Simulating Serial-Target Antibacterial Drug Synergies Using Flux

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Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis
Krueger, Andrew S.; Munck, Christian; Dantas, Gautam; Church, George M.; Galagan, James; Lehár,
Joseph; Sommer, Morten Otto Alexander
Published in:
P L o S One
Link to article, DOI:
10.1371/journal.pone.0147651
Publication date:
2016
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Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Krueger, A. S., Munck, C., Dantas, G., Church, G. M., Galagan, J., Lehár, J., & Sommer, M. O. A. (2016).
Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis. P L o S One, 11(1),
[e0147651]. https://doi.org/10.1371/journal.pone.0147651

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RESEARCHARTICLE
Simulating Serial-Target Antibacterial Drug
Synergies Using Flux Balance Analysis
AndrewS.Krueger1☯,ChristianMunck2☯,GautamDantas3,4,5,GeorgeM.Church6,
JamesGalagan1,7,JosephLehár1*,MortenO.A.Sommer2*
1 BostonUniversity,44CummingtonSt,Boston,MA,UnitedStatesofAmerica,2 TechnicalUniversityof
Denmark,NovoNordiskFoundationCenterforBiosustainability,Hørsholm,Denmark,3 CenterforGenome
Science&SystemsBiology,WashingtonUniversitySchoolofMedicine,StLouis,Missouri,UnitedStatesof
America,4 DepartmentofPathology&Immunology,WashingtonUniversitySchoolofMedicine,StLouis,
Missouri,UnitedStatesofAmerica,5 DepartmentofBiomedicalEngineering,WashingtonUniversity,
St.Louis,Missouri,UnitedStatesofAmerica,6 DepartmentofGenetics,HarvardMedicalSchool,Boston,
Massachusetts,UnitedStatesofAmerica,7 BroadInstitute,CambridgeCenter,Cambridge,Massachusetts,
UnitedStatesofAmerica
☯Theseauthorscontributedequallytothiswork.
*[email protected](JL);[email protected](MOAS)
Abstract
OPENACCESS Fluxbalanceanalysis(FBA)isanincreasinglyusefulapproachformodelingthebehaviorof
metabolicsystems.However,standardFBAmodelingofgeneticknockoutscannotpredict
Citation:KruegerAS,MunckC,DantasG,Church
GM,GalaganJ,LehárJ,etal.(2016)Simulating drugcombinationsynergiesobservedbetweenserialmetabolictargets,eventhoughsuch
Serial-TargetAntibacterialDrugSynergiesUsingFlux synergiesgiverisetosomeofthemostwidelyusedantibiotictreatments.Hereweextend
BalanceAnalysis.PLoSONE11(1):e0147651.
FBAmodelingtosimulateresponsestochemicalinhibitorsatvaryingconcentrations,by
doi:10.1371/journal.pone.0147651
divertingenzymaticfluxtoawastereaction.Thisfluxdiversionyieldsverysimilarqualitative
Editor:StephenS.Fong,VirginiaCommonwealth
predictionstopriormethodsforsingletargetactivity.However,wefindverydifferentpredic-
University,UNITEDSTATES
tionsforcombinations,wherefluxdiversion,whichmimicsthekineticsofcompetitivemeta-
Received:November8,2015
bolicinhibitors,canexplainserialtargetsynergiesbetweenmetabolicenzymeinhibitors
Accepted:January6,2016 thatweconfirmedinEscherichiacolicultures.FBAfluxdiversionopensthepossibilityfor
Published:January28,2016 moreaccurategenome-scalepredictionsofdrugsynergies,whichcanbeusedtosuggest
treatmentsforinfectionsandotherdiseases.
Copyright:©2016Kruegeretal.Thisisanopen
accessarticledistributedunderthetermsofthe
CreativeCommonsAttributionLicense,whichpermits
unrestricteduse,distribution,andreproductioninany
medium,providedtheoriginalauthorandsourceare Introduction
credited.
Microbialinfectionsareamajorburdenonsocieties,andtheemergenceofdrug-resistantbac-
DataAvailabilityStatement:Allrelevantdataare
teriaposesanincreasingthreattohumanwelfare.Drugcombinationscanovercomeresistance
withinthepaperanditsSupportingInformationfiles.
bycreatingnewtherapeuticavenuesinaccessibletosingletargetdrugs[1–3]oreliminating
Funding:MOASacknowledgesfundingfromThe
functionalredundanciesexhibitedbyrobustbiologicalnetworks[4].However,althoughcom-
LundbeckFoundation(www.lundbeckfonden.com)
binationsareincreasinglythestandardofcareformanybacterialinfections[5,6]thecomplex-
andEUFP7-HealthProgramEvotar(282004)(www.
ityofmicrobialbiologyandthevastnumberofpossibletargetcombinationsmakesfinding
cordis.europa.eu/fp7/).Thefundershadnorolein
studydesign,datacollectionandanalysis,decisionto neweffectivedrugcombinationschallenging.
publish,orpreparationofthemanuscript. Systemsbiologymayprovideasolutiontothischallenge[7–9],bymodelingmicrobialsys-
temsascomplexnetworksofinteractingcomponents.Dynamicmodelsofmicrobialfunction
CompetingInterests:Theauthorshavedeclared
thatnocompetinginterestsexist. underdrugtreatment[10,11]canprovidedetailedandaccuraterepresentationsofphenotypes,
PLOSONE|DOI:10.1371/journal.pone.0147651 January28,2016 1/18
SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
butthescaleofsuchmodelsislimitedbythescarcityofkineticmolecularreactionratemea-
surements.Graph-theoreticnetworksofmetabolicinteractionsfoundinKEGGorMetacyc
[4,12,13]canaddressthetruescaleofmicrobialbiology,butarelimitedtostaticrepresenta-
tionswithonlylimitedrelevancetodrugresponsephenotypes.
Asuccessfulapproachtowardsgenome-scalemodelingisFluxBalanceAnalysis(FBA)[14–
16],whichutilizesreactionstoichiometrytomodelmetaboliccapabilitiesatsteadystate(Fig1A).
Byintegratingthepropertiesofmetabolicnetworksintoasinglegrowthphenotype,FBAenables
predictionsofenzymaticgeneessentialityandevengeneticinteractions.FBAapproacheshave
beenusedtopredictthenutrient-dependentmetabolicphenotypeofgeneknockouts(Fig1B)
[15,17],andhavebeensuccessfullyappliedtomodelthecombinedeffectsofdoubleknockoutsin
microbialsystems[18].Recently,integrationofproteomestructurehasallowedfortheprediction
ofthetemperaturedependenceofmetabolicreactionsonagenomewidescale[19].Severalmeth-
odshavealsobeendevelopedtoincorporategeneexpressionandotherhighthroughputdatato
constrainfluxesthroughparticularreactionspredictingmetabolicstatescorrespondingtospecific
geneexpressionstates;E-fluxinparticularhasbeenusedtopredicttheimpactofdrugsgiven
expressiondata[20–24].Finally,incorporationofgeneexpressionnetworksandproteintransla-
tionprocesseshasenabledamechanisticallydetaileddescriptionofcellulartrade-offsoccurring
duringvariousgrowthphasesandnutrientlimitations[25–29].However,noneoftheabovemeth-
odologiesmodelstheeffectsofdrugdosing.Thecontinuousresponsestovaryinginhibitorcon-
centrationsareespeciallycriticalforidentifyingandinterpretingdrugcombinationeffects[10].
HerewehaveextendedFBAmodelingtosimulatedrugeffectsovermultipledoses.We
explorenewmethodsforsimulatingdrugtreatmentswithFBA,consideringbothdirecttarget
fluxrestriction[3]andamodelthatdivertsfluxtonon-productivewastepathways(Fig1).In
fluxrestriction“FBA-res”,thefluxthroughthetargetreactionisrestrictedbyavariablescalar
factor(Fig1C),whileinflux-diversion“FBA-div”,weinsteaddivertfluxtoawastereservoir
(Fig1D).Thetwomethodsyieldsimilarresultstoknockoutsimulationsforsingleagenteffects,
buthaveverydifferentpredictionsforcombinations.OnlyFBA-divpredictspotentantibiotic
synergiestargetingmetabolism.
MaterialsandMethods
Simulations
TheEscherichiaColiiAF1260modelcreatedbyBernhardPalsson’sgroupatUCSDservesas
ourbacterialmodelinthiswork[30],whichcontainsspecies-specificmetabolicreactions,
linkedtogetherinanetworkbysubstratesandproducts.Foroursimulations,wewillassume
bacterialgrowthonrichmediawithamplesuppliesofoxygen,glucose,ammonia,potassium,
sulphur,andallaminoacids.
AlldrugeffectsimulationswereperformedwithanR-scriptusingtheRpackageSybil(Sys-
temsBiologyLibraryforR)[31]andthegenome-scalereconstructionofEscherichiaColi.The
“Ec_iAF1260_flux2”modelwasdownloadedinxmlformatandaddedtotheRworkspace.
Afterdownloading,thegrowthfluxiscalculatedusingthebuilt-inoptimizationmodule“opti-
mizeProb”withthealgorithmsetto“fba”.ThetheoreticalframeworkforFBA-resmodelsdrug
perturbationsasascalarrestrictionoffluxthroughatargetedreaction.WeimplementFBA-res
byreducingthefluxboundsbyascalaralphaforeachdoseofeverytarget.Thiscreatesanew
drug-perturbedmodel.Thedrug-perturbedmodelissenttooptimizeProbwiththealgorithm
setto“fba”.Growthinhibitioniscalculatedwiththeunperturbedandperturbedgrowthfluxes.
Aftereachdoseforcombinationsorsingleagents,weresettotheoriginalmodeltoimplement
thenextperturbation.ThetheoreticalframeworkforFBA-divmodelsdrugperturbationsasa
scalardiversionofflux,whichdependsonthemagnitudeoftheperturbation(dose).We
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SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
Fig1.SimulationsofinhibitedFBAmetabolism.(A)Cartoonofatargetenzyme“j”whichactsonsubstrate“i”atasteady-statefluxv.Otherenzymesmay
j
competeforthesamesubstrate,anddownstreamreactionswillconvertallproductsto“biomass”fluxorunproductive“waste”thatisdegradedorexported.
PLOSONE|DOI:10.1371/journal.pone.0147651 January28,2016 3/18
SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
(B)Whenthetargetisknockedoutbysettingv =0,substratebacklogincreasesflowthroughotherreactions,andincreasedwasteratesreducebiomass.(C)
j
FBA-resreducesthetargetfluxbyascalarfactorα,causingapartialknockouteffect.(D)ForFBA-div,thereaction'sefficiencyisreducedbyscalingits
stoichiometriccoefficients,divertingthebacklogtowaste.Becausethisdiversionpreventsyetmorefluxfromgoingtobiomass,FBA-divyieldsstronger
ij
inhibitionlevelsthancorrespondingFBA-ressimulations.Inthisillustration,bothFBA-resandFBA-divreducethetargetfluxbythesamefactoralpha,butthe
smallerbackloginFBA-divleadstolessnon-wastenetworkfluxbeingdirectedtobiomass,leadingtoastrongertotalinhibition.
doi:10.1371/journal.pone.0147651.g001
implementFBA-divbyfirstaddingwastereactionsandwastemetabolitestothemodel.Ini-
tiallythewastemetabolitesdonotbelongtoanyreaction,andthewastereactionsconsume
wastemetabolitesirreversibly.Tosimulatedrugeffects,theamountofmetabolitesproduced
byatargetedreactionarereducedbyalphaandtheremainderofmassisconvertedintoa
wastemetabolite,whichisnowconnectedtothetargetedreaction.Wastereactionsconsume
anydivertedwastemetabolites.Inthecaseofreversiblereactions,twoirreversiblereactionsare
createdwithdifferentwastemetabolites,andthereductionbyalphaisappliedtobothreac-
tions.Thisisthedrug-perturbedmodel.Thedrug-perturbedmodelissenttotheoptimization
module“optimizeProb”withthealgorithmsetto“fba”.Growthinhibitioniscalculatedwith
theunperturbedandperturbedgrowthfluxes.Aftereachdoseforcombinationsorsingle
agents,weresettotheoriginalmodeltoimplementthenextperturbation.
Drugeffectsonatargetedmetabolicreactionwereimplementedinthegenome-scalemodel
eitherbylimitingthetargetflux(FBA-res)orlimitingtheamountofmassconvertedfromsub-
stratetoproductbydivertingmetabolicmasstoawastereaction(FBA-div).Inhibitionvalues
Inhib=1-f /f ,wheref andf arethesimulatedbiomassfluxratesforuntreatedand
treat wt wt treat
drugtreatedbacteria.InbothofourmodelimplementationstheMOMAquadraticprogram-
mingalgorithmforsimulatingperturbedbiologicalnetworkswasimplementedtofindthe
changeinbiomassflux.TheIC50valueforareactiondescribestheamountbywhichreaction
fluxmustbereducedtoinhibitgrowthby50%.ForFBA-res,fluxisdirectlyrestrictedbyasca-
lardrugconcentration,andsotheIC50isthescalarthatachievesa50%growthinhibitingflux
restriction.ForFBA-div,fluxisdivertedtoawastereaction,andsotheIC50isthevaluethat
achieves50%growthinhibitingfluxdiversion.First,acentralperturbationofα (where
cent
α =1+[Inhibitor]/K andforsimplicityK =1)wasfoundforeachtargetenzymeusinga
cent i i
bisectionsearchtoyieldhalftheinhibitionlevelofafullFBAgenedeletion(forenzymesshow-
ingnodeletionphenotype,weusedα=5,000,000sincethisvaluereproducedsyntheticlethal
interactionsin[12].Simulatedresponsecurveswerethengeneratedforeachenzyme,withfive
concentrationscenteredonthisα using3xdilutionstepsofinhibitorconcentration(α-1),
cent
coveringa~100xdynamicrange(Fig2A).Foreachpairofagents,wethengenerateddose
matricesbysimulatingcombinedinhibitorsatallpairsofthoseconcentrations(Fig2B).Gradi-
entorsecant-basedoptimizationcouldprovidefastersolutions,soreadersmaywishtoexplore
suchmethodsinfutureapplicationsofthisapproach.Completeanalysismethodsareprovided
asS1Dataset,whichincludesthemetabolicnetworkmatrix,theanalysiscode,andallsupport-
ingdatafiles.CompletesimulationresultsarealsoprovidedinS1Table.
Singleagenteffect,combinationsynergyscore,andepistasis
Weusedsimplemetricsofsingleagentandcombinedinhibitorresponses(Fig2A),basedon
maximuminhibitionlevelsmax(I)oron50%inhibitoryconcentrationsIC50.Comparingmax(I)
valuespermitscomparisonswithstandardFBAknockouts,whileIC50sallowfulleruseofthe
dose-responsivenessofinhibitors.Themaximuminhibitionmax(I)and50%crossingconcentra-
tionIC50wasmeasuredforeachtarget,andifmax(I)<0.5,IC50wassettothetopconcentration.
Synergywasthendeterminedforeachdosematrixusingeitheraneffectdifferencemax(ΔI)
or“shiftindex”SI50,comparedtothesingleagents(Fig2B).ThecombinationdataI (blue
XY
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SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
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SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
Fig2.Activityandsynergymeasuresforeachcombination.(A)Inhibitionofeachenzymewassimulatedatfiveαconcentrations,using3-folddilution
intervalscenteredontheconcentrationthatyieldedhalfofthemaximumsimulatedeffect.Notethatthe3xdilutionstepswereconstantinsimulated
concentrationα-1,sotheyarenotalwaysequalonthesecurveplotsbasedonα.Themaximuminhibitionmax(I)and50%crossingconcentrationIC50was
measuredforeachtarget(IC50=topconcentrationifmax(I)<0.5),andeachcombinationwassimulatedatall25concentrationpairs.(B)Forcombinations,
wescoredthemaximumeffectmax(I)andsynergyoverGaddum’s“bestsingleagent”referencemax(ΔI)=max{I -max(I ,I )}acrossallinhibitionsI .We
XY X Y XY
alsocalculated“potencyshiftindex”fromthe50%inhibitioncrossingconcentrations(C50 ,C50 )alongthematrixdiagonal(blue),whereSI50=max(C50 /
X Y X
IC50 ,C50 /IC50 ).Epistasistypesfor(C)FBA-resand(D)FBA-divsimulationsonthreeexampletargetpairs.Interactionswereclassifiedbasedonthe
X Y Y
singleagentandcombinationeffectandsynergy,aseithernon-interacting“None”,syntheticlethality“SL”betweeninactiveinhibitors,partialSL“PSL”
involvingoneactiveagent,orpotentiation“Pot”betweentwoactiveinhibitors.
doi:10.1371/journal.pone.0147651.g002
point)arecomparedtothecorrespondingsingleagentresponsevaluesI ,I (greenpoints),
X Y
andmax(ΔI)=max{I -max(I ,I )},showstheGaddum“bestsingleagent”expectation[32].
XY X Y
Allcombinationpointswereconsidered,withthelargestdifferenceacrossthematrixrecorded
asthescore.Positivemax(ΔI)valuescorrespondtosynergy(moreeffectthanthebettersingle
agentatcomparabledoses).Fordoseshifting,thematrixdiagonal(bluearea)iscomparedto
thetwosingleagentcurves(greenareas).Thecombination’s50%inhibitorycrossingpoint
alongthediagonalhassingleagentcomponentconcentrationsC50 andC50 ,whicharecom-
X Y
paredtothesingleagent50%inhibitoryconcentrationsIC50 andIC50 ,tocalculate
X Y
SI50=max(C50 /IC50 ,C50 /IC50 ).ThisSI50indicateswhetherthecombinationshows
X X Y Y
synergistic(SI50<1)orantagonistic(SI50>1)doseshifting,relativetotheGaddumresponse
surface.WealsocalculatedastandardLoewecombinationindexCI50=C /IC50 +C /
X X Y
IC50 ,whichmeasuressynergyrelativetoLoewedoseadditivity[33],whichisusedtodeter-
Y
minewhetheracombinationoutperformsa“drug-with-itself”shamcombination(CI50=1for
dose-additive).AllscoresforsimulatedandexperimentalcombinationsarelistedinS1Table.
Simulatedepistasiswasclassified(Fig2Cand2D)basedonthemax(I)valuesforacombi-
nationanditssingleagents.Ifacombination’smax(I)<0.05ormax(ΔI)<0.05,wesetepista-
sistonon-interaction“None”,correspondingtoaGaddum“bestsingleagent”interaction
model.Epistasiswasthensettopotentiation“Pot”ifsingleagentmax(I)>=0.5forboth
agents,syntheticlethal“SL”ifmax(I)<0.5forbothagents,orpartialsyntheticlethal“PSL”
otherwise.Toaccountforhighernoiselevelsinexperimentalcombinations,weusedthesame
classificationscheme,exceptthatepistasis=Nonewascalledwhenmax(I)<0.25ormax(ΔI)
<0.25foracombination.EpistasiscallsarerecordedinS1Table.
Proliferationassay
Toexperimentallyvalidatethepredicteddruginteractions,28drug-pairsweretestedagainstE.
coliMG1655(S3Table).Inordertoexplorethefullinteractionsurfacethedrugpairswere
testedinan8x8well2ddrug-gradientmatrixina96wellplate,inadditiontothedrugmatrix
theplatealsocontainedgradientsforeachofthesingledrugsaswellasnegativeandpositive
controls.Forboththedrugmatrixandthesingledruggradientsthehighestdrugconcentra-
tionswere4timesabovetheminimalinhibitoryconcentration(MIC).Theplateswereinocu-
latedwitha96pinreplicatorandincubated18–20hoursat37°C.Afterincubation,OD600was
readusingaBioTekH1platereader.Eachplatewasproducedinfivereplicates.Rawdataare
presentedinS4Table,andresponsescoresareinS1Table.
Results
Fluxbalanceanalysisframeworksformodelingdruginhibition
Extensivenetworksofmicrobialmetabolismhavebeenconstructedthatlinktogetherthou-
sandsofspecies-specificmetabolicreactionsminedfromtheliteratureandonlinedatabases
[34].Simulatingthebehaviorofmicrobialmetabolismrequiresnotonlythestoichiometry
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SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
capturedbysuchnetworks,butalsodetailedkineticparameterswhichareunknownformost
reactions–evenforwell-studiedmicrobeslikeE.coli.FBAaddressesthislimitationbyreplacing
thoseparameterswithlinearfluxesthroughallthemetabolicreactions,andusinglinearpro-
grammingtoderivesteady-statefluxvaluesoptimizedbasedonanobjectivefunctioncon-
structedfromexperimentalabundancesofnucleotides,aminoacidsandofanabolic
metabolites[15,16,35].FBAmodelsoptimizesteady-stateproductionoftheseessentialbuild-
ingblocks,enforcingconsistencywithlimitsimposedbythenetwork’sconnectivity,fluxlimits
andtheconservationofmassbetweenreactions.
FBAmodelshavebeenusedtosuccessfullypredicttheeffectsofgeneticknockouts[15,17].In
FBA,understeadystate,asystemofj=1...Nreactionsbetweeni=1...Mmetabolitesshould
satisfy∑ s v =0,wherev arethereactionvelocitiesands arestoichiometriccoefficientsthat
j ij j j ij
accountforreactionaffinitiesandconnectivity.FBAmodelssolveforthev thatmaximizesimu-
j
latedfluxthroughtheobjectivefunction,constrainedbythismassconservationrequirementand
anyv <v <v limits.Tomodelgeneessentialityusingthestandardknockout“FBA-ko”
j,min j j,max
approach,thetargetenzyme’sreactionrateissettov =0,afterwhichthemodelisre-optimized
j
withalinearprogrammingalgorithmtomaximizetheobjectivefunction(Fig1BandS1Fig).
Growthisrepresentedbyabiomassreactionwhichintegratestheoutputsfrommanymetabolic
pathways.ArefinementtoFBAapplies“minimizationofmetabolicadjustment”(MOMA)[36],
whichrequiresthere-optimizedreactioncoefficientstominimizetheirdistancefromtheunper-
turbedvalues,ratherthanseekingthemaximumobjectivefunctionfluxconsistentwiththe
appliedconstraints.MOMAhasbeenappliedtoE.coliandyeastmetabolicnetworksandcan
successfullypredictphenotypicresponsestosingle[36]anddoubleknockoutexperiments[18].
ExtendingFBAtodrugperturbations,weconsidertwoapproaches:our“FBA-res”(previously
describedinLeharet.al.2009[3])directlyrestrictsthetargetfluxwhileour“FBA-div”diverts
fluxtonon-productivewaste.FBA-resreducesthefluxv throughatargetedreactionbyascalar
j
factorα(Fig1CandS1Fig).Thus,insteadofFBA’sv =0constraint,wesetv!v/αandre-opti-
j j j
mizethereactionfluxes,usingMOMA.FBA-divmodelingscalesdownthetarget’sstoichiometric
coefficient,ratherthanitsmaximumreactionrate(Fig1DandS1Fig).Specifically,FBA-div
inhibitsanenzymebysettings !s /α,formetabolitestargetedbytheinhibitor,beforere-opti-
ij ij
mizingtotheobjectivefunction.Toconservemass,weintroducetransportreaction,s ,with
i(N+1)
compensatingstoichiometriccoefficientss =1-∑ s /αthatdivertexcesssubstratetoaninfi-
i(N+1) j ij
nitewastesink.WeusestandardFBAlinearprogrammingtosolvetheoptimizationproblemin
conjunctionwithourFBA-divmethodology.IncontrasttoFBA-res,thiswastediversionprevents
otherenzymesfromincreasingtheirreactionratesinresponsetotargetfluxrestriction.Thisusu-
allypredictsgreaterbiomassreductionsthanFBA-resforthesameleveloftargetfluxinhibition.
Simulatingdrugepistaticinteractions
Toevaluatetheseapproaches,wesimulatedcombinationeffectsusingstandardFBA-ko,FBA-
resandFBA-div,appliedtotheiAF1260modelofEscherichiacolimetabolism[30].Toexplore
mechanisticpatterns,wechose50enzymestocoversyntheticlethalsynergiesandantagonisms
foundusingFBA-ko[12]andsamplekeypathwaysinbacterialmetabolism(S2Table).Inhibi-
tionofeachtargetwassimulatedat5“drug”concentrationsusingFBA-resandFBA-div,in
eachcaseestimatinginhibitionbythefluxthroughthegrowthreactioninperturbedand
unperturbedstates(MaterialsandmethodsandS1Fig).Weusedthesamemethodologyto
generatecombinationresponsematricesacrossall25pairingsofsingledrugconcentrations.
Toscorethesimulationresults,weusedmetricsofsingleagentandcombinedinhibitor
responses,basedonmaximuminhibitionlevelsoron50%inhibitoryconcentrationsIC50(Fig
2Aand2B),andfocusedouranalysisonthemaximumeffectmax(I)andsynergyscoremax
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SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
(ΔI).Wealsoclassifiedsimulatedinteractionsintofourepistasistypes,basedonthedose
matrixresponseshapes(Fig2Cand2D).Theseanalyseswereperformedforall1225possible
pairwisecombinationsofour50targets(S1Table).
Thesingleagentresponseswereverysimilarbetweenmethodologies,butcombinationsdif-
feredgreatly(Fig3andS2–S4Figs).BothFBA-resandFBA-divsingleagentactivitieswere
consistentwithFBAknockouts(R~1,Fig4).Moreover,eventheIC50concentrationsshowed
astrongquantitativecorrelation(R=0.98,Fig5).Forcombinations(Fig4B),allthree
approachesmostlygeneratednon-interactingpairs,withmax(I)reflectingthemoreeffective
singleagents,andnoepistasis.However,thereisaclearincreaseinthenumberandvarietyof
interactionsbetweenFBA-ko,FBA-res,andFBA-div.WhileFBA-kosynergieswererestricted
tosyntheticlethal(SL)epistasis,somepartialsyntheticlethal(PSL)appearedinFBA-res,anda
largenumberofpotentiation(Pot)synergieswereaddedwithFBA-div.
Arrangingtheresultsbytargetpathwayrevealsinformativepatterns(Fig3andS2–S4Figs).
First,welocatedouriAF1260targetsontheiJR904[37]pathwaymaps,andthenassignedgene
identitieswithreferencetoKEGG[34].NovisualmapswerepublishedfortheiAFmodelthat
weused,soweusedtheiJRmapstoconstructourvisualdisplays.Pathwayswerethenrepre-
sentedusingconcisedescriptorslistedinS2Table.Allthreesimulationapproachesshowactive
singleagentsclusteredinpathwaysessentialforE.coligrowthinrichmedia(glycolysis,citrate
cycle,folateandmureinbiosynthesis,andcertainaminoacidpathways),andtheresponsesfor
anyparticularenzymearemoreorlessuniformwithineachsuchpathway.
Fig3.ComparingFBA-koandFBA-divinteractionsacrossmetabolicpathways.Simulatedinteractionsfor(A)FBA-koand(B)forFBA-div,inselected
metabolicpathways.Morecompletesimulationresultsareshownelsewhere(S2–S4Figs).Eachsymbolrepresentsthesimulatedresponsetoinhibitinga
singleorpairoftargets(seeFig2),withenzymesorganizedbypathwayandmetabolicreactionorderintheiAF1260model.Symbolshapeshowsthetypeof
epistasis(syntheticlethal“SL”,partialsyntheticlethal“PSL”,potentiation“Pot”,ornon-interaction“None”),sizeshowstheeffectmax(I),andcolorshowsthe
synergymax(ΔI)betweentwotargets(samescaleasFig2).Singleagentsareshownalongthebottomandrightedges.ThetrianglesforPSLepistasispoint
towardtheinactiveagentinthepairing.SingleenzymeeffectsareverysimilarbetweenFBA-koandFBA-div,butinteractionsareverydifferent.Mostnotably,
strongPotsynergiesareobservedbetweenserialtargetsinthesamepathwayunderFBA-div(A),whicharenotpredictedbyFBA-ko(B)orFBA-res(S4Fig).
doi:10.1371/journal.pone.0147651.g003
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SimulatingSerial-TargetAntibacterialDrugSynergiesUsingFBA
Fig4.Comparingsingleagentandcombinationeffectsbetweenmethods.(A)Simulatedsingleagentinhibitionsareveryconsistentbetween
methodologies.Acrossthe50simulatedinhibitors,bothFBA-resandFBA-divmethodologiesyieldedverysimilarmax(I)scorestothoseobtainedfrom
standardFBA-ko.Datawererandomlyditheredby~0.03inbothdirectionstovisuallyseparateoverlappingpoints.(B)Simulatedcombinationeffects,
however,showmanydeviationsinmax(ΔI)fromFBA-ko,andsubstantialdifferencesinepistasistypes.Acrossall1225simulatedpairs,FBA-koyielded
mostlyNone,withafewSL(2%).SimulatingwithFBA-resconvertedafewoftheNonetoPSL(5%),andFBA-divreproducedalltheFBA-ressynergiesand
convertedanother16%fromNonetoPot.Datawererandomlyditheredby~0.03toseparateoverlappingpoints.
doi:10.1371/journal.pone.0147651.g004
PLOSONE|DOI:10.1371/journal.pone.0147651 January28,2016 9/18