptionincludesuncertaintyintherequiredstatesofbothcatalystsandsubstrates.Inthisvisualisation,thisuncertaintyhasbeenshownbyusingasinglecatalysisarrowfromaboxincludingallpotentiallyactivestateofthecatalysttothebasicstateofthesubstrate(completelyunphosphorylatedforkinasereactions,orcompletelyphosphorylatedforphosphatasereactions).Whilethesesimplificationsareunsupported,includingadditionalcatalyticarrowswouldbeequallyarbitrarywiththeaddeddrawbackofmakingthefiguremorecomplex(seeSupplementaryFigureS2).Despitetheneedforimplicitassumptions,theprocessdescriptionisusefulasitisveryexplicitandintuitivetoread.

individuallyinthereactionandcontingencylistsinthe‘PubMedI-dentifier(s)’columnwiththeirPMIDnumber.

(Aietal,2002;Alepuzetal,2003;Alepuzetal,2001;AndrewsandHerskowitz,1989;AndrewsandMoore,1992;Apanovitchetal,1998;BaetzandAndrews,1999;Baetzetal,2001;Ballonetal,2006;Baoetal,2004;Baoetal,2010;Baretal,2003;Bardwelletal,1996;Bardwelletal,1998a;Bardwelletal,1998b;BenderandSprague,1986;Bilsland-Marchesanetal,2000;Blumeretal,1988;Breitkreutzetal,2001;Bruckneretal,2004;Buttyetal,1998;Chouetal,2004;Chouetal,2006;Cismowskietal,2001;Clarketal,1993;Collisteretal,2002;Cooketal,1996;Crosbyetal,2000;Cullenetal,2004;Davenportetal,1999;deNadaletal,2003;DodouandTreisman,1997;Doietal,1994;Dolanetal,1989;Dowelletal,1998;Drogenetal,2000;Elionetal,1993;Erredeetal,1993;Escoteetal,2004;Fengetal,1998;Fitchetal,2004;Flandezetal,2004;Flothoetal,2004;Friantetal,2001;Garcia-GimenoandStruhl,2000;Garrisonetal,1999;Gartneretal,1998;Gartneretal,1992;Goodetal,2009;Greenetal,2003;Guoetal,2009;Hagenetal,1986;Hagenetal,1991;HahnandThiele,2002;Heenanetal,2009;Heiseetal,2010;Hoetal,2002;Horieetal,2008;Inagakietal,1999;Inouyeetal,1997a;Inouyeetal,1997b;Irieetal,1993;Jacobyetal,1997;Jungetal,2002;Kamadaetal,1995;Kamadaetal,1996;Ketelaetal,1999;Kimetal,2010;Kimetal,2008;Kranzetal,1994;Kusarietal,2004;Lamsonetal,2002;LeeandLevin,1992;Leeuwetal,1995;Leeuwetal,1998;Lietal,1998;Liuetal,2005;MacKayetal,1991;MacKayetal,1988;Maddenetal,1997;MadhaniandFink,1997;Madhanietal,1997;Maedaetal,1995;Maedaetal,1994;Malerietal,2004;MapesandOta,2004;Martinetal,2000;14MolecularSystemsBiology2012MattisonandOta,2000;Mattisonetal,1999;Medicietal,1997;MelcherandThorner,1996;Metodievetal,2002;Miyajimaetal,1987;Murakamietal,2008;NasmythandDirick,1991;Nehlinetal,1992;NeimanandHerskowitz,1994;NernandArkowitz,1998;NernandArkowitz,1999;Nonakaetal,1995;Olsonetal,2000;OstranderandGorman,1999;Ozakietal,1996;ParaviciniandFriedli,1996;Parnelletal,2005;Pascual-Ahuiretal,2001;Peteretal,1996;Petersonetal,1994;PhilipandLevin,2001;PosasandSaito,1997;PosasandSaito,1998;Posasetal,1998;Posasetal,1996;Proftetal,2005;Proftetal,2001;ProftandSerrano,1999;ProftandStruhl,2002;Raicuetal,2005;Raittetal,2000;Rajaveletal,1999;Reiseretal,2000;Remenyietal,2005;Repetal,2000;Repetal,1999;RobertsandFink,1994;Schmelzleetal,2002;Schmidtetal,1997;Schmidtetal,2002;Schmitzetal,2002;Shietal,2005;Shimadaetal,2004;SidorovaandBreeden,1993;SiegmundandNasmyth,1996;SiekhausandDrubin,2003;Simonetal,1995;Skowyraetal,1997;Smithetal,2002;Soleretal,1995;Songetal,1996;Tabaetal,1991;TakahashiandPryciak,2007;Taoetal,2002;Tarassovetal,2008;Tatebayashietal,2003;Tatebayashietal,2007;Tatebayashietal,2006;Tedfordetal,1997;Trucksesetal,2006;Trumanetal,2009;Vadaieetal,2008;Valtzetal,1995;Varanasietal,1996;Vernaetal,1997;Vilellaetal,2005;WangandKonopka,2009;Wangetal,2005;Warmkaetal,2001;WassmannandAmmerer,1997;Watanabeetal,1994;Watanabeetal,1995;Watanabeetal,1997;WintersandPryciak,2005;Wuetal,2006;Wuetal,1999;Wuetal,1995;Wuetal,2004;Wurgler-Murphyetal,1997;Yablonskietal,1996;Yamamotoetal,2010;YesilaltayandJenness,2000;Youngetal,2002;YuanandFields,1991;Zarrinparetal,2004;

&2012EMBOandMacmillanPublishersLimitedZarrinparetal,2003;Zarzovetal,1996;Zeitlingeretal,2003;Zhanetal,1997;ZhanandGuan,1999;Zhaoetal,1995;ZhengandGuan,1994;Zhengetal,1994;Zhouetal,1993).

Themethodsusedareanintegralpartoftheresultsandareoutlinedinthatsection.Foradditionaldetails,pleaseseeSupplementaryinformation.

Supplementaryinformation

SupplementaryinformationisavailableattheMolecularSystemsBiologywebsite(www.nature.com/msb).

Conflictofinterest

Theauthorsdeclarethattheyhavenoconflictofinterest.

Acknowledgements

Wethankpastandpresentcolleaguesforhelpfuldiscussions;inparticularAkiraFunahashi,NorikoHiroiandDouglasMurrayforsuggestionsintheconceptionphase,Hans-MichaelKaltenbachforintroductiontothebipartitegraph,ClemensKu¨hnforintroductiontoNFsim,JensNielsenforthesuggestiontousematrixmultiplicationtocalculatenetworkdistanceandNinaArensforproofreading.WeacknowledgesupportfromJSPSandSSF(Japan-SwedencollaborativepostdocgranttoMK),LionsandtheSwedishResearchCouncil(toGC),theGermanMinistryforEducationandResearch(BMBF,SysMO2projectTranslucent2toEK),theEuropeanCommission(UNICELLSYS,Grant201142,AQUAGLYCEROPORIN,Grant35995,CELLCOMPUT,Grant043310andSYSTEMSBIOLOGY,Grant514169,alltoSHandEK)andfromtheMULTIDISCIPLINARYBIOSweden-Japaninitiative(Sweden:FoundationforStrategicResearchSSFandVinnova,Japan:JapanScienceandTechnologyAgencyJST)toSHandHK.WorkinthelaboratoryofSHwasalsosupportedbyagrantfromtheSwedishResearchCouncil(Grant2007-4905).

Authorcontributions:HKinitiatedthemappingproject.MKconceivedtheframework.GCandMKdevelopedtheframeworkwithinputfromalltheauthors.CFTandMKmappedtheMAPkinasenetwork.FKandRPimplementedtheframeworkwithguidancefromGCandMK.FKcreatedtherxnconsoftwaretool.MKdraftedthefirstmanuscriptwithhelpfromGC.SHandEKcontributedbiologicalandtheoreticalbackgroundknowledge,respectively.SH,EKandHKprovidedtheresearchenvironmentsandcontributedtocompletionofthemanuscript.Allauthorsread,editedandapprovedthefinalmanuscript.

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