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METABOLISM

Systems-level analysis of mechanismsregulating yeast metabolic fluxSean R. Hackett, Vito R. T. Zanotelli, Wenxin Xu, Jonathan Goya, Junyoung O. Park,David H. Perlman, Patrick A. Gibney, David Botstein,John D. Storey, Joshua D. Rabinowitz*

INTRODUCTION:Metabolism is among themost strongly conserved processes across alldomains of life and is crucial for both bio-engineering and disease research, yet we stillhave an unclear understanding of howmetabolicrates (fluxes) are determined. Qualitatively, thisdeficiency involvesmissing knowledge of enzymeregulators. Quantitatively, it involves limited under-standing of the relative contributions of enzymeandmetabolite concentrations in controlling fluxacross physiological conditions. Addressing thesegaps has been challenging because in vitro bio-chemical approaches lack the physiological con-text, whereas models of cellular metabolicdynamics have limited capacity for identifying

or quantitating specific regulatory events be-cause of overall model complexity.

RATIONALE: Flux through individual meta-bolic reactions is directly determined by theconcentrations of enzyme, substrates, products,and any allosteric regulators, as captured quan-titatively by a Michaelis-Menten–style reactionequation. Analogous to how experimental var-iation of reaction species in vitro allows for theinference of regulators and reaction equationkinetic parameters, physiological changes influx entail a change in reaction species thatcan be used to determine reaction equationson the basis of cellular data. This requires mea-

surement across multiple biological conditionsof flux, enzyme concentrations, and metaboliteconcentrations. We reasoned that chemostatcultures could be used to induce predictable andstrong flux changes, with changes in enzymesand metabolites measurable by proteomics and

metabolomics. By directlyrelating cellular flux to thereaction species that deter-mine it, we can carry outregulatory inference at thelevel of single metabolic re-actions by using cellular

data. An important benefit is that the physiolog-ical significance of any identified regulator is im-plicit from its role in determining cellular flux.

RESULTS:Here we introduce systematic iden-tification of meaningful metabolic enzyme reg-ulation (SIMMER). We measured fluxes, andmetabolite and enzyme concentrations, in eachof 25 yeast chemostats. For each of 56 reactionsfor which the flux, enzyme, and substrates weremeasured, we determined whether variation inmeasured flux could be explained by simpleMichaelis-Menten kinetics. We also evaluatedalternative models of each reaction’s kineticsthat included a suite of allosteric regulatorsdrawn from across all organisms. For 46 re-actions, we were able to identify a useful ki-netic model, with 17 reactions not including anyregulation and 29 reactions being regulated byone to two allosteric regulators. Three previouslyunrecognized cross-pathway regulatory inter-actions were validated biochemically. Theseincluded inhibition of pyruvate kinase bycitrate and inhibition of pyruvate decarboxylaseby phenypyruvate. These metabolites accumu-lated and thereby curtailed glycolytic outflowand ethanol production in nitrogen-limitedyeast. For well-supported reaction forms, wewere able to determine the extent to whichnutrient-based changes in flux were determinedby changes in the concentrations of individualreaction species. We find that substrates are themost important determinant of fluxes in gen-eral, with enzymes and allosteric regulatorshaving a comparably important role in the caseof physiologically irreversible reactions.

CONCLUSION: By connecting changes in fluxto their root cause, SIMMER parallels classic invitro approaches, but it allows simultaneoustesting of numerous regulators of many reactionsunder physiological conditions. Its application toyeast showed that changes in flux across nutrientconditions are predominantly due to metabolite,not enzyme, levels. Thus, yeast metabolism issubstantially self-regulating.▪

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The list of author affiliations is available in the full article online.*Corresponding author. Email: [email protected] this article as S. Hackett et al., Science 354, aaf2786(2016). DOI: 10.1126/science.aaf2786

Integrative analysis of fluxes and metabolite and enzyme concentrations by SIMMER. Mea-sured flux is related, on a reaction-by-reaction basis, to enzyme and metabolite concentrationsthrough a Michaelis-Menten equation. The extent to which variation in flux across experimentalconditions can be explained by the enzyme, substrates, and products is assessed. If unregulatedkinetics disagrees with the measured flux, we test a set of possible allosteric regulators todetermine which, if any, regulators are supported on the basis of improvement in fit.

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RESEARCH ARTICLE◥

METABOLISM

Systems-level analysis of mechanismsregulating yeast metabolic fluxSean R. Hackett,1 Vito R. T. Zanotelli,2 Wenxin Xu,1,3 Jonathan Goya,1

Junyoung O. Park,1 David H. Perlman,3 Patrick A. Gibney,1,4 David Botstein,1,4

John D. Storey,1,4,5 Joshua D. Rabinowitz1,3*

Cellular metabolic fluxes are determined by enzyme activities and metabolite abundances.Biochemical approaches reveal the impact of specific substrates or regulators onenzyme kinetics but do not capture the extent to which metabolite and enzymeconcentrations vary across physiological states and, therefore, how cellular reactions areregulated. We measured enzyme and metabolite concentrations and metabolic fluxesacross 25 steady-state yeast cultures. We then assessed the extent to which flux can beexplained by a Michaelis-Menten relationship between enzyme, substrate, product, andpotential regulator concentrations. This revealed three previously unrecognized instancesof cross-pathway regulation, which we biochemically verified. One of these involvedinhibition of pyruvate kinase by citrate, which accumulated and thereby curtailed glycolyticoutflow in nitrogen-limited yeast. Overall, substrate concentrations were the strongestdriver of the net rates of cellular metabolic reactions, with metabolite concentrationscollectively having more than double the physiological impact of enzymes.

Acrowning achievement of 20th-centurybiochemistry was determining the enzy-matic reactions bywhich organisms convertdiverse nutrients into energy and biomass(1). Despite the extensive knowledge ofmeta-

bolic reaction networks that resulted, themeansby whichmetabolic reaction rates (fluxes) are con-trolled remain incompletely understood, even inhighly studied model microbes. Most metabolicregulatory mechanisms were determined fromstudying the kinetics of isolated enzymes in vitro.Although powerful for discovering specific reg-ulatory interactions, this reductionist approachhas been less effective at revealing the impact ofregulation in the intact cell. Metabolic regulationin vivo depends not only on enzyme kinetics, butalso on howmuch the concentrations of substratesand products change across physiological statesand how enzymes respond in the presence of phys-iologic concentrations of othermetabolites (2–4).One framework for systematically and quan-

titatively investigating metabolic flux control incells ismetabolic control analysis. In this approach,the impact of enzyme activities on pathway fluxesis captured by their flux control coefficients (CJ

E ),which reflect the fractional change in pathwayflux (J) in response to a fractional change in en-zyme activity (E): CJ

E ¼ ðdJ=JÞ=ðdE=EÞ (2). Al-

thoughmathematically elegant, experimental as-signment of flux control has proven difficult. Themost straightforward approach involves modu-lating enzyme activities on a one-by-one basis,which is taxing, especially because flux controlmay also reside in distal cellular reactions, ratherthan in pathway enzymes themselves (3, 5–7). Forexample, the rate of glycolytic flux may be deter-mined by total cellular adenosine triphosphate(ATP) demand, rather than by glycolytic enzymeexpression (8).To take advantage of growing systems-level

data, an alternative approach is differential equa-tion modeling of metabolic dynamics. Throughfitting experimentalmetabolic concentration data,such an approach can identify quantitative kinet-ic parameters (e.g., catalytic rate constant kcat,Michaelis constant Km, and inhibition constantKi), aswell as regulatory interactions (4, 9–12). Thedifficulty is that parameter and regulator iden-tification requires a global, nonlinear search inhigh-dimensional space and accordingly workspoorly when metabolic networks are either largeor incomplete. Therefore, there is a need for robustand scalable new approaches (13).We developed a method that we term system-

atic identification ofmeaningfulmetabolic enzymeregulation (SIMMER). By combining steady-stateproteomic, metabolomic, and fluxomic data,SIMMER quantitatively evaluates the physiolog-ical mechanisms underlying flux control on areaction-by-reaction basis. Specifically, givenmea-surements of fluxes, metabolites, and enzymesacrossmultiple steady states, SIMMER testswheth-er the observed fluxes through an individual re-action can be explained by a Michaelis-Mentenrelationship between substrate, product, and en-

zyme concentrations (Fig. 1A). When a misfit isobserved, it then searches for potential regulatorsthat significantly rectify the discrepancy (Fig. 1B).Because parameters and regulators are identifiedone reaction at a time, the approach is scalable.The resulting regulatory insights are local: Theydescribe the factors determining individual reac-tion fluxes (net reaction rate), not overall controlof pathway flux. To apply SIMMER,we analyzedthe metabolome, proteome, and fluxome of yeastgrowing in 25 different steady-state conditions.SIMMER recapitulated much of known yeastmetabolic regulation and revealed previously un-recognized regulatorymechanisms. It also revealedthe quantitative contribution of substrate, product,enzyme, and allosteric effector concentrations tothe control of cellularmetabolic reaction rates,withsmall-molecule metabolites collectively playing apredominant role in determining flux.

Results

Metabolite and enzymeconcentrations and metabolic fluxesin nutrient-limited yeastYeast were grown at five different specific growthrates in chemostats in which amounts of car-bon (glucose), nitrogen (ammonia), phosphorus(phosphate), or (in appropriate auxotrophs) leu-cine or uracil were limited. Replicate experimentalmeasurementsweremade from single chemostats(14). To determine fluxes, we used flux balanceanalysis constrained by experimental measure-ments of nutrient uptake, waste excretion, andbiomass generation, including detailed analysisof biomass composition, which varied substan-tially across conditions. For example, nucleic acidcontent (mainly in the form of ribosomal RNA)was higher at fast specific growth rates (15, 16),whereas fat and polyphosphate accumulatedwhennitrogenwas limited (fig. S1).With some importantexceptions, such as more amino acid biosynthesiswhen leucine was limited and less glycolytic fluxwhen glucose was limited, flux correlated stronglywith specific growth rate. The range of fluxes thatwere equally compatible with the experimentalobservations was determined by flux variabilityanalysis (17, 18), providing fluxes with error esti-mates for 233 metabolic reactions (fig. S2). Werefer to the fluxes determined by experimentallyconstrained flux balance and variability analysis asthe “measured fluxes” to differentiate them fromsubsequent flux predictions based on metaboliteand enzyme concentrations. Thesemeasured fluxesagree well with recent studies using 13C tracers todetermine fluxes in carbon-limited yeast (figs. S3and S4) (19, 20).The relative concentrations of 106 metabolites

were previously measured across these chemostatconditionsby liquid chromatography–tandemmassspectrometry (LC-MS/MS) (21). We augmentedthese observations by determining absolute meta-bolite concentrations by an isotope ratio–basedapproach (22). Overall, metabolite abundancesdepended strongly on the limiting nutrient (fig.S5). Products derived from the limiting nutrient,such as nucleotide triphosphates in phosphorouslimitation, were depleted at slow specific growth

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1Lewis-Sigler Institute for Integrative Genomics, PrincetonUniversity, Princeton, NJ 08544, USA. 2Institute of MolecularSystems Biology, ETH Zurich, Zurich, Switzerland.3Department of Chemistry, Princeton University, Princeton,NJ 08544, USA. 4Department of Molecular Biology, PrincetonUniversity, Princeton, NJ 08544, USA. 5Center for Statisticsand Machine Learning, Princeton University, Princeton, NJ08544, USA.*Corresponding author. Email: [email protected]

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rates, whereas related metabolites lacking thelimiting element, such as nucleosides in phospho-rous limitation, accumulated.We also used an isotope ratio–based LC-MS/

MS approach to analyze the proteome. To deter-mine relative protein abundances across condi-tions, we compared each experimental sample toa common 15N-labeled internal reference sample(23, 24). Quantitative data with good reprodu-cibility were obtained for over 20,000 peptidesrepresenting 1187 proteins (fig. S6). Unlike meta-bolites, the abundances of many proteins, especial-ly that of ribosomal proteins, depended primarilyon specific growth rate, irrespective of the limitingnutrient (fig. S7). Quantitatively, the fraction of con-centration variation explained by specific growthrate alone for the proteomewas greater than thatfor the metabolome but less than that for the tran-scriptome (fig. S8) (25). The measured proteinsincluded 370 metabolic enzymes, representing

over 90% of those covered using selected reactionmonitoring–based approaches tailored for enzymequantitation (table S1) (26, 27). Much like meta-bolite abundances, amounts ofmetabolic enzymesvaried strongly depending on the limiting nu-trient. Compared with proteins overall, metabolicenzymes depended less on the specific growthrate and more on which nutrient was limitinggrowth (fig. S8). Notable nutrient-specific trendsincluded down-regulation of glycolytic enzymesand up-regulation of tricarboxylic acid (TCA) en-zymes in carbon limitation and increased levelsof amino acid biosynthetic enzymes in leucinelimitation (fig. S9). Thus, relative to transcriptsor proteins overall, the abundances of metabo-lites andmetabolic enzymes are tiedmore stronglyto the particular nutrient environment. In thecase ofmetabolites, thismay directly reflectmassaction, whereas for metabolic enzymes, it mayreflect regulation designed to maintain appropri-

ate flux as amounts of nutrients, and thus meta-bolites, change.

Integration of concentration and fluxdata through SIMMER

In total, we obtained the requisite data forSIMMER analysis (flux, enzyme concentrations,substrate concentrations, and, optionally, productconcentrations) for 56 reactions. For all reactions,we applied a reversible Michaelis-Menten rate lawthat assumes a random-order enzyme mechanismand competitive binding of substrates and products(4, 28, 29). Kinetic parameters were identifiedby nonlinear optimization tomaximize the consist-ency of the Michaelis-Menten output (based onthe measured enzyme and metabolite concen-trations) and measured flux. For 50% of the re-actions, Michaelis-Menten kinetics explainedmuch of the physiological flux variation (coeffi-cient of determination R2 > 0.35). An illustrative

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Fig. 1. Integrative analysis of fluxes and metabolite and enzyme concen-trations by SIMMER. (A) Measured flux (determined by flux balance analysisconstrained with uptake, excretion, and biomass composition data) is related, ona reaction-by-reaction basis, to enzyme and metabolite concentrations througha Michaelis-Menten equation.The extent to which variation in flux across expe-rimental conditions can be explained by enzyme and metabolite abundancesis assessed. Heatmaps reflect the measured fluxes, enzyme abundances, andmetabolite abundances. Each heatmap contains five columns grouped toge-ther for each limiting nutrient, arranged from slower to faster growth. Thegroups of five columns are arranged in the order of phosphorus, carbon, nitro-gen, leucine, and uracil limitation. Expanded heatmaps are shown in figs. S2,

S5, and S9. Scenario 1 shows the glycolytic reaction catalyzed by triose-phosphate isomerase (TPI) (see also Fig. 2), and scenario 2 shows the reactioncatalyzed by pyruvate kinase (PYK) (see also Fig. 5). Each of the bottom panelscompares measured flux (red dots) to the Michaelis-Menten predictions (bluedots) across the 25 nutrient conditions. (B) Identification of allosteric regu-lators.When a simple Michaelis-Menten expression did not account for theobserved fluxes, the impact of adding allosteric regulation by measuredmetabolites was tested. Physiologically important regulation significantlyenhances the fit to the fluxes. Scenario 1 shows regulation of PYK by fructose1,6-bisphosphate (FBP) and citrate (CIT), and scenario 2 shows the lack ofregulation of pyruvate kinase by fructose 6-phosphate (F6P).

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example is the triose-phosphate isomerase (TPI)reaction in glycolysis, which converts dihydroxy-acetone phosphate (DHAP) into glyceraldehyde3-phosophate (GAP). TPI reaction flux was lowestwhen carbonwas limited but otherwise correlatedwith specific growth rate, and this was explainedby lower enzyme amounts when carbon was lim-ited and higher substrate concentrations in fast-growing cells (Fig. 2, A and B).In the case of TPI, although the fit was not

perfect, it was not improved significantly—basedon the likelihood ratio test with q value–basedfalse discovery rate (FDR) correction (30)—by in-

cluding biochemically annotated inhibitors of theenzyme, suchasATPorphosphoenolpyruvate (PEP),as reaction regulators (31). For other reactions, how-ever, inclusion of regulators enhanced the fit. Forexample, for the first committed step of purine bio-synthesis, phosphoribosyl pyrophosphate (PRPP)amidotransferase, our metabolite measurementsincluded one putative regulator from yeast andeight from other organisms. Among these, inhi-bition byadenosinemonophosphate (AMP),whichgenerally accumulates during slow growth, sig-nificantly improved the fit (P < 0.00003; q < 0.02)(Fig. 2, C to E); all other putative regulators were

not statistically supported (P > 0.05 for each).Inhibition of the first committed step of purinebiosynthesis by AMP is a prototypical feedbackcircuit in yeast (32, 33). Thus, from a set of can-didates based on prior knowledge ofmetabolism,SIMMER identified physiologically relevant reg-ulation of yeast purine biosynthesis.We were interested in seeing whether this ap-

proach could also identify previously unrecognizedregulation. In principle, everymeasuredmetabolitecan be tested as a potential activator or inhibitorof every reaction. Themajor potential difficulty ofthis approach, however, is generating falsepositives


Fig. 2. Analysis of flux control through TPI and PRPP amidotransferase.(A) Substrate, product, and enzyme concentrations for the TPI reaction in gly-colysis.The 25 experimental conditions are laid out across the x axis as perFig. 1 (phosphorus, carbon, nitrogen, leucine, and uracil limitation). (B) Michaelis-Menten equation (where j is reaction flux) relating concentrations to flux andextent of agreement betweenmeasured fluxes (red) and the best Michaelis-Menten fit (blue, rMM). (C) Substrate, product, and enzyme concentrationsfor the PRPP aminotransferase reaction, the committed step of purine

biosynthesis. (D) Michaelis-Menten equation relating concentrations to fluxand extent of agreement between measured fluxes and the best Michaelis-Menten fit. (E) Concentrations of the reaction inhibitor AMP and extent ofagreement between measured fluxes and the best Michaelis-Menten fit af-ter including AMP as a regulator. DHAP, dihydroxyacetone phosphate; GAP,glyceraldehyde 3-phosphate; PRPP, phosphoribosyl pyrophosphate; 5PRA,5-phospho-a-D-ribose 1-diphosphate; PPi, pyrophosphate; ADE4, amido-phosphoribosyltransferase; a.u., arbitrary units; h, hours.


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as a result of correlation betweenmetabolites. Toexplore this issue, we reviewed the literature toidentify known physiological metabolic regulatoryevents. We identified 20 such “gold-standard” reg-ulators, occurring across 16 different reactions(33–35). Comprehensive testing of all metabolitesas both activators and inhibitors of these reactionsidentified an average of 49 regulators per reactionthat significantly improved the flux fit (q < 0.1 bythe likelihood ratio test). The identified regulationincluded 10 of the 20 gold standard regulatoryevents (50%), which were substantially enrichedcomparedwith other previously reportedbiochem-ical regulation of these enzymes (24%) and allothermetabolites testedas activators and inhibitors(24%) (P< 0.02; Fisher’s exact test). Nevertheless,the specificity of the predictions was low.Because the quantitative influence ofmanyme-

tabolites cannot be distinguished, we focused onputative reaction regulators, irrespective of orga-nism, drawn from theBRENDAdatabase (31). Thisallowed us to capitalize on prior knowledge whileidentifying regulation that was previously un-recognized in Saccharomyces cerevisiae. To inte-grate prior knowledgewith our newdata, we useda Bayesian approach, trained by the 20 instancesof gold standard regulation (33–35). Specifically,we used Bayes’ theorem to determine the prob-ability of each regulatory interaction, in light ofthe experimental data, on the basis of (i) its abilityto account for the measured fluxes, Pr(Data | Reg-ulation), and (ii) its prior probability, Pr(Regu-lation). A penalty for the additional parametersintroduced by regulation, based on Akaike infor-mation criteria with a correction for finite samplesizes (AICc), was also included (Fig. 3) (36). Be-cause of the small number of gold standard reg-ulatory events relative to all regulation listed inBRENDA, Pr(Regulation) is low (median, ~0.03),reflecting that, among putative regulators inBRENDA, physiologically meaningful regulationis rare a priori.We used the above strategy to assess each of

729 candidate regulators from the literature ofthe 56 reactions for which we had sufficient data.For reactions inwhichoneormore regulatorswereindividually supported, we also tested coopera-tive binding of regulators and the inclusion of asecondary regulator. For 17 reactions, generalizedMichaelis-Menten kinetics fit the data reasonablywell (R2 > 0.35) and were supported over any reg-ulation. We additionally identified 29 reactionsfor which physiologically relevant regulation wassupported, including six reactions best describedby two physiological regulators and one reactionwith cooperative regulation, for a total of 35 reg-ulatory interactions (Fig. 4 and table S2). Addition-ally, we identified 22 alternative regulators thatwere also supported [lower AICc than for the cor-respondingunregulated reactionmechanism; eachof these individually significantly improved the fit(P < 0.01)]. The distinction between top and sec-ondary predictions was generally modest, but itis unlikely to be due to noisy measurement of reg-ulators (fig. S10). Both the best-supported regula-tors and the alternative regulators were highlyenriched for gold standard regulatory interactions,

each containing five of the 20 total (P < 0.002;Fisher’s exact test), validating the overall SIMMERapproach (tables S3, S4, andS5). For each substrateand each instance of regulation, the Michaelis-Menten fit determinedmetabolite affinity (Km,Ki)solely on the basis of the cellular data. These cel-lular affinity constants correlatedwith correspond-ing values from biochemical literature (fig. S11),providing further validation (31). In addition tofive instances of gold standard yeast regulation(33–35), the 35 best-supported regulatory inter-actions included four regulators with strong invitro support in yeast but no previous evidencefor their physiological importance (37–40). Amajority of the predicted regulation had notbeen previously proposed in S. cerevisiae.

Biochemical confirmation of threepreviously unrecognized instances ofyeast allosteric regulation

To evaluate the power of SIMMER for findingunknown yeast regulatory interactions, we testedbiochemically 10 of the best-supported predictions,verifying three: inhibition of ornithine transcarba-mylase (Arg3) by alanine, pyruvate decarboxylase(Pdc1) by phenylpyruvate, and pyruvate kinase

(Cdc19) by citrate. This relatively low validationrate is due in part to the fact that true regulatoryinteractions are rare (the false-positive rate of ourtop predictions was only 3%) (tables S6 and S7). Itfurther reflects the difficulty of selecting the cor-rect true regulator from correlatedmetabolites. Forexample, we incorrectly predicted phenylpyruvateas a regulator ofDAHPsynthase; the true regulator,phenylalanine, correlateswith phenylpyruvate andwas predicted as an alternative (table S4).Arg3 sits at the branch point between carba-

moyl phosphate assimilation into arginine and itsassimilation into pyrimidines. AlthoughArg3 activ-ity is thought to be regulated through expression(33), SIMMER predicted that alanine is a physio-logical inhibitor, and we biochemically confirmedinhibition with aKi of 15 mM, which is below thetypical cellular concentration of alanine in yeast(fig. S12). Alanine concentrations are increasedunder nutrient conditions in which amino acidsaremore abundant than nucleotides (such as strin-gent limitation for phosphorus or uracil). Thus, ala-nine inhibition of Arg3 serves to dampen argininesynthesis when pyrimidines are needed instead.Pyruvate decarboxylase shunts pyruvate toward

ethanolduringyeast fermentation.Althoughpyruvate


Fig. 3. Integration of experimental data and literature knowledge to predict physiological regula-tors of yeast metabolism. Candidate reaction equations with and without regulation follow a standardMichaelis-Menten form, with substrate (S), product (P), and enzyme (E) taken from standard metabolicreconstructions, and regulators selected on the basis of reported regulators in the BRENDA database ofthe reaction in any organism (in the Michaelis-Menten equation, R = 1 implies no regulation, A is a putativemeasured activator, and l is a putative measured inhibitor). A list of 20 gold standard instances ofphysiological yeast metabolic regulation was assembled on the basis of prior literature and used todetermine the prior probability of a candidate regulator i being a physiological regulator, Pr(Regulationi).On average, Pr(Regulationi) is low, consistentwith physiological regulation being rare.The extent of fit betweenthemeasured fluxes and thosepredictedby the candidate reactionequationdeterminesPr(Data |Regulationi).By Bayes’ theorem, the product of these two probabilities is Pr(Regulationi | Data), the probability thatregulatory event i is physiologically meaningful. A penalty for the additional parameters introduced by reg-ulation was also included to yield a final determination of whether the regulatory event is supported. “Bestsupported” refers to the lowest AICc. “Other supported” refers to any alternative regulators that improveon the unregulated model (AICc < unregulated AICc).


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sits at one of the most critical branch points incentral metabolism, little is known about physio-logic regulation of pyruvate decarboxylase. InZygosaccharomyces bisporus, a spoilage yeast inthe Saccharomycetaceae family, phenylpyruvate isanalternative substrate for pyruvatedecarboxylase,whose presence inhibits pyruvate decarboxylation(Ki, ~5 mM) (41). We confirmed that, similarly toZ. bisporus Pdc, S. cerevisiae Pdc1 can makephenylacetaldehyde from phenylpyruvate, whichalso inhibits the canonical reaction with pyruvatewith aKi of between 1 and 4mM (fig. S13). Suchinhibition was not shared by the structurally re-latedmetabolites phenylalanine ora-ketoglutarate.The downstream phenylacetaldehyde product,phenylethanol, is excreted as a quorum-sensingmolecule that promotes foraging behavior innitrogen-limited yeast (42). Phenylpyruvate con-centrations are high under conditions in whichnitrogen or leucine is limited, and its inhibitionof Pdc1 apparently serves to limit carbon wasting.Thus, SIMMER revealed a previously unknownmeans of coordinating carbon and nitrogenmeta-bolism in yeast.SIMMER also identified citrate as a candidate

inhibitor of pyruvate production through the ter-minal glycolytic enzyme, pyruvate kinase (Cdc19;Pyk2 is a minor isozyme in glucose-fed cells). Be-cause of its role in glycolytic regulation and theswitch to a fetal isoform, Pkm2, in human can-cer, pyruvate kinase is among the most heavily

studied metabolic enzymes. Both human Pkm2and yeast Cdc19 are strongly activated by fructose1,6-bisphosphate (FBP) (43, 44). In yeast, uponglucose removal, FBP concentrations drop drama-tically, shutting off pyruvate kinase and therebypreparing cells for gluconeogenesis. At the higherFBP concentrations found in glucose-fed cells,however, we observed onlymoderate sensitivity ofCdc19 to FBP concentrations (Fig. 5, A and B). Thissuggested that an alternative mode of regulationmight control pyruvate kinase flux, with SIMMERpointing to citrate, or equivalently, isocitrate (whichcoeluted in ourmetabolomics method). Citrate ismore abundant than isocitrate in cells and alsoproved to be themore potent Cdc19 inhibitor,witha Ki of ~5 mM (Fig. 5C). Citrate concentrationsare high when amounts of phosphate, nitrogen,or leucine are limited.Whenphosphatewas limited,across specific growth rates, the abundance of py-ruvate kinase was high and counterbalanced byhigh concentrations of citrate, with the flux in-creasing with specific growth rate primarily be-cause of increased amounts of FBP (Fig. 5D). Incontrast, when nitrogen or leucine was limited,the flux increased with specific growth rate, pri-marily because of decreasing amounts of citrate(Fig. 5D). Thus, inhibition of pyruvate kinase bycitrate works in concert with the control of theabundance of pyruvate kinase and FBP to co-ordinate glucose catabolism with the availabilityof other essential elemental nutrients.

A common feature of the above three previouslyunknown physiological regulatory interactions isthat each spans pathways. This contrasts with thenine instances of known yeast regulation thatwere reconfirmed by SIMMER, each of which is“local” (involving interactions of metabolites andenzymes within the same pathway, including fiveinstances of standard feedback inhibition). Thus,beyond their individual importance, these newdiscoveries collectively raise the possibility thatcross-pathway regulation may be more commonand consequential than currently appreciated.

Quantitative analysis of physiologicalflux control

In addition to revealing reaction regulators, SIM-MER yields quantitative rate laws that can beanalyzed to evaluate themechanisms controllingthe rates of cellular metabolic reactions. To assessthe impact of physiological variation in enzymeand metabolite concentrations on reaction flux,we can partition the total variability in flux acrossconditions into the contributions of individualbiochemical players. Specifically, the impact ofany given biochemical species (substrate, product,enzyme, or allosteric regulator) depends on thevariance in its concentration [Var(s)] across phys-iological conditions and the sensitivity (@v=@ s) ofthe net reaction rate, v, to its concentration, s:Nor-malization to the sum across all players gives thefractional contribution of the species to the control


Fig. 4. Consistency between measured flux and Michaelis-Menten fits for 56 cellular metabolic reactions. For 29 reactions, the inclusion ofregulation by a measured metabolite was statistically supported. R2 was determined by Pearson correlation of the measured flux with the output of theMichaelis-Menten equation across the 25 experimental conditions. Reaction abbreviations are defined in table S4.


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of the net reaction rate. We term this normalizedpartitioning of physiological reaction-rate con-trol “metabolic leverage,” defined as

yk ¼@v@sk

� �2

VarðskÞXn

i¼1

@v

@si

� �2

VarðsiÞ ð1Þ

For each of the 29 metabolic reactions best de-scribed by reaction equations lacking regulationor involving regulation that was biochemicallyverified in S. cerevisiae, the relative metabolicleverage of substrate and product concentrations,allosteric effector levels, and enzyme abundancesis shown in Fig. 6A (a similar analysis involvingall of the best-supported SIMMER predictions is

shown in fig. S14). The observed distributions ofmetabolic leverage are robust across all well-fittingparameter sets (fig. S15 and table S8). For reactionsthat can change net direction as a function of en-vironmental conditions (“reversible reactions”),metabolic leveragewas divided between substrates,products, and enzymes, with no contribution fromallosteric regulation and a majority of leverage


Fig. 5. Pyruvate kinase regulation by FBP and citrate. (A) Substrate, pro-duct, enzyme, and regulator concentrations for the pyruvate kinase reactionthat controls exit from glycolysis. (B) Extent of agreement between measuredfluxes and the best Michaelis-Menten fit, with and without including FBP,citrate, or both as regulators.The improvement in fit due to both regulators wassignificant (P < 10−4). FBP is a classical activator of pyruvate kinase, whereascitrate has not previously been described as an inhibitor. (C) Biochemicalconfirmation that physiological citrate concentrations inhibit the dominantyeast pyruvate kinase isozyme (Cdc19) across the physiologically relevantrange of phosphoenolpyruvate (PEP) and FBP concentrations. (D) The

impact of cellular FBP and citrate concentrations on Cdc19 activity acrossthe 25 experimental conditions. Pyruvate kinase activity [per enzyme andassuming fixed substrate concentrations of 0.8 mM PEP and 0.2 mMadenosine diphosphate (ADP)] was determined by interpolation of the bio-chemical data shown in (C). Each data point reflects a single experimentalcondition, with the size of the point corresponding to the specific growth rate.Increasing fluxwith faster specific growth rate is accomplished in phosphorous,carbon, and uracil limitation through increasing concentrations of FBP,whereasin nitrogen and leucine limitation, it is achieved through decreasing concentra-tion of citrate.


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residing in substrates alone (Fig. 6, B and C). Forreactions that do not change net direction butare somewhat reversible, allostery made a smallcontribution, which increased for strongly forward-driven reactions (standard Gibbs free energy of re-action < –5 kJ/mol) (45), with enzymes, substrates,and allosteric regulators each playing a major role(Fig. 6, B and C). Overall, the combined impact ofmetabolites (substrates, products, and allostericeffectors) wasmore than double that of enzymes.

Discussion

Assystems-levelmeasurement technologies stead-ily improve, there is an increasingneed formethodsthat yield concrete regulatory insights from large-scale data. Previous attempts to infer metabolicregulation frommetabolomics data have typicallyfit dynamicmetabolite concentration changeswithsystems of differential equations. Although thisapproach works well for small networks, it scalespoorly, because inaccurate description of a singlereaction leads to global errors. By measuring flux,rather than inferring it on the basis of changingmetabolite concentrations, regulation can be eval-uated on a reaction-by-reaction basis, indepen-dently of the scale of the total system. Independentevaluation of each reaction equation enables rapidparameter identification and facilitates discov-ery of regulatory interactions. Because reactionrates are measured in cells, the approach is well-positioned to identify regulation that depends onthe presence of physiological concentrations ofother metabolites. We used this approach to iden-tify physiologically relevant regulation, findingthree previously unrecognized instances of cross-pathway metabolic regulation in S. cerevisiae.These included previously unknown ways of

regulating pyruvate flux: Both pyruvate produc-tion and consumption were inhibited by metab-olites that rise in concentration during nitrogenlimitation, with the main pyruvate kinase iso-zyme Cdc19 inhibited by citrate and pyruvatedecarboxylase inhibited by phenylpyruvate, thea-ketoacid analog of phenylalanine. In Escherichiacoli,a-ketoacids includinga-ketoglutarate inhibitcarbon catabolismunder low-nitrogen conditions,in part by direct inhibition of enzyme I (46, 47).Such inhibition simultaneously cuts off flow intoupper glycolysis and out of lower glycolysis, enabl-ing adjustment of glycolytic flux with onlymodestchanges in intermediate concentrations (46). Wefind that related regulatory mechanisms operatein yeast to help balance upper and lower glycolysis(43, 48), with citrate inhibiting both FBP produc-tion (49) and PEP consumption (Fig. 5). Citrate,but not phenylpyruvate, is also abundant whenamounts of phosphate are limited, suggesting acommon bottlenecking of glycolysis when eithernutrient is limiting, but differential regulation ofthe fate of the pyruvate that is formed. Beyondtheir specific importance to understanding meta-bolic control, these previously unrecognized reg-ulatory interactions also suggest some generalprinciples—namely, the importance of long-rangefeedback interactions (involvingmetabolites out-side of the immediate pathway being regulated)and of context-dependent shifts in physiological

regulators, such as a switch from FBP as thepredominant regulator of pyruvate kinase whencarbon is limited (50) to citrate when nitrogenis limited.In addition to identifying previously unrec-

ognized regulatory interactions, we evaluatedthe overall mechanisms controlling the physio-logical rates of individual metabolic reactions in

yeast, revealing a predominant role for metabo-lite concentrations, especially substrate concen-trations. This observation builds on previouswork in yeast and other microbes, which hasfound that changes in the transcriptome andproteome are insufficient to account for fluxchanges (51–54). It is in agreement with recentfindings that changes in substrate concentrations


Fig. 6. The primary determinant of net cellular metabolic reaction rates is metabolite concen-trations.To capture the impact of metabolite and enzyme concentrations on flux through individualreactions,we determined themetabolic leverage of each species—that is, the fraction of flux variabilityacross experimental conditions that is explained by variation in each species’ concentration, as deter-mined by the sensitivity of the reaction rate to the species and the variance of the species’ concen-tration across the physiological conditions. (A) Ternary plot showing the breakdown of metabolic leverageinto substrates and products (sum of leverage of all such species), enzymes, and regulators. Metabolicreactions with either no regulation or validated yeast-specific regulation are included (n = 29). (B) Thereactions in (A) are grouped according to reversibility. Reactions were classified as reversible or not, on thebasis of whether the direction of net flux changes across physiological conditions (18); they were sub-sequently divided into strongly forward-driven versus net forward on the basis of the standard freeenergy (cutoff, –5 kJ/mol) (45). (C) Pie charts showing the average metabolic leverage of substrate,product, regulator, and enzyme concentrations. Less reversible reactions are subject to greater al-losteric regulation.


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are a major contributor to overall changes in flux(53, 55).Pathway-level flux control depends both on

how individual reaction rates are determined, asassessed by metabolic leverage, and on how re-actions interact, as assessed by flux control co-efficients (2, 3, 56). For highly reversible reactions,net flux is sensitive to small shifts in substrate-to-product ratios. Such reactions respond to otherreactions, rather than themselves exerting controlover pathway flux (3), with substrate and productconcentrations dominating metabolic leverage.In contrast, strongly thermodynamically forward-driven reactions have greater pathway flux controland are major targets of allosteric regulators. Wefind that substrate concentration also plays animportant role in determining flux through thesereactions, with the role of metabolites (substrates,products, and allosteric effectors) collectively dou-ble that of enzymes.An important question regards the generality

of our observation that metabolite concentrationsexertmoremetabolic leverage than enzymes. Thisobservation was made across steady-state yeastcultures that differed in terms of their nutrient en-vironment. Byworking at steady state, we shouldin principle favor slow regulatory events, such asmodulation of enzyme concentrations, and thusit is particularly striking that metabolite concen-trations play a larger role. This indicates substan-tial inefficiency in enzyme utilization: If enzymeswere running near maximum velocity (Vmax) inall conditions, the only way to control flux wouldbe through enzyme concentrations. Instead of pri-oritizing enzyme efficiency (57), it appears thatnutrient-limited yeast overexpress enzymes (51, 52),perhaps so that they can grow quickly when nu-trient conditions improve (58). This excess enzymecapacity imparts a plasticity tometabolism (7, 57, 58),shiftingmetabolic leverage onto substrates, prod-ucts, and allosteric effectors. It is likely thatenzyme efficiency is more important in nutrient-rich conditions and that the metabolic leverageof enzymes is greater in such environments. Incases where metabolic variation occurs withoutvariation in environmental nutrient conditions(such as across organs inmammals, which are allfed by the same nutrients carried in the blood-stream), enzymes concentrations are likely to playa yet larger role. Nevertheless, even in such set-tings, many reactions rates may be determinedlargely by metabolite concentrations, becausethis allows for proper fluxes to be achieved with-out fine-grained control of enzyme concentrations.Indeed, mechanisms regulating yeast enzymeconcentrations often work at the relatively coarselevels of whole pathways (such as Arg80, Arg81,and Arg82) and even multiple pathways (suchas Gcn4) (33, 55, 59, 60). This may reflect anevolutionary prioritization of robustness andflexibility over enzyme efficiency. Alternative-ly, it could reflect that making some excess en-zyme is “cheaper” than building the machineryto more precisely control individual enzymeconcentrations.Although we have provided a relatively com-

prehensive metabolic data set and leveraged it to

both confirm canonical regulation and predictregulation that was previously unrecognized inyeast, the majority of SIMMER predictions wereinvalidated. Predicting regulation is difficultbecause most metabolites are not physiologicalregulators of a given enzyme, and erroneouspredictions can readily occur as a result of eitherunmeasured or incorrectly measured variables oran inability to discriminate between potential reg-ulators. More accurate flux measurement throughstable isotope labeling experiments (19, 20, 61),deeper metabolome coverage, and evaluation ofenzyme posttranslational regulation and subcel-lular localization (62–64) should enable a morecomplete understanding of flux regulatorymech-anisms. Moreover, extending the conditions stud-ied to additional nutrients (e.g., other carbonsources) and genetic perturbations (e.g., geneknockouts) holds the potential for breaking downcorrelations between metabolites and therebyallowing regulators to be more reliably discrimi-nated.With sufficient additional data, rather thanrelying on candidates from BRENDA, it shouldbe possible to treat all metabolites as potentialregulators.The SIMMER approach can be applied to any

pseudo–steady-state metabolic system in whichmetabolite and enzyme concentrations and fluxescan be measured under many conditions. Thismay allow identification of metabolic regulatorymechanisms in less well-studiedmicrobes. Giventhe lack of requirements for organism-specificprior knowledge, SIMMER should be applicableto most microbes that can be cultivated in che-mostats. In the meantime, considering the impor-tance of S. cerevisiae as an industrial organism,our quantitative insights into its metabolic regu-latorymechanismsmay be of immediate utility inmetabolic engineering.

Materials and methods

Overview of SIMMERSystematic identification ofmeaningfulmetabolicenzyme regulation (SIMMER) uses omic-scale datato investigate the kinetics of individualmetabolicreactions. The four primary steps constituting theSIMMER method are:1)Measure the relative concentrations ofmetab-

olites (M), enzymes (E), and fluxes ( jF) acrossdiverse conditions. Metabolites and enzymes canbe directlymeasured bymass spectrometry; fluxescannot be directly measured and accordingly areinferred from other experimental data and theknown metabolic network stoichiometry.2) For each reaction of interest, generate one

or more reaction equations that relate measuredmetabolites (M: substrates, products and puta-tive regulators), enzymes (E), and kinetic para-meters (W) to reaction flux (jP = g(M,E,W)). Inthis study, reaction equations (g) are based onMichaelis-Menten kinetics and differ in termsof inclusion of regulators.3) Fit each reaction equation to determine how

well each reaction equation’s prediction (j^P) agrees

with measured flux (jF).4) Compare alternative reaction equations to

identify which model is best supported. Prior

literature is used to assess the plausibility of eachmodel such thatmodels that are less likely a prioriwill require stronger quantitative evidence toachieve the same overall support.

Strains and culture conditions

FY derivative strains of Saccharomyces cerevisiaewere grown at 25 distinct steady states in che-mostats by simultaneouslymodulating both limit-ing nutrient and dilution rate, as per Boer et al.2010 (21). Based on previous work showing thattechnical variability substantially exceedsbiologicalvariability for omic analyses of yeast chemostats(14), each omic analysis was based on technicalreplicates derived from a single biological culture,with proteomics and fluxomics from one cultureand metabolomics from a prior culture. For eachnutrient condition, the five dilution rates were~0.05, 0.11, 0.16, 0.22, and 0.3 hours−1. The strainswere prototrophic with the exception of uracillimitation (MATa ura3-52) and leucine limitation(MATa leu2D1). Each culture was maintainedat pH 5 throughout. Culture density was routinelymeasured using a Klett Colorimeter. Culturesreached steady-state, as determined by stable den-sity over 24 hours, after ~5 to 7 days. Intracellularvolume per culture volume was determined bydirectly measuring the volume of packed cells in5-10ml of culture (PCV Packed Cell Volume Tube87005, TPP, Trasadingen, Switzerland).

Strategy for inferring metabolism-widefluxes in chemostat cultures

Our general approach for estimating metabolism-wide fluxes was tomeasure themajor inputs intometabolism and the major outputs from metab-olism (boundary fluxes) in each condition and touse these fluxes as constraints for flux balanceanalysis. Isotopic labeling was not used in thisstudy to probe internal fluxes due to limitationsrelated to cost and time.Nevertheless, our inferredfluxes agree well with those that have previouslybeen found using 13C-based metabolic flux analy-sis (MFA) of carbon-limited yeast cultures (19, 20).The generally good agreement can be understoodin terms of the sufficiency of boundary fluxes forconstrainingmany fluxes of interest. For example,glucose uptake rate and ethanol excretion rate aregenerally sufficient to determine glycolytic flux. Incontrast, certain branched internal pathways, suchas the pentose phosphate pathway, are less wellconstrained in the absence of isotope tracermea-surements. Accordingly, perhaps unsurprisingly,our successful regulation discoveries occur in gly-colysis and in anabolic pathways whose fluxesare reliably constrained based boundary fluxes,including the rate of biomass synthesis whichconstrains the anabolic fluxes.

Determining metabolite uptake andexcretion rates through 1H-NMR

Media samples for 1H-NMR analysis were pre-pared from each of the 25 chemostats by filtering10ml of culture through a 0.45 mmHNWP filter(HNWP02500,Millipore, Billerica,MA). The con-centration ofmetabolites in the flow-through (spentmedia)wasanalyzedby 1H-NMR,with2 independent



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10ml samples analyzedper chemostat.D2O, sodiumazide, and 4,4-dimethyl-4-silapentane-1-sulfonicacid (DSS) were added to final concentrations of10%, 500 mM, and 500 mM, respectively. Using a500 MHz Advance III (Bruker), 1H-NMR spectrawere collected using the following acquisitionparameters: TD = 65536, NS = 32, D1 = 10s, SW=16,O1P= 4.68, P1 = 7.2, P12 = 2400, SPW1=0.0009,SPNAM1 = Gaus1 180r.1000. NMR peaks werequantitated using rNMR (65), by choosing thecleanest peak of each metabolite and normal-izing this peak’s height relative to the 500 mMDSS internal standard. Absolute quantificationwaspossible through comparison to external stan-dards that were similarly normalized with respectto an internal DSS standard. From the steadystate concentration of metabolites in spent mediaand the culture dilution rate, the rate of excretion(ofmetabolites not present in the originalmedia)is given by:

d½Metabolite�culture=dt ¼ jexcretion −½Metabolite�culture •DR

d½Metabolite�culture=dt ¼ 0

jexcretion ¼ ½Metabolite�culture •DRð2Þ

The rate of uptake of supplied nutrients canbe found analogously by comparing the finalconcentration of nutrients to their concentra-tion in formulated media:

d½Nutrient�culture=dt ¼DR•½Nutrient�media−DR • ½Nutrient�culture−juptaked½Nutrient�culture=dt ¼ 0

0 ¼ DR • ½Nutrient�media−DR • ½Nutrient�culture −juptake

juptake ¼ ð½Nutrient�media−½Nutrient�cultureÞ •DR

ð3Þ

Limitation-dependence of yeastbiomass composition

Because the composition of yeast cells stronglyinfluences the steady-state metabolic fluxes re-quired to support biomass synthesis, the abun-dances of major biomass constituents (16) weremeasured for each of the 25 chemostat condi-tions. For each chemostat, ~200ml of culture wascollected on ice. Yeast were separated from theculture media by centrifugation at 2,600 g at 4°Cfor 30min, the pellet was resuspended in waterto remove all extracellular salts, and yeast wereagain pelleted (1600 g at 4°C for 5 min). Theresulting pellets were stored at -80°C.For dryweight, carbohydrate, protein, and phos-

phate measurement, homogenized cells wereprepared as follows: Frozen cell pellets were dehy-drated for 24 hours at 60°C using a vacuumconcentrator and weighted. About 30 mg of dryyeast was resuspended in 1 ml of homogeniza-tion buffer (0.01MKH2PO4, 1 mMEDTA, pH 7.4)with 0.5% Triton-X, mechanically homogenized(Mini-Beadbeater-16; Biospec Products, Bartles-ville, OK), and aliquoted into 96-well assay plates

(20 ml homogenized yeast per well) for spectro-photometric measurements. Sample preparationfor determination of other biomass componentsis described in the relevant subsections.Total carbohydrate: Phenol-sulfuric assay for

total carbohydrates was used to assess the totalamount of trehalose, glycogen, mannan and glu-cans found in 96-well plates of homogenizedyeast (66). Trehalose concentration, as determinedbymass spectrometry (see below), was subtractedfrom total carbohydrate, leaving a total polysac-charide fraction of dry weight.Total protein: BCA assay (Pierce BCA Protein

Assay Kit; ThermoFisher Scientific,Waltham,MA)was used to determine the relative amounts of pro-tein across the chemostat conditions,withpreviousmeasurements of yeast composition in identicalcarbon or nitrogen-limited chemostats used as anabsolute reference (15, 16).Total inorganic phosphate: A colorimetric assay

(K410-500; BioVision, Milpitas, CA) was used tomeasure inorganic phosphate. Analysis of poly-phosphate standards confirmed that sample prepa-ration steps had already hydrolyzed polyphosphatesto monomers; thus, measured phosphate was acombination of inorganic monophosphate andpolyphosphates.RNA: Frozen pellets as above were thawed

on ice, and RNA was extracted using phenol-chloroform. The relative abundance of RNA ineach sample was measured using a Bioanalyzer2100 (Agilent Technologies, Santa Clara, CA),with previous measurements of yeast composi-tion in identical carbon or nitrogen-limited chemo-stats used as an absolute reference (15, 16).Fatty acids: The concentration of fatty acids

was assessed through absolute quantification ofthe most abundant fatty acid tails (67). Frozencells were resuspensed in 0.1 M HCl/MeOH(50/50) and extracted with 0.5 ml cold (-20°C)chloroform. After removing the solvent under N2

flow, 1 ml of 90% methanol, 0.3 M KOH wasadded and samples were heated for one hour at80°C to saponify lipids. Uniformly 13C-labeledC16-0, C16-1, C18-0, C18-1 were added as internalstandards. After acidification with 100 ml glacialformic acid, saponified fatty acids were extractedtwice with 1 ml of hexane. Samples were driedunder N2 gas and resuspended in chloroform/methanol/H2O (1/1/0.3) to a final concentrationof 2 ml cell volume per ml. Fatty acids were quan-tified byLC-MSas previously described (68), exceptusing a Q-TOF 6550 (Agilent Technologies, SantaClara, CA) instead of an orbitrap mass analyzer,with absolute concentrations determined by com-paring the endogenous unlabeled peaks to theisotope-labeled standard peaks.DNA: The average DNA content of each cell

was inferred from a previously determined rela-tionship between chemostat dilution rate and thefraction of budded cells (fraction budded = 0.936 -1.971DR) (25). As budded cells are diploid andunbudded cells are haploid, deoxyribonucleotidecontent could be calculated from genome size, GCcontent and thenumber of cells per culture volume.Soluble metabolites: Intracellular pools of the

20 metabolites with a median concentration of

greater than 1 mMwere considered in definingbiomass composition. For analytical methods forsoluble metabolites, see below.

Effluxes to biomass

In a chemostat culture, continual yeast growth(and associated biomass synthesis) is balancedby the loss of yeast cells through dilution:

d½Macromolecule�=dt ¼ jsynthesis −½Macromolecule� •DR

d½Macromolecule�=dt ¼ 0jsynthesis ¼ ½Macromolecule� •DR

ð4Þ

To relate jsynthesis to metabolic fluxes, we as-sumed that the relative proportions of monomers(in protein, RNA, etc) were invariant across thechemostats conditions with the following pro-portions: Amino acids % by weight: A: 8.8%; C:0.17%; D: 8.42%; E: 9.45%; F: 4.74%; G: 4.67%;H: 2.2%; I: 5.42%; K: 9.03%; L: 8.33%; M: 1.62%;N: 2.88%; P: 4.06%; Q: 3.3%; R: 6.03%; S: 4.18%;T: 4.89%; V: 6.64%; W: 1.24%; Y: 3.96% (18);Ribonucleotides: % by weight: AMP: 24%; CMP:22%, GMP: 25%; UMP: 29% (18); Polysacchar-ides: % by weight: b-glucan: 46%; glycogen: 21%;mannan: 33% (18).Synthesis of each macromolecule pool was

represented as a single reaction, consumingmono-mers in the proportions above, along with poly-merization costs (69, 70). For example, the RNAconsumption reaction removes ATP, CTP, GTP,and UTP and liberates two phosphates per nu-cleotide assimilated. This formalism allows a singlereaction to represent each biomass component, in-cluding themeasureduncertainty in its abundanceand thereby in the associated biosynthetic flux.

Inferring metabolism-wide fluxes byusing a constraints-based approach

The stoichiometry and directionality of yeastreactions were taken from a modified versionof the YEASTNET 7 Saccharomyces cerevisiaegenome-scale model (18). Reactions were addedto allow for polyphosphate synthesis (polyphos-phate kinase: [ATP + (PO3)n → ADP + (PO3)n+1]and orotate excretion, which we observed exper-imentally. ATP consumption occurred via threeroutes: (i) a minimal ATP maintenance flux pro-portional to cell mass (1 mmole per gDW/h) (71),(ii) growth-related reactions, (iii) an unconstrainedand unproductive ATP hydrolysis reaction whichwas manually added to the model. Reactions thatnever carried flux under our experimental conditionswere removed. This resulted in 2,787 reactions in-volving 1,843 metabolites that could carry nonzeroflux. This count includes equivalent reactions andidentical metabolites duplicated across differentcompartments. The stoichiometry of the 2,787 re-actions is defined by the stoichiometric matrix (S).To determinemetabolism-wide fluxes for each

experimental chemostat condition, we determinedthe balanced flux distribution (j such thatSj=0)that conforms to our experimentally determinedboundary fluxes (j

^) as closely as possible [i.e., minX

ð j^− jÞ2] (72). Because individual boundary



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fluxes were measured with variable accuracy,analogously toweighted least squares regression,we weighted squared residuals, ðj^ − jÞ2, by theexperimental precision (s−2) of that measure-ment. Tominimize unproductivemetabolic cycles,absolute fluxes |j| were penalized by a scalar valuec(1) or c(2) (i.e., ck∈fcð1Þ; cð2Þg for each reaction k).c(1) was used for high flux reactions (glycolysis,TCA cycle, boundary fluxes and associated tran-sport reactions and the unproductive ATP hydro-lysis reaction) and c(2) (which was larger thanc(1)) was used for all other reactions.

XK

kckj jkj

was small relative to the primary penalty for mis-fitting of the experimental measurements. Theoptimal vector j can be found using quadraticprogramming:

minj

: ð^j − jÞTX−1ð ^

j − jÞ þXKk

ckjjkj

s:t: Sj ¼ 0

jmink ≤ jk ≤ jmax

k ∀k∈K ð5ÞBecause there may be multiple optimal solu-

tions {j}, we used flux variability analysis (17) todetermine the range of fluxes through each re-action (i), which give an identical minimal cost(q) in Eq. 5. This range was taken as the expe-rimentally observed flux range. This approachinvolves separately minimizing and maximiz-ing the flux through each reaction, treating q asa constraint:

min=maxj

: ji ∀i ∈ I

s:t ð ^j − jÞT

X−1ð ^j − jÞ þ

XKk

ck j jk j≤ q

Sj¼ 0jmink ≤ jk ≤ jmax

k ∀k∈K

Bothoptimizationproblemswere implementedusing the Gurobi Optimizer (73). Code to repro-duce flux estimation is available on GitHub(https://github.com/shackett/simmer).A total of 233 reactions both carried nonzero

flux under at least some conditions and werewell constrained based on flux variability anal-ysiswithmedian across conditions of (FVA range) /(midpoint of FVA range) < 0.3. These 233 reactionswere treated as candidates for further kineticanalysis.

Proteomics

To quantify the relative levels of proteins across25 chemostats, each experimental sample waspaired to an internal 15N-labeled reference sam-ple and analyzed in triplicate.Protein extraction: Yeast from 300 ml of cul-

ture volume were collected by rapid filtrationonto a 0.8 mm cellulose acetate filter (CA089025,Sterlitech, Kent, WA). The filter containing theyeast cake was folded and placed into a 50 mlconical vial, which was immediately frozen byimmersion in liquid nitrogen, followed by stor-age at -80°C. Complete yeast particle disruptionwas accomplished by placing each cryofrozenyeast-laden filter into a 50ml canister of a RetschCryoMill (Haan, Germany) precooled on dry ice

and pulverizing the total material into a finepowder by cryogenic ball milling at -196°C. Yeastprotein was extracted from the powder by resus-pension in an 80°C solution of 4% SDS, 100 mMTris pH 8, 1 mM DTT, and Halt Protease andPhosphatase Inhibitors (ThermoFisher Scientific,MA), followed by boiling for 20min with periodicagitation. Insoluble material, including filter ma-terial, was removed from the samples by centrif-ugation at 24,000 g for 20min. The concentrationof extracted protein was determined using thePierce BCAProtein Assay Kit (ThermoFisher,MA).Experimental samples were mixed 1:1 with anequal protein content of 15N-labeled referenceprotein solution. The protein reference was yeastcultured in phosphate-limited chemostats (N =2, mixed together) growing at a dilution rate of0.05 hours−1 in which (15NH4)2SO4 was the solenitrogen-source.LC-MS data acquisition: Each experimental

sample was subject to buffer-exchange into aurea-based solution, thiol reduction and alkyla-tion, and trypsin digestion using the FASP pro-cedure (74). Peptides were diluted from thedigestion solution directly into isoelectric focus-ing (IEF) buffer, placed above pH 3-10 IPG strips,and subject to IEF using the OffGel apparatusand its reagent kits (Agilent Technologies, SantaClara, CA). Twenty-four fractions were collectedfor each sample and each fraction was directlyanalyzed by nano-LC-MS/MS three times: onceusing an Agilent 6538 Q-TOF platform and twiceusing anAgilent 6550Q-TOFplatform. BothQ-TOFplatforms were equipped with Agilent 1260 nano-flow HPLC systems and an Agilent ChipCube LC/ion source interface. Large capacity Chip (II) units(150mm300ÅZorbax C18 chipwith a 160nl trapcolumn) were utilized on the 6538 platform, whilePolaris-HR-Chip 3C18 units (150 mm 180 Å 3 mmPolaris C18 chip with a 360 nl trap column) wereemployed on the 6550 system. MS was collectedusing the high resolution setting (40k resolvingpower) at 500 ms acquisition time; MS/MS wascollected on the top 3 most abundant multiplycharged species, at 250 ms acquisition time perspectrum. Raw data was converted from theAgilent .dat format intomzXML format using thesoftware Trapper (Seattle Proteome Center, Trans-proteomic Pipeline) for downstream data analysis.Peptide identification and quantification: Each

mzXML file was analyzed using Mascot (version2.2.07, Matrix Science, London, UK) with 0.01 Daparent and fragment mass tolerance, methionineoxidation as a variable modification, cysteinecarbamidomethylation as a fixed modification,and 15N Metabolic Quantitation. The Mascot re-sults files were processed through Scaffold (ver-sion 3.6.0, Proteome Software Inc., Portland, OR)with XTandem (version 2007.01.01.1, The GPM,Alberta, Canada) to confirm peptide identitiesand report peptides with at least 95% identifica-tion confidence in proteins with at least 99%identification confidence and at least 2 peptidesidentified. The ion counts for the observed pep-tidemass spectra, which represent the sumof theexperimental (light) and reference (heavy) formsof each identified peptide, were fit to theoretical

isotopologue distribution [based on the naturalabundance of isotopes and the isotopic purity of(15NH4)2(SO4)] for the experimental and referencepeptides to determine their relative abundancesand associated error estimates. Using the co-elution probability of every pair of identified pep-tides, the elution time was predicted for peptidesidentified in only a subset of the samples. The ioncounts for the experimental and reference formsof these peptides were also added together overthe elution periods of the peptide in samples with-out explicitMS2 identifications.When a peptidewas identified in multiple fractions, the ion cur-rents from each fraction were summed to achievea sample-level summary of experimental and ref-erence ion current. 13,135 peptides, where boththe experimental and reference ion was quanti-fiable in at least 15 samples, were chosen forfurther analysis. For each peptide, i, and condition,c, the log2-ratio of the experimental to referencepeptide ion current integrated areas was treated asthe peptide relative abundance, log2ðIClight

ic =ICheavyic Þ.

Protein quantification: To infer the relativeabundance of a protein from its correspondingpeptides, we need to aggregatemultiple noisy esti-mates into a single consensus. The relative abun-dance of each peptide was taken as the geometricmean of technical replicates. To downweight noi-sier peptides, each peptide’s variance was esti-mated as the mean squared error over technicalreplicates. The relative abundance (and variance) ofaprotein in each conditionwas foundbyweightingthe peptide relative abundances (x) according totheir inverse variance:

m ¼Xn

i¼1xis

−2iXn

i¼1s−2i

; s2 ¼�Xn

i¼1

s−2i

�−1

ð7Þ

The relative abundance of proteins with nomeasured peptides in a condition (4.8% of allmeasurements and only 0.3% of enzymes catalyz-ing the 56 reactions of interest) was determinedusing knn-imputation (75).

Metabolomics

The relative concentrations of 106 metaboliteswere previously measured across our 25 exper-imental conditions (21). We further determined:(i) absolute concentrations of 56 metabolites, sothat growth-associated dilution of large metab-olite pools could be accounted for and so thatmetabolite affinities could be biochemically inter-preted, (ii) uncertainty of metabolite concentra-tions (see below).Metabolite absolute concentrations: Absolute

concentrations of 56 of themetabolitesmeasuredin Boer et al. 2010were determined by comparisonto commercial standards. The approach dependedonwhether themetabolite contained nitrogen. Fornitrogen-containing metabolites, including aminoacids, unlabeled standards of known concen-tration were added into 15N-labeled phosphate-limited chemostat samples. These samples wereCBZ-derivatized and analyzed by LC-MS in neg-ative ionization mode, as per Boer et al. 2010 (21),with absolute concentrations of themetabolites in


(6)


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https://github.com/shackett/simmer


the phosphate-limited chemostat samples deter-minedbased on ratios of theunlabeled and labeledpeaks (22). For metabolites that do not containnitrogen, their relative concentrations in a fast-specific growth rate (DR = 0.30) carbon-limitedchemostat were compared to a contemporane-ous batch culture containing glucose as a carbonsource, for which absolute concentrations havebeenpreviouslydeterminedby comparison to com-mercial standards (76). Samples were analyzed byLC-MS innegativemode, as perXu et al. 2012 (43).Variance of metabolite relative abundances:

The variance of metabolite measurements (inlog2 space) was determined from four technicalreplicates per chemostat. Residuals across chem-ically similar metabolites were often highly cor-related (for example, within amino acids or withinnucleotides). Such correlations impact the errorestimates for reaction fluxes derived by pluggingthe concentrations into a Michaelis-Menten re-action equation. For example, if errors in [ATP]and [ADP] measurement are positively correla-ted, the error in the ratio ([ATP]/[ADP]) is lessthan that based on standard propagation of error,whereas the error in [ATP]*[ADP]would be great-er than that based on standard propagation oferror. To enable more accurate propagation oferror from metabolite concentrations into theMichaelis-Menten fluxes, the residual covarianceacross all metabolites was estimated (77).Since all omic measurements rely only on

technical (and not biological) replicates, varian-ces are underestimated, but only modestly as bio-logical variability is less than technical variability(14). Because subsequent analyses are based onfinding trends across a continuum of conditions(rather than looking for differences between con-ditions), underestimation of random biologicalerror does not create a systematic bias in favor offalse discoveries.

Summary of integrative omics data

Overall, we determined the relative abundancesof 106metabolites and 304 enzymes andmeasuredflux through 233 reactions. For 56 reactions, fluxeswere determined, at least one isoenzymewasmea-sured through proteomics, and major substrateswere quantified using metabolomics (table S9).For 46 of these reactions, omic measurementsfrom all conditions (N = 25) were used to assesskinetic parameters and identify regulation. Forthe remaining 10 reactions, data in one auxotro-phic limitation differed greatly (> 5-fold) from allof the native limitations and from the other auxo-trophic limitation. For example, orotate phospho-ribosyltransferase (OPRTase) flux is zero underuracil limitation due to the ura3 auxotrophy, andinclusion of uracil limitation data would inap-propriately skew the SIMMER results for theOPRTase reaction. Based on a 5-fold differencecriterion (relative to themost similar native limi-tation data), leucine limitation data were ex-cluded for 6 reactions (ALS, AGK, ASL, ASS,LEUT, OTCase) and uracil limitation data for4 reactions (ATCase, CPS, OPRTase, ODCase).In these 10 cases, SIMMER analysis was con-ducted using data from the other four limiting

nutrients (total of 20 rather than 25 experi-mental conditions).

Reaction equations

For each reaction, an equationwith no smallmole-cule regulation (generalized Michaelis-Mentenkinetics) was generated, as were alternative equa-tions involving one or more previously reportedmetabolite activators or inhibitors. Possible regu-lators of each reaction were queried based onE.C. number. Using the BRENDA database SOAPAPI, we drew on both S. cerevisiae specific reg-ulation and nonyeast regulation (31). All putativeregulators were matched to ChEBI compounds(78) and their synonyms to determine if theywereexperimentally measured. Each model of reactionkinetics was translated into a Michaelis-Mentenreaction form using an extended form of theconvenience kinetics rate law (28, 29), which as-sumes a random-order mechanism with explicitgrouping of metabolites based on binding sites:

jp ¼�X

h

Ehkhcat

� 1YikAid

YiAaii − 1

keq

YjBbjj

� �Y

n1þ

XR∈Gn

XgR

m¼1

R

KRd

� �m� �ð8Þ

E1, E2, ... are the concentrations of isoenzymesthat catalyze the reaction. Substrates (A) andproducts (B), together denoted as reactants (R),were assigned to binding sites (G) based on struc-tural atom-pair similarity using ChEBI structures(78, 79) and assignments were manually verified.Stoichiometric coefficients of substrates, productsand reactants are given by a, b, and g respectively.Previous work has shown that this reaction formcan accurately reproduce bi-bi ping-pong and se-quential mechanisms (29). To generate reactionforms containing a potential allosteric regulatorD, a pre-multiplier was applied to the Michaelis-Menten equation: for allosteric activation, D/(D +Ka), and for inhibition: 1/(1 + D/Ki). All affinityconstants (Ki, Ka, Kd) are treated equivalentlywhen fitting reaction equations and therefore weuse Kd to represent any affinity constant in sub-sequent sections.

Fitting reaction equations toexperimental data

Each reaction equation g (Eq. 8) is an algebraicrelationship that translates enzyme (E) andmeta-bolite (M) abundances and kinetic parameters[W = (Kd, kcat, Keq); |W| = # metabolites + #enzymes + 1] into predicted flux, jP = g(M, E,W).To determine the support for g, we must find aset of kinetic parameters that best approximatesFBA-determined flux (jF) with jP. In doing this,we want both an optimal parameter set [e.g., themaximum-likelihood estimator (MLE) or maxi-mum a posteriori probability (MAP) estimator ofW, W

^] and a measure of parameter uncertainty.

All parameters (Kd; kcat; Keq) were inferred ratherthan taken from literature. This approach waschosendue to lack of absolute quantitation for oneor more substrates or products of most reactions

thereby precluding comparison to literature Keq

values, the lack of reliable literature values formanykinetic parameters, andpotential for system-atic differences between biochemical and in vivoparameters. If we constrained the kinetic param-eters based on biochemical literature, such sys-tematic differences could result in over-fitting ofregulation to correct for erroneousparameter values.We assume that deviations between jP and jF

are independent and identically distributed (iid)and follow a Normal distribution with commonvariance, given by the mean squared error. Themost popular method of fitting relationships ofthe form y = g(X, W) + e, is nonlinear leastsquares (NLS) regression which aims to estimatea set of unknown parameters that minimizes theleast squares departures between y and g(X, W).While widely used, this method is poorly suitedto enzyme kinetics for three reasons: (i) NLSmaybecome trapped in local minima (80); we foundthis to be a particularly severe problem for thereaction equations used in this study, (ii) NLSmay underestimate parameter standard errorsbecause of the nonlinear relationships betweenparameters (80), (iii) NLS does not readily allowfor uncertainty in the response variable, which inour case is flux. This latter issue is particularly crit-ical for SIMMER, as the measured fluxes spanthe interval determined by flux variability analysis.To avoid the limitations of nonlinear regres-

sion, we employed a Bayesian approach to esti-mate the kinetic parameters W:

PrðWjM;E; jFÞ ¼PrðM;E; jFjWÞPrðWÞ=PrðM;E; jFÞPrðWjM;E; jFÞºPrðM; E; jFjWÞPrðWÞ

ð9ÞThe posterior distribution of W was estimated

usingMarkov ChainMonte-Carlo. Each round ofthe algorithm involves: (i) proposing a set of ki-netic parameters (W) drawn from the proposal dis-tribution, (ii) evaluating jP = g(M,E,Wproposed), (iii)determining how well jP agrees with jF (i.e., thelikelihood of Wproposed), iv) evaluating the poste-rior probability of Wproposed (Eq. 9) to determinewhetherWproposed should be accepted or rejected.Prior and proposal distribution on W: The

prior and proposal distributions for each kineticcoefficient were equivalent and constructed toappropriately reflect reaction chemistry.Since each disassociation constant (Kd) reflects

the affinity of an enzyme for a metabolite (M), thevalue of Kd is only meaningful when compared tothis metabolite’s concentration: @j

P

jP = @MM ¼ 0 when

[M] >> Kd, and@jP

jP = @MM ¼ 1 when [M] << Kd. To

symmetrically span the extremes of near un-saturation and near saturation, the prior on eachmetabolite’s Kd was a Log-Uniform distribu-tion centered about the metabolite’s median logconcentration:

Prðlog2KdÞ ∼ Unifð−15þlog2ðmedianfMg; 15þlog2ðmedianfMgÞÞ ð10Þ

The range of this distribution was chosen suchthat near unsaturation or saturation could be



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achieved across all conditions evenwhenmetaboliteconcentrations varied greatly across conditions.Similarly to Kd, the value of Keq is meaningful

only when compared to the reaction quotient Qr.The disequilibrium ratio (Qr/Keq) equals onewhenthe reaction is at equilibrium and approaches zerowhen the reaction is far from equilibrium (in theforward direction). To symmetrically spanmean-ingful values of free energy (about thermodynamicequilibrium), the prior on Keq was a Log-Uniformdistribution centered about the log of themedianreaction quotient:

Prðlog2KeqÞ ∼ Unifð−20þlog2ðmedianfQrg;

20 þ log2ðmedianfQrgÞÞ ð11ÞThe range of this distribution was chosen such

that near irreversibility could be achieved acrossall conditions even when the reaction quotientvaried greatly across conditions.For numerical reasons, kcat parameters were

not drawn from a proposal distribution, butwereinstead optimized based on the current values ofKds and Keq. Their prior probability can be con-sidered as an improper Uniform prior over thenonnegative real numbers: Pr(kcat) ~ Unif[0, ∞).Evaluating g(M, E, Wproposed): Every reaction

equation, g(M, E, W), can be represented as theproduct of a nonlinear equation, f(M, Kd, Keq),and a linear equation, h(E, kcat), where g = fh. Forthe simplest case of Michaelis-Menten kinetics:f = [S]/([S] + Km) and h = kcat[E] (i.e., Vmax).Once values of Kds and Keq have been drawn

from the proposal distribution, the fraction ofmaximumactivity of each condition (o = f(M,Kd,Keq)) can be found. This fraction of maximumactivity, scaled by the measured enzyme concen-tration and kcat, approximates measured flux(i.e., jF = kcat[E]o + e). To find the value of kcat(or multiple kcats if isozymes are measured) thatminimizes the residual squared error, we can uselinear regression to solve for kcat, treating [E]o aspredictors. To enforce that kcat values are strictlynonnegative, kcat parameters are found using non-negative least squares (NNLS). Once all coef-ficients in W have either been drawn from theproposal distribution, or directly estimated inthe case of kcats, j

P = g(M, E, Wproposed) can beevaluated. Metabolites that were not experimen-tally measured were treated as having invariantconcentrations.Determining the likelihood ofW: As is the case

for NLS, we assume that deviations between jP andjF follow aNormal distributionwith variance givenby themean squared error. If measured fluxes ( jFc )are point estimates, the log-likelihood of a proposedparameter set,W, l(W|M, E, jF) would be:

lðWjM;E; jFÞ ¼X25c¼1

log½fðx ¼ jFc ; m ¼ jPc ;

s2 ¼

X25c¼1

ðjFc − jPc Þ2

25−jWj Þ� ð12Þ

Here, f is the Normal probability densityfunction (pdf). Since we are accounting for expe-

rimental uncertainty in fluxes through flux vari-ability analysis, Eq. 12 must be modified torepresent jFc as a uniform density between somelower (jF−c ) and upper bound (jFþc ). This log-likelihood function reflects the equivalent likeli-hood of jP falling anywhere within the intervaldetermined by flux variability analysis:

lðWjM;E; jFÞ ¼X25c¼1

log1

jFþc − jF−c∫jFþc

jFc ¼jF−c

f

�x ¼ jFc ; m ¼ jPc ;

"

s2 ¼X25

c¼1ðjFc − jPc Þ2

25− jWj�djFc

#ð13Þ

Evaluating the posterior probability of pro-posed: Due to the component-wise Uniform/Log-Uniformpriors onW (Eqs. 10 and 11), the posteriorprobability ofW, Pr(W|M,E, jF), is proportional tothe likelihood (natural exponential of Eq. 13):

PrðWjM;E; jFÞºPrðM;E; jFjWÞPrðWÞPrðM;E; jFjWÞ ¼ exp½lðWjM;E; jFÞ�

PrðWÞ ∼ UnifPrðWjM;E; jFÞºexp½lðWjM;E;jFÞ�

ð14ÞAlgorithm for calculating posterior distribu-

tion of W: For a single reaction with K nonlinearkinetic parameters (K = |Kd| + |Keq| = |Kd| + 1)tracked over the course of I sets of metropolisupdates, the joint values of these kinetic param-eters can be optimized using Algorithm 1.

Algorithm 1: MCMC-NNLS inference ofkinetic parameters

Input:Metabolite concentrations (M), enzymeconcentrations (E), measured flux (jF) and a re-action equation (jP = g(M, E, W)).Output: Posterior distribution of kinetic

parameters (W).Initialization:beginfor k ← 1 to K doWcurrent

k drawn from Log-Uniform priorCalculate ocurrent = f(M, Wcurrent) using

reaction formFind kcat parameters using NNLSUpdate lcurrent = l(Wcurrent| M, E, jF)Iteration:for i ← 1 to I dofor k ← 1 to K doWproposed

k drawn from Log-Uniform priorCalculate oproposed and kcat valueslproposed = l(Wproposed| M, E, jF)draw d from Unif(0, 1)if lproposed > lcurrent

or d < expðl proposedÞexpðl proposedÞþexpðl currentÞ:

thenWcurrent = Wproposed

l current = lproposed

Wtracki ¼ Wcurrent

return Wtrack

To obtain distributions of parameter valuesthat appropriately reflect the true distribution,Pr(W| M, E, jF), the Markov algorithm was im-plemented as follows: (i) the first 8,000 samplesfrom the Markov chain were discarded (as the

initial values are determined by the starting as-sumptions regarding the parameter distribution,not the experimental data fit), (ii) thereafter, onlyevery 300th parameter set of the Markov chainwas recorded as an element of W (as values fromnearby iterations of the chain are inappropriatelyhighly correlated) until a total of 200 Markovsamples had been generated, (iii) the algorithmwas run 10 times from different initial conditions.By comparing the 10 Markov chains from eachmodel using the multivariate potential scalereduction factor (MPSRF) (81), we verified thatin all cases the distinct initial conditions hadconverged to equivalent posterior distributions.From the 10 runs of Algorithm 1, for each

reaction equation, we generated 2,000 samplesfrom the posterior distribution of W. For pur-poses of model comparison, we calculated theMAP of each model and the correspondingMAP estimate of parameters:

^W ¼ argmax

WðPrðWjM;E;jFÞÞ ð15Þ

MAP ¼ Prð ^WjM;E;jFÞ ð16Þ

When estimates of W using nonlinear leastsquares were possible (for most reaction equa-tions NLS failed to converge from over 100 initialconditions), the MAP likelihood was either indis-tinguishable from the NLS fit or substantiallyhigher (due to NLS not reaching a global leastsquares minima).Allowing for cooperativity of regulator binding:

Cooperative binding of regulators was assessedfor each literature-informed allosteric activatoror inhibitor by adding an appropriate Hill coef-ficient (n) to the pre-multiplier; for activationDn=ðDn þ kna Þ and for inhibition 1=ð1þ ðD=kiÞnÞ.Parameters for models with cooperativity wereinferred as above, with the inclusion of an addi-tional proposal distribution for theHill coefficient.The prior and proposal distributions onHill coeffi-cients were distributed as Log-Uniform: Pr(log2n) ~Unif(-3, 3). This distribution provides symmetryof negative cooperativity (n < 1) and positive co-operativity (n > 1) about noncooperativity (n = 1).Code to apply the MCMC-NNLS algorithm to

reaction-level data for the 56 studied reactions isavailable on GitHub (https://github.com/shackett/simmer).

Evaluating how well reaction forms fitgiven experimental uncertainty

Todeterminewhetherdiscrepancies betweenmea-sured fluxes andMichaelis-Menten predictions canbe accounted for by inaccurate measurements ofreaction species, the uncertainty of the Michaelis-Menten prediction based on the collective error ofall reaction species was calculated using themul-tivariate delta method (82):

VarðjPc Þ ¼@vPc@sc

� �TX @vPc@sc

� �ð17Þ

Here, s is the set of all measured enzymes andmetabolites involved in a reaction. j refer to path-way fluxes, while v are reaction-level fluxes.

Pis a

square residual covariance matrix (if 4 measuredmetabolites and2proteins=6×6matrix).Diagonal



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entries are the variance of species in condition c,and off-diagonal entries are covariances betweenspecies (i.e., how correlated is the measurementerror of two species weighted by their residualuncertainty). Covariances between proteins wereunknown and assumed to be zero, while covarian-ces betweenmetabolites were calculated as above.

Assessing regulator significance

Our general strategy was to first identify all puta-tive regulators that significantly (after FDRcorrec-tion) improved the fit. We then used a Bayesianapproach to assess the plausibility of each regu-lator. This incorporated howwell-fit a model wasin terms of its maximum a posteriori probability(Eq. 16), themodel’s a priori plausibility based onliterature evidence, and the model’s complexity.Bayesian integration of these factors allowed usto identify the most likely model.Determining regulators that significantly im-

prove fit: Each reaction equation containingregulation was compared to the unregulatedMichaelis-Menten fit for the same reaction todetermine if the improvement in fit due to regu-lation was significant given the increased numberof fitted parameters. Because we are comparingnested models with differing numbers of degreesof freedom, a likelihood ratio test was used (be-cause of Uniformpriors, the posterior probabilityof each model is proportional to the likelihood:Eq. 14). An increased likelihood (Eq. 16) indicatesbetter fit. The expected increase in fit (2 D l) dueto an irrelevant parameter will follow a c2p dis-tribution with p equaling the number of addi-tional parameters. By this approach, a p-valuewasdetermined for each regulator. Regulators thatwere not significant at a FDR of 0.1 (30) wereremoved from further consideration to yield a setof candidate regulators. Models involving multi-ple regulators were built in a step-wise fashionfrom individual significant regulators, with a morecomplex model accepted only when it was signi-ficantly superior to all simpler models.Integrating quantitative support and prior

knowledge to compare alternative models of re-action kinetics: The above approach facilitatesthe quantitative evaluation of many reactionmechanisms without regards to their plausibility.To integrate our data andprior literature know-

ledge, we took a Bayesian approach, aiming tomaximize Pr(Model | Data), where “Model” is aMichaelis-Menten equation including regulationand “Model” is “True” if the regulation is phy-siologically meaningful. Using Bayes’ theorem:

PrðModeljDataÞ ¼PrðDatajModelÞPrðModelÞ=PrðDataÞ ð18Þ

Pr(Data | Model) accounts for how well con-centrations predict fluxes and is directly assessedby Eq. 16. Pr(Data) is independent of the choiceof the model, thus:

PrðModeljDataÞºPrðDatajModelÞPrðModelÞð19Þ

After empirically estimating Pr(Model) andaccounting for differences in model complexity(see below), alternative models of kinetics for

each reaction can be simultaneously comparedbalancing each model’s plausibility and quanti-tative support.Literature support for regulation, Pr(Model):

to carryout the above strategy, we needed to es-timate the a priori probability that each testedregulator is physiologically meaningful in yeast:Pr(Model). From literature reviews and recentprimary literature (33–35), 20 reported physio-logical regulators of 16 reactions were assembled.This gold standard list was initially treated as apriori true regulation. We also constructed a listof 186 BRENDA regulators of the 16 gold standardreactions (31); we assume that the vast majority ofregulation in this list is nonphysiological. Accord-ingly, all members (except for the 20 members ofthe gold standard list) were initially treated as apriori false regulation.Using BRENDA, for each regulator, i, we de-

termined how many times it has been reportedin S. cerevisiae (xscei ), and in other species (xotheri ).We also determined the total number of regula-tors that are tested for the reaction correspond-ing to i (Ni). The log (base 2) of this number wastreated as a third covariate (xni ¼ log2Ni). Treatinggold standard regulation as true regulation (yi = 1)and other BRENDA regulators as false regulation(yi = 0), the predictive power of xsce, xother, and xn

were determined using logistic regression:

logitðΕ½yijxi�Þ ¼ logpi

1 − pi

� �¼ aþ bxi þ ei

logp^

1 − p^

� �¼ a^ þ b

^scexsce þ b^otherxother þ b

^nxn

ð20ÞThe effect of yeast annotations (b

^sce = 0.84)and nonyeast annotations (b

^other= 0.08) were bothsignificantly positive (p < 0.001), while the effect ofa higher number of total regulators (b

^n = -0.91)was significantly negative (p < 0.005). The outputof the logistic regression (i.e., p^) was applied acrossall regulators to determine the a priori Pr(Model).The prior probabilities for models with multipleregulators were the product of individual regu-lator prior probabilities. For models without anyregulation, we used a prior probability of 1. Thisequals themaximum prior probability that couldexist for any model including regulation.Predicting the most likely reaction form for

each reaction based on Pr(Model | Data): For eachreaction, Michaelis-Menten kinetics and all regu-latory reaction forms that significantly improve fitof simpler models (q < 0.1) were simultaneouslyconsidered. Thequantitative support for eachmod-el, Pr(Data |Model) (Eq. 16), and literature supportfor each regulatorymechanism,Pr(Model) (Eq. 20),were combined to estimate each model’s totalsupport, Pr(Model | Data) (Eq. 19). The relativesupport for each model was corrected for over-parameterization by using the Akaike Informa-tion Criterion with correction (AICc) (36):

AICc ¼ 2k 1þ kþ 1

n−k− 1

� �−2logðPrðModeljDataÞÞ

ð21ÞHere, n is the number of conditions and k is

the number of fitted parameters. The reaction

form with the lowest AICc was considered mostplausible. Alternative significant regulators arereported in table S4.

Experimental verification ofpredicted regulation

Ten regulators of seven reactions (ATP-PRTase:His1, DAHP Synthase: Aro3,4, G6PD: Zwf1, 6PGD:Gnd1,OTCase: Arg3, PYK:Cdc19 (Pyk1), Pyk2, PDC:Pdc1,5,6), predicted by SIMMER,were tested usingin vitro biochemistry (table S2). For the PYK andPDC reactions, whileminor isozymes exist (Pyk2,Pdc5,6), Pyk1 and Pdc1 are the predominant iso-zymes in glucose, where all of our experimentaldata were collected.Purified S. cerevisiae enzymes were com-

mercially available for G6PD, 6PGD and PDC(10127655001, P4553, P9474; Sigma-Aldrich, MO).Using proteomics, we confirmed that commercialPDC was primarily composed of Pdc1 (total spec-tral counts from Pdc1 weremore than three timeshigher than those from Pdc5 or Pdc6). A straincontaining an N-terminal 6-His affinity taggedversion of S. cerevisiae Cdc19 was obtained fromXu et al. 2012 (43). For Arg3, Aro3, Aro4, andHis1,a C-terminal 6-His affinity tag was attached to thenative gene using PCR (amplified from BY4742genomic DNA) and incorporated into a p426GALplasmid (high-copy plasmid, URA3 selectable,gene products are galactose-inducible). This plas-mid was transformed into DBY12045 (MATa,HAP1+ ura3D0) to generate strains expressingArg3-His6, Aro3-His6, Aro4-His6 and His1-His6.Protein expression of all pGal-His6-tagged strainswas induced by first growing overnight culturesuntil an OD600 of 0.6 on SC - URA media + 2%Raffinose, followed by 12 hours of induction onSC - URA media + 2% Galactose. Total proteinwas extracted through mechanical homogeniza-tion in the presence of Y-PER reagent (ThermoScientific, MA) containing 10 ml/ml EDTA-freeHALTprotease inhibitors (Thermo Scientific,MA)and 2 mM PMSF. Tagged enzymes were purifiedusing HisPur Cobalt Spin Columns (ThermoScientific, MA), and successful purification wasconfirmed by SDS-PAGE.Activities of G6PD (ZWF1), 6PGD (Gnd1), ATP-

PRTase (His1), and DAHP synthase (Aro3,4) wereassessed using previously published kinetic spec-trophotometric assays (83–85). Assays used to iden-tify or confirm previously unrecognized regulationare detailed below. Putative regulators of each en-zymewere adjusted to thepHof the reactionbuffer.Spectrophotometric (NADH-coupled) analysis

of pyruvate kinase (PYK: Cdc19) activity: Produc-tion of pyruvate by Cdc19 was coupled to NADHoxidation via lactate dehydrogenase (LDH) (86).Initial concentrations were 0.15 or 0.8 mM PEP(as indicated), 0.2 mMADP, 0.2 mMNADH, and4.3 unit/ml LDH (L2500, Sigma-Aldrich) in 50mMTris, 4 mMMgCl2, 75 mM KCl, pH 7.5 buffer. Re-action progress was tracked in real time at 340 nmand 30°C for one hour. Initial reaction velocitieswere fitted and blank (Cdc19-free) activity wassubtracted.Spectrophotometric (direct) confirmation of

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PEP (e232 = 2.84 mM−1cm−1) to pyruvate (e232 =0.6 mM−1cm−1) as the reaction progressed wastracked by capitalizing on the difference in molarabsorptivity at 232 nm between these two species(86). Initial concentrations were 0.15 and 0.4 mMPEP, 0.2 mM ADP in 50 mM Tris, 4 mM MgCl2,75 mM KCl, pH 7.5 buffer. Reaction progress wastracked in real time at 232 nm and 30°C for onehour. Initial reaction velocities were fitted andblank (Cdc19-free) activity was subtracted.Spectrophotometric (NADH-coupled) analysis

of pyruvate decarboxylase (PDC: Pdc1) activity:Production of acetaldehyde by Pdc1 was coupledto NADH oxidation via alcohol dehydrogenase(ADH). Initial concentrations were 0.1-30 mMpyruvate, 0.1 mMNADH, 3 unit/ml ADH (A7011,Sigma-Aldrich) in 200mM citric acid, pH 6.0 buf-fer. Reaction progress was tracked in real time at340 nm and 30°C for one hour. Initial reactionvelocities were fitted and blank (Pdc1-free) activitywas subtracted.NMR-based confirmation of PDC regulation:

Acetaldehyde accumulation by PDC was directlydetected using 1H-NMR. PDC was incubated at30°C for one hour in 10 mM pyruvate, 200 mMcitric acid, pH 6.0 buffer. At the end of incuba-tion, the reaction was stopped by a five-minuteincubation at 98°C. Acetaldehyde was quantifiedby 1H-NMR as above (see “Determining metabo-lite uptake and excretion rates through 1H-NMR”).Mass spectrometry based detection of acetal-

dehyde and phenylacetaldehyde produced byPDC:PDCwas incubated at 30°C for onehourwitheither 10mMpyruvate or 10mMphenylpyruvatein 200 mM citric acid, pH 6.0 buffer. An equalvolume of acetonitrile was added to quench thereactions. Acetaldehyde and phenylacetaldehydewere TSH (p-Toluenesulfonyl hydrazide) derivat-ized and quantified by LC-MS in positive ioniza-tion mode, as per Boer et al. 2010 (21).Spectrophotometric (NADP-coupled) analy-

sis of ornithine transcarbamylase (OTCase: Arg3)activity: OTCase activity was tracked by cou-pling the loss of phosphate from carbamoyl phos-phate to glycogen phosphorylase and ultimatelyNADP reduction (87). Initial concentrations were5 mM ornithine, 100 mM carbamoyl phosphate,0.8mg/ml glycogen, 0.6mMNADP+, 0.5 unit/mlglycogen phosphorylase a (P1261, Sigma-Aldrich),0.24 unit/ml phosphoglucomutase (P3397, Sigma-Aldrich), 0.85 unit/ml glucose 6-phosphate de-hydrogenase (G7877, Sigma-Aldrich), 2 mMglucose1,6-bisphosphate, 20 mM AMP in 10 mM Tris,10mMBis-Tris, 10mMCAPS, 4mMDTT, 0.4mMMgCl2, pH 7.0 buffer. Because this approach tracksphosphate liberated from carbamoyl phosphate,it was necessary tominimize both the amount ofcontaminating phosphorous and the amount ofnonenzymatic phosphate released through thespontaneous breakdown of carbamoyl phosphate.Before quantification, all reagents except carbam-oyl phosphate were combined and incubated forone hour at room temperature to consume con-taminating phosphate. Freshly prepared carbam-oyl phosphate was added to initiate the assay.Reaction progress was tracked in real time at340 nm and 30°C for one hour. The signal from

nonenzymatic breakdown of carbamoyl phos-phate was accounted for using Arg3p-free blankswhose predictable baseline could be reliably sub-tracted from assays including Arg3p.Mass spectrometry based confirmation of

OTCase regulation: Citrulline accumulation byOTCasewas directly detected using LC-MS. Arg3pwas incubated at 30°C for two hours in 5 mMornithine, 100 mM carbamoyl phosphate, 10 mMTris, 10 mM Bis-Tris, 10 mM CAPS, 4 mM DTT,0.4mMMgCl2, pH 7.0.The reaction was stoppedby the addition of -20°C extraction solvent (ace-tonitrile:methanol:water, 40:40:20). Citrulline wasquantified by LC-MS in positive ionizationmode,as per Boer et al. 2010 (21).

Metabolic leverage

The concept of metabolic leverage is to partitionthe cause of flux changes across conditions (at theindividual reaction level) into underlying changesin the concentrations of enzymes, substrates, prod-ucts, and allosteric effectors. This concept can beformulated as partitioning the environmental-driven variance in flux across conditions into thecontributions from the concentrations of therelevant molecular players. Mathematically, thisis the inverse of propagation of uncertainty. Forexample, to determine the uncertainty in a fluxcalculation via a Michaelis-Menten expression,onewould classically propagate uncertainty fromthe technical variation in individual species mea-surements (see section “Evaluating how well re-action forms fit given experimental uncertainty”).To determine metabolic leverage, instead, we de-compose the overall environmental variance influx into the variance contributed by individualreaction species:

VareðvFÞ ≈ @vP

@ s

� �TXe

@vP

@ s

� �ð22Þ

Here, Vare(vF) is the variance in measured flux

across chemostats. To focus on physiologically rel-evant variation in flux, only the 15 prototrophicchemostats limited by an elemental nutrient wereconsidered. @vP=@ s are sensitivities that describehow the reaction equations output (vP) respondsto changes in the mean concentration (acrosschemostats) of each reaction species. Sensitivitieswere evaluated at the mean concentration of allother reaction species using the best-supportedkinetic parameters.

Pe is the environmental cova-

riance matrix describing how all reaction speciescovary across the chemostat conditions. Diagonalentries are the environmental variance of eachreaction species i (Vare(si) =

Xðsi− s

iÞ2=ð15 − 1Þ).

In order to determine the individual contribu-tions of each species i, we make the simplifyingassumption that environmental covariances be-tween species are negligible and therefore

Pe

is diagonal:

VareðvFÞ ≈Xni¼1

@vP

@si

� �2

VareðsiÞ ð23Þ

The fractional contribution of each reactionspecies k to overall flux changes is its metabolicleverage (yk), which is calculated by normalizingeach term in Eq. 23 relative to their sum such

that these metabolic leverages sum to one acrossall reaction species:

yk ¼@vP

@ sk

� �2

VareðskÞXn

i¼1

@vP

@ si

� �2VareðsiÞ

ð24Þ

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ACKNOWLEDGMENTS

Data described in the paper are presented in table S9. This researchwas supported by grants from the U.S. Department of Energy(DOE) (DE-SC0012461; Office of Science Graduate FellowshipDE-AC05-06OR23100 to S.R.H.), NIH (R01CA16359-01A1, GM046406,and GM071508; R01HG002913 to J.D.S), and Agilent Technologies(Thought Leader Awards to J.D.R. and D.B.).

SUPPLEMENTARY MATERIALS

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http://www.sciencemag.org/content/354/6311/aaf2786/suppl/DC1


Systems-level analysis of mechanisms regulating yeast metabolic flux

David Botstein, John D. Storey and Joshua D. RabinowitzSean R. Hackett, Vito R. T. Zanotelli, Wenxin Xu, Jonathan Goya, Junyoung O. Park, David H. Perlman, Patrick A. Gibney,

DOI: 10.1126/science.aaf2786 (6311), aaf2786.354Science

, this issue p. 432Sciencepreviously unrecognized regulation between pathways.the concentration of small-molecule metabolites rather than changes in enzyme abundance. The analysis also revealed probability of regulatory interactions. Regulation of flux through the pathways was predominantly controlled by changes inand 370 metabolic enzymes in yeast in 25 different steady-state conditions. Bayesian analysis was used to examine the

tandem mass spectrometry) and isotope ratio measurements for 56 reactions, over 100 metabolites,−chromatographyinfluence in yeast. They monitored concentrations of metabolites, enzymes, and potential regulators by LC-MS/MS (liquid

developed a method to quantitate such regulatory et al.or fluxes through the various enzymes are controlled. Hackett Although metabolic biochemical pathways are well understood, less is known about precisely how reaction rates

Quantitation of metabolic pathway regulation

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metabolism systems-level analysis of mechanisms regulating ... · research article metabolism...

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