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Algorithms for metabolic network-based drug target identification

University of Florida Institutional Repository
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Ithankmyadvisor,Dr.TamerKahveci,forhisexceptionalguidanceduringthecourseofthisresearch.Hehasbeenaconstantsourceofmotivationandsupporttome.Iamgratefulforhisvaluabletechnicalandprofessionalmentoring.IthankDr.Ranka,forhistechnicalguidanceduringthisresearch.IalsothankDr.Jermaineforhishelpandguidance.Ihavebeenblessedwithsupportiveparentswhohavealwaysencouragedmeinallmyendeavors.Theyweremyrstteachers,andtheybelievethatknowledgeandeducationarethebestgiftstheycangivetheirchildren.Iamgratefultothemfortheirvisionandfortheirconstantsupportandencouragement.Mybrother,Balaji,ismypillarofsupport,criticandoneofmybestfriends.Hisclarityofthoughtandnewperspectiveshavealwayshelpedmerenemyideas.Myance,Ram,hasstoodbymeinallmydecisionsandhashelpedshapemycareer.HeismysoundingboardforideasandtherstpersonIturntoforguidance.Iamgratefultohavehimbymysidealways.Ialsothankallmyfriendsandthepeoplewhohavehelpedmeintimesofneed. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 6 LISTOFFIGURES .................................... 7 ABSTRACT ........................................ 8 CHAPTER 1INTRODUCTION .................................. 10 2BACKGROUNDANDRELATEDWORK ..................... 14 3PROBLEMMODELING ............................... 16 4OPTIMALALGORITHM .............................. 18 4.1StateSpaceandBasicStrategy ........................ 18 4.2OPMETPrioritizationStrategies ....................... 20 4.2.1StaticOPMET ............................. 20 4.2.2DynamicOPMET ............................ 22 4.3FilteringStrategies ............................... 24 4.3.1TargetFilter ............................... 25 4.3.2Non-targetFilter ............................ 26 5ITERATIVEALGORITHM ............................. 28 5.1Initialization ................................... 28 5.2IterativeSteps .................................. 30 5.3MaximumNumberofIterations ........................ 32 6EXPERIMENTALRESULTS ............................ 36 6.1EvaluationofOPMETAlgorithm ....................... 36 6.2EvaluationofIterativeAlgorithm ....................... 39 7CONCLUSION .................................... 46 REFERENCES ....................................... 48 BIOGRAPHICALSKETCH ................................ 52 5

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Table page 5-1IterativeSteps:I0istheinitializationstep;I1andI2aretheiterations.VRandVCrepresentthedamagevaluesofreactionsandcompoundsrespectivelycomputedateachiteration.VE=[3,0,0]inalliterations. ................. 35 6-1MetabolicnetworksfromKEGGwithidentier(Id).C,RandEddenotethenumberofcompounds,reactionsandedges(interactions)respectively. ...... 45 6-2Comparisonofaveragedamagevaluesofsolutionsdeterminedbytheiterativealgorithmversustheoptimalalgorithm. ...................... 45 6

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Figure page 3-1AgraphconstructedforametabolicnetworkwiththreereactionsR1,R2,andR3,threeenzymesE1,E2,andE3,andninecompoundsC1,,C9.Circles,rectangles,andtrianglesdenotecompounds,reactions,andenzymesrespectively.Here,C4(shownbydoublecircle)isthetargetcompound.Dottedlinesindicatethesubgraphremovedduetoinhibitionofanenzyme.(a)EectofinhibitingE2.(b)EectofinhibitingE1. ........................... 17 4-1ThebasicOPMETstrategyforahypothetical4-enzymenetwork.EnzymesareorderedasE1,E2,E3,E4.n0,n1,,n4arethenodesgenerated.Theinitialglobalcut-othresholdD=10(initializedtothetotalnumberofcompoundsinthenetwork).n1isatruesolution(shownbydoublecircle)withdamaged=5.Sinced
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Traditionalpharmacologicaldrugdiscoveryapproachesfocusedmoreonthetherapeuticeectsofdrugsthantheirside-eects.Recentadvancesinbioinformaticshavefosteredrationaldrugdevelopmentmethodsthataimtoreduceseriousside-eects.Therststepinthisapproachistheidenticationofspecicbiologicaldrugtargets(enzymesorproteins),whichcanbemanipulatedtoproducethedesiredeect(ofcuringadisease)withminimumdisruptiveside-eects. Inthisthesis,westudythepharmacologicalproblemofidentifyingtheoptimalenzyme-combination(i.e.,drugtargets)whoseinhibitionwillachievetherequiredeectofeliminatingagiventargetsetofcompounds,whileincurringminimalside-eects.Weproposetwoapproachestosolvetheproblem. Inourrstapproach,weformulatetheproblemasanoptimizationproblemonmetabolicnetworks.Wedeneagraphbasedcomputationalmodelofthenetwork,thatencapsulatestheimpactofenzymesontocompounds.WeproposeOPMET,anOptimalenzymedrugtargetidenticationalgorithmbasedonMetabolicnetworks,tosolvethisproblemoptimally.Itisabranch-and-boundalgorithmtoexplorethesearchspace.Wedevelopacostmodelandtwoenzymeprioritizationstrategies,StaticOPMETandDynamicOPMET,basedonit. 8

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Inoursecondapproach,wedevelopaheuristicsolutiontothesameproblemformetabolicnetworkswithalargenumberofenzymes.Weproposeascalableiterativealgorithmwhichcomputesasub-optimalsolutionwithinreasonabletime-boundsforlargemetabolicnetworks.Itevaluatesimmediateprecursorsofthetargetcompoundsanditerativelymovesbackwardstoidentifytheenzymeswhoseinhibitionwillstoptheproductionofthetargetcompoundswhileincurringminimumside-eects.Weshowthatthisalgorithmconvergestoasub-optimalsolutionwithinanitenumberofsuchiterations.OurexperimentsontheE.Colimetabolicnetworkshowthattheaverageaccuracyofthismethoddeviatesfromthatoftheoptimalsolutiononlyby0.02%.Thisiterativealgorithmishighlyscalable.ItcansolvetheproblemfortheentiremetabolicnetworkofE.Coliinlessthan10seconds. 9

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1 ].Toxicityand/orlackofecacycanresult,ifmetabolicnetworkcomponentsotherthantheintendedtargetareaected.Thisiswell-illustratedbytheexampleoftherecentfailureofTolcapone(anewdrugdevelopedforParkinson'sdisease)duetoobservedhepatictoxicityinsomepatients[ 2 ].Post-genomicdrugresearchfocusesmoreontheidenticationofspecicbiologicaltargets(geneproducts,suchasenzymesorproteins)fordrugs,whichcanbemanipulatedtoproducethedesiredeect(ofcuringadisease)withminimumdisruptiveside-eects[ 3 4 ].Themainphasesinsuchadrugdevelopmentstrategyaretargetidentication,validationandleadinhibitoridentication[ 5 ]. Enzymescatalyzereactions,whichproducemetabolites(compounds)inthemetabolicnetworksoforganisms.Enzymemalfunctionscanresultintheaccumulationofcertaincompoundswhichmayresultindiseases.WetermsuchcompoundsasTargetCom-poundsandtheremainingcompoundsasNon-Targetcompounds.Forinstance,themalfunctionofenzymephenylalaninehydroxylasecausesbuildupoftheaminoacid,phenylalanine,resultinginphenylketonuria[ 6 ],adiseasethatcausesmentalretardation.Similarly,mutationsinthegenethatproducesglucokinaseresultsinaformofdiabetescalledmaturity-onsetdiabetesoftheyoungtype2(MODY2)[ 7 ].Thisconditioncausesexcessiveaccumulationofglucoseintheblood(hyperglycemia),duetothemalfunctionofglucokinase.Glucokinasenormallyplaysacentralroleininsulinregulationandhenceisresponsibleformaintainingthebloodglucoselevelinthebody.Theseexamplesunderlinetheimportanceofidentifyingtheoptimalenzymesetwhichcanbemanipulatedbydrugstopreventtheexcessproductionoftargetcompounds,withminimalside-eects.Weterm 10

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Weformallystatetheoptimalenzymecombinationidenticationproblemas GivenasetoftargetcompoundsT(TC),ndthesetofenzymesX(XE)withminimumdamage,whoseinhibitionstopstheproductionofallthecompoundsinT. Lemkeetal.[ 8 9 ]denedthedamageofinhibitionofanenzymeasthenumberofcompoundswhoseproductionstopsaftertheinhibitionofthatenzyme.OurdenitionofdamageissimilartothatofLemkeinprinciple.Wedierbyexcludingthetargetcompoundsfromthedamagecomputation.Dierentenzymesandcompoundsmayhavevaryinglevelsofimportanceinthemetabolicnetwork.Ourmodelconsidersalltheenzymesandcompoundstobeofequalimportance(similartoLemke'swork).Wecanextendourmodelbyassigningweightstoenzymesandcompoundsbasedontheirroleinthenetwork.However,wedonotdiscusstheseextensionsinthisthesis. 11

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10 ]inourmodel. 11 ].Wedeveloptwoenzymeprioritizationstrategies,StaticOPMETandDynamicOPMETbasedonthecostmodel.StaticOPMETprioritizesenzymesaccordingtotheimpactoftheirinhibitionontheproductionofcompoundsinthemetabolicnetwork.Itinspectsthemostpromisingenzymesrst,forpossibleinclusionintheoptimalsubset.DynamicOPMETdynamicallyupdatestheprioritiesasthesearchspaceisexplored.Wedeveloptwolteringapproaches,namelytargetlterandnon-targetlter,whicharecombinedwiththeOPMETtoprunethesearchspacewhilestillguaranteeinganoptimalsolution.Thetargetltereliminatesasubspacewhenitisproventhatthereisnocombinationofenzymesinthisspacethatcanstoptheproductionofallthetargetcompounds(i.e.,thereisnousefuldrugtarget).Thenon-targetlterprunessubspaceswherethereisnosolutionwithadamagelessthantheoptimalsolutionfoundsofar. 12 ].Thisalgorithmisbasedontheintuitionthatwecanarriveatasolutionclosetotheoptimalonebytracingbackwardfromthetargetcompounds.Itstartsbyndingthedamageincurredduetotheremovalofeachreactionorcompoundbyevaluatingitsimmediateprecursors.Ittheniteratively 12

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WeextractedthemetabolicnetworkdataofE.ColifromtheKEGG[ 13 14 ]databaseforourexperiments.OurexperimentsontheE.Colimetabolicnetworkshowthatourrstmethod(optimalsolution)reducesthetotalsearchtimebyseveralordersofmagnitudeascomparedtotheexhaustivesearch,formedium-sizedmetabolicnetworks.DynamicOPMETprunes91.6%ofthesearchspace.Itgeneratestheoptimalenzymecombinationwithintheexploration0.005%ofthesearchspaceonaverage. OurexperimentsontheE.Colimetabolicnetworkalsoshowthattheaverageaccuracyofourapproximatemethod(iterativesolution)deviatesfromthatoftheoptimalsolutiononlyby0.02%formedium-sizednetworks.Itisalsohighlyscalable.ItcansolvetheproblemfortheentiremetabolicnetworkofEscherichiaColiinlessthan10seconds. 13

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Classicaldrugdiscoveryapproachesinvolveincorporatingalargenumberofhypotheticaltargetsintoin-vitroorcell-basedassaysandperformingautomatedhighthroughputscreening(HTS)ofvastchemicalcompoundlibraries[ 5 15 ].Post-genomicadvancesinbioinformaticshavefosteredthedevelopmentofrationaldrug-designmethodsandreductionofseriousside-eects[ 1 16 { 18 ].Thishasengenderedtheconceptofreversepharmacology[ 4 ],inwhich,therststepisTargetidentication,thesteptoidentifyproteintargets,thatmaybecriticalinterventionpointsinadiseaseprocess[ 3 19 ].ThisisfollowedbyTargetvalidation,thesteptodemonstratethatanidentieddrugtargetisprimarilyresponsibleforthetherapeuticactivityofaprovendrug[ 20 { 22 ].ThethirdstepisLeadInhibitorIdentication[ 5 ].Sincethereversepharmacologicalapproachisdrivenbythemechanicsofthedisease,itisexpectedtobemoreecientthantheclassicalapproach[ 4 ]. Rapididenticationofenzyme(orprotein)targetsneedsathoroughunderstandingoftheunderlyingmetabolicnetworkoftheorganismaectedbyadisease.Theavailabilityoffullysequencedgenomeshasenabledresearcherstointegratetheavailablegenomicinformationtoreconstructandstudymetabolicnetworks[ 23 { 25 ].Thesestudieshaverevealedimportantpropertiesofthesenetworks[ 26 { 28 ].Thevitalstepinunderstandingtherelationshipbetweenmetabolicnetworksanddrugdiscoveryistodevelopanaccuratemodelofthepathway.Theaccuracyofthemodeldetermineshowwellthecandidatetargetsreecttherealbiologicalprocess.Agoodmodelalsohastobeexibletomeetthepossiblefutureupdatesonthemetabolicnetworkswithminimalchanges.Anumberofmodelshavealreadybeendeveloped,suchasgraphs,bayesiannetworks[ 29 30 ],booleannetworks[ 31 { 33 ],logicalnetworks[ 34 35 ],dierentialequations[ 36 37 ],andstochasticmodels[ 38 39 ].Findingtherightmodelisachallengingproblem.Thisdicultyisfurtherincreasedduetoinaccuraciesinthenetworksuchasmissingenzymesorreactions. 14

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40 ].Lemkeet.alproposedthemeasureenzymedamageasanindicatorofenzymeessentiality[ 8 9 ].Recently,acomputationalapproachforprioritizingpotentialdrugtargetsforantimalarialdrugshasbeendeveloped[ 41 ].Achoke-pointanalysisofP.falciparcumwasperformedtoidentifyessentialenzymeswhicharepotentialdrugtargets.Thepossibilityofusingenzymeinhibitorsasantiparasiticdrugsisbeinginvestigatedthroughstoichiometricanalysisofthemetabolicnetworksofparasites[ 42 43 ].Thesestudiesshowtheeectivenessofcomputationaltechniquesinreversepharmacologicalapproaches. Acombinationofmicro-arraytime-coursedataandgene-knockoutdatawasusedtostudytheeectsofachemicalcompoundonagenenetwork[ 44 ].Aninvestigationofmetaboliteessentialityiscarriedoutwiththehelpofstoichiometricanalysis[ 45 ].Theseapproachesunderlinetheimportanceofstudyingtheroleofcompounds(metabolites)duringthepursuitofcomputationalsolutionstopharmacologicalproblems. 15

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Inthischapter,wedescribeourmodelofthemetabolicnetwork.Wedevelopagraphbasedmodelthatcapturestheinteractionsbetweenreactions,compounds,andenzymes.Ourmodelisavariationofthebooleannetworkmodel[ 31 32 ].LetR,C,andEdenotethesetofreactions,compounds,andenzymesrespectively.ThevertexsetconsistsofallthemembersofR[C[E.Avertexislabeledasreaction,compound,orenzymebasedontheentityitrefersto.LetVR,VC,andVEdenotethesetofverticesfromR,C,andE.Adirectededgefromvertexxtovertexyisthendrawnifoneofthefollowingthreeconditionsholds: 1.xrepresentsanenzymethatcatalyzesthereactionrepresentedbyy. 2.xcorrespondstoasubstrateforthereactionrepresentedbyy. 3.xrepresentsareactionthatproducesthecompoundmappedtoy. Figure 3-1 illustratesasmallhypotheticalmetabolicnetwork.Adirectededgefromanenzymetoareactionimpliesthattheenzymecatalyzesthereaction(i.e.,E1catalyzesR1andE2catalyzesR2andR3).Adirectededgefromacompoundtoareactionimpliesthatthecompoundisareactant.Adirectededgefromareactiontoacompoundimpliesthatthecompoundisaproduct.Inthisgure,C4isthetargetcompound(i.e.,theproductionofC4shouldbestopped).InordertostoptheproductionofC4,R2hastobepreventedfromtakingplace.Thiscanbeachievedintwoways.Onewayisbydisruptingoneofitscatalyzingenzymes(E2inthiscase).Anotherisbystoppingtheproductionofoneofitsreactantcompounds(C2orC3inthiscase).IfwestoptheproductionofC2,weneedtorecursivelylookfortheenzymewhichisindirectlyresponsibleforitsproduction(E1inthiscase).Thus,theproductionofthetargetcompoundcanbestoppedbymanipulatingeitherE1orE2. Figure 3-1(a) showsthedisruptionofE2anditseectonthenetwork.InhibitingE2resultsintheknockoutofcompoundsC5,C8andC9inadditiontothetargetcompound, 16

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(b) AgraphconstructedforametabolicnetworkwiththreereactionsR1,R2,andR3,threeenzymesE1,E2,andE3,andninecompoundsC1,,C9.Circles,rectangles,andtrianglesdenotecompounds,reactions,andenzymesrespectively.Here,C4(shownbydoublecircle)isthetargetcompound.Dottedlinesindicatethesubgraphremovedduetoinhibitionofanenzyme.(a)EectofinhibitingE2.(b)EectofinhibitingE1. 3-1(b) showstheinhibitionofE1anditseectonthesamenetwork.Inthiscase,thedamageis2(i.e.,C2andC5).TheimportantobservationisthatE1andE2bothachievetheeectofdisruptingthetargetcompound,C4.Hence,E1andE2arebothpotentialdrugtargets.However,E1isabetterdrug-targetthanE2sinceitcauseslesserdamage. 17

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Thenumberofpossiblesubsetsofenzymesthatneedtobeconsideredforndingtheoptimaldrugtargetisexponentialinthenumberofenzymes.Thisrendersexhaustivesearchinfeasiblebeyondsmallsizedmetabolicnetworks.Inthischapter,weproposeOPMET,abranchandboundalgorithmthatconsiderablyreducesthenumberofpossiblecombinationstobesearchedwhilestillguaranteeingtondanoptimalsolution,formedium-sizednetworks(networkswithatmost32enzymes).Section 4.1 describesthebasicbranchandboundstrategy.Aspartofanyeectivebranchandboundstrategyitisimportanttondagoodsolutionquickly.Thisallowsforeectiveltering(orpruning)ofsubspacesthatcanbeguaranteednottohavebettersolutionthatthebestfoundsofar.Ourprioritization(Section 4.2 )andltering(Section 4.3 )strategiesachievethisgoal. LetE=fEij8i,1imgdenotethesetofenzymesforametabolicnetwork.Thesearchspaceismodeledasatreestructure.Everynodeofthistreecorrespondstoastateinthesearchspaceanditisrepresentedbya4-tuple([e1,e2,,em],k,d,remove).Here,1,,misapermutationof1,2,,m.Therstparametercorrespondstothestateofalltheenzymes(i.e.,eicorrespondstoenzymeEi).ei=1ifEiisinhibited.Otherwise,ei=0.Theparameterkindicatesthattherstkenzymesareconsideredatthatsearchstate.Thedecisiontoinhibitornotinhibithasbeenxedforenzymesfrom1tok1andwenowsetek=1andei=0,8i,k
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Backtrackinginvolvesfollowingsteps.FirstwepickthetopnodefromtheactivenodesstackA.LetN=([e1,e2,,em],k,d,remove)denotethisnode.Wethensetek+1=0(indicatingthenodewearebacktrackingfrom)andek+2=1inN(i.e.,weinhibittheenzymeek+2).Theresultingnodebecomesthenodetobeevaluatedinthenextstep.Thersttwocasesabovestopexpandingthetreeatthecurrentnode.Theformeroneimpliesthatthecurrentnodeisapossiblesolution(noden1inFigure 4-1 ).Thelatteroneimpliesthatthecurrentnodeincurstoomuchdamagetoleadtoapossiblesolution.Thethirdcasehappenswhenthecurrentnodedoesnotstopproductionofallthetargetcompounds,butthedamageislowerthanthedamageofthecurrentbest 19

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4-1 ).Suchnodesmayproduceapossiblesolution(noden4inFigure 4-1 )withtheinhibitionofmoreenzymes.Thus,theyneedtobeexploredfurthertoensurethatwendanoptimalsolution.Thesearchterminateswhentherearenomorenodestoexplore.Atthisstage,thecurrenttruesolutionistheoptimalsolution. 3-1 ,theproductionofC7isnotstoppedaftertheinhibitionofE1orE2individually.However,C7isremovedifE1isinhibitedaswellasE2.Thus,damagevaluesofindividualenzymesarenotgoodindicatorsofthecombineddamageoftheseenzymes. 20

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Wedenetheweightofanedgeastheweightofthenodeforwhichitistheoutgoingedge. InordertocomputethecostofEi,wesettheweightofEitozero(i.e.,W(Ei)=0).Theweightsofallthereactionandcompoundnodesareassignedprogressivelybyabreadth-rstsearch,accordingtotheabovescheme.TheweightsofallthenodesandedgeswhichcanbereachedfromEiarerecomputedtoreectthechange.TheeectofdeletingE1isshowninFigure 4-2 .Wedeneanimpactvectorforeachenzymebasedontheeectsofitsinhibition. 21

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kfor1ik,andvi=(nk nk)fork
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Weproposeanincrementalalgorithmbyusingtheimpactvectorofindividualenzymes.Wepredicttheremainingfractionofallthecompoundsafterinhibitionofeachenzymewiththehelpofitsimpactvector.ThisalgorithmisdescribedinFigure 4-3 .LetR=[r1;r2;;rn]denotetheremainingfractionsofcompounds(step1).Here,ri2[0;1]correspondstocompoundCi,8i.Weinitializeri=1,8iindicatingthatallcompoundsarebeingproducedwithoutanydisruption.LetVbethenormalizationvectorasgiveninDenition 2 .LetI(Ei)betheimpactvectorofenzymeEi(seeDenition 1 ).AteverystepoftheDynamicOPMETalgorithm,letN=([e1,e2,,em],k,d,remove)bethenodecurrentlybeingevaluated(i.e.,thedecisiontoinhibitornotinhibithasbeenxedfore1,e2,,ek1)(step2).Wenowneedtodecidewhichenzymehastobeevaluatednext.InStep3a,foreveryenzymeintheremainingenzymeset(ei,8i,kim),wecomputethenewremainingfractionsofcompounds(Ri).ThisisdonebyaVectorDirectProductofRandtheimpactvectorofEi(I(Ei)).VectordirectproductisdenedasXY=[x1y1;x2y2;;xnyn],whereX=[x1,,xn]andY=[y1,,yn].TheresultingvectorRiisanapproximationtotheimpactofinhibitionoftheenzymeEiinadditiontoalreadyinhibitedenzymes.ThisisjustiedsincethequantityofacompoundeliminatedbyacombinationincludingEiwillbeatleastasmuchasthequantityeliminatedbyEialone.Agoodcandidateenzymeatthisstepistheonethatensuresthatlesserofthetargetcompoundsremainafteritsinhibition.Also,itshouldensurethatthenontargetcompoundssuertheminimumpossibledamage.Ourcostmodelsatisestheserequirements.InStep3b,wecomputethecostofeachenzymeas 23

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ThecostofndingthebestenzymeateachsteptakesO(mn),wheremandndenotethenumberofenzymesandcompoundsinthemetabolicnetworkrespectively.ThisisbecauseavectorproductcostsO(n),andO(m)suchproductsarecarriedout. 1 :LetE=fE1,E2,,Ergbeasetofenzymes.LetCjbeacompoundinthemetabolicnetwork.Letdi,1ir,denotetheimpactofEionCj.Letdi(Rk),1ir,denotetheimpactofEionRk.Weneedtoshowthatthefollowingruleshold: WerstconsiderthecasewhenareactionRkisstoppedandprovethatRule2holds,giventhatRule1iscorrect. 24

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4.2 ),di(Rk)=minfdi(Ck)g,CkisthesetofallinputcompoundsofRk.Thus,1di(Rk)=maxf1di(Ck)g.Hence, WenowconsiderthecasewhentheproductionofacompoundCjstopsandprovethatRule1holds,giventhatRule2iscorrect.IfEremovesCj,itmeansthatallthereactionsthatproduceCjhavebeenstopped.LetR1;R2;;RtbethereactionsthatproduceCj.ForeachreactionRk;1kt,oneofthethefollowingtwocaseshastobetrue. 4.2 ),1dj(Cj)1 (1di(Cj))=1Ptj=1(1di(Rj)) Next,wedescribeourlteringstrategies. 25

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4.1 ).Ifacombinationdoesnotdeletethetargetcompoundset,theeortspentiswasted.Filteringsuchcombinationswillimprovetheperformanceofthesearchvastly.ThisisthemotivationbehindourTargetlter. Thetargetltereliminatesabulkofthesearchspacewhenitisproventhatthereisnocombinationofenzymesinthisspacethatcanstoptheproductionofallthetargetcompounds(i.e.,thereisnousefuldrugtarget).ThislteringstrategyisbasedonTheorem 1 .Formally,letnodeN=([e1,e2,,em],k,d,False)beanodeinthesearchspace.LetTdenotethesetoftargetcompounds.BacktrackifkXi=1(1di(C))ei+nXi=k+1(1di(C))<1;9C2T: 4.1 ).ThislterutilizesTheorem 1 similartotheTargetFilter.Theideaisasfollows.AtagivennodeN,foreachtargetcompound,C,wendtheminimumnumberofenzymes,msuchthatmXi=1(1di(C))ei1: 26

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ThebasicOPMETstrategyforahypothetical4-enzymenetwork.EnzymesareorderedasE1,E2,E3,E4.n0,n1,,n4arethenodesgenerated.Theinitialglobalcut-othresholdD=10(initializedtothetotalnumberofcompoundsinthenetwork).n1isatruesolution(shownbydoublecircle)withdamaged=5.Sinced
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Inthischapter,wedevelopascalableiterativealgorithmthatndsasub-optimalsolutiontotheenzyme-targetidenticationproblemquickly.Ouralgorithmisbasedontheintuitionthatwecanarriveatasolutionclosetotheoptimalone,bytracingbackwardsfromthetargetcompounds.Weevaluatetheimmediateprecursorsofthetargetcompoundsanditerativelymovebackwardstoidentifytheenzymes,whoseinhibitionwillstoptheproductionofthetargetcompoundswhileincurringminimumdamage.Ouralgorithmconsistsofaninitializationstepfollowedbyiterations,untilsomeconvergencecriteriaissatised.LetE,RandCdenotethesetsofenzymes,reactionsandcompoundsofthemetabolicnetworkrespectively.LetjEj,jRjandjCjdenotethenumberofenzymes,reactionsandcompoundsrespectively.Theprimarydatastructuresarethreevectors,namelyanenzymevectorVE=[e1,e2,,ejEj],areactionvectorVR=[r1,r2,,rjRj],andacompoundvectorVC=[c1,c2,,cjCj].Eachvalue,ei,inVEdenotesthedamageofinhibitionofenzyme,Ei2E.Eachvalue,ri,inVRdenotesthedamageincurredbystoppingthereactionRi2R.Eachvalue,ci,inVCdenotesthedamageincurredbystoppingtheproductionofthecompoundCi2C. 28

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ConsiderthenetworkinFigure 5-1 .ColumnI0inTable 5-1 showstheinitializationofthevectorsforthisnetwork.Inthisgure,C1isthetargetcompound(i.e.,theproductionofC1shouldbestopped).Inordertostopitsproduction,wehavetopreventR1fromtakingplace.Thiscanbeaccomplishedintwoways:(1)Bydisruptingoneofitscatalyzingenzymes(E1inthiscase).Figure 5-1(b) showstheeectsofdisruptingE1.Thedamagee1ofE1isthree,asinhibitingE1stopstheproductionofthreenon-targetcompoundsC2,C3andC4.(2)Bystoppingtheproductionofoneofitsreactantcompounds(C5inthiscase).TostoptheproductionofC5,weneedtorecursivelylookfortheenzymecombinationwhichisindirectlyresponsibleforitsproduction(E2andE3).SincethedisruptionofE2orE3alonedoesnotstoptheproductionofanynon-targetcompound,theirdamagevaluesarezero.Hence,VE=[3,0,0].Thedamagevaluesforreactionsarecomputedastheminimumoftheircatalyzers(r1=r2=e1andr3=r4=e2).Hence,VR=[3,3,0,0].Thedamagevaluesforcompoundsarecomputedfromthereactionsthatproducethem.Forinstance,R1andR2produceC2. 29

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4 ).ThereisnoneedtoupdateVEsincetheenzymesarenotaectedbythereactionsorthecompounds.Next,wedescribetheactionstakentoupdateVRandVCateachiteration.Welaterdiscussthestoppingcriteriafortheiterations. Thiscomputationisintuitivesinceareactioncanbedisruptedbystoppingtheproductionofanyofitsinputcompounds.Thedamageofalltheinputcompoundsarealreadycomputedinthepreviousiteration(say(n1)thiteration).Therefore,atiterationn,thesecondtermoftheminfunctionconsiderstheimpactofthereactionsandcompoundsthatareawayfromRjbynedgesinthegraphforthemetabolicnetwork.LetE(Rj)denotethesetthatcontainstheenzymesthatproducedthenewdamagerj.Alongwithrj,wealsostoreE(Rj).Weupdateallrj2VRusingthesamestrategy.Notethat 30

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ColumnsI1andI2inTable 5-1 showtheiterativestepstoupdatethevaluesofthevectorsVRandVC.InI0,wecomputethedamager1forR1astheminimumofitscurrentdamage(three)andthedamageofitsprecursorcompound,c5=1.Hence,r1isupdatedto1anditsassociatedenzymesetischangedtofE2;E3g.TheothervaluesinVRremainthesame.WhenwecomputethevaluesforVC,c1isupdatedto1,asitsnewassociatedenzymesetisfE2;E3gandthedamageofinhibitingbothE2andE3togetheris1.Hence, 31

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SpaceComplexity:Thenumberofelementsinthereactionandcompoundvectorsis(jRj+jCj).Foreachelement,westoreanassociatedsetofenzymes.Hence,thespacecomplexityisO((jRj+jCj)jEj). TimeComplexity:ThenumberofiterationsofthealgorithmisO(jRj)(seeSection 5.3 ).ThecomputationaltimeperiterationisO(G(jRj+jCj)),whereGisthesizeofthegraph.Hence,thetimecomplexityisO(jRjG(jRj+jCj)).

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4 and 3 )fromanyenzymeEitoareactionRj(oracompoundCk).Thevaluerj(orck)remainsconstantafteratmostniterations. 4 and 3 )fromanyenzymeinEicorrespondingtoei2VEtoCk. 33

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2 holds. 34

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(b) IterativeSteps:I0istheinitializationstep;I1andI2aretheiterations.VRandVCrepresentthedamagevaluesofreactionsandcompoundsrespectivelycomputedateachiteration.VE=[3,0,0]inalliterations. [1,3,0,0],[1,3,3,3,1] [1,3,0,0],[1,3,3,3,1]

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WeextractedthemetabolicnetworkinformationofEscherichiaColi(E.Coli)fromKEGG[ 13 14 ]( 6-1 showsthemetabolicnetworkschosen,alongwiththeiridentiersandthenumberofcompounds(C),reactions(R)andedges(Ed).Theedgesrepresenttheinteractionsinthenetwork. Foreachnetwork,weconstructedquerysetsofsizesone,twoandfourtargetcompounds,byrandomlychoosingcompoundsfromthatnetwork.Eachquerysetcontains10querieseach.WeranourexperimentsonanIntelPentium4processorwith2.8GHzclockspeedand1-GBmainmemoryrunningLinuxoperatingsystem. 1.Numberofnodesgenerated:Itrepresentsthetotalnumberofenzymecombinationstestedtocompletethesearch.Thelesserthenumberofnodesgenerated,thebettertheperformanceofthemethod. 2.Optimalnoderank:Thisindicatesthenumberofnodesexploredbeforethemethodarrivesattheoptimalsolution.Asmalloptimalnoderankindicatesthattheoptimalcombinationisfoundquickly. 3.Executiontime:Thisindicatesthetotaltimetakenbythemethodtonishthesearchandconcludethatitfoundanoptimalsolution. 36

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4.2 )aswellasNon-targetlterandTargetlter(seeSection 4.3 ).Wecomparethemethodsweimplementedtoanexhaustivesearchwhichenumeratesandtestsallpossiblecombinationsofenzymes(2n,wherenisthenumberofenzymes). Table 6-1 showstheaveragenumberofnodesgeneratedandtheaverageoptimalnoderankoftherandomordering,staticOPMETanddynamicOPMET,ascomparedtoanexhaustivesearch.TheresultsshowthatDynamicOPMETisthebeststrategyforallthetestednetworks.Itgeneratestheleastnumberofnodesinalltheexperiments.AllthemethodsgeneratesignicantlylargenumberofnodesforN17.Thisisbecausethenumberofreactionsandcompoundsofthisnetworkismuchlargerthantheothernetworks,resultinginmoreinteractionsinthenetwork(seeTable 6-1 ).BothDynamicandStaticOPMEThavesmallOptimalNodeRanks.DynamicOPMEThasthelowestoptimalnoderankonanaverage.Onanaverage,itarrivesattheoptimalsolutionwithinthegenerationof0.008%ofthenumberofnodespossibleinanexhaustivesearch.Thisissignicantlybetterthantherandomorderingwhicharrivesattheoptimalsolutionwithinthegenerationof11%.ThedierencebetweentheOptimalNodeRanksandthenumberofnodesgeneratedforStaticandDynamicOPMETshowsthattheyndoptimalresultsquicklybutstillevaluatemanynodestoensurethatthatresultisoptimal. WeuseDynamicOPMETintherestoftheexperimentsasithasthebestperformance. 37

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Figure 6-2(a) showstheaveragenumberofnodesgenerated.Thecombinedltersshowthebestpruning.Onanaverage,thecombinedltersprune91.5%ofthenodesgeneratedinthemethodwithoutlters.WealsoseethatmostofthisbenetisobtainedfromtheTargetFilter(itlters91.4%ofthenodesgeneratedbythemethodwithoutlters).Thecombinedltergeneratesonly12700nodesforN24(0.004%ofanexhaustivesearch). Figure 6-2(b) showstheaverageexecutiontime.WeseethattheaverageexecutiontimeshowsatrendsimilartoFigure 6-2(a) .Thisestablishesthattheexecutiontimeisproportionaltothenumberofnodesgenerated.Thecombinedlterreducestheexecutiontimebyanorderofmagnitudeascomparedtothemethodwithoutltersonanaverage. Figure 6-2(c) showstheaverageoptimalnoderank.AllthemethodshavethesameoptimalnoderankfornetworksexceptN24.ThissuggeststhatDynamicOPMETyieldedtheoptimalsolutionasearlyaspossibleforthesenetworks.ForN24,thecombinedltershowsthatlteringstrategiescanalsoleadtoadvancementinndingtheoptimalsolution.ForN24,Targetlterarrivesattheoptimalsolution99%earlierandthecombinedltersarriveattheoptimalsolution99.9%earlierthanthemethodwithoutlters(theadditional0.9%improvementisobtainedfromthenon-targetlter). Weobservethatthetargetlterismoreecientthanthenon-targetlterandthecombinedlterhasthebestperformance.WeuseDynamicOPMETwithcombinedltersintherestoftheexperiments. 38

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6-3 showstheaveragenumberofnodesgenerated.Thereisnoclearcorrelationbetweenthetargetsetsizeandthenumberofnodesexplored.Thenetworktopologydetermineshowthetargetsetsizeaectsthenumberofnodesgenerated.Thetargetcompoundsetcancontainhighlycorrelatedcompounds(deletedbytheinhibitionofalmostthesamesetofenzymes)orunrelatedcompounds(locatedindierentpartsofthenetwork).Ifthetargetsetconsistsofcorrelatedcompounds,anincreaseinthetargetsetsizedecreasestheaveragenumberofnodesgenerated.ThiscanbeseenforN14,N17,N20andN24(from2to4targetcompoundqueries).Thenumberofnodesgeneratedforthetwo-targetsetsis62%lesserthansingletargetsetsonanaverage.Forthefour-targetsets,thisvalueis75%lesser.Ontheotherhand,ifthetargetsetconsistsofunrelatedcompounds,anincreaseinthetargetsetsizeincreasestheaveragenumberofnodesgenerated.Theaveragenumberofnodesincreasesby1.2timeswhenwegofromsingletargettotwo-targetsetsandby2.2timeswhenwegofromthetwo-targettothefour-targetsets. Figure 6-4 showsthattheaverageoptimalnoderankincreasessublinearlywiththenumberoftargetcompounds.Onanaverage,Thetwo-targetqueriesarriveattheoptimalsolutionaftergenerationof1.8timesmorenodesthanthesingletargetqueries.Similarly,thefour-targetqueriesgenerate3.8timesmorenodesthanthesingletargetqueriesbeforearrivingattheoptimalsolution.Thissuggeststhatasthetargetsetsizeincreases,thenumberofenzymecombinationsthatneedtobetestedbeforewendtheoptimalsolutionincreases. 1.Executiontime:Thetotaltime(inmilliseconds)takenbythemethodtonishexecutionandreportifafeasiblesolutionisidentiedornot. 2.Numberofiterations:Thenumberofiterationsperformedbythemethodtoarriveatasteady-statesolution. 39

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Weimplementedtheproposediterativealgorithmandanexhaustivesearchalgorithmwhichdeterminestheoptimalenzymecombinationtoeliminatethegivensetoftargetcompoundswithminimumdamage.WeimplementedthealgorithmsinJava. 6-2 showsthecomparisonoftheaveragedamagevaluesofthesolutionscomputedbytheiterativealgorithmversustheoptimalalgorithm.WehaveshowntheresultsonlyuptoN32,astheoptimalalgorithmtooklongerthanonedaytonishfornetworksslightlylargetthanN32.WecanseethatthedamagevaluesofourmethodexactlymatchthedamagevaluesoftheoptimalalgorithmforallthenetworksexceptN24.ForN24,theaveragedamageoftheiterativesolutiondiersfromthatoftheoptimalsolutionbyonly0.02%.Thisshowsthattheiterativealgorithmisagoodapproximationoftheoptimalalgorithm.Theslightdeviationindamageisthetradeoforachievingthescalabilityoftheiterativealgorithm(describednext). 6-5(a) plotstheaverageexecutiontimeofouriterativemethodforincreasingsizesofmetabolicnetworks.Therunningtimeincreasesslowlywiththenetworksize.Asthenumberofenzymesincreasesfrom8to537,therunningtimeincreasesfromroughly1to10seconds.Thelargestnetwork,N537,consistsof537enzymes,andhence,anexhaustiveevaluationinspects25371combinations(whichiscomputationallyinfeasible).Thus,ourresultsshowthattheiterativemethodscaleswellfornetworksofincreasingsizes.Thispropertymakesourmethodanimportanttoolforidentifyingtherightenzymecombinationforeliminatingtargetcompounds,especiallyforthosenetworksforwhichanexhaustivesearchisnotfeasible. Figure 6-5(b) showsaplotoftheaveragenumberofiterationsforincreasingsizesofmetabolicnetworks.Theiterativemethodreachesasteadystatewithin10iterationsinallcases.Thevariousparameters(seeTable 6-1 )thatinuencethenumberofiterationsarethenumberofenzymes,compounds,reactionsandespeciallythenumberofinteractionsin 40

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(b)Averageexecutiontimeinmilliseconds ComparisonofOPMETorderingstrategies thenetwork(representedbyedgesinthenetworkgraph).Largernumberofinteractionsincreasethenumberofiterationsconsiderably,ascanbeseenfornetworksN22,N48,N96,N537,wherethenumberofiterationsisgreaterthan5.Thisshowsthat,inadditiontothenumberofenzymes,thenumberofcompoundsandreactionsinthenetworkandtheirinteractionsalsoplayasignicantroleindeterminingthenumberofiterations.Ourresultsshowthattheiterativealgorithmcanreliablyreachasteadystateandterminate,fornetworksaslargeastheentiremetabolicnetworkofE.Coli. 41

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(b)Averageexecutiontimeinmilliseconds (c)Averageoptimalnoderank ComparisonofOPMETlteringstrategies 42

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AveragenumberofnodesbygeneratedbyDynamicOPMETwithcombinedlters. Figure6-4. AverageoptimalnoderankbygeneratedbyDynamicOPMETwithcombinedlters. 43

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(b) Evaluationofiterativealgorithm.(a)Averageexecutiontimeinmilliseconds.(b)Averagenumberofiterations 44

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MetabolicnetworksfromKEGGwithidentier(Id).C,RandEddenotethenumberofcompounds,reactionsandedges(interactions)respectively. N42Otheraminoacid6963208 biosynthesis N13Xenobiotics4758187 N48Lipid134196654 biodegradation N14CitrateorTCAcycle2135125 N52Purine67128404 N17Galactose3850172 N59Energy7282268 N20Pentosephosphate2637129 N71Nucleotide102217684 N22GlycanBiosynthesis5451171 N96Vitaminsand145175550 Cofactors N24Glycerolipid3249160 N170Aminoacid543781210 N28Glycine,serine3646151 N180Carbohydrate2475011659 andthreonine N32Pyruvate2151163 N537EntireNetwork98817905833 Comparisonofaveragedamagevaluesofsolutionsdeterminedbytheiterativealgorithmversustheoptimalalgorithm. IterativeDamage2:518:731:633:391:470:59 OptimalDamage2:518:731:633:171:470:59

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Ecientcomputationalmethodsarerequiredtoidentifytheoptimalenzyme-combination(i.e.,drugtargets)whoseinhibitionwillachievetherequiredeectofeliminatingagiventargetsetofcompoundswhileincurringminimalside-eects.Inthisthesis,weproposedtwosolutionstothispharmacologicalproblem.Inourrstwork,weproposedanoptimalsolutionformedium-sizedmetabolicnetworks.Inoursecondwork,weproposedanapproximatesolutionforalargesizedmetabolicnetwork. Intheoptimalmethod,weformulatedtheoptimalenzyme-combinationidenticationproblemasanoptimizationproblemonmetabolicnetworks.Wedenedagraphbasedcomputationalmodelofthenetworkthatencapsulatestheimpactofenzymesontocompounds.WeproposedOPMET,abranch-and-boundalgorithmtoexplorethesearchspace.Wedevelopedacostmodelandtwoenzymeprioritizationstrategies,StaticOPMETandDynamicOPMETbasedonit.Wealsodevelopedtwolteringstrategiestoprunethesearchspacewhilestillguaranteeinganoptimalsolution.Thelterscomputeanupperboundtothenumberoftargetcompoundsdeletedandalowerboundtotheside-eectrespectively. OurexperimentsontheE.Colimetabolicnetworkshowthatouroptimalmethodsreducedthetotalsearchtimebyseveralordersofmagnitudeascomparedtotheexhaustivesearch.TheoptimalsolutionisreachedbyDynamicOPMETwithintheexplorationof0.005%ofthetotalsearchspaceonanaverage,provingthatourmethodsareeectiveinapproximatingtheimpactofanenzymeonacompound.TheDynamicOPMETwithcombinedlterspruned91.6%ofthesearchspaceonaverage. Inoursecondmethod,wedevelopedanapproximatesolutiontotheoptimalenzyme-combinationidenticationproblemforlarge-sizedmetabolicnetworks,forwhichanoptimalsolutionisnotfeasible.Weproposedascalableiterativealgorithmwhichcomputesasub-optimalsolutiontothisproblemwithinreasonabletime-bounds.Ouralgorithmisbasedontheintuitionthatwecanarriveatasolutionclosetotheoptimal 46

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Inthisthesis,wehavedevelopedafoundationfordevelopingeectivesolutionstopharmacologicalproblems,throughanalysisofmetabolicnetworks.Wearecurrentlyworkingtoimprovetheaccuracyofournetworkandcostmodelsinmodelingthemetabolicnetwork'sbehavior.Wearealsodevelopingmethodswhichwillecientlyprovidesolutionstothesameproblemforlargermetabolicnetworks. 47

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[1] CapranicoG.Arationalselectionofdrugtargetsneedsdeeperinsightsintogeneralregulationmechanisms.CurrentMedicinalChemistry-Anti-CancerAgents,4(5):393{394,Sep2004. [2] DeaneK.H.O.,SpiekerS.,andClarkeC.E.Catechol-O-methyltransferaseinhibitorsversusactivecomparatorsforlevodopa-inducedcomplicationsinParkinson'sdisease.CochraneDatabaseofSystematicReviews,4,2004. [3] SmithC.Hittingthetarget.Nature,422:341{347,Mar2003. [4] TakenakaT.Classicalvsreversepharmacologyindrugdiscovery.BJUInternational,88(2):7{10,Sep2001. [5] DrewsJ.Drugdiscovery:ahistoricalperspective.Science,287(5460):1960{1964,Mar2000. [6] SurteesR.andBlauN.Theneurochemistryofphenylketonuria.EuropeanJournalofPediatrics,159:109{13,2000. [7] GloynA.L.Glucokinase(GCK)mutationsinhyper-andhypoglycemia:maturity-onsetdiabetesoftheyoung,permanentneonataldiabetes,andhyperinsulinemiaofinfancy.HumanMutation,22(5):353{62,Nov2003. [8] MombachJ.C.,LemkeN.,daSilvaN.M.,FerreiraR.A.,IsaiaE.,andBarcellosC.K.Bioinformaticsanalysisofmycoplasmametabolism:importantenzymes,metabolicsimilarities,andredundancy.ComputersinBiologyandMedicine,36(5):542{52,May2006. [9] LemkeN.,HerediaF.,BarcellosC.K.,dosReisA.N.,andMombachC.M.Essentialityanddamageinmetabolicnetworks.Bioinformatics,20(1):115{119,Jan2004. [10] Ocampoet.al.TargeteddeletionofmNth1revealsanovelDNArepairenzymeactivity.MolCellBiol.,22(17):6111{21,Sep2002. [11] SridharP.,KahveciT.,andRankaS.OPMET:Ametabolicnetwork-basedalgorithmforoptimaldrugtargetidentication.Technicalreport,CISEDepartment,UniversityofFlorida,Sep2006. [12] SridharP.,KahveciT.,andRankaS.Aniterativealgorithmformetabolicnetwork-baseddrugtargetidentication.PSB2007OnlineProceedings,2007. [13] KanehisaM.Adatabaseforpost-genomeanalysis.TrendsinGenetics,13(9):375{6,1997. [14] KanehisaM.andGotoS.KEGG:Kyotoencyclopediaofgenesandgenomes.NucleicAcidsRes.,28(1):27{30,Jan2000. 48

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[15] WessG.Howtoescapethebottleneckofmedicinalchemistry.DrugDiscoveryToday,7(10):533{535,May2002. [16] DavidovE.J.,HollandJ.M.,MarpleE.W.,andNaylorS.Advancingdrugdiscoverythroughsystemsbiology.DrugDiscoveryToday,8(4):175{183,Feb2003. [17] BroderS.andVenterJ.C.Sequencingtheentiregenomesoffree-livingorganisms:thefoundationofpharmacologyinthenewmillennium.AnnualReviewofPharmacologyandToxicology,40:97{132,Apr2000. [18] ChandaS.K.andCaldwellJ.S.Fulllingthepromise:drugdiscoveryinthepost-genomicera.DrugDiscoveryToday,8(4):168{174,Feb2003. [19] `ProteomeMining'canzeroinondrugtargets.DukeUniversityMedicalNews,Aug2004. [20] JacksonL.K.andPhillipsM.A.Targetvalidationfordrugdiscoveryinparasiticorganisms.CurrentTopicsinMedicinalChemistry,2(5):425{438,May2002. [21] NuttallM.E.Drugdiscoveryandtargetvalidation.CellsTissuesOrgans,169(3):265{271,2001. [22] SchwardtO.,KolbH.,andErnstB.Drugdiscoverytoday.CurrentTopicsinMedicinalChemistry,3(1):1{9,Jan2003. [23] JeongH.,TomborB.,AlbertR.,OltvaiZ.N.,andBarabasiA.-L.Thelarge-scaleorganizationofmetabolicnetworks.LetterstoNATURE,407:651{654,Oct2000. [24] PapinJ.A.,PriceN.D.,WibackS.J.,FellD.A.,andPalssonB.O.Metabolicpathwaysinthepost-genomeera.TRENDSinBiochemicalSciences,28(5):250{258,May2003. [25] TeichmannS.A.,RisonS.,ThorntonJ.M.,RileyM.,GoughJ.,andChothiaC.TheevolutionandstructuralanatomyofthesmallmoleculemetabolicpathwaysinEscherichiacoli.JMB,311:693{708,2001. [26] MaH.,ZhaoX.,YuanY.,andZengA.P.Decompositionofmetabolicnetworkintofunctionalmodulesbasedontheglobalconnectivitystructureofreactiongraph.Bioinformatics,20(12):1870{1876,2004. [27] AritaM.ThemetabolicworldofEscherichiacoliisnotsmall.PNAS,101(6):1543{1547,Feb2004. [28] HatzimanikatisV.,LiC.,IonitaJ.A.,andBroadbeltL.J.Metabolicnetworks:enzymefunctionandmetabolitestructure.CurrentOpinioninStructuralBiology,14(3):300{306,2004. [29] PearlJ.Probabilisticreasoninginintelligentsystems.MorganKaufmann,SanFrancisco,1988.

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[30] FriedmanN.,LinialM.,NachmanI.,andPe'erD.Usingbayesiannetworkstoanalyzeexpressiondata.JCB,7(3-4):601{20,2000. [31] SomogyiR.andSniegoskiC.A.Modelingthecomplexityofgeneticnetworks:understandingmulti-geneandpleiotropicregulation.Complexity,1:45{63,1996. [32] KaumanS.A.Theoriginsoforder:self-organizationandselectioninevolution.OxfordUniversityPress,NewYork,1993. [33] AkutsuT.,MiyanoS.,andKuharaS.Identicationofgeneticnetworksfromasmallnumberofgeneexpressionpatternsunderthebooleannetworkmodel.PacicSymposiumonBiocomputing,4:17{28,1999. [34] ThieryD.,ColetM.,andThomasR.Formalisationofregulatorynets:alogicalmethodanditsautomatization.Math.ModellingSci.Computing,2:144{151,1993. [35] ThomasR.,ThieryD.,andKaufmaunM.Dynamicalbehaviourofbiologicalregulatorynetworks-I:biologicalroleoffeedbackloopsandpracticaluseoftheconceptoftheloop-characteristicstate.BulletinofMathematicalBiology,57:247{276,1995. [36] Cornish-BowdenA.Fundamentalsofenzymekinetics.PortlandPress,London,1995. [37] VoitE.O.Computationalanalysisofbiochemicalsystems:apracticalguideforbiochemistsandmolecularbiologists.CambridgeUniversityPress,Cambridge,2000. [38] ArkinA.,RossJ.,andMcAdamsH.H.Stochastickineticanalysisofdevelopmentalpathwaybifurcationinphagelambda-infectedEscherichiacolicells.Genetics,149(4):1633{1648,1998. [39] GillespieD.T.Exactstochasticsimulationofcoupledchemicalreactions.J.Phys.Chem.,81:2340{2361,1977. [40] JeongH.,OltvaiZ.N.,andBarabasiA.L.Predictionofproteinessentialitybasedongenomicdata.ComPlexUs,1:19{28,2003. [41] YehI.,HanekampT.,TsokaS.,KarpP.,andAltmanR.B.Computationalanalysisofplasmodiumfalciparummetabolism:organizinggenomicinformationtofacilitatedrugdiscovery.GenomeResearch,14:917{924,2004. [42] Cornish-BowdenA.Whyisuncompetitiveinhibitionsorare?:apossibleexplanation,withimplicationsforthedesignofdrugsandpesticides.FEBSLetters,203(1):3{6,Jul1986. [43] Cornish-BowdenA.andHofmeyrJ.S.Theroleofstoichiometricanalysisinstudiesofmetabolism:anexample.JournalofTheoreticalBiology,216:179{191,May2002. [44] Imotoet.al.Computationalstrategyfordiscoveringdruggablegenenetworksfromgenome-wideRNAexpressionproles.InPSB2006OnlineProceedings,2006.

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[45] ImielinskiM.,BeltaC.,HalaszA.,andRubinH.InvestigatingmetaboliteessentialitythroughgenomescaleanalysisofE.coliproductioncapabilities.Bioinformatics,21(9):2008{16,Jan2005.

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PadmavatiSridharwasbornonDecember6,1981,inChennai,India.SheearnedherB.TechininformationtechnologyfromSriVenkateswaraCollegeofEngineering,aliatedtotheUniversityofMadras,in2003.Aftergraduation,sheworkedasanAssistantSystemsEngineeratTataConsultancyServices,India,forayear.PadmavatijoinedtheComputerandInformationScienceandEngineeringdepartmentattheUniversityofFloridaasagraduatestudentinFall2004.Here,sheworkedintheareaofbioinformaticswithDr.TamerKahveci.SheearnedherMasterofSciencedegreeincomputerengineeringinDecember2006. 52


Permanent Link: http://ufdc.ufl.edu/UFE0017682/00001

Material Information

Title: Algorithms for metabolic network-based drug target identification
Physical Description: Mixed Material
Language: English
Creator: Sridhar, Padmavati ( Dissertant )
Kahveci, Tamer ( Thesis advisor )
Ranka, Sanjay ( Reviewer )
Jermaine, Dr. ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Computer Engineering thesis, M.S
Dissertations, Academic -- UF -- Computer and Information Science and Engineering

Notes

Abstract: Traditional pharmacological drug discovery approaches focused more on the therapeutic effects of drugs than their side-effects. Recent advances in bioinformatics have fostered rational drug development methods that aim to reduce serious side-effects. The first step in this approach is the identification of specific biological drug targets (enzymes or proteins), which can be manipulated to produce the desired effect (of curing a disease) with minimum disruptive side-effects. In this thesis, we study the pharmacological problem of identifying the optimal enzyme-combination (i.e., drug targets) whose inhibition will achieve the required effect of eliminating a given target set of compounds, while incurring minimal side-effects. We propose two approaches to solve the problem. In our first approach, we formulate the problem as an optimization problem on metabolic networks. We define a graph based computational model of the network, that encapsulates the impact of enzymes onto compounds. We propose OPMET, an Optimal enzyme drug target identification algorithm based on Metabolic networks, to solve this problem optimally. It is a branch-and-bound algorithm to explore the search space. We develop a cost model and two enzyme prioritization strategies, Static OPMET and Dynamic OPMET, based on it. Static OPMET prioritizes enzymes according to their impacts, such that the most promising enzymes are inspected first, for possible inclusion in the optimal subset. Dynamic OPMET dynamically updates the priorities as the search space is explored. We also develop two filtering strategies to prune the search space while still guaranteeing an optimal solution. Our experiments on Escherichia Coli (E.Coli) metabolic network show that OPMET can reduce the total search time by several orders of magnitude as compared to the exhaustive search. In our second approach, we develop a heuristic solution to the same problem for metabolic networks with a large number of enzymes. We propose a scalable iterative algorithm which computes a sub-optimal solution within reasonable time-bounds for large metabolic networks. It evaluates immediate precursors of the target compounds and iteratively moves backwards to identify the enzymes whose inhibition will stop the production of the target compounds while incurring minimum side-effects. We show that this algorithm converges to a sub-optimal solution within a finite number of such iterations. Our experiments on the E.Coli metabolic network show that the average accuracy of this method deviates from that of the optimal solution only by 0.02 %. This iterative algorithm is highly scalable. It can solve the problem for the entire metabolic network of E.Coli in less than 10 seconds.
Subject: algorithm, drug, enzyme, identification, metabolic, network, target
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 52 pages.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

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Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0017682:00001

Permanent Link: http://ufdc.ufl.edu/UFE0017682/00001

Material Information

Title: Algorithms for metabolic network-based drug target identification
Physical Description: Mixed Material
Language: English
Creator: Sridhar, Padmavati ( Dissertant )
Kahveci, Tamer ( Thesis advisor )
Ranka, Sanjay ( Reviewer )
Jermaine, Dr. ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Computer Engineering thesis, M.S
Dissertations, Academic -- UF -- Computer and Information Science and Engineering

Notes

Abstract: Traditional pharmacological drug discovery approaches focused more on the therapeutic effects of drugs than their side-effects. Recent advances in bioinformatics have fostered rational drug development methods that aim to reduce serious side-effects. The first step in this approach is the identification of specific biological drug targets (enzymes or proteins), which can be manipulated to produce the desired effect (of curing a disease) with minimum disruptive side-effects. In this thesis, we study the pharmacological problem of identifying the optimal enzyme-combination (i.e., drug targets) whose inhibition will achieve the required effect of eliminating a given target set of compounds, while incurring minimal side-effects. We propose two approaches to solve the problem. In our first approach, we formulate the problem as an optimization problem on metabolic networks. We define a graph based computational model of the network, that encapsulates the impact of enzymes onto compounds. We propose OPMET, an Optimal enzyme drug target identification algorithm based on Metabolic networks, to solve this problem optimally. It is a branch-and-bound algorithm to explore the search space. We develop a cost model and two enzyme prioritization strategies, Static OPMET and Dynamic OPMET, based on it. Static OPMET prioritizes enzymes according to their impacts, such that the most promising enzymes are inspected first, for possible inclusion in the optimal subset. Dynamic OPMET dynamically updates the priorities as the search space is explored. We also develop two filtering strategies to prune the search space while still guaranteeing an optimal solution. Our experiments on Escherichia Coli (E.Coli) metabolic network show that OPMET can reduce the total search time by several orders of magnitude as compared to the exhaustive search. In our second approach, we develop a heuristic solution to the same problem for metabolic networks with a large number of enzymes. We propose a scalable iterative algorithm which computes a sub-optimal solution within reasonable time-bounds for large metabolic networks. It evaluates immediate precursors of the target compounds and iteratively moves backwards to identify the enzymes whose inhibition will stop the production of the target compounds while incurring minimum side-effects. We show that this algorithm converges to a sub-optimal solution within a finite number of such iterations. Our experiments on the E.Coli metabolic network show that the average accuracy of this method deviates from that of the optimal solution only by 0.02 %. This iterative algorithm is highly scalable. It can solve the problem for the entire metabolic network of E.Coli in less than 10 seconds.
Subject: algorithm, drug, enzyme, identification, metabolic, network, target
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 52 pages.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0017682:00001


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ALGORITHMS FOR METABOLIC NETWORK-BASED DRUG TARGET
IDENTIFICATION



















By
PADMAVATI SRIDHAR,


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2006

































Copyright 2006

by
Padmavati Sridhar



































I dedicate this thesis to my parents who have shaped me into who I am 4 -~i.









ACKENOWLED GMENTS

I thank my advisor, Dr. Tamer K~ahveci, for his exceptional guidance during the

course of this research. He has been a constant source of motivation and support to me.

I am grateful for his valuable technical and professional mentoringf. I thank Dr. Ranka,

for his technical guidance during this research. I also thank Dr. Jermaine for his help and

guidance.

I have been blessed with supportive parents who have ahr-l- .- encouraged me in all my

endeavors. They were my first teachers, and they believe that knowledge and education

are the best gifts they can give their children. I am grateful to them for their vision and

for their constant support and encouragement.

My brother, B I1 i 0 is my pillar of support, critic and one of my best friends. His

clarity of thought and new perspectives have ahr-l- .- helped me refine my ideas.

My fiance, Ram, has stood by me in all my decisions and has helped shape my

career. He is my sounding board for ideas and the first person I turn to for guidance. I am

grateful to have him by my side .ll.-- li- ;.

I also thank all my friends and the people who have helped me in times of need.











TABLE OF CONTENTS


page

ACK(NOWLEDGMENTS .......... . .. .. 4

LIST OF TABLES ......... ..... .. 6

LIST OF FIGURES ......... .... .. 7

ABSTRACT ............ .......... .. 8

CHAPTER

1 INTRODUCTION ......... ... .. 10

2 BACKGROUND AND RELATED WORK( .... .. 14

3 PROBLEM MODELING . ..._.. ... 16

4 OPTIMAL ALGORITHM . ..._. ... 18

4.1 State Space and Basic Strategy . ..... .. 18
4.2 OPMET Prioritization Strategies . ..... 20
4.2.1 Static OPMET ......... .. 20
4.2.2 Dynamic OPMET ......... .. 22
4.3 Filtering Strategies ......... . 24
4.3.1 Target Filter ......... .. 25
4.3.2 Non-target Filter ......... ... 26

5 ITERATIVE ALGORITHM ......... .. 28

5.1 Initialization ......... ... .. 28
5.2 Iterative Steps ......... . .. 30
5.3 Maximum Number of Iterations . ...... .. 32

6 EXPERIMENTAL RESULTS ......... ... 36

6.1 Evaluation of OPMET Algorithm . .... 36
6.2 Evaluation of Iterative Algorithm . ..... 39

7 CONCLUSION ......... . .. .. 46

REFERENCES ............. ........... 48

BIOGRAPHICAL SK(ETCH ......... . .. 52









LIST OF TABLES
Table page

5-1 Iterative Steps: lo is the initialization step; II and I2 are the iterations. 15 and
Vc represent the damage values of reactions and compounds respectively computed
at each iteration. 15 = [3, 0, 0] in all iterations. ... .. .. 35

6-1 1\etabolic networks from K(EGG with identifier (Id). C, R and Ed denote the
number of compounds, reactions and edges (interactions) respectively. .. .. 45

6-2 Comparison of average damage values of solutions determined hv the iterative
algorithm versus the optimal algorithm. ...... .. . 45










LIST OF FIGURES

Figure page

3-1 A graph constructed for a metabolic network with three reactions R1, R2, and
R3, three enzymes El, E2, and E3, and nine compounds C1, C9. C1TC16S,
rectangles, and triangles denote compounds, reactions, and enzymes respectively.
Here, C4 (Shown by double circle) is the target compound. Dotted lines indicate
the subgraph removed due to inhibition of an enzyme. (a) Effect of inhibiting
E2. (b) Effect of inhibiting El. ......... ... 17

4-1 The basic OPMET strategy for a hypothetical 4-enzyme network. Enzymes
are ordered as El, E2, E3, E4- nO, n1, n4 are the nodes generated. The initial
I1. Ju~l cut-off threshold D = 10 initializedd to the total number of compounds in
the network). nl is a true solution (shown by double circle) with damage d = 5.
Since d < D, D is updated to 5. nl is saved and the subtree rooted at nl is
pruned. The method backtracks tO n0. n82 n3 arT fRISe nodes generated along
the search with damage d < D. us is a true node with d = 2. As d < D, D
is updated to 2 and the method backtracks to search the unexplored space for
solutions with d < D(indicated by the dashed edge). .. .. .. 27

4-2 Effect of deletion of enzyme El on the weights of reactions and compounds in
the network. .. ... . .. 27

4-3 Dynamic OPMET procedure for enzyme evaluation. .. . .. 27

5-1 (a)A graph constructed for a metabolic network with four reactions R1, R4, three
enzymes E1, E2 and E3, and five compounds C1, Cs. Circles, rectangles, and tri-
angles denote compounds, reactions, and enzymes respectively. Here, C1 (shown by
double circle) is the target compound. (b)Effect of inhibiting E1. Dotted lines indi-
cate the subgraph removed due to inhibition of enzyme E1. ... .. .. 35

6-1 Comparison of OPMET ordering strategies ..... .. . 41

6-2 Comparison of OPMET filtering strategies ..... .... . 42

6-3 Average number of nodes by generated by Dynamic OPMET with combined
filters. ......... ... . 43

6-4 Average optimal node rank by generated by Dynamic OPMET with combined
filters. ......... ... . 43

6-5 Evaluation of iterative algorithm. (a)Average execution time in milliseconds.
(b)Average number of iterations ...... ... .. 44









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

ALGORITHMS FOR METABOLIC NETWORK(-BASED DRITG TARGET
IDENTIFICATION

By

Padnmavati Sridhar

December 2006

C'I .Ir~: Tanter K~ahveci
Major Department: Computer and Information Science and Engineering

Traditional pharmacological drug discovery approaches focused more on the

therapeutic effects of drugs than their side-effects. Recent advances in bioinforniatics

have fostered rational drug development methods that aim to reduce serious side-effects.

The first step in this approach is the identification of specific biological drug targets

(enzymes or proteins), which can he manipulated to produce the desired effect (of curing a

disease) with nxininiun disruptive side-effects.

In this thesis, we study the pharmacological problem of identifying the optimal

enzynte-combination (i.e., drug targets) whose inhibition will achieve the required effect

of eliminating a given target set of compounds, while incurring nxininial side-effects. We

propose two approaches to solve the problem.

In our first approach, we formulate the problem as an optimization problem on

metabolic networks. We define a graph hased computational model of the network, that

encapsulates the impact of enzymes onto compounds. We propose OPM~ET, an Optimal

enzyme drug target identification algorithm hased on Metabolic networks, to solve this

problem optimally. It is a branch-and-hound algorithm to explore the search space.

We develop a cost model and two enzyme prioritization strategies, Static OPMET and

Dynamic OPMET, based on it.










Static OPMET priorities enzymes according to their impacts, such that the most

promising enzymes are inspected first, for possible inclusion in the optimal subset.

Dynamic OPMET dynamically updates the priorities as the search space is explored. We

also develop two filtering strategies to prune the search space while still guaranteeing an

optima~l solution. Our experilments on Eischerichia C/ol ~i(.C/oli) metabolic network show

that OPMET can reduce the total search time by several orders of magnitude as compared

to the exhaustive search.

In our second approach, we develop a heuristic solution to the same problem for

metabolic networks with a large number of enzymes. We propose a scalable iterative

algorithm which computes a sub-optimal solution within reasonable time-bounds for

large metabolic networks. It evaluates immediate precursors of the target compounds

and iteratively moves backwards to identify the enzymes whose inhibition will stop the

production of the target compounds while incurring minimum side-effects. We show

that this algorithm converges to a sub-optimal solution within a finite number of such

iterations. Our experiments on the E. Coli metabolic network show that the average

accuracy of this method deviates from that of the optimal solution only by 0.02 This

iterative algorithm is highly scalable. It can solve the problem for the entire metabolic

network of E. Coli in less than 10 seconds.









CHAPTER 1
INTRODUCTION

Motivation: Traditional drug discovery approaches focus more on the efficacy of

drugs than their toxicity (untoward side effects). Lack of predictive models that account

for the complexity of the inter-relationships between the metabolic processes often leads

to drug development failures [1]. Toxicity and/or lack of efficacy can result, if metabolic

network components other than the intended target are affected. This is well-illustrated

by the example of the recent failure of Tolcap~one (a new drug developed for Parkinson's

disease) due to observed hepatic toxicity in some patients [2]. Post-genomic drug research

focuses more on the identification of specific biological targets (gene products, such as

enzymes or proteins) for drugs, which can he manipulated to produce the desired effect

(of curing a disease) with minimum disruptive side-effects [3, 4]. The main phases in

such a drug development strategy are target identification, validation and lead inhibitor

identification [5].

Enzymes catalyze reactions, which produce metabolites (compounds) in the metabolic

networks of organisms. Enzyme malfunctions can result in the accumulation of certain

compounds which may result in diseases. We term such compounds as TI ,11 I C'om-

pounds and the remaining compounds as Non-TIr,1I I compounds. For instance, the

malfunction of enzyme Ich. ,..;; l le s:.:.0... h t;, Jr~ ..nl.; -. causes buildup of the amino acid,

phenylalanine, resulting in phenylketonuria [6], a disease that causes mental retardation.

Similarly, mutations in the gene that produces glucokinase results in a form of diabetes

called maturity-onset diabetes of the young type 2 (110DY2) [7]. This condition causes

excessive accumulation of glucose in the blood (hyperglycemia), due to the malfunction of

glucokinase. Glucokinase normally phI i- a central role in insulin regulation and hence is

responsible for maintaining the blood glucose level in the body. These examples underline

the importance of identifying the optimal enzyme set which can he manipulated by drugs

to prevent the excess production of target compounds, with minimal side-effects. We term










the side-effects of inhibiting a certain enzyme combination as the IArl,,~ri.: caused to the

metabolic network.

Problem definition: Let R, C, and E denote the set of reactions, compounds, and

enzymes of a metabolic network respectively. Given a large metabolic network and a set

of target compounds, we consider the problem of identifying the set of enzymes whose

inhibition eliminates all the target compounds and inflicts minimum damage on the rest

of the network. Formally, we define the IArl,, .qi: of inhibiting an enzyme as the number

of non-target compounds whose production is stopped by the inhibition of that specific

enzyme. Evaluating all enzyme combinations in order to identify the combination with

minimum damage is not feasible for metabolic networks with a large number of enzymes.

This is because, the number of enzyme combinations, i.e., 2|E| i, inCTreSeS exponentially

with the number of enzymes. Efficient and precise heuristics are needed to tackle this

problem.

We formally state the optimal enzyme combination identification problem as

Given a set of target compounds T (T C C), find the set of enzymes X

(X C E) with minimum damage, whose inhibition stops the production of all

the compounds in T.

Lemke et al. [8, 9] defined the damage of inhibition of an enzyme as the number of

compounds whose production stops after the inhibition of that enzyme. Our definition

of IArl,, rli: is similar to that of Lemke in principle. We differ by excluding the target

compounds from the damage computation. Different enzymes and compounds may

have varying levels of importance in the metabolic network. Our model considers all the

enzymes and compounds to be of equal importance (similar to Lemke's work). We can

extend our model by assigning weights to enzymes and compounds based on their role in

the network. However, we do not discuss these extensions in this thesis.










For simplicity, we also assume that the input compounds to all reactions are present

in the network and that there are no external inputs. Also, we are not incorporating

back-up enzyme activities [10] in our model.

Contribution: In this thesis, we study the pharmacological problem of identifying

the optimal enzyme-combination (i.e., drug targets) whose inhibition will achieve the

required effect of eliminating a given target set of compounds, while incurring minimum

damage. In this section, we formally defined the problem. Further, we develop a graph

based computational model of the metabolic network and propose two methods to solve

the problem, based on this model. We discuss them briefly here.

* Graph-based model: We define a graph based computational model of the
metabolic network that encapsulates the impact of enzymes onto compounds. We
formulate the optimal enzyme combination identification problem as an optimization
problem on this graph. We develop a cost model that takes both the observed and
potential damage (i.e, side-effects) resulting from the inhibition of an enzyme set into
account, for the cost computation.

* Optimal solution: We propose a branch-and-bound algorithm, OPM~ET, an
Optimal enzyme drug target identification algorithm based on Metabolic networks,
to explore the search space and produce an optimal solution. This work is published
as a technical report [11]. We develop two enzyme prioritization strategies, Static
OPM~ET and D include. OPM~ET based on the cost model. Static OPMET priorities
enzymes according to the impact of their inhibition on the production of compounds
in the metabolic network. It inspects the most promising enzymes first, for possible
inclusion in the optimal subset. Dynamic OPMET dynamically updates the priorities
as the search space is explored. We develop two filtering approaches, namely in /* A
filter and non-r4,,l ai Aflter, which are combined with the OP MET to prune the search
space while still guaranteeing an optimal solution. The target filter eliminates a
subspace when it is proven that there is no combination of enzymes in this space
that can stop the production of all the target compounds (i.e., there is no useful drug
target). The non-target filter prunes subspaces where there is no solution with a
damage less than the optimal solution found so far.

* Approximate solution: We develop a scalable iterative algorithm as an approximation
to the optimal enzyme combination detection problem. This work is published in PSB
2007 Online Proceedings [12]. This algorithm is based on the intuition that we can
arrive at a solution close to the optimal one by tracing backward from the target
compounds. It starts by finding the damage incurred due to the removal of each
reaction or compound by evaluating its immediate precursors. It then iteratively










improves the damage by considering the damage computed for the immediate
precursors. It converges when the damage values cannot he improved any further.
We prove that the number of iterations is at most the number of reactions on
the longest path from any enzyme to the target compounds in the underlying
pathway. To the best of our knowledge, this is the first polynomial time solution for a
metabolic-network hased drug target identification problem.

We extracted the metabolic network data of E. Coli fr~om the KEG 13 4]daabs
for our experiments. Our experiments on the E. C'ol mea oi network-- show--- that-'- our- first

method (optimal solution) reduces the total search time by several orders of magnitude

as compared to the exhaustive search, for medium-sized metabolic networks. Dynamic

OPMET prunes 91.6 .of the search space. It generates the optimal enzyme combination

within the exploration 0.005 of the search space on average.

Our. experilments on the Ei. oli metabolic network also show that the average

accuracy of our approximate method iterativee solution) deviates from that of the optimal

solution only by 0.02 .for medium-sized networks. It is also highly scalable. It can solve

the problem for the entire metabolic network of Escherichia Coli in less than 10 seconds.

Thesis organization: The rest of the thesis is organized as follows. C'!s Ilter 2

discusses the background and related work. ('! .pter 3 describes our proposed network

model. ('!s Ilter 4 presents the proposed OPMET algorithm with static and dynamic

prioritization and filtering strategies. ('!s Ilter 5 presents the proposed iterative algorithm

for determining the enzyme combination whose inhibition achieves the desired effect of

inhibiting the production of target compounds. ('! .pter 6 discusses experimental results of

testing our methods on the E. Coli metabolic network. ('! .pter 7 presents the future work

and concludes the thesis.









CHAPTER 2
BACKGROUND AND RELATED WORK(

Classical drug discovery approaches involve incorporating a large number of

hypothetical targets into in-vitro or cell-based .I-- li-- and performing automated high

throughput screening (HTS) of vast chemical compound libraries [5, 15]. Post-genomic

advances in bioinformatics have fostered the development of rational drug-design methods

and reduction of serious side-effects [1, 16-18]. This has engendered the concept of reverse

phrI'I''' ..J.''I ,'1i [4], in which, the first step is TI, i. L .J.;./.I.: el..>,n, the step to identify

protein targets, that may be critical intervention points in a disease process [:3, 19]. This

is followed by TI, i. A validation, the step to demonstrate that an identified drug target is

primarily responsible for the therapeutic activity of a proven drug [20-22]. The third step

is Lead Inhibitor I I. ,./I.:. el..>,n [5]. Since the reverse pharmacological approach is driven by

the mechanics of the disease, it is expected to be more efficient than the classical approach

[4].

Rapid identification of enzyme (or protein) targets needs a thorough understanding of

the underlying metabolic network of the organism affected by a disease. The availability

of fully sequenced genomes has enabled researchers to integrate the available genomic

information to reconstruct and study metabolic networks [2:325]. These studies have

revealed important properties of these networks [26-28]. The vital step in understanding

the relationship between metabolic networks and drug discovery is to develop an accurate

model of the pathway. The accuracy of the model determines how well the candidate

targets reflect the real biological process. A good model also has to be flexible to meet the

possible future updates on the metabolic networks with minimal changes. A number of

models have already been developed, such as graphs,' l.i-o -1 Io networks [29, :30], boolean

networks [:31-3:3], logical networks [:34, :35], differential equations [:36, :37], and stochastic

models [:38, :39]. Finding the right model is a challenging problem. This difficulty is further

increased due to inaccuracies in the network such as missing enzymes or reactions.










The potential of an enzyme to be an effective drug target is considered to be related

to its essentiality in the corresponding metabolic network [40]. Lemke et. al proposed

the measure i .;I,,.- I/****l'9: as an indicator of enzyme essentiality [8, 9]. Recently, a

computational approach for prioritizing potential drug targets for antimalarial drugs has

been developed [41]. A choke-point analysis of P.falciparcum was performed to identify

essential enzymes which are potential drug targets. The possibility of using enzyme

inhibitors as antiparasitic drugs is being investigated through stoichiometric an~ llh--;

of the metabolic networks of parasites [42, 43]. These studies show the effectiveness of

computational techniques in reverse pharmacological approaches.

A combination of micro-array time-course data and gene-knockout data was used

to study the effects of a chemical compound on a gene network [44]. An investigation of

metabolite essentiality is carried out with the help of stoichiometric analysis [45]. These

approaches underline the importance of studying the role of compounds metabolitess)

during the pursuit of computational solutions to pharmacological problems.









CHAPTER 3
PROBLEM MODELING,

In this chapter, we describe our model of the metabolic network. We develop a graph

based model that captures the interactions between reactions, compounds, and enzymes.

Our model is a variation of the boolean network model [31, 32]. Let R, C, and E denote

the set of reactions, compounds, and enzymes respectively. The vertex set consists of all

the members of R U CU E. A vertex is labeled as reaction, compound, or enzyme based

on the entity it refers to. Let VR, VC, and VE denote the set of vertices from R, C, and

E. A directed edge from vertex x to vertex y is then drawn if one of the following three

conditions holds:

1. x represents an enzyme that catalyzes the reaction represented by y.

2. x corresponds to a substrate for the reaction represented by y.

3. x represents a reaction that produces the compound mapped to y7.

Figure 3-1 illustrates a small hypothetical metabolic network. A directed edge from

an enzyme to a reaction implies that the enzyme catalyzes the reaction (i.e., El of Ir l. 0

R1 and E2 CatalyZeS R2 and R3). A directed edge from a compound to a reaction implies

that the compound is a reactant. A directed edge from a reaction to a compound implies

that the compound is a product. In this figure, Cq is the target compound (i.e., the

production of Cq should be stopped). In order to stop the production of Cq, R2 has to be

prevented from taking place. This can be achieved in two v- .--s. One way is by disrupting

one of its catalyzing enzymes (E2 in this case). Another is by stopping the production

of one of its reactant compounds (C2 Or C3 in this case). If we stop the production of

C2, We need to recursively look for the enzyme which is indirectly responsible for its

production (El in this case). Thus, the production of the target compound can be stopped

by manipulating either El or E2-

Figure 3-1(a) shows the disruption of E2 and its effect on the network. Inhibiting E2

resuts n te kockout f cmponds@, s andl C9 in addition to the target compound,













R2R




------Disrupted pathway ---------- Disrupted Pathway
(a) (b)
Figure 3-1. A graph constructed for a metabolic network with three reactions R R2,
and R3, three enzymes El, E2, and E3, and nine compounds C Cg*
Circles, rectangles, and triangles denote compounds, reactions, and enzymes
respectively. Here, Cq (shown by double circle) is the target compound.
Dotted lines indicate the subgraph removed due to inhibition of an enzyme.
(a) Effect of inhibiting E2. (b) Effect of inhibiting El.


C/. Note~ thati the~ productionI of 7 is not stopped since it is produced by R1 even after

the inhibition of E2. We term the effect of disrupting non-target compounds as the side-

effect of manipulating E2. We define the number of non-target compounds knocked out

as the A~rlsa,,rl the manipulation of an enzyme set causes to the metabolic network. In

this case, the damage of inhibiting E2 is 3 (iO., g5 C8 andu C9). Figure: 3-1(b) shows

the inhibition of El and its effect on the same network. In this case, the damage is 2

(i.e., C2 and C5). The important observation is that El and E2 both achieve the effect of

disrupting the target compound, CQ. Hence, El and E2 are both potential drug targets.

However, El is a better drug-target than E2 SillCe 11 CauseS leSSer damage.









CHAPTER 4
OPTIMAL ALGORITHM

The number of possible subsets of enzymes that need to be considered for finding the

optimal drug target is exponential in the number of enzymes. This renders exhaustive

search infeasible beyond small sized metabolic networks. In this chapter, we propose

OPMET, a branch and bound algorithm that considerably reduces the number of possible

combinations to be searched while still guaranteeing to find an optimal solution, for

medium-sized networks (networks with at most 32 enzymes). Section 4.1 describes the

basic branch and bound strategy. As part of any effective branch and bound strategy it is

important to find a good solution quickly. This allows for effective filtering (or pruning) of

subspaces that can be guaranteed not to have better solution that the best found so far.

Our prioritization (Section 4.2) and filtering (Section 4.3) strategies achieve this goal.

4.1 State Space and Basic Strategy

In this section we discuss our modeling of the search space and the basic underlying

strategy of the OPMET algorithm. We develop a systematic and flexible enumeration of

the search space and use it to build our efficient search strategy to find optimal results.

Let E = {Ei| Vi, 1 < i < m} denote the set of enzymes for a metabolic network. The

search space is modeled as a tree structure. Every node of this tree corresponds to a state

in the search space and it is represented by a 4-tuple ([e,,, e,,, exm], k, d, remove).

Here, xtl, xm, is a permutation of 1, 2, m. The first parameter corresponds to the

state of all the enzymes (i.e., ex, corresponds to enzyme Ei). ex, = 1 if Ei is inhibited.

Otherwise, ex, = 0. The parameter k indicates that the first k enzymes are considered at

that search state. The decision to inhibit or not inhibit has been fixed for enzymes from 1

to k 1 and we now set e,, = 1 and ex, = 0, Vi, k < i < m. The damage incurred due

to inhibited enzymes at that state is represented by d. The final parameter, remove, is a

boolean variable. It takes value True if the inhibited enzymes stop the production of all

the target compounds. Otherwise, it is set to False. We call a node with remove = True

as a true node, and a node with remove = False as a false node. Figure 4-1 shows part of










the search tree for a hypothetical 4-enzyme network. The tuple for node nl indicates that

enzyme El is inhibited and it is a true node with damage d = 5. k = 1 since the decision

to inhibit or not has been fixed only for one enzyme.

OP MET algorithm: We start with the root node ([0, 0, 0], 0, 0, False)

indicating that all enzymes are present in the network. As the search space is traversed,

we keep the true node with the minimum damage found so far as the current true solution

and store the associated damage value as D, the 11g l..1.l cut-off threshold. D is initialized

to the number of compounds in the network. At any point, we have an active set of nodes

A, stored in a stack structure. A contains the nodes currently being considered. Let node

NV = ([exr, exrr,, -- exm]~, k, d, remove) be the node on top of this stack (i.e., the node to

be evaluated). There are three cases:

* Case 1: N has damage d > D. In this case we prune the subtree rooted at NV. We
then backtrack.

* Case 2: NV is a true node with damage d < D. In this case, we save NV as the current
true solution and update D with the damage value of NV. We then backtrack.

* Case 8: NV is a false node with damage d < D. In this case, we insert NV in the active
set A for backtracking purposes. We then create a new node M~ by setting exey, = 1
in NV (i.e., we inhibit the enzyme E,, ). The resulting node is M~ ([e,,, ex,,,
exm], k + 1, d', remove'). The node M~ is evaluated in the next step similarly.

Backtrackingf involves following steps. First we pick the top node from the active

nodes stack A. Let NV = ([e,,, e,,, exm], k, d, remove) denote this node. We then

set e,,, = 0 (indicating the node we are backtracking from) and e,,,, = 1 in NV (i.e.,

we inhibit the enzyme e,, ). The resulting node becomes the node to be evaluated in

the next step. The first two cases above stop expanding the tree at the current node.

The former one implies that the current node is a possible solution (node nl in Figure

4-1). The latter one implies that the current node incurs too much damage to lead to a

possible solution. The third case happens when the current node does not stop production

of all the target compounds, but the damage is lower than the damage of the current best










solution (nodeS n2 and n3 in Figure 4-1). Such nodes may produce a possible solution

(node n4 in FiguTO 4-1) With the inhibition of more enzymes. Thus, they need to be

explored further to ensure that we find an optimal solution. The search terminates when

there are no more nodes to explore. At this stage, the current true solution is the optimal

solution.

4.2 OPMET Prioritization Strategies

In this section we present our cost model as the basis for enzyme evaluation and

our resulting enzyme prioritization strategies. The purpose of ordering enzymes by a

priority measure is to test the combinations with a high likelihood of deleting the target

compounds first. We develop the following two enzyme prioritization strategies which are

described in more detail in the rest of the section:

* Static OPMET: We pre-order the enzymes according to a priority measure and
apply the OPMET algorithm.

* Dynamic OPMET: We dynamically select the next enzyme to inhibit based on the
partial solution.

4.2.1 Static OPMET

The simplest way to order the enzymes is to sort them in ascending order of damage.

However, this is inaccurate for several reasons. First, since damage is defined in terms

of non target compounds, it does not reflect the impact of an enzyme on the target

compounds. Second, the inhibition of an enzyme can make a compound more vulnerable

even if the compound is not removed entirely. For example, in Figure 3-1, the production

of C7 is not stopped after the inhibition of El or E2 individually. However, C7 is removed

if El is inhibited as well as E2. Thus, damage values of individual enzymes are not good

indicators of the combined damage of these enzymes.

Cost Model: We develop a cost model as the basis for enzyme ordering in OPMET.

This cost model takes both the observed and potential damage (side-effects) resulting from

the inhibition of an enzyme set into the cost computation. For each enzyme Ei E E, we










compute a weight W(Ei) as W(Ei) = 0 if Ei inhibited and W(Ei) = 1 otherwise. We

assign rational weights (fractions between 0 and 1) to the reaction and compound nodes

and the edges. Intuitively, the weight of a node or edge denotes the rate at which that

node or edge appears in the network. We then use these weights to compute the cost of

EG. The weight of each node depends on the weights of the incoming edges and the type of

the node (i.e., reaction or compound):

* Cost Rule 1: Let Rj be a reaction node. Let I, 1 < i < k, denote the weights of
the incoming edges to Rj. We compute the weight of Rj as W(Rj) min ,{te' }.
This computation is intuitive since a reaction takes place only if all the inputs are
present .

* Cost Rule 2: Let Cj be a compound node. Let I, 1 < i < k, denote the weights
of the incomin~g edges to Cy. W/ie compute the wevigh~t of C, a~s W(C,) (Ef ,{ This weight evaluates to zero (i.e., Cj disappears from the system) only if all the
reactions that produce it stops.

We define the weight of an edge as the weight of the node for which it is the outgoing

edge.

In order to compute the cost of Ei, we set the weight of Ei to zero (i.e., W(Ei) = 0).

The weights of all the reaction and compound nodes are assigned progressively by a

breadth-first search, according to the above scheme. The weights of all the nodes and

edges which can be reached from Ei are recomputed to reflect the change. The effect of

deleting El is shown in Figure 4-2. We define an impact vector for each enzyme based on

the effects of its inhibition.
Definition 1. Given a network with a compounds, Cy .Lt (C)dnt h

weight of the node corresponding to Cj after the inhibition of t.'.c;,I,, Ei. We I. I;,..: the

impact vector of Ei as I(Ei) =[Wi(Cz), Wi(C2>l '; i(Cn)]. We term Wi(Cj) as theC

impact of Ei on Cj, Vj. M

The impact vector of an enzyme approximates the amount of each compound

that remains after the inhibition of that enzyme. Every entry of the impact vector is

a fractional number between 0 and 1, where 0 indicates that the corresponding compound










does not exist after inhibition of the corresponding enzyme. We define the cost of an

enzyme as follows:

Definition 2. Given a network with a compounds, Cj, 1 < j < n. Assume that the

compounds Cj, Vj, 1 < j < k < n constitute the set of Iary,ll compounds. Assume that

the remaining compounds @,l Vj, k 1 < j < n constitute the non-f ore,li compounds. Let

I(Ei) = [Wi(C1), Wi(C,)] denote the impact vector of Ei. We I. I;,:: the cost of Ei as

cost(E,)= I(E,) V',: where: V =[vi1, :, v,] is the normalization victor: t=" o
1 < i < k. and I = -(n'\ -k) for k <( i

Each target compound contributes a positive value and each non-target compound

contributes a negative value to the cost of an enzyme. This is justified since the cost

promotes removal of target compounds and demotes the removal of non-target compounds.

The magnitude of the contribution of a compound increases linearly with the amount of

that compound that diminishes from the system after the inhibition of the corresponding

enzyme .

In order to benefit from the pruning power of OPMET cases 1 and 2 (see Section 4.1),

we need to compute the permutation xxl, xm carefully. The earlier we place the

enzymes in the optimal solution in this permutation, the better, as OPMET reaches the

optimal solution earlier under such an ordering. Thus, reaching the solution with the

smallest possible damage value (i.e., the optimal solution) increases the chances of pruning

the remaining nodes of the search tree. We propose to sort the enzymes in ascending order

of cost value. This is because a small cost value indicates that the corresponding enzyme

has a large impact on target compounds and low impact on non-target compounds.

4.2.2 Dynamic OPMET

Static OPMET priorities enzymes based on their individual potential to be part

of the solution. However, this model does not account for the combined damage of a set

of enzymes. Finding the damage of a set of enzymes is non-trivial. This is because the

combined damage depends on the overlap of the reactions catalyzed by these enzymes as










well as their individual damages. Enzymes that catalyze almost the same set of reactions

have less combined damage compared to enzymes that catalyze disjoint reaction sets.

This is due to the overlap of the damage of the enzymes in the former case. We develop a

dynamic strategy, Dynamic OPMET. It sorts the enzymes on the fly. At a high level, this

strategy evaluates the current state at every step and picks the enzyme-to-inhibit for the

next step based on this evaluation.

We propose an incremental algorithm by using the impact vector of individual

enzymes. We predict the remaining fraction of all the compounds after inhibition of each

enzyme with the help of its impact vector. This algorithm is described in Figure 4-3.

Let R = [rl, r2, ru] denote the remaining fractions of compounds (step 1). Here,

ri E [0, 1] corresponds to compound Ci, Vi. We initialize ri = 1, Vi indicating that all

compounds are being produced without any disruption. Let V be the normalization vector

as given in Definition 2. Let I(Ei) be the impact vector of enzyme Ei (see Definition 1).

At every step of the Dynamic OPMET algorithm, let NV = ([e,,, e,,, exm]~, k, d,

remove) be the node currently being evaluated (i.e., the decision to inhibit or not inhibit

has been fixed for e,,, e,,, ex,_z) (step 2). We now need to decide which enzyme has

to be evaluated next. In Step 3a, for every enzyme in the remaining enzyme set (e,,, Vi,

k < i < m), we compute the new remaining fractions of compounds (Ri). This is done by

a Vector Direct Product of R and the impact vector of Ei (I(Ei)). Vector direct product

is defined as X e Y = [xlyl, x292, n~yn Where X = [xl, x,] and Y = [yl,

y,]. The resulting vector Ri is an approximation to the impact of inhibition of the

enzyme Ei in addition to already inhibited enzymes. This is justified since the quantity

of a compound eliminated by a combination including Ei will be at least as much as the

quantity eliminated by Ei alone. A good candidate enzyme at this step is the one that

ensures that lesser of the target compounds remain after its inhibition. Also, it should

ensure that the non target compounds suffer the minimum possible damage. Our cost

model satisfies these requirements. In Step 3b, we compute the cost of each enzyme as









the dot product of Ri and V. In step 4, we pick the enzyme (Ej) with the minimum cost.

Thus, this strategy chooses the the next best enzyme to inhibit dynamically.

The cost of finding the best enzyme at each step takes O(mn), where m and a denote

the number of enzymes and compounds in the metabolic network respectively. This is

because a vector product costs O(u), and O(m) such products are carried out.

4.3 Filtering Strategies

So far, we have described how OPMET traverses the state space. In this section we

propose two filtering strategies to eliminate large portions of the search space quickly while

still guaranteeing the optimal solution. The following theorem establishes a relationship

between the impact of enzymes and their damage.

Theorem 1. Let E = {El, E2, Er } be a set of ;..oto Let Cj be a compound in the
metabolic network, rk. Le d4(C ) 1 < i < r, denote the impctofEsonCy If the inhibition

of all the ,:..ater. in E stops the production of Cj, then CE (1 d,(C,)) '> 1. M

Proof of Theorem 1: Let E = {El, E2, Er } be a set of enzymes. Let Cj be a

compound in the metabolic network. Let di, 1 < i < r, denote the impact of Ei on Cj. Let

di(Rk), 1 < i < r, denote the impact of Ei on Rk. We need to show that the following
rules hold:

Rule 1: If the inhibition of all the enzymes in E stops the production of Cj, then

C=1(1 d,(C,)) > 1.

Rule 2: If the inhibition of all the enzymes in E stops a reaction Rk, then CE (1 -

d (~> > 1.

We first consider the case when a reaction RkIS iS topped and prove that Rule 2 holds,

given that Rule 1 is correct.

Case 1: 3 E E E such that Ej catalyzes Rk. Hence, the inhibition of Ej stops Rk*

The impact of Ej on Rk, is 1 dj Rk) = 1. Therefore, CE (1 di(Rk)) > .

Rule 2 holds.










Case 2: o enzym E eE catalyzes Rkc. This implies that E removes Ci,whcisa

input to Rk. From Rule 1, C~(1 d (Ci)) > 1. From the Cost Model (see Cost Rule 1

in Section 4.2), di(Rk) min di(Cl' k / kis the set of all input compounds of Rk. Thus,
1 4(R) =maX 1 di k)}I. Hence,
2=1( -iR~ d4R 1 d

Rule 2 holds.

We now consider the case when-- the- p-roduction of ,,, a opud ysos n rv

that Rule 1 holds, given that Rule 2 is correct. If E removes Cj, it means that all the

reactions that produce Cj have been stopped. Let R1, R2, Rt be the reactions that

produce Cj. For each reaction Rk, 1 < k < t, one of the the following two cases has to be

true.

Case 1: 3 E E E such that Ej catalyzes Rk. Hence, the inhibition of Ej stops Rk.

The impact of Ej on Rk, is 1 dj Rk) = 1. Fr-om the Cost Model (see Cost Rule 2 in

Section 4.2), 1 dy (Cj) > ,. Since all the t input reactions of Cj have been stopped,

pr (1 d4C ))> 1xt > 1

Rule 1 holds.

Case 2: No enzyme E E E directly catalyzes Rk. But since RkIS iS topped by the

inhibition of enzymes in E, C~(1 d (Rk)) > 1 (Rule 2). Also given that t reactions

produce Cj,
(1~~ d1(Ci) = 1





Rule 1 holds.

Next, we describe our filtering strategies.

4.3.1 Target Filter

As we traverse the state space considerable effort is spent evaluating combinations

which might yield a solution with damage value less than D, the global cut-off threshold










(see Section 4.1). If a combination does not delete the target compound set, the effort

spent is wasted. Filtering such combinations will improve the performance of the search

vastly. This is the motivation behind our T o9. I flter.

The target filter eliminates a bulk of the search space when it is proven that there

is no combination of enzymes in this space that can stop the production of all the target

compounds (i.e., there is no useful drug target). This filtering strategy is based on

Theorem 1. Formally, let node NV = ([e,,, e,,, exm]~, k, d, False) be a node in the

search space. Let T denote the set of target compounds. Backtrack if



i=1 i=k+1

In this inequality, the first term indicates the impact of enzymes, which are currently

part of the solution set, on the target compounds. The second term represents the impact

of the remaining enzymes on the target compounds.

4.3.2 Non-target Filter

The motivation behind this filtering strategy is to quickly determine if there is any

solution in the subtree with a damage d < D, the global cut-off threshold (see Section 4.1).

This filter utilizes Theorem 1 similar to the Target Filter. The idea is as follows. At a

given node NV, for each target compound, C, we find the minimum number of enzymes, m

such that


i= 1
This gives us the minimum number of enzymes needed to delete C. Let mmax be the

maximum value of m for any target compound (i.e, we will need at least mmax enzymes to

delete the entire target compound set). Now, we sort the remaining enzymes (enzymes not

considered so far) in the ascending order of their damage values. Let dmax be the damage

of the enzyme at index mmax. If dmax in addition to the damage incurred so far is greater

than D, we prune the sub tree rooted at NV.











n "o[()())() (). () False]
E-1 Ep()


n 2[()100, 2, 1, False]
E -1


na ~[(11() 3, 2, Truel


Figure 4-1.


























Figure 4-2.




1. Let N
2. Let R
*/


The basic OPMET strategy for a hypothetical 4-enzyme network. Enzymes
are ordered as El, E2, E3, E4- no0 n1 4 are the nodes generated. The
initial 11l. .l..rl cut-off threshold D = 10 initializedd to the total number of
compounds in the network). nl is a true solution (shown by double circle)
with damage d = 5. Since d < D, D is updated to 5. nl is saved and the
subtree rooted at nl is pruned. The method backtracks tO n0. n2, n3 arT fRISe
nodes generated along the search with damage d < D. us is a true node with
d = 2. As d < D, D is updated to 2 and the method backtracks to search the
unexplored space for solutions with d < D(indicated by the dashed edge).


/E1


Disrupted Pathway


Effect of deletion of enzyme El on the weights of reactions and compounds in
the network.



= ([e, r, eX25,.. e 67m], k, d, remove) be the node currently being evaluated.
=[rT, rg, r,] /* ri E [0, 1] corresponds to the remaining fraction of compound C,, Vi


3. For every candidate enzyme ei E {e' ex ,-- ,em
(a) Ri R 0I(E,) /* Compute new ratio */
(b) Cost(E,) Ri VT /* Cost of inhibiting E, */
4. Let j = arg min {~Cost(E3)}
5. R = Rj /* Update the ratio after inhibition of the enzyme with least cost */
6. Select E, as the next enzyme to inhibit.



Figure 4-3. Dynamic OPMET procedure for enzyme evaluation.









CHAPTER 5
ITERATIVE ALGORITHM

In this chapter, we develop a scalable iterative algorithm that finds a sub-optimal

solution to the enzyme-target identification problem quickly. Our algorithm is based

on the intuition that we can arrive at a solution close to the optimal one, by tracing

backwards from the target compounds. We evaluate the immediate precursors of the

target compounds and iteratively move backwards to identify the enzymes, whose

inhibition will stop the production of the target compounds while incurring minimum

damage. Our algorithm consists of an initialization step followed by iterations, until some

convergence criteria is satisfied. Let E, R and C denote the sets of enzymes, reactions and

compounds of the metabolic network respectively. Let |E|, |R| and |C| denote the number

of enzymes, reactions and compounds respectively. The primary data structures are three

vectors, namely an it .;;;;;.- vector VE = 61l, 62, *, 6|E|], a reaction vector VR = [rl, T2,

S, rlR ], and a compound vector Vc = [cl, c2, C|C|]. Each value, ei, in VE denotes

the damage of inhibition of enzyme, Ei E E. Each value, ri, in VR denotes the damage

incurred by stopping the reaction Ri E R. Each value, ci, in Vc denotes the damage

incurred by stopping the production of the compound Ci e C.

5.1 Initialization

Here, we describe the initialization of vectors VE, VR, and Vc. We initialize VE firSt,

VR second, and Vc last.

Fr.:.;,l,,.- vector: The damage ei, Vi, 1 < i < |E|, is computed as the number of

non-target compounds whose productions stop after inhibiting Ei. We find the number of

such compounds by doing a breadth-first traversal of the metabolic network starting from

Ei. We calculate the damage ei associated with every enzyme Ei E E, Vi, 1 < i < |E|, and

store it at position i in the enzyme vector VE.

Reaction vector: The damage rj is computed as the minimum of the damages of

the enzymes that catalyze Rj, Vj, 1 < j < |R|. In other words, let E,,, E,,, Ex,

be the enzymes that catalyze Rj. We compute the damage of rj as rj = min {e,,).









This computation is intuitive since a reaction can be disrupted by inhibiting any of its

catalyzers. We calculate rj associated with every reaction Rj E R, Vj, 1 < j < |R| and

store it at position j in the reaction vector VR. Let E(Rj) denote the set of enzymes that

produced the damage rj. Along with rj, we also store E(Rj). Note that in our model, we

do not consider back-up enzyme activities for simplicity.

Coemp~ound vector: The damage ck, Vk, 1 < k < |C|, is computed by considering the
re~actionls that produce: Ck. Let R,,, R,,, Rxj be the^ rea^ctions thatC produce. ^ C We

first compute a set of enzymes E(Ck~) foT CIk aS E(Ck~) = E(R,,) U E(R,,) U U E(R,,).

We then compute the damage value ck aS the number of non-target compounds that is

deleted after ~lthe inibitionI~U of aIllthe enz~ymles in1 E(\Ck). This~ compIutation is based on

the observation that a compound disappears from the system only if all the reactions that

produce it stop. We calculate Ck aSSociated with every compound Ck, E C, 1 < k < |C| and

store it at position k in the compound vector Vc. Along with ck, We alSO Store E(Ck~)*

Consider the network in Figure 5-1. Column Io in Table 5-1 shows the initialization of

the vectors for this network. In this figure, C1 is the target compound (i.e., the production

of Ci should be stopped). In order to stop its production, we have to prevent R1 from

taking place. This can be accomplished in two v--i~.- (1) By disrupting one of its

catalyzing enzymes (El in this case). Figure 5-1(b) shows the effects of disrupting El.

The damage el of El is three, as inhibiting El stops the production of three non-target

compounds C2, C3 and C4. (2) By stopping the production of one of its reactant

compounds (Cg in this case). To stop the production of Cg, we need to recursively

look for the enzyme combination which is indirectly responsible for its production (E2

and E3). Since the disruption of E2 or E3 alone does not stop the production of any

non-target compound, their damage values are zero. Hence, VE = [3, 0, 0]. The damage

values for reactions are computed as the minimum of their catalyzers (rl = T2 = 61

and T3 = 4 = 62). Hence, VR = [3, 3, 0, 0]. The damage values for compounds are

computed from the reactions that produce them. For instance, R1 and R2 produce C2-










E(R1) = E(R2) = {El}. Therefore, c2 = 61. However, the combined damage of E2 and

E3 IS 1. Hence, cs is equal to the damage of inhibiting the set E(R3) U E(R4) = {E2, E3)

which is 1. Thus, cs = 1. Thus, the production of the target compound can be stopped

by manipulating either El or a combination of E2 and E3. The optimal solution is the

enzyme combination whose disruption has the minimum damage on the network (E2 and

E3 in this case).

5.2 Iterative Steps

We iteratively refine the damage values in vectors VR and Vc in a number of steps. At

each iteration, the values are updated by considering the damage of the precursor of the

precursors. Thus, at nth iteration, the precursors from which a reaction or a compound is

reachable on a path of length up to n are considered. We define the length of a path on

the graph constructed for a metabolic network as the number of reactions on that path

(see Definition 4). There is no need to update VE Since the enzymes are not affected by

the reactions or the compounds. Next, we describe the actions taken to update VR and Vc

at each iteration. We later discuss the stopping criteria for the iterations.

Reaction vector: Let C,, C,,, C,, be the compounds that are input to Rj. We

update the damage of rj as rj = min~rj, min z,(cmi))

The first term of the min function denotes the damage value calculated for Rj during

the previous iteration. The second term provides the damage of the input compound with

the minimum damage found in the previous iteration.

This computation is intuitive since a reaction can be disrupted by stopping the

production of any of its input compounds. The damage of all the input compounds

are already computed in the previous iteration ( wi (n 1)th iteration). Therefore, at

iteration n, the second term of the min function considers the impact of the reactions and

compounds that are away from Rj by n edges in the graph for the metabolic network. Let

E(Rj) denote the set that contains the enzymes that produced the new damage rj. Along

with rj, we also store E(Rj). We update all rj E VR using the same strategy. Note that










the values rj can be updated in any order, i.e., the result does not depend on the order in

which they are updated.

Compound vector: The damage ck, Vk, 1 < k < |C|, is updated by considering the

damage computed for Ck, in the previous iteration and the damages of the reactions that

produce Ck~. Let R,,, R,,, Rx, be the reactions that produce Ck~. We first compute a

set of enzymes as E(R,,) U E(R,,) U U E(R,,). Here, E(R,,), 1 < t < j, is the set of

enzymes computed for Rt after the reaction vector is updated in the current iteration. We

then update the damage value ck aS Ck, = min Ck, damage(UL=, E(Rxei))}.

The first term here denotes the damage value computed for Ck, in the previous

iteration. The second term shows the damage computed for all the precursor reactions in

the current step. Along with ck, We alSO Store E(Ck~), the set of enzymes which provides

the current minimum damage ck.

Condition for convergence: At each iteration, each value in VR and Vc either

remains the same or decreases by an integer amount. This is because a min function is

applied to update each value as the minimum of the current value and a function of its

precursors. Therefore, the values of VR and Vc do not increase. Furthermore, a damage

value is ahr-l-w an integer since it denotes the number of deleted non-target compounds.

We stop our iterative refinement steps when the vectors VR and Vc do not change in two

consecutive iterations. This is justified, because, if these two vectors remain the same after

an iteration, it implies that the damage values in VR and Vc cannot be minimized any

more using our refinement strategy.

Columns II and I2 in Table 5-1 show the iterative steps to update the values of the

vectors VR and Vc. In lo, we compute the damage rl for R1 as the minimum of its current

damage (three) and the damage of its precursor compound, cg = 1. Hence, rl is updated

to 1 and its associated enzyme set is changed to {E2, E3}. The other values in VR remain

the same. When we compute the values for Vc, cl is updated to 1, as its new associated

enzyme set is {E2, E3} and the damage of inhibiting both E2 and E3 together is 1. Hence,










VR = [1, 3, 0, 0] and Vc = [1, 3, 3, 3, 1]. In I2, We find that the values in VR and Vc do

not change anymore. Hence, we stop our iterative refinement and report the enzyme

combination E2, E3 aS the iterative solution for stopping the production of the target

compound, C1.

Complexity analysis: We now discuss the complexity of our iterative algorithm.

Space Complexity: The number of elements in the reaction and compound vectors

is (|R| + |C|). For each element, we store an associated set of enzymes. Hence, the space

complexity is O((|R| + |C|)~ I E|).

Time Complexity: The number of iterations of the algorithm is O(|R|) (see

Section 5.3). The computational time per iteration is O(G (|R| + |C|)), where G is

the size of the graph. Hence, the time complexity is O(|R|G o (|R| + |C|)).

5.3 Maximum Number of Iterations

In this section, we present a theoretical analysis of our proposed algorithm. We show

that the number of iterations for the method to converge is finite. This is because the

number of iterations is dependent on the length of the longest non-self-intersecting path

(see Definitions below) from any enzyme to a reaction or compound.

Definition 3. In a given metabolic network, a non-self-intersecting path is a path which

traces i t.;, vertex: on the path ~rer. A once.

For simplicity, we will use the term path instead of non-self-intersecting path in the

rest of this section.

Definition 4. In a given metabolic network, the length of a path from an .;..an;.- Ei to a

reaction Rj or compound Ck, iS I. I;,:. .1 aS the number of unique reactions on that path.

Note that the reaction Rj is counted as one of the unique reactions on the path from

enzyme Ei to Rj.

Definition 5. In a given metabolic network, the preceding path of a reaction Rj (or a

compound Ok~ iS I. I;,:.. G S the l6Rgth Of the l089681 path fTOm it,:;; ,:.;;i,,o in that network

to Rj (or Ck~).










Theorem 2. Let VE = 61,i 621 .. I 6E| VR = [li, T21 .. I r FR|], and Vc = [cl, c2; '

C|C|] be the e..u;,I, reaction and compound vectors ,n Ic.~. :.l; ; Let a be the length of
the longest path (see D. ~i,!~n il4i and 8) frmJ .; .co;-Est eato R o

compound Ck ). The Ualue Ty (OT Ck TemtinS CONStatR af1Te at most n ifTertOnS.
Proof: We prove this theorem by an induction on the number of reactions on the

longest path (see Definitions 4 and 3) from any enzyme in Ei corresponding to ei a VE tO

Gk -

BASIS: The basis is the case when the longest path from an enzyme Ei is of length

1 (i.e., the path consists of exactly one reaction). Let Rj be such a reaction. This implies

that there is no other reaction on a path from any Ei to Rj. As a result, the value

rj remains constant after initialization. Let Ck, be a compound such that there is at

mos8~Ult: one~U recion fro anly enzl~ymel to G~. Let R,,, R,,, Rx, be the reactions

that produce Ck~. Because of our assumption there is no precursor reaction to any of

these reactions. Otherwise, the length of the longest path would be greater than one.

Therefore, the values r,,, r,,, rx, and the sets E(R,,), E(R,,), E(R,,) do

not change after initialization. The value Ck is computed as the damage of E(Ck~)

E(R,,) U E(R,,) U U E(R,,). Thus, Ck remains unchanged after initialization and the

algorithm terminates after the first iteration.

INDUCTIVE STEP: Assume that the theorem is true for reactions and compounds that

have a preceding path with at most n 1 reactions. Now, we will prove the theorem for

reactions and compounds that have a preceding path with a reactions. Assume that Rj

and Ck, denote such a reaction and a compound. We will prove the theorem for each one

separately.

Proof for Rj: Let C,,, Ox,, Ox, be the compounds that are input to Rj. The

preceding path length of each of these input compounds, wi Cx, is at most n. Otherwise,

the preceding path length of Rj would be greater than n.










C'rse 1: If the preceding path length of C,, is less than n, by our induction

hypothesis, c~s would remain constant after (n 1)th iteration. Thus, the input compound

C~s will not change the value of rj after oth iteration.

C'rse 2: If the preceding path length of C,, is n, then Rj is one of the reactions

on this path. In other words, C~s and Rj are on a cycle of length n. Otherwise, the

preceding path length of Rj would be greater than n. Recall that at each iteration, the

algorithm considers a new reaction or a compound on the preceding path starting front

the closest one. Thus, at oth iteration of computation of rj, the algorithm completes the

cycle and considers Rj. This however will not modify rj. This is because the value of rj

monotonically decreases (or remains the same) at each iteration. Thus, the initial damage

value computed front Rj is guaranteed to be no better than r y after n 1 iterations. We

conclude that rj will remain unchanged after oth iteration.

Proof for Ok~: Let R,,, R,,, R,j he the reactions that produce Ok~. The preceding

path length of each of these reactions, ;?i R,, is at most n. Otherwise, the preceding path

length of Ok, would be greater than n.

C'rse 1: If the preceding path length of R,s is less than n, by our induction

hypothesis r,, would remain constant after (n 1)th iteration. Thus, the reaction

R,s will not change the value of ck after oth iteration.

Case 2: If the preceding path length of R,s is n, then front our earlier discussion for

proof of Rj, r,, remains unchanged after oth iteration. Therefore R,, will not change the

value of Ck after oth iteration. Hence, by induction, we show that the Theorem 2 holds.



































Figure 5-1. (a)A graph constructed for a metabolic network with four reactions R R4,
three enzymes E1, E2 and E3, and five compounds C1, Cs. Circles, rectangles,
and triangles denote compounds, reactions, and enzymes respectively. Here, C1
(shown by double circle) is the target compound. (b)Effect of inhibiting E1. Dotted
lines indicate the subgraph removed due to inhibition of enzyme E1.




















Table 5-1. Iterative Steps: lo is the initialization step, II and I2 are the iterations. VR
and Vc represent the damage values of reactions and compounds respectively
computed at each iteration. VE = [3, 0, 0] in all iterations.

Io II I2

VR, VC [3, 3, 0, 0], [3, 3, 3, 3, 1] [1, 3, 0, 0], [1, 3, 3, 3, 1] [1, 3, 0, 0], [1, 3, 3, 3, 1]


C5

,,
E1~I R2

C4

()


i\ -I R3
R1
,IL I\
Cz,



\Cq)

(b)









CHAPTER 6
EXPERIMENTAL RESULTS

We extracted the metabolic network information of Escherichia Coli (E. Coli) from

K(EGG [13, 14] (f tp ://f tp .genome .j p/pub/kegg/pathways/eco/) The metabolic

network in K(EGG has been hierarchically classified into smaller networks according

to their functionality. We performed experiments at different levels of hierarchy of the

metabolic network and on the entire metabolic network, that is an .I_ regfation of all the

functional subnetworks. We devised a uniform labeling scheme for the networks based

on the number of enzymes. According to this scheme, a network label begins with 'N'

and is followed by the number of enzymes in the network. For instance, 'N20' indicates

a network with 20 enzymes. Table 6-1 shows the metabolic networks chosen, along with

their identifiers and the number of compounds (C), reactions (R) and edges (Ed). The

edges represent the interactions in the network.

For each network, we constructed query sets of sizes one, two and four target

compounds, by randomly choosing compounds from that network. Each query set contains

10 queries each. We ran our experiments on an Intel Pentium 4 processor with 2.8 GHz

clock speed and 1-GB main memory running Linux operating system.

6.1 Evaluation of OPMET Algorithm

We evaluate the performance of our first solution, the OPMET algorithm, for

medium-sized networks(at most 32 enzymes) using the following three criteria:

1. Number of nodes generated: It represents the total number of enzyme combinations
tested to complete the search. The lesser the number of nodes generated, the better
the performance of the method.

2. Optimal node rank: This indicates the number of nodes explored before the
method arrives at the optimal solution. A small optimal node rank indicates that the
optimal combination is found quickly.

3. Execution time: This indicates the total time taken by the method to finish the
search and conclude that it found an optimal solution.










We intpleniented the OPMET algorithm with a random enzyme ordering, Static

OPMET and Dynamic OPMET (see Section 4.2) as well as Non-target filter and Target

filter (see Section 4.3). We compare the methods we intpleniented to an exhaustive search

which enunterates and tests all possible combinations of enzymes (2': where n is the

number of enzymes).

Evaluation of prioritization strategies: We compare our static and dynamic

OPMET algorithms with a random ordering of enzymes and an exhaustive search. We do

not include our filtering strategies here as the goal is to focus on the enzyme ordering. We

present the results only up to a network of size 20 enzymes. This is because, beyond this,

the search space grows rapidly, necessitating the use of filtering strategies.

Table 6-1 shows the average number of nodes generated and the average optimal

node rank of the random ordering, static OPMET and dynamic OPMET, as compared

to an exhaustive search. The results show that Dynamic OPMET is the best strategy

for all the tested networks. It generates the least number of nodes in all the experiments.

All the methods generate significantly large number of nodes for N17. This is because

the number of reactions and compounds of this network is much larger than the other

networks, resulting in more interactions in the network (see Table 6-1). Both Dynamic

and Static OPMET have small Optimal Node Ranks. Dynamic OPMET has the lowest

optimal node rank on an average. On an average, it arrives at the optimal solution within

the generation of 0.008 .of the number of nodes possible in an exhaustive search. This is

significantly better than the random ordering which arrives at the optimal solution within

the generation of 11 The difference between the Optimal Node Ranks and the number

of nodes generated for Static and Dynamic OPMET shows that they find optimal results

quickly but still evaluate many nodes to ensure that that result is optimal.

We use Dynamic OPMET in the rest of the experiments as it has the best performance.










Evaluation of filtering strategies: We measure how much our filtering strategies

reduce the search space. The experiments are performed for Dynamic OPMET without

filters, with Target Filter, Non-target Filter and both of these filters together.

Figure 6-2(a) shows the average number of nodes generated. The combined filters

show the best pruning. On an average, the combined filters prune 91.5 of the nodes

generated in the method without filters. We also see that most of this benefit is obtained

front the Target Filter (it filters 91.4 .~ of the nodes generated by the method without

filters). The combined filter generates only 12700 nodes for N24 (0.004 .~ of an exhaustive

search).

Figure 6-2(b) shows the average execution time. We see that the average execution

time shows a trend similar to Figure 6-2(a). This establishes that the execution time is

proportional to the number of nodes generated. The combined filter reduces the execution

time by an order of magnitude as compared to the method without filters on an average.

Figure 6-2(c) shows the average optimal node rank. All the methods have the same

optimal node rank for networks except N24. This el__o-1-;- that Dynamic OPMET yielded

the optimal solution as early as possible for these networks. For N24, the combined

filter shows that filteringf strategies can also lead to advancement in findings the optimal

solution. For N24, Target filter arrives at the optimal solution 99 .earlier and the

combined filters arrive at the optimal solution 99.9 .earlier than the method without

filters (the additional 0.9 .~ intprovenient is obtained front the non-target filter).

We observe that the target filter is more efficient than the non-target filter and the

combined filter has the best performance. We use Dynamic OPMET with combined filters

in the rest of the experiments.

Scalability in the number of targets: We evaluate how Dynamic OPMET with

combined filter scales with increasing target set size. The target sets compared are of sizes

one, two and four.










Figure 6-3 shows the average number of nodes generated. There is no clear correlation

between the target set size and the number of nodes explored. The network topology

determines how the target set size affects the number of nodes generated. The target

compound set can contain highly correlated compounds (deleted by the inhibition of

almost the same set of enzymes) or unrelated compounds (located in different parts

of the network). If the target set consists of correlated compounds, an increase in the

target set size decreases the average number of nodes generated. This can he seen for

N14, N17, N20 and N24 (from 2 to 4 target compound queries). The number of nodes

generated for the two-target sets is 62 .lesser than single target sets on an average. For

the four-target sets, this value is 75 lesser. On the other hand, if the target set consists

of unrelated compounds, an increase in the target set size increases the average number

of nodes generated. The average number of nodes increases by 1.2 times when we go from

single target to two-target sets and by 2.2 times when we go from the two-target to the

four-target sets.

Figure 6-4 shows that the average optimal node rank increases sub linearly with the

number of target compounds. On an average, The two-target queries arrive at the optimal

solution after generation of 1.8 times more nodes than the single target queries. Similarly,

the four-target queries generate 3.8 times more nodes than the single target queries before

arriving at the optimal solution. This -II__- -R that as the target set size increases, the

number of enzyme combinations that need to be tested before we find the optimal solution

mecreases.

6.2 Evaluation of Iterative Algorithm

We evaluate our proposed iterative algorithm using the following three criteria:

1. Execution time: The total time (in milliseconds) taken by the method to finish
execution and report if a feasible solution is identified or not.

2. Number of iterations: The number of iterations performed hv the method to
arrive at a steady-state solution.










:3. Average damage: The average number of non-target compounds that are
eliminated when the enzymes in the result set are inhibited.

We intpleniented the proposed iterative algorithm and an exhaustive search algorithm

which determines the optimal enzyme combination to eliminate the given set of target

compounds with nxininiun damage. We intpleniented the algorithms in Java.

Evaluation of accuracy: Table 6-2 shows the comparison of the average damage

values of the solutions computed by the iterative algorithm versus the optimal algorithm.

We have shown the results only upto N:32, as the optimal algorithm took longer than one

dei to finish for networks slightly largest than N:32. We can see that the damage values of

our method exactly match the damage values of the optimal algorithm for all the networks

except NV24. For NV24, the average damage of the iterative solution differs front that of

the optimal solution by only 0.02-' This shows that the iterative algorithm is a good

approximation of the optimal algorithm. The slight deviation in damage is the tradeoff for

achieving the salability of the iterative algorithm (described next).

Evaluation of scalability: Figure 6-5(a) plots the average execution time of our

iterative method for increasing sizes of metabolic networks. The running time increases

slowly with the network size. As the number of enzymes increases front 8 to 5:37, the

running time increases front roughly 1 to 10 seconds. The largest network, N15:37, consists

of 5:37 enzymes, and hence, an exhaustive evaluation inspects 2537 1 combinations (which

is computationally infeasible). Thus, our results show that the iterative method scales well

for networks of increasing sizes. This property makes our method an important tool for

identifying the right enzyme combination for eliminating target compounds, especially for

those networks for which an exhaustive search is not feasible.

Figure 6-5(b) shows a plot of the average number of iterations for increasing sizes of

metabolic networks. The iterative method reaches a steady state within 10 iterations in all

cases. The various parameters (see Table 6-1) that influence the number of iterations are

the number of enzymes, compounds, reactions and especially the number of interactions in












10000000

S1000000

S100000









N14 N17 N20
Pathway identifier

MExhaustive Search M Random Order 0 Static Priority n Dynamic Priority

(a) Average number of nodes generated

1000000

100000











N14 N117 N20
Pathway Identifier

M Random Order a Static Priority 0 Dynamic Priority

(b) Average execution time in milliseconds


Figure 6-1. Comparison of OPMET ordering strategies



the network (represented by edges in the network graph). Larger number of interactions

increase the number of iterations considerably, as can be seen for networks NV22, NV48,


NV96, N\1537, where the number of iterations is greater than 5. This shows that, in addition

to the number of enzymes, the number of compounds and reactions in the network and

their interactions also pIli wa significant role in determining the number of iterations. Our

results show that the iterative algorithm can reliably reach a steady state and terminate,

for networks as large as the entire metabolic network of E. Coli.
















10000000





110 000



100


N14 N17 N20 N24 N28 N32
Pathway Identifer

HNoFilter HNon-TargetFilter OTargetFilter BCombinedFilters

(a) Average number of nodes generated


N14 N17 N20 N24 N28 N
Pathway Identifier

aNoFilter a Non-TargetFilter 0 Targetfilter a CombinedFilters

(b) Average execution time in milliseconds


(c) Average optimal node rank


Figure 6-2. Comparison of OPlMET filteringf strategies






































Figure 6-3. Average number of nodes by generated by Dynamic OPMET with combined
filters.


100000

10000

S1000

o 100

10iii I


N14 N17 N20 N24 N28 N32
Pathway identifier

1-Target M2-Target 04-Target


Figure 6-4. Average optimal
filters.


node rank by generated by Dynamic OPMET with combined























10000


e, 1000


S100-


10-


1


10



S7
6
S5
4
e,3
S2





Pathway Identifier


zzzzzz00


zzzzzzzzzzzi

Pathway Identifier


(b)


Figure 6-5. Evaluation of iterative algorithm. (a)Average execution time in milliseconds.
(b)Average number of iterations


















Table 6-1. 1\etabolic networks from K(EGG with identifier (Id). C, R and Ed denote the
number of compounds, reactions and edges (interactions) respectively.

Id Metabolic Network C R Ed Id Metabolic Network C R Ed
NON Polvketide 11 11 33 N42 Other amnito acid 69 63 208
biosynthesis
N13 Xenobiotics 47 58 187 N48 Lipid 134 196 654
biodegradation
N14 C'itrate or TC'A cycle 21 35 125 N52 Purille 67 128 404
N17 Galactose 38 50 172 N59 Energy 72 8'> '68
N20 Pentose phosphate 26: 37 120 N71 Nucleotide 10'> '17 684
N22 Glveall Biosynthesis 54 51 171 N96 Vitalitils and 145 175 550
Cofactors
N24 Glveerolipid 32 49 160 N170 Amnito acid 54 378 1210
N28 Op .1, serille 36 46 151 N180 Carbohydrate 247 501 1650
and threonine
N32 Pyrrivate 21 51 163 N537 Entire Network 988 1700 5833


Table 6-2. Comparison of average damage values of solutions determined by the iterative
algorithm versus the optimal algorithm.









CHAPTER 7
CONCLUSION

Efficient computational methods are required to identify the optimal enzynte-combination

(i.e., drug targets) whose inhibition will achieve the required effect of eliminating a given

target set of compounds while incurring nxininial side-effects. In this thesis, we proposed

two solutions to this pharmacological problem. In our first work, we proposed an optimal

solution for niedium-sized metabolic networks. In our second work, we proposed an

approximate solution for a large sized metabolic network.

In the optimal method, we formulated the optimal enzynte-combination identification

problem as an optimization problem on metabolic networks. We defined a graph hased

computational model of the network that encapsulates the impact of enzymes onto

compounds. We proposed OPMET, a branch-and-hound algorithm to explore the search

space. We developed a cost model and two enzyme prioritization strategies, Static

OPMET and Dynamic OPMET based on it. We also developed two filtering strategies to

prune the search space while still guaranteeing an optimal solution. The filters compute

an upper bound to the number of target compounds deleted and a lower bound to the

side-effect respectively.

Our experiments on the E. C'oli metabolic network show that our optimal methods

reduced the total search time by several orders of magnitude as compared to the

exhaustive search. The optimal solution is reached by Dynamic OPMET within the

exploration of 0.005 of the total search space on an average, proving that our methods

are effective in approximating the impact of an enzyme on a compound. The Dynamic

OPMET with combined filters pruned 91.6 of the search space on average.

In our second method, we developed an approximate solution to the optimal

enzynte-combination identification problem for large-sized metabolic networks, for which

an optimal solution is not feasible. We proposed a scalable iterative algorithm which

computes a sub-optinmal solution to this problem within reasonable tinte-bounds. Our

algorithm is based on the intuition that we can arrive at a solution close to the optimal










one by tracing backward front the target compounds. We evaluated the ininediate

precursors of a target compound and iteratively moved backwards, to identify the

enzymes, whose inhibition stopped the production of the target compound while incurring

nmininiun damage. We showed that this approximate method converges within a finite

number of such iterations. In our experiments on E. C'oli metabolic network, the accuracy

of a solution computed by the iterative algorithm deviated front that of the optimal

solution only by 0.02 Our iterative algorithm is highly scalable. It solved the problem

for even the entire metabolic network of E. C'oli (which has at least 500 enzymes) in less

than 10 seconds.

In this thesis, we have developed a foundation for developing effective solutions to

pharmacological problems, through an~ ll-h- of metabolic networks. We are currently

working to improve the accuracy of our network and cost models in modeling the

metabolic network's behavior. We are also developing methods which will efficiently

provide solutions to the same problem for larger metabolic networks.









REFERENCES


[1] Capranico G. A rational selection of drug targets needs deeper insights into general
regulation mechanisms. Current M~edicinal C'I, I,,.i ry Anti-Cancer Agents,
4(5):393-394, Sep 2004.

[2] Deane K(.H.O., Spieker S., and Clarke C.E. Catechol-O-methyltransferase inhibitors
versus active comparators for levodopa-induced complications in Parkinson's disease.
Cochrane Database of S;,ich ol..: Reviews, 4, 2004.

[3] Smith C. Hitting the target. Nature, 422:341-347, Mar 2003.

[4] Takenaka T. Classical vs reverse pharmacology in drug discovery. BJU International,
88(2):7-10, Sep 2001.

[5] Drews J. Drug discovery: a historical perspective. Science, 287(5460):1960-1964, Mar
2000.

[6] Surtees R. and Blau N. The neurochemistry of phenylketonuria. European Journal of
Pediatrics, 159:109-13, 2000.

[7] Gloyn A.L. Glucokinase (GCK() mutations in hyper- and hypoglycemia:
maturity-onset diabetes of the young, permanent neonatal diabetes, and
hyperinsulinemia of infancy. Human M~utation, 22(5):353-62, Nov 2003.

[8] Mombach J.C., Lemke N., da Silva N.M., Ferreira R.A., Isaia E., and Barcellos C.K(.
Bioinformatics analysis of mycoplasma metabolism: important enzymes, metabolic
similarities, and redundancy. Computers in B..~~I J.m;, and M~edicine, 36(5):542-52, May
2006.

[9] Lemke N., Heriidia F., Barcellos C.K(., dos Reis A. N., and Mombach C.M.
Essentiality and damage in metabolic networks. Bioinformatics, 20(1):115-119,
Jan 2004.

[10] Ocampo et. al. Targeted deletion of mNth1 reveals a novel DNA repair enzyme
activity. M~ol Cell Biol., 22(17):6111-21, Sep 2002.

[11] Sridhar P., K~ahveci T., and Ranka S. OPMET: A metabolic network-based algorithm
for optimal drug target identification. Technical report, CISE Department, University
of Florida, Sep 2006.

[12] Sridhar P., K~ahveci T., and Ranka S. An iterative algorithm for metabolic
network-based drug target identification. PSB 2007 Online Proceedings, 2007.

[13] K~anehisa M. A database for post-genome analysis. Trends in Genetics, 13(9):375-6,
1997.

[14] K~anehisa M. and Goto S. K(EGG: K~yoto encyclopedia of genes and genomes. Nucleic
Acids Res., 28(1):27-30, Jan 2000.










[15] Wess G. How to escape the bottleneck of medicinal chemistry. Drug Discovery T c.rt;,
7(10):533-535, May 2002.

[16] Davidov E.J., Holland J.M., Marple E.W., and Naylor S. Advancing drug discovery
through systems biology. Drug Discovery T ../.r ;, 8(4):175-183, Feb 2003.

[17] Broder S. and Venter J.C. Sequencing the entire genomes of free-living organisms: the
foundation of pharmacology in the new millennium. Annual Review of Ph,~r ,Ient..J..~~I,i
and TI.:...J..it ~;, 40:97-132, Apr 2000.

[18] CI.! .1.01 S.K(. and Caldwell J.S. Fulfilling the promise: drug discovery in the
post-genomic era. Drug Discovery T ../r ;, 8(4):168-174, Feb 2003.

[19] 'Proteome Mining' can zero in on drug targets. Duke University Medical News, Aug
2004.

[20] Jackson L.K(. and Phillips M.A. Target validation for drug discovery in parasitic
organisms. Current Top~ics in M~edicinal Clo, ne,.n;, 2(5):425-438, if li- 2002.

[21] Nuttall M.E. Drug discovery and target validation. Cells Tissues Ollr ga
169(3):265-271, 2001.

[22] Schwardt O., K~olb H., and Ernst B. Drug discovery today-. Current Top~ics in
Medicinal Clo, I,,.iry, 3(1):1-9, Jan 2003.

[23] Jeong H., Tombor B., Albert R., Oltvai Z. N., and Barabasi A.-L. The large-scale
organization of metabolic networks. Letters to NATURE, 407:651-654, Oct 2000.

[24] Papin J.A., Price N.D., Wiback S.J., Fell D.A., and Palsson B.O. Metabolic pathi- .1-<
in the post-genome era. TRENDS in Biochemical Sciences, 28(5):250-258, if li- 2003.

[25] Teichmann S.A., Rison S., Thornton J.M., Riley M., Gough J., and Chothia C.
The evolution and structural .Ilr Irhow: of the small molecule metabolic pathi- .1-< in
Escherichia coli. JM~B, 311:693-708, 2001.

[26] Ma H., Zhao X., Yuan Y., and Zeng A.P. Decomposition of metabolic network into
functional modules based on the global connectivity structure of reaction graph.
Bioinformatics, 20(12):1870-1876, 2004.

[27] Arita M. The metabolic world of Escherichia coli is not small. PNAS,
101(6):1543-1547, Feb 2004.

[28] Hatzimanikatis V., Li C., lonita J.A., and Broadbelt L.J. Metabolic networks:
enzyme function and metabolite structure. Current Op~inion in Structural B:. J.- ~it
14(3):300-306, 2004.

[29] Pearl J. Probabilistic reasoning in intelligent st;,/. rt,- Morgan K~aufmann, San
Francisco, 1988.










[30] Friedman N., Linial M., Nachman I., and Pe'er D. Using 'l. li ,o ~ networks to analyze
expression data. JOB, 7(3-4):601-20, 2000.

[31] Somogyi R. and Sniegoski C.A. Modeling the complexity of genetic networks:
understanding multi-gene and pleiotropic regulation. Consp~~il. ;, 1:45-63, 1996.

[32] K~auffman S.A. The origins of order: self-organization and selection in evolution.
Oxford University Press, New York, 1993.

[33] Akutsu T., Miyano S., and K~uhara S. Identification of genetic networks from a
small number of gene expression patterns under the boolean network model. Pi .
Symp~osium on B*'**** uL,,;.:( 4:17-28, 1999.

[34] Thieffry D., Colet M., and Thomas R. Formalisation of regulatory nets: a logical
method and its automatization. M~ath. M~odelling Sci. Comp~uting, 2:144-151, 1993.

[35] Thomas R., Thieffry D., and K~aufmaun M. Dynamical behaviour of biological
regulatory networks-I: biological role of feedback loops and practical use of the
concept of the loop-characteristic state. Bulletin of M~athematical B..~~I J..;,i 57:247-276,
1995.

[36] Cornish-Bowden A. Fundamentals of .;..one.- kinetics. Portland Press, London, 1995.

[37] Voit E.O. Comp~utational r,:..;&;-.: of biochemical s;,;lent- a practical guide for
biochemists and molecular biologists. Cambridge University Press, Cambridge, 2000.

[38] Arkin A., Ross J., and McAdams H.H. Stochastic kinetic analysis of developmental
pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics,
149(4):1633-1648, 1998.

[39] Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys.
C'I,; I; 81:2340-2361, 1977.

[40] Jeong H., Oltvai Z.N., and Barabasi A.L. Prediction of protein essentiality based on
genomic data. ComPlex;Us, 1:19-28, 2003.

[41] Yeh I., Hanekamp T., Tsoka S., K~arp P., and Altman R.B. Computational analysis of
plasmodium falciparum metabolism: organizing genomic information to facilitate drug
discovery. Genome Research, 14:917-924, 2004.

[42] Cornish-Bowden A. Why is uncompetitive inhibition so rare?: a possible explanation,
with implications for the design of drugs and pesticides. FEBS Letters, 203(1):3-6,
Jul 1986.

[43] Cornish-Bowden A. and Hofmeyr J. S. The role of stoichiometric analysis in studies
of metabolism: an example. Journal of Theoretical B..~~I J..;,i 216:179-191, May 2002.

[44] Imoto et. al. Computational strategy for discovering dr-i_ 110~ gene networks from
genome-wide RNA expression profiles. In PSB .'thb:r Online Proceedings, 2006.










[45] Imielinski 1\., Belta C., Halasz A., and Rubin H. Investigating metabolite essentiality
through genome scale analysis of E. coli production capabilities. Bioinformatics,
21(9):2008-16, Jan 2005.









BIOGRAPHICAL SKETCH

Padmavati Sridhar was born on December 6, 1981, in ('11. H!!Isi India. She earned her

B.Tech in information technology from Sri Venkateswara College of Engineering, affiliated

to the University of 1\adras, in 2003. After graduation, she worked as an Assistant

Systems Engineer at Tata Consultancy Services, India, for a year.

Padmavati joined the Computer and Information Science and Engineering department

at the University of Florida as a graduate student in Fall 2004. Here, she worked in the

area of bioinformatics with Dr. Tamer K~ahveci. She earned her 1\aster of Science degree

in computer engineering in December 2006.