Delft University of Technology
Current state and challenges for dynamic metabolic modeling
Vasilakou, Eleni; Machado, Daniel; Theorell, Axel; Rocha, Isabel; Nöh, Katharina; Oldiges, Marco; Wahl, S. Aljoscha DOI 10.1016/j.mib.2016.07.008 Publication date 2016 Document Version Final published version Published in
Current Opinion in Microbiology
Citation (APA)
Vasilakou, E., Machado, D., Theorell, A., Rocha, I., Nöh, K., Oldiges, M., & Wahl, S. A. (2016). Current state and challenges for dynamic metabolic modeling. Current Opinion in Microbiology, 33, 97-104.
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Current
state
and
challenges
for
dynamic
metabolic
modeling
Eleni
Vasilakou
1,
Daniel
Machado
2,
Axel
Theorell
3,
Isabel
Rocha
2,4,
Katharina
No¨h
3,
Marco
Oldiges
3,5and
S
Aljoscha
Wahl
1Whilethestoichiometryofmetabolismisprobablythebest
studiedcellularlevel,thedynamicsinmetabolismcanstillnot
bewelldescribed,predictedand,thus,engineered.Unknowns
inthemetabolicfluxbehaviorarisefromkineticinteractions,
especiallyallostericcontrolmechanisms.Whilethe
stoichiometryofenzymesispreservedinvitro,theiractivityand
kineticbehaviordiffersfromtheinvivosituation.Nexttothis
challenge,itisinfeasibletotesttheinteractionofeachenzyme
witheachintracellularmetaboliteinvitroexhaustively.Asa
consequence,thewholeinteractingmetabolomehastobe
studiedinvivotoidentifytherelevantenzymesproperties.In
thisreviewwediscusscurrentapproachesforinvivo
perturbationexperiments,thatis,stimulusresponse
experimentsusingdifferentsetupsandquantitativeanalytical
approaches,includingdynamiccarbontracing.Nextto
reliableandinformativedata,advancedmodeling
approachesandcomputationaltoolsarerequiredtoidentify
kineticmechanismsandtheirparameters.
Addresses
1DepartmentofBiotechnology,DelftUniversityofTechnology,vander
Maasweg9,2629HZDelft,TheNetherlands
2
InstituteforBiotechnologyandBioengineering,UniversityofMinho, Braga,Portugal
3InstituteofBio-andGeosciences,IBG-1:Biotechnology,
ForschungszentrumJu¨lich,52425Ju¨lich,Germany
4
SilicoLife,Braga,Portugal
5
InstituteofBiotechnology,RWTHAachenUniversity,WorringerWeg1, D-52056Aachen,Germany
Correspondingauthor:Wahl,SAljoscha(s.a.wahl@tudelft.nl)
CurrentOpinioninMicrobiology2016,33:97–104
ThisreviewcomesfromathemedissueonMicrobialsystems biology
EditedbyRalfTakorsandVictordeLorenzo ForacompleteoverviewseetheIssueandtheEditorial
Availableonline26thJuly2016
http://dx.doi.org/10.1016/j.mib.2016.07.008
1369-5274/#2016ElsevierLtd.Allrightsreserved.
Introduction
Modelingofmicrobialsystemshastwomajoraims:(1)to provideasystemicunderstandingofcellularbehaviorand (2)toguidethedesignofmicrobialhost,tooptimize,for
example,theproductionofchemicals.Metabolicnetwork analysis has guided the genetic engineering of cells, leadingtosignificantlyimprovedproductionhosts[1,2]. Especially,steady-stateanalysishasdeliveredinsightsto metabolicfluxesinmanydifferentmicroorganisms[3]. This includes the discovery of unknown pathways and activities including unusualroutes in carbohydrate me-tabolisminpathogenichosts[4],aminoaciddegradation pathways[5]oruncommon shuntsincyanobacteria[6]. However, most current models fail to predict cellular operation [7].The metabolic flux not only depends on theenzymeconcentration,butavarietyofcellular func-tions and mechanisms, like transcription, translation, post-translational modifications and allosteric control. Foreachlevel,techniqueshavebeendevelopedto mon-itor changesin vivo,but the integration of data and its interpretation remain highly challenging. Experimental datasetsformodelingareoftenderivedfromwell-defined andcontrolledenvironmentalconditions,whereascellsin production processesare faced with sub-optimal condi-tions, for example, limited oxygen, switching substrate availability or product inhibition. Such environmental factors are one source leading to a limited accuracy of modelpredictionsfordynamicprocess conditions. Without doubt, metabolism is thebest studied cellular level. For mostcommon hosts like Escherichiacoli, Sac-charomyces cerevisiae,Bacillus subtilis,Corynebacterium glu-tamicum and many more, the metabolic network stoichiometry is arguably completely described [8,9]. Unknownsinmetabolicactivityarisefromkinetic inter-actions, especiallyallosteric control mechanisms.While the stoichiometry of enzymes is preserved in vitro, its activity and behavior differs from the in vivo situation [10]. As a consequence, the whole interacting metabo-lomehastobestudiedtoidentifytheenzymatic proper-ties invivo [11].Experiments andmodeling of enzyme kinetic networks have been pioneered by Reuss et al. [12,13] using stimulus–response experiments (SRE). While crucial newinsights have been generated, these approaches only partly succeeded to identify enzyme mechanisms(structural)or kinetic(quantitative) param-eters[7].
Therearedifferentaspectsthatleadtonon-identifiability (i.e.,theinabilityofthedatatosufficientlydeterminethe
model’s structure and its quantitative parameters): (1) Carbon effluxesfromcentral carbonmetabolism cannot be quantified with sufficient accuracy during the short term of the experiment. (2) Parallel reaction rates and reaction cycles cannot be distinguished. (3) Parameter estimationqualityremains low becauseof high correla-tions of the model parameter and limited regulatory information content of intracellular concentration mea-surements[14].
The review focuses on approachesto overcomenamed challenges, especially approaches that (1) increase the informationcontent byaddition of isotopic tracers, like
13
C,(2)combinatorialapproachesthatallowforinference ofdifferentenzymekineticmechanisms,(3)novel devel-opmentsin parameterestimation.
Coupling
experimental
observations
with
modeling
approaches
Identificationof invivokineticmechanismsis challeng-ingasthesystemcanonlybeperturbedbyextracellular stimuli and/or genetic modifications (Figure 1). The experiments have therefore to be designed with the modelingandtherequiredmodelresolutionandaccuracy inmind.Inparticular,theexperimentaldatamustshow precisequantitativepropertiestodistinguishbetweenthe differenthypotheses anddeliversufficientaccuracyand coveragefortheparameteridentification.Thesecriteria,
comingfromthestudyaimandthemodelingapproach, definethemeasurementsandapproachesneeded,thatis, to decide whether additional, quantitative metabolite measurementsneedto bedevelopedor complementary observables,likecarbon labeling[15],arerequired.
Experimental
approaches
The aim to reach predictive kinetic models requires sufficient informative experimental data for parameter identification. In this context, the term ‘informative’ means accurate, robust and quantitative data gathered for relevant conditions. Commonly, metabolic flux is observed under steady-state conditions, while dynamic fluxestimationismorechallenginginseveral experimen-tal and computational aspects. The aim of this review article is not a complete description of all variants of experimental approaches, but to emphasize how they contributetotheconstructionofkineticmetabolic mod-els.Alltheseexperimentalapproacheshaveincommon thatthey must beconducted underwell-controlled, re-producibleconditions.
Toidentifykineticparametersfromsteady-state experi-ments,theanalysisofaseriesofdifferentsteady-statesis required[16–18].Anobviouschallengeinsuchaseriesof experimentsistokeepthecellularpropertiescomparable. To this end, continuous cultivation in chemostat with differentdilution rateshasbeenemployed.
98 Microbialsystemsbiology
Figure1 • Extracellular Perturbations • Genetic Perturbations Experimental Approach Modeling Approach Biological Question Parameters Identification • Mechanistic Kinetics • Approximative Kinetics • Piecewise Affine Functions • Ensemble Modeling • Cybernetic Approach Biological Insights Literature Advanced Constraints Advanced Optimization Sampling Extraction Quenching Analytical Techniques 13C Labeling
Current Opinion in Microbiology
Modelingandtheexperimentalapproacharedeterminedbythebiologicalquestion,thatis,theapproachesneedtobefine-tunedtoidentifythe relevantparameters.Thebiologicalsystemneedstobeperturbedbymodificationofthemetabolicnetwork(usinggeneticmodifications)and/or theextracellularconditions(substratepulse,temperature,amongothers).Theresponseofthesystemismonitoredusing(advanced)analytical methodsincluding13Ctracingtoprovidetheresearcherwithquantitativeinvivodata.Thedataisthenusedtocalibratemetabolicmodelswhich needtobechosenbasedonthebiologicalquestionandavailabledata.Modelingandparameterestimationdeliversinformationonthe intracellularkineticsincludingkineticfeaturesofthereactionstepsandallowsfornewbiologicalinsights.
Tokeeptheenzymaticpropertiesconstantwhile gather-ingsufficientinformationonthekineticmechanisms,the socalledstimulus–responseexperimentwasproposedby Theobaldetal.[12]andbecameawidely-used,yetvery challenging approach. More specifically, the cells are exposed to strongand abrupt perturbationsinsubstrate supply in ashorttimeframe,that is,much shorter than protein turnover times. Pioneering work has been performed in yeast and bacteria by substrate pulses [12,18–23]. An experimental challenge in SREs is the rapidmonitoringofintracellularmetabolites,thatis,rapid sampling,quenchingandanalysisofthelowconcentrated intracellularmetabolites byquantitativeanalytical tech-niques. The available setups range from fast manual sampling [13] to automated sampling devices coupled toconventionalbioreactors[24,25]orplug-flowbioreactor units liketheBioScope[26,27].
Besides precise analytical determination of metabolite concentrations,thequantificationatintracellularlevelsis influencedbyimperfectquenchingproceduresthathave to be considered [28,29], that is, aspects of metabolite leakageorsignificantpresence ofmetabolitesalreadyin culturesupernatant.However,procedureslikethe differ-entialmethodwithtotalbrothextraction[30]or metabo-lite balancingincludingerrorpropagationwith all three typesofsamples(i.e.cellextract,quenchingandculture supernatant)[31]havebeendevelopedtoovercomethis. Nevertheless,suchmethodsneedtobevalidatedforeach novelmicrobial species.
SREsgenerateacomprehensivetimecourseof intracel-lularmetaboliteconcentrationsintime,thatcanbeused toidentifyreactionkineticparameters[32]andputative regulatory mechanisms[33].Forexample,Chassagnole etal.[19]designedadynamicmodelaccountingforthe phosphotransferase system (PTS), glycolysis and the pentose-phosphate pathway in E. coli. Using the data ofintracellularmetaboliteconcentrations afterthe dis-turbance of steady-state with a glucose pulse, it was shown thatthe PTSadjustsinsub-secondstothenew condition and exhibits a major flux control in E. coli metabolism.
TheSREapproachhasalsobeenappliedtoother micro-organisms with the aim to highlight the importance of compartmentationfortheregulationofglycolysisinyeast [12],toshedlightonthevaline/leucinepathwaykinetics in C. glutamicum [20], or to study the dependency of penicillin-Gproductiononthemechanisms oftransport ofphenylaceticacidandtheproductoverthecell mem-branein Penicilliumchrysogenum[18,23].
WhileSREswithsinglepulsearehighlyinformativeto obtain insights into microbial kinetics and metabolic responses, itisnotyetclearifthistypeofperturbation mimics well the ‘non-laboratory’ biotechnological
conditions experienced by cells in large-scale bioreac-tors,especiallywhenthenetworkhasbeenconditioned tothesubstrate limitedsteady-state beforethe pertur-bation. There is evidence from literature that the metabolic response of the first substrate pulse differs from aseries ofperturbations inE. coli [34].
To study such ‘training’ phenomena where metabolic networks are ‘trained’ underperiodically changing con-ditions, a series of scale-down approaches have been applied. Block-wisefeeding regimeshavebeenusedin scale-downexperiments,generatingarepetitivedynamic environment.Oneofthefirststudiesapplyingblock-wise feeding investigated the impact of dynamics on the energymetabolisminyeaststrains[35],especially evalu-atingtheyieldofbiomassandproductsincomparisonto steady-state conditions. Later,this type of feast/famine experimentswasusedtostudymetabolisminvivo,with focusonstoragemetabolisminP.chrysogenum[36]andS. cerevisiae[33].
Suarez-Mendez etal.[33]alsoshowedthatthiskindof experimentalregimenotonlysimulatesthecell transi-tion fromsubstrate excess tostarvationconditions,but alsofacilitatesthereproducibilityofmetabolicresponse measurements.Especially,several(identical)cyclescan be sampled allowing for higher time-resolution and replicate measurements compared to the single-pulse experiment.
Continuousdynamicperturbationscanalsobegenerated in two-compartment bioreactors that mimic large-scale conditions.Thisefficientscale-downapproachcan simu-lateinhomogeneityinsidelarge-scalebioreactors,by cir-culating cells between either two stirred-tank reactors (STR-STR)orfromoneSTRtoaplugflowreactor(PFR) [37,38].
While all these experimental setups can generate fre-quent observationsandhigh coverageof metabolic con-centration profiles, the relevant information for the identificationofkineticparametersmightstillbelimited, especially for branch-point metabolic nodes[39]. In re-centyears,theselimitationshavebeenovercomewiththe use of 13C tracerexperiments, a powerful method that enablesthequantificationofintracellularfluxesand pro-vides reliable information on parallel or bidirectional reactions [40,41]. In 13C based metabolic flux analysis (MFA), 13C-labeled substrates are fed and the labeling enrichment istracedthroughthemetabolic network by either mass spectrometry-based techniques or nuclear magnetic resonance spectroscopy (NMR) [42]. In the traditionalisotopicsteady-statemethodonlythelabeling data of themetabolites is requiredto inform about the particular flux distribution, whereas under isotopic dy-namicconditions,boththelabelingandconcentrationsof metabolitesneedtobemeasured[14].Linketal.[43]
used13Cisotopic labelingtoidentify allosteric metabo-lite–protein interactions (allosteric mechanisms) that haveanimpact ontheswitchbetweengluconeogenesis toglycolysisin E.coli.The cellswereculturedonfilter materialallowingforaveryfastexchangeofthe cultiva-tion medium, for example switching from glucose to pyruvate.Theauthorsmeasuredthemetabolicresponse tosuchshifts andappliedamodelingapproach,usinga large set of different kinetic hypothesis to identify the mostrelevantallostericmechanisms.
High-throughput
opportunities
and
developments
Theexperimentalapproachesdiscussedcanonly gener-ate resultsfor one strainunder one perturbation condi-tion. In recent years, high-throughput experimental approaches have been developed to miniaturize the experiments and study more strains and conditions in parallel.Afirstcharacterizationofmetabolicphenotypes can be obtained from the analysis of the extracellular space(metabolicfootprinting)[44].
Fuhreretal.[45]screenedtheintracellularmetabolomeof several E. coli mutants, using a microtiter cultivation system coupled to flow-injection mass-spectrometry. Thissystemallowsforupto1400samplemeasurements perday. Hollinshead et al. [46] haveapplied metabolic fingerprintingtogetherwith13Ctracingusingaseriesof differenttracersubstrates,allowingtoidentifykey meta-bolicfluxphenotypesof lesscommonmicroorganisms. Whiletheclassicalmilliliterscalecultivationcanonlybe performedin batchmode,novelsystemscombine auto-matedliquid-handlingandopticalsensorstocontrolsmall scalecultivations[47].Forexample,theBiolectorsystem canhandle 48parallelcultivationwells[48].Heuxetal. [49] developed a robotic flux profiling system from isotopicfingerprintsthatenablesthegenerationof20flux profilesperdaythough.
Analytical
techniques
Toobtainasmuchinformationaspossibleaboutthe13C patterns of metabolites, advancedanalytical techniques areofmajorimportance.Massspectrometryandtandem massspectrometry arethemost commondevices.With theambitionof kineticmodeling in mind,the focus in this review is on quantitative approaches, while untar-getedapproachesareonly brieflytouched.
Theambitionofquantitativeintracellularmeasurements notonly requireshighly sensitiveinstrumentsto detect the low concentrated metabolites, but also a careful samplepreparation.Continuousimprovementsand vali-dationofprotocolsforneworganismsarecrucialtoensure gooddataquality.Especially,thecellularmatrixis chal-lenging,asionizationissensitivetovaryingbackgrounds. Standardadditionorintroductionofinternalstandardsis
requiredtocorrect formatrixeffects. In2005,Mashego et al. [50,51] introduced an internal standard for each metabolite,bytheadditionofU-13Clabeledcellextract, whichis,sincethen,frequentlyappliedincurrent quan-titative metabolomics. This internal standard can be added at an early stage of the sample processing and enablestocorrectforlossesduringtheprocessing[31,52]. For measuringisotopiclabeling,precisely themass iso-topomer distribution of intracellular metabolites, mass spectrometry, coupled to gas-chromatography or liquid chromatography,hasshownsignificantadvancesinrecent years.Tandemmassspectrometryhasproventoenhance the sensitivity and additionally increase the resolution, withrespecttothelabelingcompositionbyMS/MS[53]. Therefore, the metabolic flux estimation can be im-proved,compared to single MS or NMR based techni-ques[14,54,55].
Next to these targeted, quantitativeapproaches, untar-getedapproachesarenecessaryforthedeterminationof novel metabolites and pathways. Since they provide broader coverage, untargeted metabolomics data is ex-tremely complex and software tools are indispensable. Examples are the XCMS platform [56] for traditional metabolomics and X13CMS [57], and DynaMet[58], MathDAMP[59],or MIDMax[60]for identificationof isotopiclabelingenrichmentsindetectedmetabolites.
Modeling
approaches
The parameterizedkineticmodel shouldbe ableto (1) reproducetheexperimentalobservations,(2)allowforthe predictionofgeneticorenvironmentalperturbation.With predictivemodelsathand, optimizationofthehost and theprocessconditionswilldelivermoreefficient biopro-cesses. The advances in technology have enabled the construction of detailed mechanistic models that link metaboliteconcentrationswithenzymeactivities.Major limitationsofpracticalapplicabilityarethesheeramount ofmodelparameterslackingidentifiability,thesizeofthe networkor theaccuracyof thekineticexpressions[61]. Here it is important to recognize that for predictive models not necessarily all parameters are required to be well determined [62]. This perception unlocks the use of sampling approaches, where average model pre-dictions over a range of parameters are investigated. Approximativekineticformatsareasuitablealternative, astheyarerepresentedbycanonicalequationsand usu-ally contain fewer parameters. Some of the earliest approaches include power–law formats (GMA, S-Sys-tems)and linearizedformats (log-lin,lin-log).However, these formats can lead to inconsistent thermodynamic states,aproblemthatisaddressedbyrecentformatssuch asmodular ratelawsandconveniencekinetics[61,63]. Althoughkinetic parameters canoften be found in the literature,theyaredeterminedusinginvitroexperiments
that can differ significantly from in vivo conditions. Hence, the final step to obtain a working model is to calibrateitsparametersusinginvivodata.Thequalityof calibration will depend on the model complexity and amountofavailabledata.Trueestimatesofsome param-eters maynot be possible due to structural or practical identifiabilityproblems[64].
Ensemblemodelingapproachisapowerfulapproachto tackletheseproblems[65–69].Itconsistsonbuildingan ensemble ofalternative models thatcomplieswith ex-perimental observations. In especial, models with dif-ferent complexity are generated and compared with respect to their ability to reproduce key features of the data. To overcome data scarcity and inaccuracies (noise),samplingbasedapproacheshavebecome popu-lartoyieldsurrogatesformissingknowledgein parame-ter values. Sampling of metabolite concentrations, kineticparameters,enzymelevelsandfluxeshavebeen used to identify average properties on asystem level, even when the available data is insufficient for actual parameter inference [70,71,72,73].Having fast simu-lators and smart stochastic sampling schemes at hand, Bayesian approaches couldemerge as the ‘swiss army knife’ that unlocks the consistent incorporation of all prior knowledge.
Irrespective of the biological question, modeling includes several common elements. In particular, fast and accurate numerical integrators, robust parameter fittingandadvancedstatisticaltoolsarerequired, capa-ble to deal with the non-linear and often ill-posed dynamic problems. Particularly, badly determined or non-identifiable parameters, often non-intuitively cor-related pose distinct numerical challenges to model calibration. Parameter uncertainty is addressed by the calculation of confidence intervals, often using the Fisherinformationmatrix,bootstrappingorprofile like-lihoods.For addressinguncertaintyinpotentially non-identifiableparameters,profilelikelihoodshaveproven the mostreliable[74].Withadynamic modelathand, analysisfortheratelimitingandcontrollingstepscanbe performed.OnefrequentlyusedapproachisMetabolic Control Analysis, a sensitivity analysis framework [75–77].MCA computestheeffectsofsmallparameter perturbationsresultinginfluxcontrolcoefficientswhich describe the effect of a change in the activity of an enzymeon all networkfluxes.
Conclusions
and
outlook
Withpredictive kineticmodelsathand, thedesign and understanding ofmicrobialcellfactories couldreceivea boost in development. The construction of valid meta-bolic models is highly challenging and requires further developments, in both experimentaland computational approaches:
- Designexperimental systems that generate sufficient perturbations, while still being representative for natural and industrial environments and allow for accuratemonitoringof thecellulardynamics.
- Developtheseplatformsforhigh-throughput analysis, tostudyaseriesof externaland internalconditions. - Rigorous dynamical systems theory and systems
analysisto elucidate mathematical structures thatcan bebeneficially exploited[78].
- Newcomputationaltoolsforparameterexplorationand identificationinhigh-dimensional(>100)spaces. - Enhancement of model building frameworks (like
KiMoSys[79]forkineticmodeling)byvariousfeatures toassistmodelerswiththecomplextasksofgathering andintegratingtheavailableinformation.
- Establish comprehensive model databases (like Bio-Models [80] for kinetic modeling). To this end, standards,structuredrepositoriesfortheexperimental omics data and associated protocols (meta-data) are needed[81].
Ultimately,predictivemetabolicmodelscouldthen inte-grate into whole-cell models, which also include tran-scription, translation and post-translational mechanisms [82].Nexttocell-focusedmodels,theintegrationofthe extracellular environment with spatial inhomogeneity due totransport limitation(mixing) arerelevant for the developmentof industrialbioprocesses[83,84].
Acknowledgements
TheauthorsEV,AT,KN,IR,MO,DMandAWarepartoftheERA-IB fundedconsortiumDYNAMICS(ERA-IB-14-081,NWO053.80.724).
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