ANovelApproachtoEvaluatetheProductionKineticsofExt

ANovelApproachtoEvaluatetheProductionKineticsofExtracellularPolymericSubstances(EPS)byActivatedSludgeUsingWeightedNonlinearLeast-SquaresAnalysisBING-JIENI,†RAYMONDJ.ZENG,‡FANGFANG,†JUANXU,†GUO-PINGSHENG,†ANDHAN-QINGYU*,†DepartmentofChemistry,UniversityofScienceandTechnologyofChina,Hefei,230026,China,andAdvancedWaterManagementCentre,TheUniversityofQueensland,St.Lucia,QLD4072,AustraliaReceivedJanuary14,2009.RevisedmanuscriptreceivedMarch30,2009.AcceptedApril2,2009.Thispaperdevelopsanovelandconvenientapproachforevaluationofproductionkineticsofextracellularpolymericsubstances(EPS)byactivatedsludge.Inthisapproach,theweightedleast-squaresanalysisisemployedtocalculateapproximatedifferencesinEPSconcentrationbetweenmodelpredictionsanddata.AniterativesearchroutineintheMonteCarlomethodisutilizedforoptimizationoftheobjectivefunctionbyminimizingthesumofsquaredweightederrors.ApplicationoftheapproachinthisworkshowsthatthefractionofsubstrateelectronsdivertedtoEPSformation(kEPS)is0.23gCODEPSg-1CODSwithabacterialmaximumgrowthrateof0.32h-1.Theobtainedparametersarefoundtobereasonableastheyaregenerallybounded.ThevalidityofthisapproachisconfirmedbyboththeindependentEPSproductiontestsandtheEPSdatareportedinliterature.ItalsocorrectstheoverestimationofcellularproductionandidentifiesthatkEPSisthekeyparameterinEPSproductionkinetics.Furthermore,thisapproachcouldestimatethekineticparametersaccuratelyusingfewdatasetsorevenoneset,whichbecomesveryattractivefortheprocesseswheredataarecostlytoobtain.IntroductionExtracellularpolymericsubstances(EPS)comefromthenaturalsecretionsofmicroorganismswhichrefertoarichmatrixofbiopolymers,suchaspolysaccharides,proteins,nucleicacids,andothers(1,2).Theyplayanimportantroleintheaggregationofmicrobialcells,theformationofanactivegel-likestructurethatmaintainscellcohesion,gov-erningthemicrobialphysiology,stabilizationofsludgestructure,andprotectionofmicrobesagainstnoxiousenvironmentalconditions(3-5).ItisalsofoundthatEPSareimportantsinksforelectronsandcarbonderivedfromtheoriginalsubstrate(6,7).ThediversionofelectronsandcarbonforEPSproductioncouldotherwisebeinvestedinthecellyieldandthegrowthrate(5,6).IgnoringEPSformationcouldleadtoanoverestimationoftruecellulargrowthrates,whichshouldhavesignificantimplicationsontheperformanceofactivatedsludgesystems.Therefore,theformationkineticsofEPSinbiologicalwastewatertreatmentprocessesshouldbeexplored.SeveralapproacheshavebeenusedtomodelEPSproductionkinetics.KreftandWimpenny(8)developedamodelofbiofilminwhichtheEPSproductionwasdescribedbyagrowthratedependentandanindependentterm.LaspidouandRittmann(5,6)formulatedamodelthatEPSproductionwasproportionaltothesubstrateutilizationrate.Thebiochemicalreactionsinthesemodelsareexpressedusingnonlinearequations,resultingincomplexityoftheirmodelsanddifficultyinestimatingkineticparametersforEPSproduction.Theevaluationofmicrobialandenzymaticreactionratesrequiresrepresentativeratedataandaneffectivemethodforfittingrateequationstotheexperimentaldata.TheintegratedMonod-basedequationisfoundtobeusefulforevaluationofkineticparametersthroughprogresscurvesfromafewbatchexperimentsorevenonebatchexperiment(9).Weightednonlinearleast-squaresanalysisisanapproachthatcanbeusedtominimizedifferencesbetweenexperi-mentaldataandmodelpredictionswhenitisnecessarytouseanimplicitexpressioninthemodel(9).Ontheotherhand,theMonteCarlosimulationisapracticalwayofimitatingtheinherentrandomnessinbiologicalsystemsusingdeterministicmodels(10-15).Thissimulationtechniquehasbeenusedforthedesignandupgradeofwastewatertreatmentplants,aswellasgeneratingdifferentwastewatercompositionsforposteriorprocessperformanceevaluation.Italsohasawideapplicationinhydrologicalmodelingfield(16).Thispaperaimstodevelopanovelandconvenientapproachfordeterminingthebest-fitvaluesforkineticcoefficientsofEPSproductionbyactivatedsludgeandtheirpracticalidentifiabilityusingacombinationofweightedleast-squaresanalysisandMonteCarlomethod.Thenexperimentalandliteraturedataareusedtovalidatethisapproach.Finally,thecomparisonbetweenthisnovelapproachandothersisperformedtoobtainbetterunderstandingofEPSproductionkineticsoverall.Tothebestofourknowledge,thismightbethefirstattempttoevaluatetheEPSproductionkineticsbyactivatedsludgeusingtheweightednonlinearleast-squaresandtheMonteCarlomethod.MaterialsandMethodsMonod-BasedKineticsforEPSProduction.AMonod-basedkineticsforEPSformationbyactivatedsludgeisevaluatedinthiswork(detailsaregivenintheSupportingInformation(SI)).TherateofEPSformationisproportionaltotherateofsubstrateutilization(5),andthekineticequationisexpressedasfollows:dXEPSdt)kEPSµHYHSSKS+SSXH(1)whereXHistheactivebacteria(mgCODL-1),XEPSistheproducedEPS(mgCODL-1),SSistherate-limitingexternalsubstrate(mgCODL-1),tistime(h),kEPSistheEPSformationcoefficient(gCODEPSg-1CODS),µHisthemaximumspecificgrowthrateofactivebiomass(h-1),YHistheyieldforactivecellsynthesis(gCODXg-1CODS),andKSisthehalf-maximum-rateconcentrationforSS(gCODSm-3).*Correspondingauthorfax:[phone];e-mail:[e-mail].†UniversityofScienceandTechnologyofChina.‡TheUn