Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis

19 Pages·2016·3.61 MB·English

Simulating Serial-Target Antibacterial Drug
Synergies Using Flux Balance Analysis
Citation
Krueger, Andrew S., Christian Munck, Gautam Dantas, George M. Church, James Galagan,
Joseph Lehár, and Morten O. A. Sommer. 2016. “Simulating Serial-Target Antibacterial
Drug Synergies Using Flux Balance Analysis.” PLoS ONE 11 (1): e0147651. doi:10.1371/
journal.pone.0147651. http://dx.doi.org/10.1371/journal.pone.0147651.
Published Version
doi: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.
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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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(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
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