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RESEARCHARTICLEOpenAccessSolvinggapmetabolitesandblockedreactionsingenome-scalemodels:applicationtothemetabolicnetworkofBlattabacteriumcuenotiMiguelPonce-de-León1,FranciscoMontero1*andJuliPeretó2*AbstractBackground:Metabolicreconstructionisthecomputational-basedprocessthataimstoelucidatethenetworkofmetabolitesinterconnectedthroughreactionscatalyzedbyactivitiesassignedtooneormoregenes.
Reconstructedmodelsmaycontaininconsistenciesthatappearasgapmetabolitesandblockedreactions.
Althoughautomaticmethodsforsolvingthisproblemhavebeenpreviouslydeveloped,therearemanysituationswheremanualcurationisstillneeded.
Results:Weintroduceageneraldefinitionofgapmetabolitethatallowsitsdetectioninastraightforwardmanner.
Moreover,amethodforthedetectionofUnconnectedModules,definedasisolatedsetsofblockedreactionsconnectedthroughgapmetabolites,isproposed.
ThemethodhasbeensuccessfullyappliedtothecurationofiCG238,thegenome-scalemetabolicmodelforthebacteriumBlattabacteriumcuenoti,obligateendosymbiontofcockroaches.
Conclusion:Wefoundtheproposedapproachtobeavaluabletoolforthecurationofgenome-scalemetabolicmodels.
Theoutcomeofitsapplicationtothegenome-scalemodelB.
cuenotiiCG238isamoreaccuratemodelver-sionnamedasB.
cuenotiiMP240.
BackgroundMetabolicreconstructionisthecomputational-basedprocessthataimstoelucidatethenetworkofmetabolitesinterconnectedthroughreactionscatalyzedbyactivitiesassignedtooneormoregenes[1-5].
Thereconstructionprocessbeginswiththefunctionallyannotatedgenomeofanorganism.
Then,theidentificationofthosegeneswhoseputativeproductscatalyzesomebiochemicalreac-tion,i.
e.
geneproductswithanassignedenzymecommis-sionnumber(EC)ortransportcommissionnumber(TC),shouldbedone.
Thisrelationalinformationcanbeorga-nizedintheso-calledgene-protein-reactionassociationtables(GPR)[1].
InafurtherstepGPRtableswillbeusedtoinfercandidatemetabolicpathwayscodedintheorgan-ism'sgenome[2].
Inordertoautomatetheprocessofreconstructionofatargetorganism'smetabolicnetwork,computationalmethodshavebeenpreviouslydevelopedthatwillyieldafirstdraft[6-8].
Thisfirstdraftcanbeusedtoformu-lateamathematicalrepresentationofanorganism'sme-tabolism,termedasgenome-scalemodel(GSM).
TheConstraint-Based-Modeling(CBM)isanapproachthatcombinesthestoichiometricanalysiswithoptimizationtechniquestostudygenome-scalemodels[9-14].
TheCBMhasbeensuccessfullyusedtopredictmetaboliccap-abilitiessuchasgrowthrates,aswellassystemsresponsestoenvironmentalorgeneticperturbations[15-18].
WhenapplyingCBMtoaninitialdraftofametabolicmodel,itisusualtofindinconsistenciesthatcanhavedifferentcauses.
Intheinitialstagesofametabolicrecon-struction,duetoannotationerrors,aswellastheexis-tencesofunknownenzymefunctionality,GPRassociationscanbeincorrectlyestablished.
Thus,somereactionsmaybenotincludedinthemodeldraft.
Asaconsequence,*Correspondence:framonte@quim.
ucm.
es;Juli.
Pereto@uv.
es1DepartamentodeBioquímicayBiologíaMolecularI,FacultaddeCienciasQuímicas,UniversidadComplutensedeMadrid,CiudadUniversitaria,Madrid28045,Spain2DepartamentdeBioquímicaiBiologiaMolecularandInstitutCavanillesdeBiodiversitatiBiologiaEvolutiva,UniversitatdeValència,C/JoséBeltrán2,Paterna46980,Spain2013Ponce-de-Léonetal.
;licenseeBioMedCentralLtd.
ThisisanopenaccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114http://www.
biomedcentral.
com/1752-0509/7/114somemetabolicpathwayswillcontaingapsthatwillcreatedead-endmetabolites[19].
Thesemetabolitesappearinthemodelasonlyproducedoronlyconsumedbyreactions,andhencewillneverreachasteadystatedifferentthanthetrivial,andthentheywillneverparticipateinafeasibleso-lution.
Theywillinturnblockanyreactioninwhichtheyareinvolved.
Therearetwoclassesofdead-endmetabo-lites:i)Root-Non-Producedmetabolites(RNP)i.
e.
metabo-litesthatareonlyconsumedbysystem'sreactions,andii)Root-Non-Consumed(RNC)thatincludesthosemetabo-litesthatareonlyproducedbythenetworkbutneverconsumed[20].
DetectionofRNPandRNCcanbeconductedbysimplyscanningtherowsofthestoichiometricmatrix.
However,theabsenceofflowthroughmetabolitesRNP(orRNC)couldbepropagateddownstream(orupstream)byblockingreactionsandthus,additionalmetaboliteswouldbecomegaps(seeFigure1).
ThosemetabolitesthatbecomeagapasaconsequenceofsomeRNPmetabolitearetermedDownstream-Non-Produced(DNP).
Inasym-metricway,Upstream-Non-Consumed(UNC)metabo-litesaredefinedasthosemetabolitesthatbecameagapasaconsequenceofsomepresentRNCmetabolite[20].
Ingeneral,thedetectionofdead-endmetabolitesandblockedreactionsisreferredcommonlyasthegapfind-ingproblem[6,7,19,20].
Model'sgapscanbesolvedbyaddingoneormorere-actionsthatallowconnectingadead-endmetabolitewithothermetabolitesofthenetwork,aprocessknownasgap-filling[6,20].
Insomecases,theincorporatedre-actionscanbemappedintosomecodinggene.
However,therearesomesituationswhereevenifasetofcandi-datereactionsthatfillthegapshasbeensuccessfullypredicted,itcouldnotbepossibletofindthegenesthatcodefortheseactivities.
Insuchcasesthereactionsarecalledorphanreactions.
Methodstopredictcandidategenestobeassignedtoorphanreactionshavealsobeenpreviouslydeveloped[21,22].
Thus,thereconstructionofmetabolicmodelsisaniterativeprocessinwhichtheCBMplaysanimportantroletodetectinconsistenciesthatshouldberesolvedorcuratedinordertoimprovemodelformulation[23].
Automatedmethodsformodelcurationhavebeenpreviouslydeveloped(foracomprehensivereviewthereaderisreferredto[24]).
Inordertosolvethegap-fillingproblem,anoptimization-basedmethodtoiden-tifytheminimumnumberofreactiontobeincludedinthemodelhasbeenproposedbydifferentauthors[20,23].
ThesemethodsrelyintheuseofMixedIntegerLinearProgramming(MILP)combinedwithuniversalreactiondatabasessuchasKEGG[25],BiGG[26]orMetaCyc[27].
Otherproposedapproachesarebasedontheuseofexperimentalinformationtodetectinconsist-encieswithmodelpredictionsthatmaysuggesterrorsinmodelformulation[28,29].
Eventhoughautomatedmethodsformetabolicnet-workcurationareofanundoubtedhelptoimprovemodelformulation,theremaybesituationswherethemanualinspectionsofacuratorarestillneeded.
Thisiscertainlythecaseofthereconstructionofnetworksfromgenomesthatsufferreductiveevolution(e.
g.
intracellularbacterialsymbionts)andcodeforminimizedmetabo-lisms.
Duringtheestablishmentofsymbiosis,metabolicredundancieswiththehostcanresultinthelossofen-zymaticstepsintheendosymbiontnetwork,leadingtotheemergenceofobligatemetaboliccomplementation.
Thesesharedmetabolicabilitiestaketheformofinter-ruptedpathwayswhentheendosymbioticnetworkisreconstructed.
Thus,theproblemofgap-fillingisacomplexdecisionmakingprocesswhereavisualrepre-sentationoftheinconsistenciescanhelptoamodel'scuratortounderstandhowgapmetabolitesandblockedFigure1Descriptionofgapmetabolites.
Aschematicrepresentationwherethefourclassesofgapmetabolitesareshownasaconsequenceofmissingreactions.
Redcrossesindicatetheabsenceofsomereaction.
Dottedandcontinuousarrowsrepresentblockedandnon-blockedreac-tions,respectively.
Yellowandgreencirclesrepresentgapandnon-gapmetabolites,respectively.
Metabolitesarelabeledaccordingtoitsclass.
Ina)theabsenceofareaction,causesmetaboliteAtobecomeaRoot-Non-Producedmetabolite(RNP)andthiseffectpropagatesdownstreamgen-eratingnewgapmetabolites(Downstream-Non-Produced,DNP)andblockedreactions.
Inb)theabsenceofreactionsconsumingHmakesitaRoot-Non-consumedmetabolite(RNC)andthiseffectpropagatesupstreamcausingothermetabolitestobecomeUpstream-Non-Consumed(UNC),inasymmetricmannerrespecttocasea).
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page2of15http://www.
biomedcentral.
com/1752-0509/7/114reactionsarerelatedandthusfindthenatureoftheseinconsistencies.
InthispaperwepresentamethodthatcombinestheCBMwithanalgorithmtocomputeConnectedCompo-nentsoverbipartite-graphs.
Thepresentedmethodal-lowsthedetectionoftheisolatedsetsofblockedandgapmetabolitesandthewayinwhichtheseareinter-connectedinwhatwehavetermedunconnectedmod-ules(UM)(seeIdentificationofUnconnectedModulesinsectionMethods).
Then,theanalysisofeachindividualunconnectedmodulesimplifiesandclarifiesthevisualrepresentation,andhencecanbeusedtodecidehowgapsshouldbefilledduringthecurationofthemodel.
TheavailabilityofaccurateGSMisespeciallyrelevantinthecaseofbacterialobligate(primary)endosymbiontssinceitisnotpossiblethecultureofthesemicroorgan-ismsandhencethereisanintrinsicdifficultyforobtain-ingdirectexperimentaldatafromthesystem.
Inthiscase,modelingcanserveasanappropriateproxyforfunc-tionalcharacterizations.
Forinstance,metabolicmodelinghasbeensuccessfullyusedinthecaseofBuchneraaphidi-cola(obligateendosymbiontofaphids)toevaluatetheroleoftheendosymbiontandthehostinnitrogenmetabolism[30],inSodalisglossinidius(facultativeendosymbiontoftse-tseflies)tocharacterizeintermediatestepsduringthereductionofthenetworkasaresultoftheinteractionwiththehostmetabolism[31],andinBlattabacteriumcuenoti(obligateendosymbiontofcockroaches)tobetterunder-standthestrikingconservationoftheendosymbiontme-tabolismalongtheevolutionarytimeaswellasitsputativeroleinthenitrogeneconomyofthesystem[32].
InthispaperwehaveusedtheGSMfromB.
cuenoti(iCG238)totesttheproposedmethodofcuration.
OurstudyallowsupgradingiCG238toamoreaccuratemodelversionnamediMP240,anditcanbeusedasaguideforsystemsbiologyexperimentalexplorationsoftheinteractionbe-tweencockroachesandtheirendosymbionts.
MethodsConstraint-basedmodelingThestudyofthestructuralpropertiesofbiochemicalre-actionsnetworkreliesontheanalysisofthestoichiomet-ricmatrix[33,34].
LetdenotebyNthestoichiometricmatrixassociatedtoacertainmetabolicnetworkwithmrowsandncolumnscorrespondingtothenumberofmetabolitesandreactions,respectively.
InthefollowingIandJwillrefertothesetofmetaboliteindexes(rows)andreactionindexes(columns),respectively.
Moreover,thesetofreactionindexesJwillbepartitionedintotwodisjointsubsets:thesetJINTwhichcontainstheindexesofinternalfluxes,i.
e.
thebiochemicalreactionsthattakeplaceinsidethecell,aswellthetransportreactionsthatoperatebetweenthecellandthesurroundingmedium.
Ontheotherhand,thesetJEXcontainstheindexesoftheexchangefluxes,whicharetheauxiliaryvariablesusedtorepresenttherateatwhichcertainmetabolitesareconsumedorproducedbythesystem[35].
Therewillbeonlyoneexchangefluxpermetaboliteandthesefluxeswillbeassociatedtothemetabolitesbelongingtotheextra-cellularcompartment.
Byconvention,theactivityoftheexchangefluxesisdefinedaspositiveornegativeifthemetaboliteisproducedorconsumedbythesystem,re-spectively[35].
TheCBMapproachrelaysontheuseofdifferentkindsofconstraintsrepresentedbymathematicalequationstodefinethesocalledfluxspaceF,i.
e.
thesetofallfluxdis-tributionscompatiblewiththegivenconstraints[9,36,37].
Thesteadystateconditionisimposedoverthemassbal-anceequationofeachmetaboliteofthenetworkyieldingthefollowinghomogeneoussystemoflinearequations:N:v01wherethevectorvisafluxdistributioncompatiblewiththesteady-statecondition.
Moreover,lowerandupperboundsareimposedovereachreactiontorepresentadd-itionalconstraints.
Forinstance,thethermodynamiccon-straintsthatmakesomereactionstobeirreversiblearerepresentedbysettingtozerothelowerbound.
Besides,thesurroundingenvironmentofametabolicsystemcanbemodeledbysettingboundsovertheexchangefluxes.
Forexample,ifagivenmetaboliteisavailableinthemediumandthuscanbeconsumedbythesystem,thelowerboundofthecorrespondingexchangefluxshouldhaveanegativevalue.
Thelowerandupperboundsim-posedovereachfluxcanbewrittenasthefollowingsys-temsoflinearinequalities:vlbj≤vj≤vubjjJ2wherevjistheactivitythroughthefluxj,whereasvlbjandvubjareitslowerandupperbounds,respectively.
Together,thehomogeneoussystemoflinearequations(1)andthesystemoflinearinequalities(2)yieldsthemathematicalrepresentationofthefluxspaceF,expressedas:FvRn:N:v0;vlbj≤vj≤vubjjJno3BlockedreactionsAreactioninametabolicmodelisdefinedasblockedunderagivenmediumconditionifitcannotdisplayasteady-statefluxotherthanzero:jJBlockedvj0;vF4whereJBlockedisthesetofblockedreactionindexes.
Thissetcanbecomputedsolvingasetoflinearprograms,asPonce-de-Leónetal.
BMCSystemsBiology2013,7:114Page3of15http://www.
biomedcentral.
com/1752-0509/7/114proposedbyBurgardetal.
[38].
Theapproachconsistsincalculatingtheminimumandmaximumfluxvaluethrougheachreactionofthesystem.
Whenthemax-imumandminimumvaluesfoundforagivenreactionarebothequaltozero,thereactionissaidtobeblockedunderthedefinedmediumcondition.
Theformulationofthesetoflinearprogramsisthefollowing:Min=Max:vjjJs:t:Nv0vlbj≤vj≤vubjjJ5GapmetabolitesGapmetabolitesinGSMaredefinedasthosevertexesofthenetworkthroughwhichtherecanbenosteadystateflow[24].
WhilethedetectionofRNPandRNCmetabo-lites(seetheIntroductionforaproperdefinition)isstraightforwardbyscanningofeachrowofthestoichio-metricmatrixN,thecaseofdetectingUNPandDNCmetabolitescannotbeaccomplishedbyasimpleinspec-tionoftheentriesofN[20].
However,basedonthedef-initionofblockedreaction(4)wefoundawaytodefinegapmetabolitesthatallowitsidentificationinastraight-forwardmanner.
Definition:ametabolite∈Iinanetworkundersteady-stateisagapifandonlyifallthereactionsinwhichitsparticipate(eitherasreactantorasproduct)belongstothesetofblockedreactionsJBlocked.
Thisstate-mentimpliesthattherecannotexistsastationaryflowthroughthismetabolite.
Thus,ifwenamethesetofreactionsinwhichame-taboliteparticipateas:σijJ:Nij≠0iI6then,thesetofgapmetabolitesIGapIcanbedefinedasfollows:i∈IGapσiJBlocked7Hence,thedetectionofgapmetabolitescanbeaccom-plishedbyfindingthesetJBlockedandapplyingequations(6)and(7)foreachmetabolite.
Thegivendefinitionforagapmetabolitedoesn'tmakeanydistinctionbetweenthedifferentclassesofgapdefined(i.
e.
RNP,RNC,UNP,DNC).
AlthoughthereisnogeneralprocedurefortheclassificationofgapmetabolitesasRNP,RNC,UNP,orDNConcetheyhavebeenfound,thisispossibleinsimplecases.
Forexample,ifagapmetaboliteisinvolvedonlyinanirreversiblereactionbywhichitisconsumed,orifallthereactionsinwhichthismetaboliteisinvolvedareirre-versibleandinallitisconsumed,thenmetabolitewillbeaRNP.
Asimilarreasoningcanwearguedforthesym-metriccase,leadingtotheidentificationofaRNC.
Formorecomplexcases,avisualinspectionoftheunderling"UnconnectedModule"(seesection:IdentificationofUn-connectedModules)mayhelptotheclassification.
Thecoenzymepseudo-gapproblemIngeneralgapmetabolitescanbeidentifiedusingitsre-lationtothesetofblockedreactionsJBlockedasitwasex-plainedinprevioussubsection.
However,therecouldbesomespecialmetabolitesthatarenot"gap"underthedefinitiongivenby(7).
Neverthelessthesemetabolitesmaybethecausethatcertainreactionsgetblocked,astheexampledepictedinFigure2shows.
ThemetaboliteDisnotagapbutthemassbalancesequationforD*im-pliesthatv5isequaltov6,andthemassbalanceequa-tionforDimpliesv4+v6=v5.
Asaconsequenceoftheserelationsv4isrestrictedtozero,i.
e.
v4isablockedreaction.
Thiseffectpropagatesdownstreamtov3,v2andv1.
ThisiswhywenameDasapseudo-gapmetab-olite.
Inordertounblockv4,whichintermwillunblockv1,v2andv3,theremustbeaddedasinkforDorD*.
Thesekindsofsituationsmaytakeplacewhenthebio-syntheticpathwayofacoenzymeispresentinamodel,buttherearenofluxesdrainingordegradingthecoen-zymeproducedbythispathway.
Thesemetabolitesmaybeinvolvedinconservedmoieties,andinsuchcasestheywillbeconsumedandregeneratedinacyclicman-ner.
Asaconsequencetheycouldnotbedetectedasgapmetabolitesbecausetheywillparticipateinatleasttwoactivereactions.
However,ifthebiosyntheticpathwayforacoenzymeisincludedinametabolicmodel,thenetproductionofacoenzymewillnotoccurundersteadystateunlesssomefluxconsumesit.
Hence,thereactionsinvolvedinthebiosynthesispathwaymaybecomeblocked.
Acommonapproachtosolvethisproblemistoincludethecoenzyme-likemetaboliteintothebiomassequationoralternativelytointroduceanexchangefluxthatcandrainthemetaboliteoutofthesystem.
Eitherofthesetwosituationsisequivalenttotheadditionoftheabove-mentionedsink.
Thewaytodetectthepseudo-gapmetabolitesmaybesummarizedasfollow.
WhenanUMoverlapwiththebiosyntheticpathwayofacertaincofactor,twodifferentsituationscanbefound:thecofactorisincludedintheUMasagaporitisnot.
Ifitisagap,thecofactormustbeincludedinthebiomassequationinordertosolvetheUM(see"UM3-Pyridoxal5-phosphatebiosyntheticpathway"undersectionResultsanddiscussionasenex-ample).
IfthecofactorisnotincludedintheUM(i.
e.
isnotagap),thenitisquiteprobablethatthecofactormaybeinvolvedinaconservationrelationwhichcon-nectthecofactortoactivereactionsandforthisreasonisnotdetectedasagapunderthedefinitiongivenbyequation(7).
However,evennotdetectedasgap,theco-factorcouldbetheunderlyingcausethattheUMbecomePonce-de-Leónetal.
BMCSystemsBiology2013,7:114Page4of15http://www.
biomedcentral.
com/1752-0509/7/114blocked,andforthisreasonwastermedthecofactora"pseudo-gap"ashasbeenpointedoutatthebeginningofthissection(asanexample,see"UM1-Menaquinolbio-syntheticpathway",undersectionResultsanddiscussion).
Theconservationrelationscanbedetectedbytheanalysisoftheconservedmoieties,whichwerecalculatedasprevi-ouslydescribed[33].
Finally,byaddingthecorrespondingcofactortothebiomassequationtheUMcanbesolved.
Identificationofunconnectedmodules(UM)Whenanalyzingthesetofblockedreactionsandgapmetabolitesofametabolicmodel,itiscommontofindrelationsbetweenbothsetsduetothefactthatblockedreactionsmaybeconnectedwithotherblockedreactionsthroughgapmetabolite.
Insomecases,blockedreac-tionsaredirectlyconnectedtoaRNP/RNCmetabolite.
However,thismaybenotthecaseofotherblockedreac-tionsthatmaybenotlinkeddirectlytoaRNPorRNCmetabolite.
Forexample,asitcanbeseeninFigure1a,reactionv3,althoughblocked,isnotdirectlyconnectedtoaRNPmetabolite(A),butindirectlythroughmetabol-itethroughasetDNCmetabolites(BandC)andotherblockedreactions(v1andv2).
Similarlyoccursinthesymmetriccase(Figure1b).
Asaconsequenceoftheserelations,itispossibletosystematicallyestablishhowtheblockedreactionsareconnectedthroughthegapmetabolites.
Anymetabolicnetworkcanberepresentedasadi-rectedbipartitegraphbyconsideringthesetsofvertexV=IUJ[39,40].
Then,adirectededgeorarcwillexistbetweenametaboliteandareactionifthemetaboliteparticipatesinthereaction.
Thedirectionofthearcwillbeincidenttothereactionifthemetaboliteisareactantandincidenttothemetaboliteifitisaproduct.
Inthefollowing,thegraphassociatedtoametabolicnetworkwillbereferredasthemetabolicgraph.
Oncethemetabolicgraphisconstructeditispossibletoconsideranypossiblesub-graphbyselectingapairofsubsetsI'IandJ'Jofmetabolitesandreactionsre-spectively.
Inparticular,itispossibletoconsiderthesub-graphdefinedbythesubsetofvertexV=IGapUJBlocked.
Thissub-graphwillcontaintherelationthatexistsbetweengapmetabolitesandblockedreactions.
Moreover,thesetofconnectedcomponentscanbecomputedoverthisgraph.
Inthiscontext,eachconnectedcomponentcanbeinterpretedasa"module"ofthemetabolismthatbecomesinactiveorunconnected,possiblyasaconse-quenceofmodelinconsistencies,suchasthepresencesofasetofRNP/RNCmetabolites.
ForthisreasonthesetofconnectedcomponentwillbereferredasanUnconnectedModules(UM).
Insimplecases,thereasonthatcausesacertainUMtobeunconnectedfromtherestofthenetworkmaybefoundbyvisualinspectionofthegraphrepresentingtheUM.
InsuchcasesconnectivityrestoringoftheRNCandRNPmetabolitespresentintheUMmay,ingeneral,solvetheproblemoftheUNCandDNPmetabolites.
ThesetofelementaryoperationsthatcanbeappliedtosolveUMshasbeendiscussedbyKumarandcollabora-tors[20],anditincludes:additionofbiochemicalreac-tionsoftransport,incorporationofexchangefluxesandrelaxationofirreversibilityconstraintofsomereactions.
Morecomplexsituationsmayincludecasessuchasthepseudo-gapproblemdescribedintheprevioussection.
FluxbalanceanalysisTheFluxBalanceAnalysis(FBA)isanapproachthatcombinesthedescriptionofthefluxspaceFdefinedbyequation(3)withoptimizationtechniquestofindafluxdistributionvthatmaximizesthegrowthrate[17,37,41].
ThisproblemcanformulatedasalinearprogramandcanbesolvedwithstandardtechniquesofLinearPro-gramming(LP).
Max:vBiomasss:t:Nv0vlbj≤vj≤vubjjJ8wherethefluxvBiomassrepresentsthegrowthrateoftheorganism.
Thisflux,alsorefereedasthebiomassequa-tion,includesallthemetabolitesthatarebiomasscom-ponents,initsspecificproportions[42,43].
Figure2Pseudo-gapmetabolites.
Schematicrepresentationofasituationwherethereisametabolitenotdetectedasgap(metaboliteD)becauseofitsparticipationinnon-blockedreactions.
However,thesetofnon-blockedreactionsinwhichitparticipatesformsaloopandthereisnonetproduction/consumptionofthemetabolite.
Asaconsequence,thepathwayofsynthesisofDbecomesblocked.
ThecolorandlinecodesarethesameasinFigure1.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page5of15http://www.
biomedcentral.
com/1752-0509/7/114In-silicoknockoutexperimentsThefragilityanalysisofanetworkwasperformedbysimu-latingknockoutexperimentsforeachmetabolicgeneincludedinaGSM.
Anin-silicoknockoutexperimentforagivengeneconsistsinboundtozerothefluxforeachre-actioncodedbythegene,whichareinferredthroughtheGRPassociationtable.
Afterso,FBAisusedtofindthemaximalvalueofthebiomassreactionunderthegeneticperturbation.
Iftheoptimalvalueofbiomassreactionislowerthanacertainthreshold,theknockoutissaidtobelethal(i.
e.
essential),otherwisethegeneisnotessential.
Theprocedureisperformedoverallthegenesinthemodel.
MinimalmediumpredictionTheminimalmediummaybedefinedasthesmallersetofmetabolitesthatshouldbepresentinthemediumconditioninorderafeasiblefluxdistributionvtoexist,withabiomassproductionrategreaterthanzero.
TheminimalmediumwascalculatedbysolvingaMILPalgo-rithmaspreviouslydescribed[44-46].
TheMILPalgo-rithmisthefollowing:Min:XjJEXyjs:t:Nv0vlbj≤vj≤vubjjJINTvBiomass≥vlbBiomassvlbjyj≤vjjJEXyj0;1fgjJEX9Thealgorithmrequirestheincorporationofasetofbinaryyjvariables,oneforeachexchangefluxjJEX.
Moreover,asetofconstraintsthatrelateseachbinaryvariablewithitscorrespondingexchangesfluxshouldbeincorporatedtotheproblem.
Then,wheneverabinaryvariabletakesthezerovalue,thecorrespondingex-changefluxisconstrainedtotakeavaluegreaterorequalthanzero.
Additionally,thelowerboundcorre-spondingtothebiomassproductionfluxshouldbesettoacutoffvaluegreaterthanzeroinordertoguaranteeapositivegrowthrate.
Finally,theoptimizationtargetisdefinedinsuchawaythatminimizesthenumberofac-tiveexchangefluxeswithanegativevalue.
Duetothefactthateachexchangefluxisrelatedwithoneextracel-lularmetabolitethisisequivalenttofindtheminimalsetofmetabolitesthatthesystemmustconsumeinordertoproduceabiomassfluxgreaterthanzero.
DetectionofreactionsubsetsAReactionSubsets(RS)[47,48]orFullCouplingSets[38]inastoichiometricnetworkisagroupofreactionsthatoperatetogetherinfixedfluxproportionsforanyfluxdistribution.
Duetothefactthattherelationsbe-tweenenzymesandreactionsarenotalwaysbiunivocal,thereactionsubsetdoesnotalwaysmatchtheconceptofEnzymeSubsetpreviouslyintroducebyPfeifferetal.
[49],andforthisreasonthetermReactionSubsetseamsmoreappropriate[48].
TheRSsarestructuralinvariantofnetworkandforthattheyareindependentonthekin-eticparametersofthesystem.
Moreover,theyshedvalu-ableinformationthatmayhelptounderstandhowthenetworkisregulated[50].
ForthesereasonstheconceptRSisimportantfortheanalysisofmetabolicnetworks.
Inordertocomputereactionsubsetthefollowingpre-processingstepswereappliedtothenetwork.
First,rowsandcolumnscorrespondingtogapmetabolitesandblockedreactionrespectivelywereremovedfromthestoichiometricmatrix.
Asitwaspreviouslydescribed[38],theconstantbiomasscompositionimposedbythestoichiometryofthebiomassequationwasrelaxedbyremovingthecorrespond-ingcolumn,whileallowingeachbiomasscomponenttobedrainedfromthesysteminanindependentway.
Then,theidentificationofRSwasdonebyusingthealgorithmde-scribedin[49].
ComputationaltoolsConstraint-Basedanalysiswasperformedusingthepython-basedtoolboxCOBRApy[51].
LPandMILPproblemsweresolvedusingtheGurobiSolver[52]accededthroughCOBRApy.
IdentificationofconservationrelationswasdonebycomputationthesetofextremeraysusingthePolcopackage[53].
IdentificationofRSwasdonebyusinganimplementationbasedonPython[54,55]ofthealgorithmdescribedin[49].
Thedetectionofthecon-nectedcomponentsofagraphwasdoneusingtheim-plementationofthealgorithmavailableintheiGraphlibrary[56].
GraphsweredrawnusingtheyEdGraphEditor[57].
AllcomputationwasdoneonadesktopcomputerwithanIntelCorei7CPU950processor,with23.
5GiB,runningunderFedora17LinuxOS.
ResultsanddiscussionThefirststepintheanalysisoftheGSMofB.
cuenotiiCG238wastofindthesetsJBlockedandIGapofblockedreactionsandgapmetabolites,respectively.
Theresultsshowedthat69reactionsoveratotalof419(~16%)areblockedunderanymediumcondition.
Usingthisinforma-tionasetof58metabolitesoveratotalof364(~15%)weredetectedasgaps.
Abipartitegraphrepresentationofthemetabolicnetworkwasconstructed,andthesub-graphdefinedbythesubsetofvertexIGapUJBlockedwasselected(seeIdentificationofUnconnectedModulesinsectionMethods).
Computationofconnectedcomponentsoverthissub-graphallowsidentifying10UM.
Afterso,eachgapmetabolitewasclassifiedinoneofthefourcat-egories:RNP,RNC,UNCandDNP.
AdescriptionofeachPonce-de-Leónetal.
BMCSystemsBiology2013,7:114Page6of15http://www.
biomedcentral.
com/1752-0509/7/114differentUMfoundiniCG238issummarizedinTable1,whichwassortedaccordingtothenumberofreactionsin-cludedineachUM.
WhenanalyzingthereactionsparticipationofeachUM,itwasfoundthatinmanyofthecasesthesetofreactionsbelongingtoanUMoverlappedwithknownbiochemicalsubsystems(ormetabolicpathways).
Forexample,allthereactionincludedinUM1belongstothemenaquinolbiosyntheticpathway.
ItisworthtonotethatinsomecasesUMscouldbecomposedbyaniso-latedreactionasthecasesofUM9andUM10.
AftertheidentificationofallUMapplyingtheproposedapproach,eachsub-graphwasdrawnindependently.
Visualinspec-tionofeachgraphwasdonetodetectpossibleinconsist-enciesinthenetworkformulationthatmayhelptocarryoutthemanualcurationofaGSM.
UM1-MenaquinolbiosyntheticpathwayThebiggestUMfoundinthemetabolicmodel(UM1)wasfirstanalyzed.
Figure3showsthegraphthatrepre-sentstheUM.
AvisualinspectionoftheseFigureshowsthatUM1includesallthereactionsandmetabolitethatconformsthemenaquinolbiosyntheticpathway.
TheFigurealsoshowsthatfromthe21gapmetabolitesin-cludedintheUM,twoareRNPmetabolites(mevalonate,2-Octaprenyl-6-methoxy-1,4-benzoquinol),andoneisanRNCmetabolite(2-Octaprenyl-3-methyl-6-methoxy-1,4-benzoquinol),whiletheremainingmetabolitesarethenupstream/downstreamgapmetabolites.
Mevalonateisaprecursorforthebiosynthesisofisopen-tenyldiphosphatethatinturnisinvolvedinthebiosyn-theticpathwayofmanycofactorssuchasmenaquinoland2-demetyl-menaquinol.
Aninspectionofthecurrentgen-omeannotationofB.
cuenoti[58]wasdonetolookforcandidategenescodingforenzymesbelongingtothemevalonatebiosyntheticpathway.
However,noneofthosegeneswereidentifiedindicatingaplausiblepartiallossofthemevalonatebiosyntheticpathway.
Asaconsequenceofthisputativelosttrait,mevalonateshouldbehypothet-icallyimportedfromtheenvironment(i.
e.
theinsecthost),asituationthatwouldsuggestanewcaseofmetaboliccomplementationbetweenthebacterialendosymbiontanditshost.
Infavorofourhypothesiswepointoutthatthemevalonatepathwayplaysakeyroleininsectmetab-olismastheprecursorofjuvenilehormone(JH)anditisactiveinthefatbodyofB.
germanica([59]andreferencestherein).
Indirectevidenceoftheabilityofmevalonatetodiffuseandreachtheendosymbiontisgivenbyfeedingex-perimentsusingmevalonateasaprecursorofJHsynthesisinthecorporaallata([59]andreferencestherein).
Moreover,thelocustagBLBBGE_110hasbeenanno-tatedasahomologtoubiE[58],whichcodesforanen-zyme,aC-methyltransferase,thatcatalyzesreactionsinbothubiquinone(Q)andmenaquinone(MK)biosyn-thesis[60].
InQbiosynthesis,UbiEcatalyzesthecon-versionof2-octaprenyl-6-methoxy-1,4-benzoquinoneto2-octaprenyl-3-methyl-6-methoxy-1,4-benzoquinone(EC2.
1.
1.
201).
InMKbiosynthesis,UbiEcatalyzesthecon-versionofdemethylmenaquinonetomenaquinone(EC2.
1.
1.
163).
WhilethegenomeofBlattabacteriumhaspu-tativegenesthatcodefortheremainingactivitiesfortheMKbiosynthesis,ithasnotanyotherannotatedgenethataccountsfortheactivitiesoftheQbiosynthesis.
Asacon-sequencetheactivityEC2.
1.
1.
201hasnobiologicalmean-inginthemetabolicnetworkofB.
cuenotiandforthatreasonitshouldnotbeincludedinthemodel.
Assumingacaseofmetaboliccomplementationbe-tweenthebacteriaanditshostwheremevalonateisaTable1DescriptionofUMsUMRelatedtosubsystemNo.
reactionsNo.
metabolitesRNPRNC1MenaquinolBiosynthesis2321Mev,2ombzl2ommbl2NucleotideSalvagePathway2215-Hxan,xan,r1p,2dr1p,thym,ura3Pyridoxal5-phosphateBiosynthesis76-4hthr4LipopolysaccharideBiosynthesis44-u3hga5SirohemeBiosynthesis44-uppg36ArginineandProlineMetabolism22-1pyr5c7Transport,Extracellular(Fe2+)22-Fe2+8Transport,Extracellular(K+)22-K+9SuperoxideDismutase11O2–-10Acyl-CarrierProteinSynthase11apoACP-Total685884UMidentifiedinB.
cuenotiiCG238GSM.
Metaboliteabbreviations:Mev(mevalonate),2ombzl(2-Octaprenyl-6-methoxy-1,4-benzoquinol),2ommbl(2-Octaprenyl-3-methyl-6-methoxy-1,4-benzoquinol),hxan(Hypoxanthine),xan(Xanthine),r1p(Ribose-1-phosphate),2dr1p(2-deoxy-D-Ribose-1-phosphate,thym(Thymine),ura(Uracil)1pyr5c(1-Pyrroline-5-carboxylate),4hthr(4-Hydroxy-L-threonine),u3hga(UDP-3-O-(3-hydroxytetradecanoyl)-D-glucosamine),uppg3(Uroporphyrinogen),apoACP(apoprotein[acylcarrierprotein]).
TherelationbetweenanUMandasubsystemwasestablishedaccordingtothemostfrequentsubsystemassociatedtothereactionsoftheUM.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page7of15http://www.
biomedcentral.
com/1752-0509/7/114Figure3UM1scheme.
SchematicrepresentationofthebiggestUMfoundinB.
cuenotiiCG238model,whichincludesallthereactionsbelongingtotheMenaquinolBiosyntheticPathway.
Metabolitesarerepresentedbynamelabelsandcoloredaccordinglytoitscategory(yellowforRNPandRNC;blackforDNPandUNC);reactionsarerepresentedassquareswithitsassociatedECnumber.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page8of15http://www.
biomedcentral.
com/1752-0509/7/114metabolitesuppliedbythehost,atransportfluxthatallowtheuptakeofmevalonatebythecellwasincorpo-ratedtothemodel.
AftersoUMwhererecomputedjusttofindoutthatUM1wasstillnon-functional.
Anewin-spectionofthegraphshowedthatthereweretwo"deadend"reactions(EC2.
5.
1.
31andEC3.
3.
1.
1)forwhichnoproductswereincludedasRNCmetabolites.
Acloserin-spectionofthesereactionsshowedthefollowing:reac-tionEC2.
5.
1.
31producesundecaprenyldiphosphate,ametabolitethatworksasacoenzymeinthebiosynthesisofmurein,whereasreactionEC3.
3.
1.
1isthelaststepinthebiosynthesisofmenaquinol,whichisaknowncoen-zymethatoperatesasanelectroncarrier.
Asitisex-plainedinsectionMethods(Thecoenzymepseudo-gapproblem),bothmetaboliteswerethenincludedinthebiomassequation.
Afterso,UM1wascompletelysolved,meaningthatallreactionsgotunblocked(Additionalfile1:FigureS1).
UM2-NucleotidesalvagepathwayInthiscase,thesetof22reactionscontainedintheUMbelongstothenucleotidesalvagepathway.
Thesetofgenescodingfortheseactivitieswasanalyzedanditwasfoundthat12ofthereactionsareorphans,i.
e.
theydonothaveanassociatedcodinggene(seeFigure4).
Theremaining10reactionsweregroupedaccordingtoitscod-inggeneandthisshowedthat3genescodetheseactivitiesinthefollowingway:sevenreactions,thatcorrespondtotheactivity2.
4.
2.
1,areassignedtogeneBLBBGE_377[GenBank:CP001487],annotatedaspurine-nucleosidephosphorylase;tworeactionsdefinedbytheactivitiesEC3.
1.
5.
1areassociatedtogeneBLBBGE_612[GenBank:CP001487];finally,theactivityEC3.
5.
4.
1isassignedtothegeneBLBBGE_353[GenBank:CP001487].
DuetothegreatnumberoforphanreactionscontainedinUM2andbasedonthefactthatallofthesereactionsarepredictedasblocked,thefirststeptoanalyzethisUMwastore-moveitsorphanreactions.
Afterso,thesetofUMswererecalculatedtoevaluatetheimpactofthesechanges.
ItwasfoundthattheUMsplitsintotwoUMs:oneofthemformedbyallthereactionsassociatedwiththeactivitiesEC2.
4.
2.
1togetherwiththetworeactionsassociatedwithactivityEC3.
1.
5.
1;theotheronewascomposedbytheisolatedreactionEC3.
5.
4.
1.
Inbothsituations,mostofthemetabolitesinvolvedintheUMswereclassifiedasRNPorRNC(Additionalfile1:FigureS2b).
Withthepurposeofevaluatingthefunctionalassign-mentofthesethreegenes,acloseinspectionofthegen-omeannotationwasdone.
First,itwasfoundthattheannotationofBLBBGE_612[GenBank:CP001487]doesnothavestrongevidencesupportingthatthisgenecodefortheactivityEC3.
1.
5.
1.
Thus,consideringthelackofinformationsupportingtheassociationbetweenthegeneandtheactivityandtakingintoaccountthatthemodelpredictsthatbothreactionsassociatedwithactivityEC3.
1.
5.
1areblocked,itismoreplausibletoassumethattheactivitydoesnottakeplaceinthemetabolismoftheendosymbiont.
Second,theassociationoftheenzymeFigure4UM2scheme.
SchematicrepresentationoftheUM2thatcorrespondstotheNucleotideSalvagePathway.
ReactionsandmetabolitesarerepresentedasinFigure1.
However,inthiscasethereactionswithnogeneassociation(i.
e.
orphanreactions),orwrongECassignations,arerepresentedwithroundedrectanglesandhighlightedinyellow.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page9of15http://www.
biomedcentral.
com/1752-0509/7/114activitiesEC2.
4.
2.
1andEC3.
1.
5.
1togenesBLBBGE_377andBLBBGE_353[GenBank:CP001487],respectively,issupportedbythegenomeannotation.
However,theactivityEC2.
4.
2.
1appearstohaveabroadsubstratespecificityandsevendifferentreactionsassoci-atedwiththisactivityareincludedinmodeliCG238,allofthempredictedtobeblockedbecausetheirdirectconnec-tiontoanRNP,anRNCortoboth.
Inthecaseoftheac-tivityEC3.
1.
5.
1thereactionbecomesisolatedbeingoneofitssubstratesandoneofitsproductsaRNPandaRNCmetabolites,respectively.
Duetothecomplexityofthissituationandintheabsenceofexperimentalevidencethatcouldhelptosolvethesemetabolicpuzzlesitwasnotpos-sibletofindtheroleoftheseactivitiesinthemetabolismofthebacterium,andthusthesetofgeneswithitsassoci-atedactivitieswereexcludedfromthemodeluntilnewex-perimentaldatashedsomelightoverthisproblem.
UM3-Pyridoxal5-phosphatebiosyntheticpathwayThesevenreactionsinvolvedinthissub-graphcorres-pondtothecompletePyridoxal-5-phosphatepathway(Additionalfile1:FigureS3).
Pyridoxal-5-phosphate,alsocalledVitaminB6,functionsasacofactorofdiffer-entenzymesinvolved,amongothers,intransaminationreactionsrequiredforthesynthesisandcatabolismofaminoacids.
Duetoitsimportanceinmetabolism,thismetabolitewasincludedinthebiomassequationinthesamewaythatithasbeendonewithothercofactorsandcoenzymes.
AsaresultallthereactionsintheUMbe-comeunblocked.
Itisworthtonotethatanimals,inpar-ticularinsects,donotpossessanybiosyntheticpathwayforpyridoxal-5-phosphate,andforthisreasontheyneedtotakeitfromtheirdietinordertosurvive[61].
AsaconsequenceB.
cuenotimayprovideitshostwiththismetabolite,suggestinganothercaseofpossiblemetaboliccomplementation.
UM4-LipopolysaccharidebiosyntheticpathwayTheUM4iscomposedbyalinearchainoffourreac-tionsthatarerelatedtothebiosyntheticpathwaysofdifferentmembranelipids.
Thefirsttworeactionsareinvolvedinthepalmitatebiosyntheticpathway.
However,thesereactionsarenotbiochemicallydefined,buttheyareinturnthecondensationofasetofreactions.
Forexample,thefirstreactionlabeledasC120SNisthenetsumof19activitiesthatproducedodecanoyl-ACPfromacetoacetyl-ACP.
Moreover,thereactionKAS16isalsothecondensationoftheactivitiesEC2.
3.
1.
41andEC1.
1.
1.
100(Additionalfile1:FigureS4).
Theothertwore-actionsoftheUMarethefirstandsecondstepsoftheLipidIVAbiosyntheticpathway.
UM4wasreformulatedbydecomposingthereactionsC120SNandKAS16initscorrespondingactivities.
Afterso,thestructureoftheUMwasanalyzedtofindthefollowing.
First,theactivitiesEC4.
2.
1.
58andEC4.
2.
1.
59,seemtobeorphaninICG238.
Second,theactivitiesassignedtotheLipidIVAbiosyntheticpathwaywereallorphanexceptfortheactivityEC3.
5.
1.
108,whichwasassignedtothegeneBLBBGE_037[GenBank:CP001487].
Thisscenariosug-geststhatthispathwaymaybeabsent,andthusitcouldbetheconsequencesofanerrorintheannotationofBLBBGE_037[GenBank:CP001487].
Indeed,itwasfoundthatthesetoforthologgenesidentifiedinthegenomeofothersequencedgenomesfromdiverseB.
cuenotistrainshavebeenannotatedascodingfortheactivitiesEC4.
2.
1.
58andEC4.
2.
1.
59.
Asaconsequence,theannotatedactivityofBLBBGE_037[GenBank:CP001487]waschan-gedfromEC3.
5.
1.
108toEC4.
2.
1.
58andEC4.
2.
1.
59.
TheremainingorphanactivitypresentintheLipidIVApath-waywasalsoremovedfromthemodelbecauseitisas-sumedthatthispathwayisnotpresentinthemetabolismofB.
cuenoti.
UM5-SirohemebiosyntheticpathwayAlinearchainoffourreactionscomposestheUM5,wherethelastreactionproducesuroporphyrinogenIII,whichwasfoundtobeaRNC(seeTable1).
Thismetab-oliteactsassubstrateinthebiosynthesisofsiroheme,aprostheticgroupwhichcatalyzesthereductionofsulfitetosulfideandofnitritetoammoniaintheassimilationanddissimilationofsulfurandnitrogencompounds[62].
AfteraninspectionofB.
cuenotigenomeannotation,itwasfoundthatallthecodinggenesofthebiosyntheticpathwayofsirohemearepresent.
However,theyhadnotbeenpreviouslyincludedinthemetabolicmodel.
Thepathwayconsistsinfourreactions(arrangedinalinearpathway)codedbytwogenes:BLBBGE_281[GenBank:CP001487]thatcodestheenzymewithactivityEC1.
3.
1.
76andthegeneBLBBGE_278[GenBank:CP001487]whichcodesanenzymethatcatalyzesactivitiesEC2.
1.
1.
107andEC4.
99.
1.
4.
Sincesirohemeisanimportantcofactorinvolvedinsulfurandnitrogenmetabolism,thecellwouldhavetobeabletomaintaincertainpoolofthiscofactor.
Hence,duringthebacterialgrowthphase,theorganismwillneedsomeproductionofsiroheme.
Inordertotakeintoac-countthisfact,sirohemewasincludedintothebiomassequation.
Afterincludingthismodificationtothemodel,FBAwasappliedtofindametabolicstatethatmaximizesbiomassproduction.
Asexpected,itwasfoundthatthefourreactionsincludedinUM5andthefournewreac-tionsaddedtothemodelshowednon-zerofluxunderop-timalstate(Additionalfile1:FigureS5).
UM6-ProlinebiosyntheticpathwayInthiscasetworeactionswerefound:N-acetylornithinedeacetylasecodedbygeneBLBBG_320(withnocorre-spondingECnumber)andL-glutamate5-semialdehydePonce-de-Leónetal.
BMCSystemsBiology2013,7:114Page10of15http://www.
biomedcentral.
com/1752-0509/7/114dehydrataseannotatedtobespontaneous.
Bothreactionswereannotatedasbelongingtotheprolinebiosyntheticpathway.
Inthisscenariosuggestthatthepathwayonlylacksthelastreactionstepinordertobeabletopro-duceproline(Additionalfile1:FigureS7).
HoweveracloserlooktotheannotationofgeneBLBBG_320showsthatithasbeenassignedtocodethefollowing3activities:1.
N-Acetyl-L-glutamate5-semialdehyde+H2O→Acetate+L-Glutamate5-semialdehyde2.
N-acetyl-L-ornithine+H2O→L-ornithine+acetate3.
N-succinyl-L,L-2,6-diaminopimelate+H2O→L,L-diaminopimelate+succinateReaction(1)couldnotbefoundintheBRENDAdata-base.
HoweveritwasfoundasanentryinBiGGdata-base[26].
Forthesereasonitisnotclearwhereasthereactionhasbeenbiochemicallycharacterizedornot.
Inaddition,experimentalresultsshowthatprolineisthemostabundantaminoacidinthecockroach'shemolymph[63]supportingthehypothesisthatprolineisprovidedbythehost.
Asaconsequence,consideringUM6asananno-tationerrorseemsamoreplausiblehypothesisandthustheseactivitieswerenotincludedinthenewversionofthemetabolicmodel.
UM7–UM10-ThecaseofisolatedreactionsInthecasesofUM7andUM8,bothofthemcorrespondtotransportreactionsassociatedtotwodifferentions:Fe2+andMg2+and,theassociatedexchangefluxes.
Bothionsareincludedinthebiomassequationasdescribedbyotherauthors[19,42]andinthiswaybothUMsgotunblocked(Additionalfile1:FigureS6).
TheisolatedreactionthatdefinesUM9issuperoxidedismutase(EC1.
15.
1.
1),areactionthattogetherwiththeactivityEC1.
11.
1.
6worksasadetoxificationpathwayagainstfreeradicalssuchassuperoxideandhydrogenperoxide(Additionalfile1:FigureS7b).
BothactivitieshaveanassociatedcodinggeneandthereisalsoexperimentalinformationsuggestingtheaerobiccharacterofB.
cue-noti[32].
Takingtogetherthesefactsitisexpectedthatsuperoxidedismutaseplaysanimportantroleinthemetabolismoftheendosymbiont.
ThegraphanalysisshowedthesuperoxideasaRNPmetabolite.
Theex-planationofthepreviousfindingrelyinthefactthattheprocessesoffreeradicalformation,e.
g.
asbyproductofaerobicrespiration,isoutofthescopeofthemodelandhencethemodeldoesnotincludeanyreactionprodu-cingsuperoxide.
UM10isalsoacaseofanisolatedreaction(EC2.
7.
8.
7)whichcatalyzestheactivationoftheapoproteinintoacyl-carrier-protein(ACP),beenthisproductahighlycon-servedcarrierofacylintermediates,importantforfattyacidsynthesis(Additionalfile1:FigureS7c).
TheprocessofproteinbiosynthesisisnotincludedinthemetabolicmodelofB.
cuenoti(neithertheDNAnorRNAbiosyn-thesis)andforthatreasonthemodeldoesn'tincludeanyreactionproducingtheapoprotein.
Asaconsequence,theapoproteinbecomesaRNPmetabolitethatblockstheac-tivityEC2.
7.
8.
7.
AsinthecaseofUM9,somemetabolite(e.
g.
theapoprotein)isproducedbyametabolicprocessthatisoutofthescopeofthemodelandthusappearsasadead-end.
ModelupdateThecurationprocessdescribedintheprevioussectionresultedintheremovalof6genesassociatedto6reac-tionsfromiCG238andtheadditionof8newgenescorre-spondingtoatotalof9reactions.
Thus,thenewmodelversionhastwomoregenes(240)andforthisreasonhasbeennamedasiMP240.
Moreover,thereassignmentandtheinclusionofactivitiesaswellastheremovaloforphanactivitiesleadtoeliminationof73reactions(71reactionsplus2exchangefluxes)fromiCG238andtheinclusionof59newreactions(56reactionsplus3exchangefluxes)iniMP240(seeAdditionalfile2).
SincenoexperimentaldatawasavailableforBlattabacteriumBge,chemicalcompos-itionofE.
coli,adaptedfrom[19],wasused.
Inparticular,thestoichiometriccoefficientsofthenewcofactorin-cludedtothebiomassofiMP240,werethosefoundinE.
colimodeliJO1366.
EvenifBlattabacteriumandE.
coliarephylogeneticallyverydistantorganisms,itisworthtonotethatthesecoefficientsareapproximationsoftheorderofmagnitudemeanttocapturetheneedsofanor-ganismduringgrowthinaqualitativelyfashion.
Forade-tailedcomparisonbetweenbothmodelsseeAdditionalfile3.
ComparativeanalysisofthereactionsubsetsThecurationprocessinvolvedadditionandremovalofreactionandmetabolitesaswellaschangesintheformu-lationofthebiomassequation.
Thesechangesaffectedthestoichiometricmatrix,andthenresultedindifferentstruc-turalpropertiesofthenetwork.
Inparticular,wehaveana-lyzedtheorganizationoftheReactionSubsets(RS).
Table2summarizesthenumberofRSidentifiedforthetwomodels,aswellthenumberofreactionwithineachRS.
TheJaccardindexwasusedasameasureofsimi-laritybetweentheRSfromthetwomodels.
ThisindexwascalculatedforeachpairofRSasthecardinalityoftheintersectionoverthecardinalityoftheunionbetweenbothRSs.
Thusitsvalueisboundedbetween0and1.
Thehighertheindexvalue,thehigheristhenumberofreac-tionsharedbybothRS.
ThemajordifferencefoundinthereorganizationwasthepresenceofaRScomposedby19reactionspresentiniMP240butnotfoundiniCG238.
ThisdifferenceisduePonce-de-Leónetal.
BMCSystemsBiology2013,7:114Page11of15http://www.
biomedcentral.
com/1752-0509/7/114tothefactthatmodeliCG238hasallthese19reactionscondensedinasinglestep(Additionalfile1:FigureS4).
ThisisalsothecaseofboththeRSthatcontains13reac-tionsandoneoftheRScomposedby7reactionsfoundediniMP240.
Moreover,thereisanotherRSof7reactionsonlypresentiniMP240thatcorrespondstothePyridoxalBiosyntheticPathway.
ThispathwaywasblockediniCG238,andhencecannotbedetectedasanRS.
Add-itionally,therearethreeRSalmostequalinbothmodels,butdifferinginonlyonereaction.
Forexample,theRSof18reactionsiniMP240correspondstotheRSpresentiniCG238thatcontains17reactions.
Despitethedifferencesdescribedabove,nomajorchangeswerefoundintheor-ganizationsofRSbetweenbothmodels.
ComparisonofminimalmediumThein-silicominimalsetofcompoundsneededfortheendosymbiontinordertoproduceallbiomasscompo-nentswaspredictedforbothmodelversions(iCG238andiMP240),usinganoptimizationalgorithm(seeMin-imalMediumPredictioninMethodssection).
Table3showstheresults.
Asitcanbeseen,allthemetabolitesincludedintheminimalmediumpredictedformodeliCG238areincludedintheminimalmediumpredictedforiMP240,exceptfor(S)-Dihydroorotate.
Thismetab-oliteisaprecursorinthebiosynthesisofpyrimidines.
ThereasonforthisdifferenceisthatiCG238didnotincludetheactivityEC3.
5.
2.
3,whichcatalyzestheconver-sionofN-carbamoyl-L-aspartateinto(S)-Dihydroorotate,andthusthemodelpredictsthat(S)-Dihydroorotateshouldbeuptakenfromanexternalsource.
TheactivityEC3.
5.
2.
3hasbeenfoundtobecodedbythegeneBLBBGE_317[GenBank:CP001487],anditsinclusioninthenewmodelpredictsthat(S)-Dihydroorotatecanbeproducedbythemetabolismoftheendosymbiont.
ThepredictionsusingthemodeliMP240alsosuggestsixnewcompoundsthatneedtobepresentinthemediuminorderfortheorganismtobeabletogrow.
Thesesetsofmetabolitesinclude:i)mevalonate,whichisneededtosynthesizemenaquinoland2-demetyl-menaquinol;ii)glycerol,whichisphosphorylatedbytheactivityEC2.
7.
1.
30,andusedinthebiosynthesisofphos-phatidylglycerolspecies.
InmodeliGC238glycerol-3-phosphateisproducedfromdihydroxyacetonephosphatethroughthereactionEC1.
1.
5.
3operatinginreversesense.
However,itwasnotpossibletofoundanyevidencesuggestingthatthereactionEC1.
1.
5.
3couldoperateinareversiblemanner.
Hence,ifthereactionisconsideredasirreversible,thenthecellcannotproduceglycerol-3-phosphate.
Thenglycerolshouldbeuptakenfromthemediumandphosphorylatedinsidethecell.
iii)Porpho-bilinogenthatisconvertedintohydroxymethylbilane,thefirstprecursorinthesynthesisofsiroheme,whichinturnrequiresFe2+;iv)thecaseofK+andMg2+areTable2ComparisonofRSNo.
reactionsinRSiMP240iCG238J1.
0J.
752272821–38631(+1)4241–5432–6332–73111(+1)8–1––9433–1011–1(+1)11–1––131–––17–1––181––1(1)201–––ThefirstcolumnindicatesthenumberofreactionsthatbelongtoaRS.
ThesecondandthirdcolumnsindicatehowmanyRSwithagivennumberofreactionareinmodeliMP240andiCG238,respectively.
ThefourthcolumnshowshowmanyRSpairsareequalinbothmodelsandforagivennumberofreactions.
Inthelastcolumns,thenumberoutoftheparenthesisindicatehowmanyRSwithaJaccardindexgreaterthan0.
75havebeenfound,takingasthereferencepointthemodeliMP240.
ThenumberinparenthesisindicatesthedifferenceofreactionsbetweenapairofRSinthefollowingway:apositivenumbermeansthattheRSiniCG238hasthisnumberofadditionalreactionswhereasanegativeindicatetheopposite.
Table3MinimalmediumMediumcomponentsiMP240iCG238ThiaminRequiredRequiredNicotinateRequiredRequiredSodiumRequiredRequiredL-GlutamineRequiredRequiredSulfateRequiredRequired(R)-PantothenateRequiredRequiredPhosphateRequiredRequiredL-AsparagineRequiredRequiredL-ProlineRequiredRequiredGlycineRequiredRequiredO2RequiredRequired(S)-Dihydroorotate–Required(R)-MevalonateRequired–GlycerolRequired–PorphobilinogenRequired–Fe2+Required–K+Required–Mg2+Required–Comparativetableshowingthein-silicopredictedminimalmediumforthenewversionmodeliMP240andpreviousversioniCG238.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page12of15http://www.
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com/1752-0509/7/114trivial:theseionsbecomerequiredintheminimalmediumaftertheirinclusionintothebiomassequation.
NetworkfragilityThesetofessentialmetabolicgeneswerecomputedbyanin-silicoanalysisofthemodeliMP240.
Theseresultswerethencomparedwiththesetofessentialgenespre-viouslypredictedformodeliCG238[32].
Figure5sum-marizestheresultsofthecomparativeanalysisbetweenbothmodels.
Thesetof172genes(~72.
3%)predictedasessentialiniCG238remainsasessentialiniMP240.
Inaddition,asetof30geneswaspredictedasessentialiniMP240,resultingintotalof202metabolicgenespre-dictedasessential(~84%).
AsitisdepictedinFigure5,25ofthose30geneswerepresentinthepreviousver-sionofthemodel(iCG238),whiletheremaining5arenewgenes.
Thisincreaseinthepredictednetworkfragilityob-tainedaftermodelcurationisexplained,ingreaterex-tent,duetotheadditionofnewcomponentstothebiomassequation.
Forexample,thegenescodingforthebiosyntheticpathwayofmenaquinolwherepredictedasnon-essentialinmodeliCG238becausethecofactorwasnotincludedinthebiomassequation.
However,theco-factormustbeessentialtotheorganism,duetoitsstrictaerobiosis,andthenitshouldbeincludedasabiomasscomponent.
Asaconsequencemostofthegenescodingthebiosyntheticpathwayofmenaquinolarepredictedasessentialinthenewscenario.
Moreover,the5newgenesincludediniMP240thatarepredictedasessentials,in-cludetwogenesthatcodeforthreestepsinthebiosyn-thesisofsiroheme,twogenesthatcodeforthetransportofnicotinamideandMg+2,andthegenethatencodeFtsl,anessentialcelldivisionprotein.
ConclusionInthispaperwehaveintroducedageneraldefinitionofgapmetabolitethatallowsitsdetectioninastraightfor-wardmanner,evenforthecasesofupstream-non-producedanddownstream-non-consumedmetabolites.
Moreover,amethodforthedetectionofUnconnectedModules(UM),definedasisolatedsetsofblockedreac-tionsconnectedthroughgapmetaboliteshavebeenpro-posed.
ThevisualrepresentationofUMcanshedusefulinformationthatmayhelpthemodel'scuratortosolveinconsistencies.
Furthermore,thepresentapproachcanbecombinedwithexistingtoolsinordertofindasetofmodelmodificationsthatsolvestheinconsistenciesandthusimprovesmodel'spredictions.
ThismethodwasappliedtothecurationoftheGSMofthecockroachendosymbiontB.
cuenotiiCG238.
Inthiswayeveryblockedreactiondetectedinthemodelwassuccessfullyunblockedoralternativelyremoved,inthosecaseswheretherewasnotenoughinformationsupportingtheexistenceofsuchreactions.
Asanex-ample,thosereactionsfoundasblockedandwithnogeneassociationwereexcluded.
Moreover,newreactionswereaddedtothemodelbasedonthecarefulrevisionofthegenomeannotationthatallowstheidentificationofgenefunctionspreviouslynotincluded,aswellasthein-corporationofnewcompoundsintothebiomassequation.
AsaconsequenceofmodelcurationanewGSMversionofB.
cuenoti,namedasiMP240,isproposed.
Theimpactofthesemodifications,withrespecttosomestructuralpropertiesofthenetworks,wasanalyzedbyperformingdifferentin-silicoanalysisovereachmodel'sversion.
Asafinalcommentary,themethodherepresentedcanbeconsideredasasemi-automaticapproachthathastheadvantageofallowingaquickrepresentationofFigure5DifferencesbetweenmodelsiCG238andiMP240.
VenndiagramrepresentingthemaindifferencesbetweenmodelsiCG238andiMP240.
Thesetsdrawnwithathincontinuouslinerepresentsthegenesincludedineachmodel.
Thesetdelimitedbythicksolidlinerepresentsthesetofgenespresentinbothmodels,i.
e.
theintersection.
Finally,setsdefinedbydottedlinesindicategenespredictedasessentialbythein-silicosimulationsovereachmodel.
Ponce-de-Leónetal.
BMCSystemsBiology2013,7:114Page13of15http://www.
biomedcentral.
com/1752-0509/7/114thegapsofthemodelbutthatneedsthesupervisionofanexpertinthebiologyofthestudiedorganism.
Thisissuemaybeseenasadrawbackofthemethodbut,asinthecaseofautomaticgenomeannotation,thereisatrade-offbetweenthedegreeofautomationofthemetabolicre-constructionandthequalityofthegeneratedmodel.
AdditionalfilesAdditionalfile1:SchematicrepresentationofUMs.
ThefilecontainsschemesandabriefdescriptionofeachUM.
Additionalfile2:NewGSMmodelofB.
cuenotiiMP240.
Spreadsheetwiththemodeldescription.
ThefilecontainsthreesheetscorrespondingtoMetabolites,Reactions,andExchangeFluxes,respectively.
Additionalfile3:ComparativetableiCG238vsiMP240.
Spreadsheetdescribingthemaindifferencesbetweenbothmodelversions.
Thefilecontainsthreesheets:thefirstoneincludesthegenesaddedaswellthegenesthatwereremoved;thesecondonepresentstheremovedreactions;andthethirdoneshowsthesetofaddedreactions.
AbbreviationsRNP:Root-non-produced;RNC:Root-non-consumed;DNP:Downstream-non-produced;UNC:Upstream-non-consume;UM:Unconnectedmodule;FBA:Fluxbalanceanalysis;CBM:Constraintbasedmodeling;GSM:Genomescalemodel;RS:Reactionssubset;LP:Linearprogramming;MILP:Mixedintegerlinearprogramming;GPR:Gene-protein-reaction;EC:Enzymecommissionnumber;TC:Transportcommissionnumber.
CompetinginterestsTheauthorsdeclarethattheyhavenocompetinginterests.
Authors'contributionsJP,FMandMPLpresentedtheoriginalideaoftheworkanddesignedthestudy.
MPLconceivedthealgorithmicprocedure,implementedthecode,andcarriedoutthein-silicoexperiments.
Allauthorscontributedindesigningresearch,analyzingthedata,andwritingthepaper.
Allauthorshavereadandapprovedthemanuscript.
AcknowledgmentsMPLwouldliketothankFundaciónParqueCientíficodeMadridforallowinghimtocarryouttheresearchactivitiescorrespondingtothispaper.
FinancialsupportfromSpanishGovernmentisgratefulacknowledged(grantreferences:BFU2009-12895,BFU2012-39816).
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