Methanosarcina acetivorans is a model archaeon with renewed interest due to its unique reversible methane production pathways. However, the mechanism and relevant pathways implicated in (co)utilizing novel carbon substrates in this organism are still not fully understood. This paper provides a comprehensive inventory of thermodynamically feasible routes for anaerobic methane oxidation, co-reactant utilization, and maximum carbon yields of major biofuel candidates by M. acetivorans.M. acetivorans is introduced  by integrating information from two previously reconstructed metabolic models , modifying 17 reactions, adding 24 new reactions, and revising 64 gene-protein-reaction associations based on newly available information. The new model establishes improved predictions of growth yields on native substrates and is capable of correctly predicting the knockout outcomes for 27 out of 28 gene deletion mutants. By tracing a bifurcated electron flow mechanism, the iMAC868 model predicts thermodynamically feasible (co)utilization pathway of methane and bicarbonate using various terminal electron acceptors through the reversal of the aceticlastic pathway.Here, an updated genome-scale metabolic model of Archaea.This effort paves the way in informing the search for thermodynamically feasible ways of (co)utilizing novel carbon substrates in the domain The online version of this article (doi:10.1186/s12934-015-0404-4) contains supplementary material, which is available to authorized users. Methane, the second most important greenhouse gas, is regulated primarily by microbial processes . A renew3− [42− [Methanosarcina acetivorans for which trace methane oxidation has been observed [The global methane cycle is predominantly controlled by anaerobic methanotrophic archaea (ANME) in anoxic environments , 12 and 3−  or SO42−3− [42− . Despite3− [42− , 22. Of observed , 24 implobserved , 26.M. acetivorans, a strictly anaerobic marine methanogen possessing one of the largest known archaeal genomes [M. acetivorans remain largely uncharacterized. Two genome-scale metabolic (GSM) models, iVS941 [M. acetivorans cell extracts grown with methane  motivates an update in the existing genome-scale models to incorporate recent findings and to allow for the analysis of methane utilization in silico. genomes , has eme genomes  and vers genomes , 30. Whi genomes –34, rele, iVS941  and iMB7, iVS941 , for thi, iVS941 –42. ReceM. acetivorans to postulate pathways for reversing methanogenesis while maintaining overall thermodynamic feasibility. We first generated an up-to-date GSM model for M. acetivorans by combining information from two earlier models  along with the most recent data from literature and databases. M. acetivorans has transcriptome and proteome profiles that differ depending on growth substrate [3+, NO3−, SO42−, and MnO2 as external electron acceptors. Overall ΔG ≤ 0 is imposed as a constraint to ensure thermodynamic feasibility of methanogenesis reversal in the presence of an external electron acceptor. The interplay between externally supplied electron acceptors and various by-products is analyzed. The feasibility of methanotrophy by resting cells is assessed when all carbons coming from methane and bicarbonate are converted into acetate, formate, CO2, and methyl sulfide, the known byproducts of M. acetivorans’ metabolism [In this paper we make use of a revamped GSM for ubstrate , 34. We tabolism , 43 sometabolism  as end p+/H+ ratio for sodium/proton antiporter (Mrp) and ATP synthase. Among the charge re-balanced reactions, those involving cofactor F420 in the methylotrophic pathway and ATP synthase also required proton rebalancing to accurately account for proton exchange across the cell membrane. The number of Na+ pumped out by ferredoxin-dependent methanophenazine reductase (Rnf) was updated from three Na+ in iMB745 [+ per methanophenazine reduced in accordance with experimental findings [+ and H+ gradients [+/H+ ratio recapitulating the growth yields on native substrates was estimated to be 2:1 for Mrp and 3:1 and 1:2 for ATP synthase, respectively. The two identified solutions for ATP synthase are rendered equivalent by the reversible 2:1 antiport of Na+/H+ across the cell membrane by Mrp, which makes one intracellular H+ equivalent to two extracellular Na+. We also added an F420-dependent NADP reductase to the iMAC868 model , which functions as a source of NADPH for cell biosynthesis.iMAC868 contains 868 genes, 845 reactions, and 718 metabolites  growing with acetate due to the unknown role of the enzymes in acetate-grown cells [mch [420 for NADPH production in acetate-grown cells thereby rendering mch (methenyl-H4SPT cyclohydrolase) essential. Comparing with the iVS941 model, the iMAC868 model correctly predicts the essentiality of rnf, mtr, and the membrane-bound hdr due to the updated GPRs and ion transport stoichiometries included in this model.Upon correcting 64 GPRs based on updated gene annotations  bifurcates yielding a high-potential electron reducing Fe3+ to Fe2+ (Em = +770 mV) and a low-potential electron reducing ferredoxin (Em = −420 mV). Flavin-based electron bifurcation is common among anaerobic microbes including methanogens [3+ on the outer aspect of the cytoplasmic membrane, the bifurcation event occurs either at the cytoplasm or the membrane. Bifurcation in the membrane depends on the Rnf complex, abundant in acetate-grown M. acetivorans, which interacts with ferredoxin and contains two FMN-bound subunits that are possible sites for electron bifurcation [M. acetivorans [3+ takes place. Finally, an electron transfer reaction is included in the model to transfer the electrons from reduced methanophenazine to an externally supplied electron acceptor based on its reported in vivo essentiality [2. The addition of prospective biofuel molecule production pathways for ethanol [In order to allow for methanotrophy, the iMAC868 model was customized to enable three new processes: (1) reversal of methyl-coenzyme M reductase (Mcr) reaction, (2) inclusion of a cytosolic methyltransferase (CmtA), and (3) inclusion of a mechanism enabling electron bifurcation and its subsequent discharge to an external electron acceptor. The methyl-coenzyme M reductase of an anaerobic methanotroph (ANME-MCR), capable of oxidizing methane , was apptivorans , 24, 48,tivorans , and thenotrophy . CmtA [5notrophy  serves aetyl-CoA . Two flahanogens , 53. Alturcation . Oxidatiurcation . Methanotivorans . Oxidatintiality , 20, 55.ntiality  and organtiality . These a ethanol , butanol ethanol , and iso ethanol  to the m2 and biomass as the main products of methanotrophy using all tested electron acceptors. Methane is oxidized to methyl-H4SPT by ANME-MCR and Mtr (or CmtA), a part of which is oxidized via the methylotrophic pathway to produce intracellular CO2. The remaining methyl-H4SPT is used to produce acetyl-CoA, the primary building block for all biomass precursors. Additional carbon fixation occurs via reductive carboxylation by Cdh and Por. Acetyl-CoA is also converted to acetate, generating ATP via substrate-level phosphorylation  of the supplied electron acceptor is less than 50.5 kJ/electron-pair  compared to SO42− reduction (ΔG = 44.53 kJ/electron-pair). This thermodynamic advantage for Fe3+ allows for the co-utilization of bicarbonate up to a maximum HCO3−/CH4 ratio of 0.44 with complete incorporation of all substrate carbons into biomass. However, the endergonic nature of bicarbonate uptake disallows HCO3−/CH4 co-utilization for increasing biomass yield under sulfate-dependent methanotrophy. Methanotrophy using NO3− and MnO2 also allows for co-utilization of bicarbonate as both electron acceptors have ΔGred greater than −20 kJ/electron-pair , constrained only by stoichiometry for both Fe2 production remains non-essential during ferric-dependent methanotrophy as revealed by the model , thereby restricting maximum achievable biofuel yield  as opposed to CO2 reduction by acetyl-CoA synthesis, causing all electrons to be generated by the ANME-MCR. During sulfate-dependent methanotrophy, none of the products could be produced with the complete carbon conversion efficiency due to the fact that coupling biofuel production with SO42− reduction remains thermodynamically infeasible  is necessary to maintain thermodynamic feasibility of the observed solution spaces  to methyl sulfide. Increasing Fe3+ uptake allows more flux through the methylotrophic pathway, thereby generating additional intracellular CO2 for an increased acetate production of up to a maximum of 0.71 mol/mol-methane at an Fe3+ uptake of 2.2 mol/mol-methane  and methane was feasible for certain ratios leading to improved carbon yields for acetate and biofuel molecules. Re-routing of a fraction of carbon towards CO2 was found to be a recurring mechanism for driving growth and production within thermodynamically constrained metabolic states. Finally, the availability in excess of inorganic electron acceptors resulted in a switch between substrate-level and chemiosmotic ATP synthesis. Thermodynamic constraints were often the limiting factor in product yields. Unsurprisingly, the inability to completely reverse the aceticlastic pathway in the absence of an external electron acceptor was confirmed.An updated genome-scale metabolic reconstruction (iMAC868) for the archaeon The theoretical limits of external electron acceptor utilization possibilities to drive the reversal of methanogenesis were thoroughly explored. Key challenges that confound the fidelity of model predictions are still unknown sodium gradient requirements, substrate-dependent regulation and the detailed mechanism of electron transport from internal electron carriers to their external counterparts. Shedding light to these questions will require systematic experimental investigations to confirm or refute electron flow paths guided by the rapidly expanding modeling infrastructure.M. acetivorans, iMAC868, was constructed by appending genes and reactions from iVS941 to iMB745. The stoichiometric coefficients of the ions associated with the membrane-bound electron transport chain were updated based on recent findings. This includes Rnf, ATP synthase and the Na+/H+ antiporter Mrp. All reactions in the model were checked for mass and charge balances and corrected if necessary. Five reactions from amino acid, two from tRNA, one from cofactor biosynthesis pathways, three from methanogenesis, and three metabolite transport reactions required elemental and charge rebalancing. The biomass equation formulation of iMB745 model was adopted in the new iMAC868 model as reported previously [−1. The medium composition was assumed to be a defined high-salt medium [http://www.gnu.org/software/glpk/) and Gurobi (http://www.gurobi.com) solvers in Matlab using COBRA toolbox [The updated genome-scale metabolic model for eviously . It was eviously . The iMAt medium . The modt medium . FBA opt toolbox . Flux va toolbox . Both FBI = {i|i = 1,2,…,M} = Set of metabolites in the stoichiometric modelJ = {j|j = 1,2,…,N} = Set of reactions in the stoichiometric modelJex = {j|j = 1,2,…,Nex} = Set of exchange reactions in the stoichiometric modelSets:vj = Flux of reaction vbiomass = Flux of the biomass formation reactionVariables:Sij = Stoichiometric coefficient of metabolite UBj = Upper bound for the flux of reaction LBj = Lower bound for the flux of reaction Parameters:biomass) is estimated to be 3750 J/gDCW. This value is identified so as the overall stoichiometries for growth on acetate and methanol (see below) remain thermodynamically feasible:All standard transformed ΔG values were calculated at pH of 7, temperature of 25 °C and ionic concentration of 0.25 M  listed ivj separately subject to stoichiometric and thermodynamic constraints.In the above LP problem, the flux of the biomass is maximized subject to the constraints of stoichiometry (1), thermodynamics (2), metabolic network fluxes (3), fixed uptake of methane (4), minimum requirements of maintenance ATP of 2.5 mmol/gDCW-h (5), and fixed ΔG values of input/output metabolites to/from the system (6). Flux ranges for target products were obtained by iteratively solving the above LP problem to minimize and maximize all M. acetivorans grown with acetate and methanol [Step 1k in the total gene set K, the value ck was calculated as the ratio of protein abundance for cells grown on substrate 1 to cells grown on substrate 2 where substrate 1 and 2 can be any of acetate or methanol.Calculate the ratio of protein abundance under different growth substrates. For each gene Step 2ck with a pre-defined cutoff value . If the ratio ck is below or equal to the cutoff value then gene k is added to a candidate list G for which the feasibility of removing the corresponding reactions is evaluated.Compare the ratio Step 3G. The GPR for each reaction is re-evaluated assuming that all genes in list G are eliminated. If re-evaluation of the GPR reveals no associated gene then the reaction is added to the set Jexp that contains the candidate reactions for removal.Re-evaluate GPRs within list Step 4Jexp that can be removed from the model without dropping the biomass yield below the experimental value:The following mathematical formulation is used to identify the maximum number of reactions in the set Gene-protein-reactions (GPRs) associations in the iMAC868 model were thoroughly assessed and 64 GPRs were corrected using a list of 781 newly revised gene annotations Jon = {j|j = 1, 2, …, Non} = Set of reactions for which the evaluation of their GPR indicates active reactionsJoff = {j|j = 1, 2, …, Noff} = Set of reactions for which the evaluation of their GPR indicates inactive reactionsSets:vbiomass = Flux of the reaction producing biomassyj = Binary variable associated with flux of vjVariables:vbiomass,exp = The experimentally measured biomass yield for the given substrateParameters:yj is minimized subject to the limitations on stoichiometry (7), the flux of the reactions for which proteomic data is available but their GPRs are not evaluated because ck is greater than the cutoff value (8), the flux of all other metabolic network reactions which do not belong to set Jexp along with those belong to set Jon (9), and the flux reactions which belong to set Joff (10), and the flux of the reaction producing biomass being equal or greater than the experimentally measured biomass yield for the given substrate (11).Here, the sum of binary variables EAE corresponding to the ΔGred (kJ/electron-pair) of the specific electron acceptor described in Table Electron acceptor reactions are modeled using “electron acceptor equivalents (EAE)”, which serves to drain electron pairs from the model. Each electron pair is drained from reduced methanophenazine. The general form of the electron acceptor reaction used in this model is:+/H+ stoichiometric ratios of ATP synthase and Mrp matching best the observed growth yields, Flux Balance Analysis (FBA) was used as described earlier in this section. FBA optimization problems were solved at varying Na+/H+ ratios of 3:1, 1:1, 1:3, 2:1, and 1:2 for ATP synthase and at varying Na+/H+ ratios of 3:1, 2:1, 1:1, 1:2, and 1:3 for Mrp. These ratios were selected based on recent findings involving archaeal ATP synthase and their dependence on Mrp. Welte and Deppenmeier [+ or Na+) are required to synthesize one molecule of ATP based on the measured electrochemical ion gradients available for a limited number of methanogens. Jasso-Chavez et al. [M. acetivorans. The objective function was the maximization of cellular growth. This procedure was repeated for both acetate and methanol as sole carbon sources. The sum squared error (SSE) between the predicted and observed growth yields were calculated and results are shown in Table To find the optimal Napenmeier  estimatez et al.  proposed


Escherichia coli metabolic flux have played a key role in computational studies of cellular metabolism at the genome scale. We sought to develop a next-generation constraint-based E. coli model that achieved improved phenotypic prediction accuracy while being frequently updated and easy to use. We also sought to compare model predictions with experimental data to highlight open questions in E. coli biology.Constraint-based models of E. coli K–12 MG1655 metabolic network. The model is automatically generated from the current state of EcoCyc using the MetaFlux software, enabling the release of multiple model updates per year. EcoCyc–18.0–GEM encompasses 1445 genes, 2286 unique metabolic reactions, and 1453 unique metabolites. We demonstrate a three-part validation of the model that breaks new ground in breadth and accuracy: (i) Comparison of simulated growth in aerobic and anaerobic glucose culture with experimental results from chemostat culture and simulation results from the E. coli modeling literature. (ii) Essentiality prediction for the 1445 genes represented in the model, in which EcoCyc–18.0–GEM achieves an improved accuracy of 95.2% in predicting the growth phenotype of experimental gene knockouts. (iii) Nutrient utilization predictions under 431 different media conditions, for which the model achieves an overall accuracy of 80.7%. The model’s derivation from EcoCyc enables query and visualization via the EcoCyc website, facilitating model reuse and validation by inspection. We present an extensive investigation of disagreements between EcoCyc–18.0–GEM predictions and experimental data to highlight areas of interest to E. coli modelers and experimentalists, including 70 incorrect predictions of gene essentiality on glucose, 80 incorrect predictions of gene essentiality on glycerol, and 83 incorrect predictions of nutrient utilization.We present EcoCyc–18.0–GEM, a genome-scale model of the Significant advantages can be derived from the combination of model organism databases and flux balance modeling represented by MetaFlux. Interpretation of the EcoCyc database as a flux balance model results in a highly accurate metabolic model and provides a rigorous consistency check for information stored in the database. Escherichia coli K–12 MG1655 metabolic network. A series of E. coli constraint-based models have been published by the group of B. Palsson [E. coli dating back more than twenty years [E. coli modeling, and have seen a range of applications [Constraint-based modeling techniques such as flux balance analysis (FBA) have become central to systems biology ,2, enabl Palsson -6, extenty years -10. Thesications -13 incluE. coli metabolic models, we aimed to illustrate the benefits of integrating metabolic modeling into model organism databases by developing an E. coli model derived directly from the EcoCyc bioinformatics database [Motivated by the widespread use of database . First, Second, we sought to make the model easy to understand and operate. Our goal was a high level of model accessibility and readability through (a) tight web-based integration of the model with extensive model query and visualization tools, and (b) a model representation that captures extensive information that enriches the model and aids its understanding, such as metabolic pathways, chemical structures, and genetic regulatory information. Metabolic models are not just mathematical entities that output predictions; they are also artifacts that scientists interact with in multiple ways. If a model can be quickly and easily understood, scientists are more likely to trust its predictions, and the model is easier to reuse, to modify and extend, to learn from, and to validate through inspection. These aspects of a metabolic model depend strongly on how the model is represented, on the software tools available to interactively inspect the model, and on how tightly integrated the model is with those software tools.E. coli metabolism.Third, we sought to produce a model that is frequently updated to integrate new knowledge of E. coli metabolic model to identify errors in EcoCyc, and open problems in E. coli biology, by performing in-depth investigations of the disagreements between the phenotypic predictions of the model and experimental results.Fourth, we sought to use the EcoCyc-derived E. coli K–12 MG1655 that is directly derived from the EcoCyc model organism database (http://EcoCyc.org) built on the genome sequence of E. coli K–12 MG1655. The model is implemented using the MetaFlux [We present EcoCyc–18.0–GEM, a constraint-based genome-scale metabolic model for MetaFlux  componenE. coli metabolic models. EcoCyc–18.0–GEM is an advance over previous stoichiometric models of E. coli metabolism in four respects: in its size; in its accuracy; in its form, readability and accessibility; and in its update frequency. Here we summarize these results; these points will be expanded in subsequent subsections.The EcoCyc–18.0–GEM generated from EcoCyc 18.0 encompasses 1445 genes, 2286 unique cytosolic and periplasmic reactions, and 1453 unique metabolites. Table The MetaFlux component of Pathway Tools translates Pathway/Genome Database (PGDB) reactions and compounds into constraint-based metabolic models. Our methodology of fusing systems-biology models and bioinformatics databases has several advantages because of strong synergies between these approaches. Databases and models both require extensive literature-based curation and refinement. It is more efficient to perform that curation once in a manner that benefits a database and a model, than to duplicate curation efforts for a database project and a modeling project. Furthermore, the modeling process identifies errors, omissions, and inconsistencies in the description of a metabolic model, and therefore drives correction and further curation of the database if the two efforts are coupled. We made more than 80 EcoCyc updates as a result of comparing model predictions with experimental data and literature for this work. In addition, bioinformatics database curation methods such as the use of evidence codes and citations to provide data provenance, and the incorporation of mini-review summaries that describe enzymes and pathways, benefit systems-biology models, which typically lack data provenance and explanations.Advances in model size. Compared with iJO1366, EcoCyc–18.0–GEM represents a 6% increase in the number of genes, a 23% increase in the number of unique cytosolic and periplasmic reactions, and a 28% increase in the number of unique metabolites. The size of EcoCyc–18.0–GEM is currently exceeded only by the more mathematically complex ME-model of O’Brien et al.[en et al., which iAdvances in model accuracy. We conducted a threephase validation of EcoCyc–18.0–GEM to assess its accuracy . A liteAdvances in model update frequency. Because the MetaFlux component of Pathway Tools generates constraint-based models directly from the EcoCyc PGDBs, as the database is refined through new curation, those refinements are automatically incorporated into newly generated versions of the model. We release new versions of the EcoCyc-based model three times per year; previous models were updated every four years [E. coli.ur years -6. Althoet al., with several revisions stemming from differences in content and functionality between EcoCyc and the iJO1366 model. Gene essentiality in constraint-based models is principally determined by the biomass demands of the cell. Inclusion of a metabolite in the biomass metabolite set forces the genes required for manufacture of that metabolite to become essential in the simulation.Refinement of EcoCyc–18.0–GEM began with the validation of the biomass, nutrient, and secretion metabolite sets, which are detailed at length in Additional file et al. The core biomass metabolite set is a biomass metabolite set that is defined with the aim of maintaining quantitative accuracy with regards to cell performance while predicting the observed experimental essentiality data as accurately as possible. Because much of this work focuses on testing the minimum requirements for cell growth, we frequently employed the core biomass metabolite set in our simulations. We use the term “expanded biomass set” to refer to our version of the wild-type biomass metabolite set described in Orth et al., because we do not wish to imply that the simulated cells always represented the wild-type state.A wild-type biomass metabolite set, which is derived from measurement of the biomolecular composition of healthy, growing cells, is not representative of the minimal set of biomass metabolites required for cell survival. Because biomass metabolites not truly required for cell survival will generate false simulation predictions of essentiality in their biosynthetic pathways, the concept of a core biomass metabolite set was developed by Feist The biomass metabolite sets described here underwent several revisions reflecting differences in scope between EcoCyc–18.0–GEM and iJO1366. Whereas iJO1366 is a purpose-built model developed using the COBRA Toolbox with input from KEGG, EcoCyc, and other databases, EcoCyc is a database with its own schema whose entries are programmatically transformed into an FBA model. The specific metabolites present in iJO1366 therefore cannot always be matched with the specific metabolites generated from EcoCyc by MetaFlux on a one-to-one basis. Several biomass metabolites represented as distinct within iJO1366, such as phosphatidylethanolamines with different chain lengths and saturations, are summed under the heading of a single representative metabolite in the EcoCyc–18.0–GEM biomass set. Additionally, not all processes covered in EcoCyc–18.0–GEM are covered in iJO1366, and the reverse is also true. As a result, the biomass metabolite sets differ slightly. Additional file 2, 2, minerals appropriate to the biomass objective function, and MOPS buffer (usable as a sulfur source) where appropriate. Because of passive diffusion at the high concentration of ammonium used in experimental culture, amtB), whereas all other nutrients are supplied in the periplasmic space.We constructed standard nutrient sets based on culture conditions reflecting experiments in glucose or glycerol minimal media and on the model’s capability to use substrates. Those substrates include glucose or glycerol as appropriate, O E. coli metabolism and dead-end metabolites [E. coli culture media.Finally, we developed a large set of secreted compounds that could be supplied across all growth conditions explored with our model. It contains both plausible products of abolites  within tWe verified the metabolic reachability of each component within the EcoCyc biomass metabolite set by supplying nutrients representing an aerobic glucose minimal medium and setting the production of each individual metabolite in turn as the optimization goal of MetaFlux, and repaired gaps by means of literature-based manual curation of EcoCyc and expansion of the relevant metabolite sets.E. coli FBA.We next confirmed that simulations of aerobic growth on glucose run with maximization of ATP production as their objective made appropriate use of the glycolytic and TCA cycle pathways and agreed with previous work on 2O → ADP + Pi + H + as the objective function to be maximized by MetaFlux. The fluxes resulting from the maximization of ATP production on glucose under aerobic conditions were compared with fluxes from COBRA Toolbox [+ translocated per 2 e -, as proposed by Treberg et al.[+ translocated per 2 e -, as proposed by Wikstrom and Hummer [+ per 2 e - view of translocation stoichiometry, future versions of EcoCyc will be changed to reflect this fact.The maximization of ATP production under aerobic conditions was studied by setting the ATP consumption reaction ATP + H  Toolbox  simulatirg et al.) and thed Hummer ). The exbo oxidase reaction stoichiometry is written in terms of whole molecules of oxygen, while iJO1366 CYTBO3_4pp is written in terms of half-molecules (1 O 2 consumed vs. 0.5 O 2).Further numerical differences are due to a technical consideration: EcoCyc cytochrome After completing our basic validation of biomass production and energy generation, we maximized the rate of EcoCyc–18.0–GEM biomass metabolite set production under several minimal media conditions and ensured that we obtained results comparable to the iJO1366 results for the same conditions obtained using the COBRA Toolbox. Divergences were addressed by literature-based manual curation of EcoCyc and modification of MetaFlux reaction sets. We further compared the extracellular flux distributions resulting from these simulations with the experimental data obtained in carbon-limited chemostat environments under both aerobic and anaerobic conditions.Tables 2 uptake observed experimentally lend support to a lower practical efficiency of proton translation stoichiometry in vivo, perhaps augmented by respiratory inefficiencies such as futile cycling and generation of reactive oxygen species. Both models secrete the expected 1:2:1 mix of acetate, formate, and ethanol during anaerobic growth on glucose that Varma et al.[et al., in which ethanol, then formate, and finally acetate production are eliminated as the cell’s oxygen supply becomes completely sufficient to support aerobic respiration. Figures The behavior of MetaFlux/EcoCyc–18.0–GEM simulations was very similar in most regards to the behavior of COBRA/iJO1366 simulations. Respiration and fermentation rates scaled with nutrient uptake at comparable rates. The generally higher rates of O ma et al. original2 and CO 2 than the simulated fluxes, suggesting a degree of respiratory inefficiency not properly modeled by FBA. Similarly, small quantities of succinate and lactate were produced by experimental fermentation, indicating a degree of divergence from metabolic optimality in vivo. Broader cellular constraints such as regulation, protein crowding, pathway enzyme synthesis requirements, and pathway-throughput limits underlie these differences [et al.[Comparisons between FBA-predicted extracellular fluxes and experimental fluxes show that EcoCyc–18.0–GEM and iJO1366 FBA predictions agree more closely with each other than with experimental flux results, although the correspondence between simulation and experiment was quite close for the experimental fluxes under consideration. This result was expected given the adaptation of the iJO1366 biomass function for use in EcoCyc–18.0–GEM, the use of iJO1366 and preceding reconstructions as benchmarks in the development of EcoCyc–18.0–GEM, and the use of EcoCyc as a reference in the construction of iJO1366 and its predecessors. The experimental measurements generally demonstrate higher fluxes of the respiratory gases O ferences ,26,27. Ss [et al..in silico FBA screens of gene KOs have been applied in a variety of metabolic engineering efforts [E. coli KO library collections with well-characterized growth behavior provide an important tool for flux model validation.One of the most exciting aspects of genome-scale flux modeling is the ability to rapidly test computational gene knockouts (KOs) for their effects on metabolic function. Gene KO simulation is useful both for prediction and for validation:  efforts -31, and FBA gene KO essentiality prediction depends on two types of database associations between genes and chemical reactions: genes whose products catalyze reactions, and genes whose products are reaction substrates . Simulation gene KOs are carried out by identifying all reactions involving the gene, and then identifying all other genes capable of catalyzing the reactions or supplying the substrates thus identified. Reactions for which no isozymes or alternative substrate supplies are found are removed from the FBA stoichiometric network. An FBA solution is then calculated for the new model. If the simulated gene KO has caused the deletion of one or more reactions required for the synthesis of a biomass metabolite, generation of the full biomass metabolite set will be blocked and the FBA simulation returns a no-growth result. Such a result represents a prediction of gene essentiality. If the complete biomass metabolite set can still be produced in spite of the simulated gene knockout, the FBA simulation returns a growth result, indicating a prediction of gene non-essentiality.et al.[et al.[E. coli gene deletion strains for growth on LB rich media and MOPS minimal media with 0.4% glucose. We conducted our glycerol minimal media tests using the gene knockout essentiality data of Joyce et al.[The experimental essentiality data used in our tests consisted of two major datasets. The first, used to study gene essentiality on rich and glucose minimal media, was the deletion study of Baba et al. as updatl.[et al., which tce et al., an expaE. coli gene deletions strongly affect growth on various types of minimal media, but are nonessential to growth on rich media. Because the FBA simulation result is treated as a binary test (growth or no-growth), gene deletions that strongly affect growth on minimal media without producing a completely lethal phenotype must be defined either as experimentally essential or as experimentally nonessential.Several et al. The narrow glucose essentiality criteria treat as essential those Baba et al. and Yamamoto et al. gene deletion mutants with OD600 ≤ 0.005 after 24 and 48 hr growth on glucose minimal media. This requires no perceptible growth over a long period. The broad essentiality criteria was originally defined in relative terms by Joyce et al., as the slowest-growing ninth of all Keio collection deletion mutants.Two representative perspectives on this definition are the narrow essentiality criteria of no observable growth in minimal media and the broad essentiality criteria used by Orth et al. to have OD ≤ 0.091 after 24 hr growth on glucose minimal media, which indicates impaired growth over a shorter period. The practical difference between these two perspectives is illustrated in Figure et al. As the figure illustrates, the broad essentiality criteria include a population of cells with severe growth defects that is not contained in the narrow essentiality data. The comparison between narrow and broad essentiality criteria can be expanded to glycerol minimal media by comparing narrow glycerol essentiality criteria of no observed growth on rich media with the glycerol essentiality criteria of Orth et al., again derived from the criteria of Joyce et al. involving successive division into thirds.In absolute terms, that approach treats as essential those deletion mutants measured by Baba et al. Differences in essentiality predictions between the two data sets illustrated the differences between standard cell composition under nominal conditions and the minimal composition required for cell growth.In order to examine criteria for experimental gene essentiality more deeply and to illustrate the effect of defining a core biomass metabolite set, we conducted essentiality testing using both the expanded and core biomass metabolite sets proposed by Orth et al. and Joyce et al. Gene KO simulations capable of generating any growth at all were scored as nonessential, whereas gene KOs blocking generation of the biomass metabolite set were scored as essential.We simulated single gene KOs on glucose and glycerol minimal media for the 1445 genes in EcoCyc–18.0–GEM to test whether the resulting EcoCyc–18.0–GEM gene deletion mutants were capable of generating core and expanded biomass metabolite sets from sets of nutrients based on the experimental culture media of Baba We compared the results of this simulated essentiality screen with experimental gene essentiality results based on both narrow and broad gene essentiality criteria. Incorrect essentiality predictions were addressed by literature-based manual curation of EcoCyc and modification of MetaFlux metabolite sets. Final essentiality prediction results after curation are summarized in Tables E. coli literature. Our examination covered two types of incorrect gene deletion growth predictions. The first type was a false positive growth prediction. These genes, which are experimentally essential under the conditions tested by Baba et al., were predicted to be nonessential by EcoCyc–18.0–GEM. The second type was a false negative growth prediction. These genes, which are not experimentally essential under the conditions tested by Baba et al., were predicted to be essential by EcoCyc–18.0–GEM.Tables E. coli biology, false predictions resulting from interesting facets of experimental or simulation methods, and other situations of special relevance. Table E. coli metabolism contains several isozymes and opportunities for reversibility, and presents a challenge to FBA essentiality predictions in the absence of complete regulatory modeling. Table et al. experimental growth conditions, insufficiently expressed isozymes, and cases of enzyme inhibition all fall into this category. Table E. coli K–12 literature. Table Tables et al. in E. coli core metabolism with reference to the then-current state of EcoCyc. Constraint-based model improvement and gap-filling based on gene essentiality predictions derived from the work of Baba et al. have been examined for the COBRA family of constraint-based models of E. coli metabolism by Reed et al.[et al.[et al.[Several of the false gene essentiality predictions described within these tables were discussed in the work of Kim and Copley, who examined the essentiality conclusions of Baba ed et al., Kumar el.[et al., Kumar al.[et al., Barua el.[et al., Orth anl.[et al.,144, andl.[et al.. Our revl.[et al. gap-fillAdditional file E. coli respiration for 428 types of media, including 22 conventional types of minimal growth media and 383 Biolog Phenotype Microarray (PM) wells. The 383 Biolog PM media conditions represent a high-throughput method of evaluating metabolic phenotypes in culture based on a tetrazolium dye assay of cellular respiration. Each well in a Biolog 96-well PM plate contains a standard minimal media composition plus a nutrient source that is varied across the PM plate, with the element supplied by the varying nutrient source dependent on the type of Biolog PM plate in use [Observation of culture growth on various nutrient sources is a foundation of microbiology . EcoCyc e in use -149.E. coli growth on the 22 common conventional minimal growth media; (2) consensus estimates of respiration based on four different experimentalists’ measurements of aerobic Biolog 96-well plates PM1–4, representing 313 conflict-free growth observations; and (3) an anaerobic Biolog PM1 plate assay surveying carbon source utilization in the absence of oxygen, representing 96 anaerobic growth observations. Biolog PM data stored in EcoCyc measures utilization of nutrients as sources of carbon (PM1–2), nitrogen (PM3), sulfur (PM4), and phosphorus (PM4).We evaluated the performance of EcoCyc–18.0–GEM in predicting growth for the following available datasets: (1) aerobic et al.[et al.[et al. in our analysis of Biolog PM results because of variation in culture conditions and a high degree of conflict with other datasets under both aerobic and anaerobic conditions [Conventional media compositions and growth results were drawn from the literature. Aerobic Biolog PM nutrient utilization assay results were compiled from four different datasets captured in EcoCyc: (1) from our own experiments; (2) from a dataset obtained from B. Bochner; and from the recent publications of (3) AbuOun et al. and (4) l.[et al.. Anaerobnditions . See the3+ in the medium was replaced with Fe 2+. Anaerobic simulations were prepared identically to those performed for aerobic growth, except for the removal of oxygen from the nutrient set, inclusion of the formate-hydrogen lyase reaction, and the removal of the protoheme and pyridoxal 5’-phosphate synthesis requirement from the biomass.Growth on a given type of media was tested by constructing simulated MetaFlux nutrient sets corresponding to the contents of the media in question and comparing EcoCyc–18.0–GEM growth predictions with experimental growth results. Due to the absence of enterobactin iron uptake modeling in EcoCyc, Fe Literature-based EcoCyc curation and appropriate modifications of MetaFlux metabolite sets were used to address incorrect nutrient utilization predictions. The final results for PM array validation after curation are listed in Table The overall accuracy of nutrient utilization prediction across all aerobic and anaerobic PM and conventional growth media is 348/431 (80.7%). Tables E. coli enzymes are inhibited by ADP?” “What transcriptional regulators affect the expression of the enzymes for reaction X?” Their ability to answer these questions rapidly and accurately is strongly dependent on the model representation, the software tools available for querying and visualizing that representation, the tightness with which those tools are integrated with the model, and the presence of additional enriching information for the model.Scientists naturally need to ask many questions of a metabolic model, such as “What are the chemical structures of all substrates in reaction X, and is X chemically balanced?” “What metabolic pathway(s) is reaction X a member of, and what are the adjacent reactions?” “Which E. coli models are represented as spreadsheet files and as SBML files, making it tedious or impossible for non-programmers to answer the preceding questions directly from those files. Although SBML files can be imported into software tools such as the RAVEN Toolbox [E. coli models do not capture (nor can SBML capture) additional enriching information that, while not required for the mathematical operation of a model, greatly enhances our ability to validate and understand a model, and to answer the preceding questions. Examples of such enriching information present in EcoCyc–18.0–GEM are metabolite chemical structures, arrangements of reactions within metabolic pathways, and gene regulatory information. Note that introducing ad-hoc definitions of these data  in the SBML “Notes” field, or introducing SBML links to external databases, would be considered out of bounds: since pathways are not captured formally in the SBML specification today, there is no guarantee regarding interoperability of software tools with such ad-hoc data.Existing  Toolbox  and rbio Toolbox , in pracE. coli gene regulatory network; constructing structured queries such as: find all reactions of a given metabolite; find all enzymes utilizing a given cofactor; and presentation of text summaries and citations that explain and support aspects of the model. In general, other tools for metabolic model visualization tend to be less comprehensive, and to be less closely coupled to the model; see [EcoCyc–18.0–GEM is highly understandable because it can be interactively queried and visualized through the EcoCyc web site and desktop Pathway Tools software, which supports visualization of metabolic pathways and reaction diagrams; metabolite pages that depict metabolite structures and all reactions a metabolite is involved in; depiction of gene/reaction connections and of genome organization via a genome browser; navigation through the del; see -186 for E. coli models because EcoCyc–18.0–GEM fluxes can be immediately painted onto the EcoCyc Cellular Overview, a zoomable diagram of the complete metabolic map of E. coli that allows immediate visual inspection of flux patterns. Although other software tools exist for visualizing flux patterns on metabolic networks, e.g., the RAVEN Toolbox, they are unlikely to be easily usable with previous E. coli models. For example, RAVEN Toolbox requires that the user manually construct the metabolic network diagram, which could take days or weeks of effort. In contrast, Pathway Tools generates metabolic map diagrams algorithmically from a PGDB.The reaction fluxes computed from EcoCyc–18.0–GEM are more understandable than those from previous E. coli metabolic network, representing gene function with an unprecedented degree of accuracy.EcoCyc–18.0–GEM demonstrates the advantages of literate modeling based on comprehensive organism databases. It provides comprehensive genome-scale coverage of the E. coli, and visualization of pathways and reactions within the model as they change throughout the course of construction. As part of EcoCyc, EcoCyc–18.0–GEM will receive frequent updates to remain abreast of recent research developments.Integration of EcoCyc–18.0–GEM into the EcoCyc database gives investigators working with the model access to the full Pathway Tools bioinformatics and data visualization suite. This allows construction of complex database queries involving the full range of biochemical entities within The process of EcoCyc–18.0–GEM construction and validation resulted in more than 80 updates to EcoCyc. These included expansion and revision of periplasmic phosphatase activities many updates to sugar transport and phosphotransferase system modeling; correction of incorrect compartment assignments; fixes for L-lactate dehydrogenase action; revisions to glutathione hydrolysis; new transport reactions for compounds identified as nutrient sources during Biolog PM testing; addition of MOPS catabolism via the alkanesulfonate pathway; removal of several incorrect reactions and gene-protein relationships; numerous fixes to reaction reversibility and directionality; several compound class reassignments to correct issues with reaction instantiation; mass rebalancing for several reactions; and revisions to ATP synthase proton stoichiometry. These updates are outlined in Additional file E. coli have been introduced as part of this effort. Biomass metabolite sets have been revised to reflect the work of Orth et al., and additional updates have been made on the basis of the validation process in order to create the most accurate final product possible.The MetaFlux software has also been improved as a result of the FBA validation of EcoCyc. These improvements include upgrades to compartmentalization handling, gene deletion code, and electron transfer reaction handling. MetaFlux solution and log files have been updated to contain additional statistical information and provide a more detailed explanation of the metabolic network construction process to the user. Numerous updates and revisions to the MetaFlux model of E. coli modelers and experimentalists were raised in the course of EcoCyc–18.0–GEM development. By highlighting these questions and presenting them within the context of EcoCyc as a reference database, we address the interests of the general metabolic modeling audience and of E. coli experimentalists interested in using models to explore their results and generate new leads for research. We summarize these questions here.Many questions of interest to in vivo deviations from theoretical in silico optimality.Experimental measurements of respiratory fluxes in glucose-fed aerobic chemostat culture are higher than those predicted by simulation, and small quantities of succinate and lactate are generated in experimental anaerobic fermentations, suggesting interesting A small number of metabolic byproducts must be removed directly from the cytosol in the secretion set because of a lack of known salvage or excretion pathways. The fate of these metabolites is of interest.E. coli function in varying environments.Several incorrect essentiality predictions are associated with unclear cellular biomass requirements, pathways with potential alternate routes of catalysis, uncertain determinations of essentiality on glucose minimal media, and ambiguous or missing gene function. Similarly, nutrient utilization predictions have identified a number of compounds that lack clear pathways of entry into metabolism but are capable of supporting respiration and/or growth. Resolution of these uncertainties would improve our understanding of http://brg.ai.sri.com/ptools/. The simulation tests were constructed by using Lisp scripting and the Pathway Tools Lisp API, documented at http://brg.ai.sri.com/ptools/api/. Further details on the construction of EcoCyc–18.0–GEM can be found within Additional file The data used for this project were obtained from EcoCyc version 18.0, and the bioinformatics and flux analysis procedures documented here were performed in either the Web or desktop environment of the Pathway Tools 18.0 software. Pathway Tools can be downloaded, along with documentation and example files, at E. coli BW25113 on glucose is included as Additional file EcoCyc–18.0–GEM development employed the MetaFlux component of Pathway Tools, documented in the Pathway Tools User’s Guide and in . All simWe note that the choice of stoichiometric representation of equations can affect flux balance solutions when minimization of summed flux is used as part of the objective function; see  for furtBriefly, MetaFlux creates a stoichiometric metabolic flux network at run time from the metabolites and reactions contained in a Pathway Tools PGDB. During network construction, MetaFlux removes PGDB reactions that are: ambiguously instantiated (see below); unbalanced or having an undetermined balance state; disconnected from the network; marked as physiologically irrelevant; involved in polymerization; involved in polymer segment or protein modification; lacking substrates on one side; containing substrate entities that are described only by strings; possessed of variable stoichiometry; or have more than 10,000 permutations that must be checked during instantiation. MetaFlux then instantiates reactions containing compound classes, replacing the class reactions with mass-balanced reactions containing instances of the relevant compound classes. The resulting set of metabolites and reactions constitutes the metabolic flux network operated on by MetaFlux. Enzymatic reaction and gene-protein relationship data encoded in the PGDB are used to associate the reactions of the network with enzymes and genes as appropriate.E. coli genome-scale reconstruction were employed in order to validate the EcoCyc FBA simulations and to provide a point of comparison to existing reference models. The iJO1366 simulations were performed using the COBRA Toolbox 5.0.0 within MATLAB R2010a and cobrapy 0.2 within Python 2.7.6. All iJO1366 simulations used taxicab norm minimization of fluxes as described in the documentation for the optimizeCbModel function.COBRA ,188 simuet al. and modified according to our research findings and experimental data on gene essentiality. The ATP turnover requirement for growth-associated maintenance costs (GAM) was set to 53.95 mmol ATP/gCDW, while the ATP turnover requirement for non-growth-associated maintenance costs (NGAM) was set to 3.15 mmol ATP/gCDW, per Orth et al.Biomass metabolite sets were constructed using the wild-type and core biomass sets of Orth μ of 1.0 hr -1 (one new gram of cell dry weight per gram of cell dry weight per hour).All coefficients of the biomass metabolite set represent millimoles (mmol) of each metabolite required per gram of cell dry weight (gCDW). Coefficients of the nutrient and metabolite sets represent specific uptake and output fluxes, in millimoles of each metabolite supplied per gram of cell dry weight per hour (mmol/gCDW/hr). An overall biomass flux of 1.0 thus represents a specific growth rate Aerobic glucose chemostat data for experimental comparisons were obtained from . AnaerobE. coli MG1655 was obtained from the Yale Coli Genetic Stock Center, pre-grown on nutrient agar and used to inoculate the plates following Biolog instructions. The data were collected and analyzed using the OmniLogH PM system, which records the color change every 15 min for each well in the 96 well assay plates. All incubations were performed at 37°C over 48 hr. For the complete details of all PM assay conditions, please refer to the original publications.The protocols followed in our PM experiments are as follows: PM plates 1–4 containing 190 sole carbon sources, 95 sole nitrogen sources, 59 sole phosphate sources and 35 sole sulfur sources were used in this analysis. The PM nutrient-source assay is an assay of respiration based on the generation of NADH by carbon metabolism and the subsequent reduction of a tetrazolium redox dye by NADH. As such, it does not directly measure either the cell growth simulated by FBA biomass objectives or the uptake of noncarbon sources. However, checkpoint linkage of carbon-source catabolism to nitrogen, phosphorus, and sulfur source catabolism enables the tetrazolium redox dye assay to probe the metabolism of non-carbon sources . BochnerBiolog PM results are stored within the EcoCyc database and are accessible via the Pathway Tools API and EcoCyc website. Individual Biolog PM assay scores for each well were compared across experimental datasets to establish a consensus for comparison with EcoCyc–18.0–GEM simulation. Because simulations of nutrient utilization were scored according to growth or no growth, experimental Biolog PM results indicating ‘normal’ and ‘low’ respiration were combined into a ‘positive’ result. The majority of Biolog PM tests (313/383) displayed a consensus of either respiration or no respiration across all four experimental datasets used. In 70 of 383 cases, no clear consensus could be reached. These divergent cases were omitted from the nutrient-utilization assay validation because no reliable conclusion could be reached regarding the results. See Additional file DSW, IMK, and PDK receive fees from SRI International commercial licensing of Pathway Tools.PDK and DSW conceived and designed the experiments. DSW constructed the model and conducted the simulations. DSW analyzed the data. IMK, AM, and DSW curated the database. DSW and PDK wrote the manuscript. AM and ITP performed phenotype microarray experiments. All authors read and approved the final manuscript.Supplementary information text and table descriptions.Click here for fileSupplementary tables (11 tables).Click here for fileMetaFlux .fba file demonstrating simulation of aerobic growth of E. coli BW25113 on glucose.Click here for file


E.coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E.coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.In simple organisms like  E.coli. Although they often give good results in practice, they normally rely on heuristic considerations like “evolution has tuned metabolic fluxes to optimize growth, hence optimizing growth gives reasonable fluxes”. The main result of this paper is to show that metabolic adaptation naturally leads to optimal growth, in the sense that the flux distribution associated to optimal growth is the dominant attractor of the fitness landscape of the metabolic adaptation process.In modeling metabolic networks, concepts like biomass optimization are often used to determine flux distributions of simple organisms such as  Constraint-based computational methods such as Flux Balance Analysis (FBA) are nowadays widely used when investigating metabolism of bacteria and other simple unicellular organisms , 2. WithE.coli, the short-term metabolic response to genetic and environmental perturbations is characterized by a growth arrest and by the activation of a number of latent pathways, a strategy which can favor the survival of the organism at the expenses of efficient biomass production  and u = [u1 … un], and S is the stoichiometric matrix. The FBA optimal flux vector is given byg = ξTv is the growth rate, i.e., the linear combination of fluxes that constitutes the biomass reaction. When the optimum is degenerate, a secondary optimization criterion can be used to discriminate among equivalent optimal solutions. For example, overall enzyme investment is minimized by the pFBA solution vpFBA, which corresponds to minimization of the sum of the  fluxes [In FBA , the pol) fluxes .k = {vk, Γk}k = 0,1,2,…, where v0 is a randomly chosen initial condition in Γ0 = Γ. The stochastic process can be summarized as follows. At step k, assume the population of bacteria has an homogeneous metabolism, i.e., all cells have the same nk active reactions with the same fluxes vk−1 (this corresponds to a specific sampling of our Markov chains). From vk−1, it is possible to obtain nk + 1 different phenotypes, corresponding to the resilencing of one of the enzymes (nk possibilities) or to the current phenotype remaining unchanged for another step. The nk possible silencings of a reaction yield the nk reduced polytopes Γk,i = Γk−1 ∩ {ℓi = ui = 0}, i = 1, …, nk. The corresponding fluxes vk,i are computed via a MOMA projection on these reduced polytopes:Following , we assuvk,i leads to a possible growth rate: gk,i = ξTvk,i, i = 1, …, nk. Viable phenotypes have gk,i > 0 while non-viable phenotypes  have gk,i = 0. In what follows these growth rates will be placed on the diagonal of a fitness matrixgk,0 represents the current growth rate.Each choice of nk + 1 possible choices gk,i, it is possible to associate selection probabilities through a basic replicator equation which uses the gk,i as fitness function. Denote pk,i, i = 0, 1, …, nk, the probabilities (or frequencies) associated to the gk,i. If Δt is the time duration of each step, then the replicator equation isuniform priors: at the begin of the time interval the selection probability is pk(0) = 1/(nk + 1), where non-uniform priors: at the begin of the time interval the selection frequencies are not uniform but are themselves expressible as a Boltzmann distributionβk has the interpretation of an inverse temperature. In this case, at the end of the time interval we obtainA through derivation of these selection probabilities is available in the To the pk(Δt) has the meaning of transition probability between the current state 𝓢k−1 = {vk−1, Γk−1} and the possible states achievable at the k-th step 𝓢k,i = {vk,i, Γk,i}, i.e., i = 0, 1, …, nk. Since the fluxes vk,i can take any value between lower and upper bound, the corresponding transition matrix is infinite dimensional. However, in order to understand the properties of the stochastic process we are considering, it is useful to look at its projection over the subspace of active reactions . In terms of this projection, the possible states of the Markov chain are the 2r possible combinations of the r reactions of the network, see r = 4. Denote 𝓩1, …, 𝓩r2 these discrete states and Pij = ℙ(Xk = 𝓩i ∣ Xk−1 = 𝓩j) the corresponding transition probabilities. As in our model the resilencings are irreversible, P is triangular, i.e., it is completely reducible, see P is the result of a projection, it is P = P(v), i.e., the exact transition probabilities pk depend on the values of the fluxes and hence on v0. However, even in the complete model the fully reducible structure is preserved. In particular it follows that a certain number of states 𝓩i must correspond to ergodic classes, i.e., “absorbing” states in which the Markov chain stabilizes. Full reducibility implies that each ergodic class is composed of a single state. Periodic chains of states are impossible.In both cases described above E.coli [E.coli central metabolism , hence numerical computations are necessarily limited to a fraction of all possible trajectories. For this study, some 105 trajectories have been generated, starting from randomly chosen initial conditions in the polytope of admissible fluxes Γ and using various forms for the priors.The metabolic adaptation process described in Methods and in E.coli . In ordegFBA, and for nearly 50% of all trajectories the growth at the end-point is ≥ 0.85 gFBA, see g/gFBA < 0.85. Much more remarkable is the correlation between the end-point flux distribution v and the flux distribution given by the pFBA criterion vpFBA: the mean of the correlation is 0.96 and the median is 0.98, with 88% of all trajectories achieving a correlation of at least 0.9, see vpFBA, regardless of the biomass they can produce, see Fig. A of Given the irreversibility of the resilencing, the number of steps required to reach an end-point state can be computed from the trajectories. A trajectory is considered absorbed into an end-point state  when no further silencing happens for 5 consecutive steps. With this stopping condition, the expected time until absorption of our trajectories is 24.6 ± 4.1 steps. Except for pathological initial conditions , all trajectories stabilize to flux vectors of positive growth. Nearly 20% of all trajectories reach the maximal growth computed by the FBA criterion, The time evolution of the 3D histogram of vpFBA, although through slightly different paths. None of the trajectories of the second row of Fig. D of gFBA. However, all of the end-points flux vectors become aligned with vpFBA (correlation higher than 0.97). In this case the two values of g reached by the trajectories correspond to two different ergodic states, as can be seen by the grouping of the number of active reactions eventually reached. It should be observed how for this phenotype of non-optimal growth the number of reactions is much less than for vpFBA. This is indeed a constant pattern in our metabolic adaptation strategy. As can be seen in Fig. G of R of active reactions of v and g are positively correlated: for strains that have sub-optimal growth more resilencings are possible i.e., more directions with slow but positive Δg exist and are explored. In fact, Fig. G of L of a trajectory is inversely correlated with the growth g of v.Examples of the resulting trajectories are shown in Figs. D-F of vpFBA, i.e., to alternative FBA optima. An example of such trajectory is shown in Fig. E of vpFBA, a few do not (one is shown in green), and stabilize in an alternative FBA flux vector of correlation 0.75 with vpFBA. Cases like this lead to a correlation corr which decreases when vk falls into the basin of attraction of a local maximum other than vpFBA. In the ensemble of the trajectories, however, these situations are unfrequent: if we look at the average of all trajectories, corr is always monotonically increasing, regardless of the final g achieved, see g is monotonically growing on the vast majority of the trajectories , then the convergence rate to v becomes aligned with vpFBA, the growth rate it can produce depends on the norm of v. In fact, v‖ at ergodicity and g: when the recursive process of silencings and adjustments leads to a v which is smaller in norm than vpFBA, also the corresponding g will be smaller than gFBA.It follows directly from the linearity of the expression for the biomass that when a trajectory v of norm comparable to vpFBA, one can look at how many of the bounds that delimit the polytope of admissible fluxes at step k, Γk, become active during the adaptation . Fig. N of v‖ < ‖vpFBA‖) tend to saturate less than those achieving higher growth. Hence fluxes that tend to stay in the interior of the polytope rarely will reach a high ‖v‖. From Fig. O of In order to understand when an initial condition can lead to an end-point 3 genes differentially expressed [Mathematically, the dynamical model used in this paper to describe metabolic adaptation has many aspects in common with standard evolutionary models based on natural selection . The onlxpressed . A similxpressed . After av0, is chosen randomly in the polytope Γ, which implies that at the begin of the Markov chain most reactions are already active.As shown in , differeE.coli mutants can be reproduced closely by the metabolic adaptation process described in the Methods section. Proceeding in this way corresponds to fixing specific initial conditions on the Markov chains, and following the specific family of trajectories that results from them (activatory phase included). It becomes then interesting to see what happens when these “nominal” trajectories are compared to more general trajectories in which the initial fluxes v0 are randomly chosen in Γ. For glucose as single carbon source, the two types of trajectories are compared in Fig. M of vpFBA. Notice how the pgi mutant has a secondary peak at low correlation: this corresponds to a less frequent second phenotype of lower growth, described in [When instead the effect of a specific perturbation can be explicitly included in the FBA model, then the Markov chains can be used to investigate also the early stages of the transient, with the activation of the latent pathways. This is the point of view taken in , where tribed in . Such a ribed in  and the A number of possible optimality criteria alternative to biomass optimization have been investigated in the literature , 28–30. vpFBA, as Figs. J-L of vpFBA). On the contrary, in the case of all reversible reactions the ratio g/gFBA achieved by the trajectories is even better than in g of 0.91gFBA and a median value of 0.997gFBA, see Fig. L of It is shown in  that in a priori guarantee that a greedy fitness landscape constructed in this way i) may be regular; ii) may achieve maximal growth, and iii) may lead to flux distributions that resemble those of the pFBA. In our trajectories, in fact, what we observe is that the fitness landscape is rugged, but the plethora of local maxima have all a very small basin of attraction, as opposed to the global maximum which attracts around 50% of all trajectories when we count based on growth. If instead we look at normalized flux distributions then the basin of attraction of vk on vpFBA. The robustness of the convergence is also reflected in the low sensitivity to the randomness of the Markov chains, see It is worth remarking that the method used in this paper is fundamentally different from a dynamical FBA . In the In conclusion, one can say that simple flux reorganization rules based on local fitness are sufficient to drive the cell toward a more efficient use of the metabolic resources. It is quite remarkable that most of the trajectories end up in the pFBA optimum, without knowing it, and without ever using growth rate to update metabolic fluxes . Clearly this fact provides a further evidence in favor of the FBA criterion, and one could even speculate that it provides a more fundamental principle, from which FBA follows as a corollary.S1 textDetails of the population dynamics model and of the selection probabilities. Further considerations of the method and on its applicability.(PDF)Click here for additional data file.


NADPH regeneration capacity is attracting growing research attention due to its important role in resisting oxidative stress. Besides, NADPH availability has been regarded as a limiting factor in production of industrially valuable compounds. The central carbon metabolism carries the carbon skeleton flux supporting the operation of NADPH-regenerating enzyme and offers flexibility in coping with NADPH demand for varied intracellular environment. To acquire an insightful understanding of its NADPH regeneration capacity, the elementary mode method was employed to compute all elementary flux modes (EFMs) of a network representative of central carbon metabolism. Based on the metabolic flux distributions of these modes, a cluster analysis of EFMs with high NADPH regeneration rate was conducted using the self-organizing map clustering algorithm. The clustering results were used to study the relationship between the flux of total NADPH regeneration and the flux in each NADPH producing enzyme. The results identified several reaction combinations supporting high NADPH regeneration, which are proven to be feasible in cells via thermodynamic analysis and coincident with a great deal of previous experimental report. Meanwhile, the reaction combinations showed some common characteristics: there were one or two decarboxylation oxidation reactions in the combinations that produced NADPH and the combination constitution included certain gluconeogenesis pathways. These findings suggested cyclization pathways as a powerful way for NADPH regeneration capacity of bacterial central carbon metabolism. When oral (OH•) . The cenal (OH•) ,5. Certaal (OH•) . TBrookeal (OH•) ,8. The ral (OH•) .+ [Pseudomonas fluorescens, which results in more NADPH generation and an inhibition of NADH generation[Escherichia coli, we also found that oxidative stress could induce a transition in the central carbon metabolism system from its normal condition to a sub-optimal condition, where more NADPH could be generated[In these anti-oxidative metabolites, it is reduced nicotinamide adenine dinucleotide phosphate (NADPH) that has the central role in the cells' anti-oxidative defense strategies in most organisms. It is the shared carrier for all the cellular reducing power and the primary participant in anti-oxidation. Through+ . Therefo+ ,5. For eeneration. In Eschgenerated.Escherichia coli[Escherichia coli NAD-dependent glyceraldehyde 3-phosphate dehydrogenase (GAPDH) with a NADP-dependent enzyme from Clostridium acetobutylicum [Clostridium acetobutylicum in Corynebacterium glutamicum and almost trebled the NADPH availability [Besides, NADPH provides basic reducing equivalence for reductive whole-cell biotransformation and NADPH-dependent enzymes play important roles in manufacturing industrially valuable compounds. As a result, the bioavailability of NADPH within the cell is often the rate-limiting factor for the over-production of desired compounds and improving NADPH regeneration capacity becomes one of the objects of current metabolic engineering. Siedlerchia coli. Martı´nutylicum . Jiang elability .Although the central carbon metabolism system is not very complicated, combinations of its various sub-pathways result in substantial flexibility and diveThe theoretical analysis presented in this work uses the concept of “elementary flux modes/extreme pathways” (EFMs) as its base ,20,21. AElementary flux modes have been applied successfully in metabolic network analysis for several cases. For example, Figueiredo et al. established all potential NAD synthesis and degradation pathways by use of EFMs, and found that substrate specificity differed significantly in species like yeasts and humans. ThroughIn this study, using a central carbon metabolism networks modified from that one reconstructed by Palsson et al., all EFME.coli’s biomass composition was taken to represent the biomass synthesis. In total, 72 reactants and 97 reactions are involved, of which 20 reactions are responsible for exchange of intracellular and extracellular materials. The network captures a full representation of the central carbon metabolism of bacterium In contrast, this network does not contain the compartment information. However, it would also be applicable to eukaryotic organisms, since the transportations between compartments would not affect the elementary flux mode enumeration. The reversibility of the reactions is defined mainly based on original articles and the BRENDA database[+ dependent and NADP+ dependent) were considered in this study. No other restriction was applied in the computation.The metabolic networks for EFM computing and subsequent analyses are detailed in  database. For exa2) and to simultaneously generate D–Ribulose-5–phosphate and NADPH. “ICDHyr” catalyzes isocitrate oxidation to generate 2-Oxoglutarate and NADPH. “ME2” produces PYR and NADPH via malate oxidative decarboxylation. Thus, NADPH regeneration flux of the central carbon metabolism system could be defined as:The NADPH fluxes are as follows: “G6PDH2r” catalyzes G-6-PDH to simultaneously generate 6-phospho-D-glucono-1,5-lactone and NADPH. “GLUDy” catalyzes Glutamate to simultaneously generate 2-Oxoglutarate and NADPH. “GLUSy” catalyzes the transamination between 2-Oxoglutarate and Glutamine, thereby generating 2-molecular Glutamate by consuming 1 NADPH molecule. “GND” catalyzes 6-Phospho-D-gluconate to release carbon dioxide  of sample number for each category could be considered as an indicator of the degree of balance in clustering. Among the 49 clustering results, the optimal cluster number was determined by combining Q and SD.ΔfGi'° is the formation free energy of chemical compound i, m is the number of compound categories that participate in the reaction, ni is the stoichiometric coefficient of compound i in the reaction, R is the universal gas constant, T is Kelvin temperature of 37°C that is optimal for growth of most organisms, and xi is the activity or concentration of compound i.The most common criterion to evaluate the thermodynamic availability of a reaction is the change in Gibbs free energy under physiological condition. The Gibbs free energy for a given reaction (or reaction group) can be calculated as ,32:ΔrG'E. coli from Chassagnole et al. and Bennett et al. was used as the representative value under normal physiological conditions [-5M and a maximum of 0.02M, and the intracellular H ion concentration was set to pH = 7 as previously described[fGi'° could not be measured for most materials, the group contribution method was used to calculate the value [The concentration value of corresponding metabolites in nditions ,34. Sincnditions , the randescribed. As ΔfGihe value ,37.fG' value from Eq  was taken as the primary testing result, and the response surface chart is shown in The optimal clustering results are shown in Mean flux values of the cluster center are shown in E. coli’s metabolic enzymes could form an NADPH generation network, during which ME flux demonstrated significant up-regulation. Moreover, due to the poor correlation between ME and G6PDH, the fluxes of both reactions could be increased at the same time, through certain biological operations.Briefly, either G6DPH or GND could bear a large flux themselves, so they are major contributors to total NADPH generation. Specifically, the maximal total NADPH flux can be obtained if both G6PDH and GND fluxes are high while other reactions have nearly zero flux. Meanwhile, ME plays an important role in total metabolism flux. One certain suboptimal value of total NADPH flux is achieved by increasing ME flux and decreasing other fluxes. Singh et al. reported that serial operation of Contrarily, ICDH contributes less to NADPH flux, which might be attributed to the small ICDH flux. Only when the whole tricarboxylic acid cycle is at a high level does the ICDH contribution to NADPH increase to 50%. That indicates that although ICDH is an important NADPH-generating enzyme during general physiological functioning, it does not have the potential to increase. In addition, GLUDy and GLUSy always have similar fluxes, so the generated and consumed NADPH cancels each other out. Therefore, this branch does not make an obvious contribution to NADPH generation.Based on the above distributions, it could be observed that it is difficult to amplify the fluxes of these reactions simultaneously without changing the topology structure of the metabolism network, because of the trade-off between different reactions. To activate the NADPH generation capacity of the central carbon metabolism pathway, emphasis should be put on G6PDH, GND, and ME rather than on the other two pathways that have little space for improvement.Several different cyclized flux modes with high NADPH availability were observed in the clustering results, namely the PP-EMP cycle, PP-ED-EMP cycle 1, PP-ED-EMP cycle 2, and ME-PPC cycle, ME-GLX cycle and ME-TCA cycle . The cheE. coli’s NADPH generation. As seen in Afterwards, the structural constitutions of the elementary modes with high NADPH generation capacity were analyzed. The mode corresponding to The two NADPH generation modes in top of 2 for 2 NADH and 2 NADPH regeneration.The other three modes are related to malic enzyme. In bottom of In 2. This process generates 1 mol NADH and NADPH.In The above six modes have some shared characteristics. Firstly, to enable high NADPH productivity, all six modes form an open loop based on a combination of various metabolism pathways. The loop is necessarily open otherwise it is not allowed in thermodynamics. Secondly, these open loops are conservative in structure. There is always a carbon skeleton input reaction for each loop as shown in black in Chemical thermodynamic analysis is required to verify whether the elementary modes obtained from mathematical analysis can operate under normal physiological conditions. For chemical reactions/combinations, the framework for thermodynamic analysis is already relatively mature ,32,36, bTo be representative, the values measured in the steady logarithmic growth phase were considered to be the stress-free under natural physiological conditions ,34. BaserGm’, highest possible ⊿rGm’, and lowest possible ⊿rGm’ were computed, with the results shown in rGm’, the top end of the bar chart is the highest possible ⊿rGm’, and the bottom end is the lowest possible ⊿rGm’. For the PP-EMP cycle, the values were -40.9, -10.3, and -71.5 kCal/mol, respectively. For the PP-ED-EMP cycle 1, the values were 2.34, 15.6, and -53.0 kCal/mol. For the PP-ED-EMP cycle 2, they were -22.1, 0.144, and -46.9kCal/mol. For the ME-PPC cycle, they were -2.32, 14.5, and -27.8kCal/mol. The physiological⊿rGm’s of ME-GLX and ME-TCA cycle are both less than zero. From the thermodynamic values, it can be seen that the PP-EMP cycle, PP-ED-EMP cycle 2 and ME related cycles are physiologically preferred and can happen under natural physiological condition. The lowest possible ⊿rGm’ of the PP-ED-EMP cycle 1 was significantly less than zero, while the activity of metabolites changed while super-oxidative stress occurred[Then, the normal ⊿ occurred. This coEscherichia coli and confirmed that it was due to a partial cyclization of the pentose phosphate pathway by 13C metabolic flux analysis [Corynebacterium glutamicum. TheΔpfkA mutant strain reached a yield of 4.8 mol NADPH mol-1 glucose while theΔgapA mutant reached a yield of 7.9 mol NADPH mol-1 glucose[E. coli are subject to oxidative stress, the PP-EMP cycle reduces the glycolysis pathway and increases the pentose phosphate pathway [The physiologically feasibility proposed by the thermodynamic analysis has placed our calculation and analysis on solidated and safe position. However, the prediction capacity and confidence of the framework should be confirmed in context of real experiments. After a thorough mining of current literature of related topics, most of these cyclized pathways calculated has indeed been reproduced in other experimental reports. Siedler et al. doubled the NADPH regeneration rate by deleting the phosphofructokinase gene pfkA in analysis . Immedia1 glucose. Both si pathway ,40. ThisPseudomonas under oxidative stress from clinical infection, and found that carbon metabolism flux completely transferred from the EMP pathway to G6PDH. Moreover, most 6-phospho-D-glucono-1,5-lactone entered the ED pathway after G6PDH, rather than through the non-oxidative branch[Pseudomonas fluorescens SBW2 wild type underwent a significantly high flux in gluconeogenic pathway, which together with a vigorous ED pathway formed a PP-ED-EMP cycle 1 as in this study. This flux distribution had contributed to an obviously higher NADPH production than that of a mutant strain [Gluconobacter oxydans 621H degrade the glucose via partially cyclic Pentose Phosphate Pathway and Entner-Doudoroff pathway, which are no other than the EMP-PP cycle and PP-ED-EMP cycle 1[Secondly, PP-ED-EMP cycles are also observed. Berger et al. investigated the flux distribution of ve branch. This sit strain . MoreoveP cycle 1.Saccharomyces cerevisiae, the ME-PPC cycle was activated by malic enzyme, malate dehydrogenase and pyruvate carboxylase. This metabolic shunt achieved a transhydrogenase-like shunt [3) treatment. In one genotype, the increase in PPC activity was quite well correlated to the increase in NADP-ICDH activity and NADP-ME activity. This phenomenon resembled the activation of ME-TCA cycle [Additionally, the ME related cycles are also common in physiological experiment. In a xylose-fermenting recombinant ke shunt . Dghim eCA cycle .NADPH regeneration capacity of central carbon metabolism system was better understood through computation of its EFMs. An SOM clustering algorithm was applied to EFMs with high NADPH productivity, and 16 categories were obtained. The relationship between each NADPH generating enzyme and total NADPH flux was discussed. Several cyclic pathways that supported high NADPH generation were found, and proved to be totally feasible in cells via thermodynamic analysis. Comparison with previous studies suggested that these pathways were indeed NADPH generation strategies used by various organisms. Meanwhile, the pathways showed some shared characteristics: an open loop was formed based on the combination of various metabolism pathways, and one or two decarboxylation oxidation reactions in the loop generate NADPH; there are also certain gluconeogenesis pathways in some loop’s constitution. Our results suggested that analyzing the relationships between various metabolism pathways at an overall systematic level facilitates the understanding of metabolic-related changes—this not only indirectly validates the flexibility of the bacteria’s operation on metabolism branches, but provides a new perspective for designing combinations of different metabolic reactions to achieve desired cofactor availability and internal environment.S1 Appendix(DOC)Click here for additional data file.S2 Appendix(DOC)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.


Nucleotide degradation is a universal metabolic capability. Here we combine metabolomics, genetics and biochemistry to characterize the yeast pathway. Nutrient starvation, via PKA, AMPK/SNF1, and TOR, triggers autophagic breakdown of ribosomes into nucleotides. A protein not previously associated with nucleotide degradation, Phm8, converts nucleotide monophosphates into nucleosides. Downstream steps, which involve the purine nucleoside phosphorylase, Pnp1, and pyrimidine nucleoside hydrolase, Urh1, funnel ribose into the nonoxidative pentose phosphate pathway. During carbon starvation, the ribose-derived carbon accumulates as sedoheptulose-7-phosphate, whose consumption by transaldolase is impaired due to depletion of transaldolase’s other substrate, glyceraldehyde-3-phosphate. Oxidative stress increases glyceraldehyde-3-phosphate, resulting in rapid consumption of sedoheptulose-7-phosphate to make NADPH for antioxidant defense. Ablation of Phm8 or double deletion of Pnp1 and Urh1 prevent effective nucleotide salvage, resulting in metabolite depletion and impaired survival of starving yeast. Thus, ribose salvage provides means of surviving nutrient starvation and oxidative stress. In natural environments, microbes face myriad environmental stressors including starvation for essential nutrients, such as carbon, nitrogen and phosphorous. Yeast has evolved metabolic responses to these stressors, which enable their survival and effective resumption of growth when conditions improve. Recent evidence suggests that these metabolic responses are substantially hardwired in metabolic enzymes themselves . In paraA particularly important function of these kinases is to control levels of ribosomes, which constitute about 10% of yeast dry weight. This is achieved through regulation both of ribosome production and of ribosome degradation via autophagy (ribophagy) . RibosomThe carbonaceous product of nucleotide degradation is ribose-5-phosphate, which must be converted into glycolytic intermediates in order to extract energy and generate anabolic precursors. Such conversion is carried out by the nonoxidative pentose phosphate pathway, a series of five reversible reactions whose net stoichiometry is 3 ribose-5-phosphate ←→2 fructose-6-phosphate (F6P)+1 glyceraldehyde-3-phosphate . Both F6E. coli could also utilize the glycolytic enzyme phosphofructokinase (Pfk1) to phosphorylate S7P into SBP, which is further converted to erythrose-4-phosphate (E4P) and glycolytic intermediate dihydroxyacetone phosphate , the direct product of RNA degradation, increased only slightly. Nucleosides and bases, however, rapidly accumulated to greater than 10-fold basal levels  to measure the changes in the metabolome profile of l levels . Moreove13C-glucose for 70 min followed by carbon starvation , AMP-activated protein kinase (SNF1), and target of rapamycin complex 1 (TORC1). PKA is an inhibitor of macroautophagy but is inactivated upon glucose removal . SNF1 is species . Thus, b species . To test species . Thus, Tin vitro  . In contlower Km ; thus, PP levels . Thus, wPNP1 or URH1 or both. Following carbon starvation, the pnp1 strain accumulated more of the nucleosides, inosine and guanosine and less of the bases hypoxanthine and guanine than did wild-type cells; similarly urh1 accumulated more uridine and cytidine and less uracil  and pyrimidine uridine hydrolase (Urh1) have been shown to catalyze these reactions . To inves uracil . Adenosiectively . StrainsPGM3, but not PGM1 or PGM2, led to accumulation of ribose-1-phosphate and upstream purines in the ribose salvage pathway (PRM15.Further metabolism of ribose-1-phosphate requires its conversion to ribose-5-phosphate. Phosphoglucomutase 3 (Pgm3) has been proposed to be a phosphoribomutase capable of catalyzing this conversion . Consist pathway . Thus, PS. cerevisiae cannot utilize ribose as the sole carbon source, in the absence of glucose, it did assimilate extracellular ribose, albeiet at a slow rate  has been annotated as a ribokinase due to its similarity to ribokinases in other organisms. While low rate . Rbk1 delow rate . Thus, aTKL1/TKL2), preventing conversion of pentose phosphates into sedoheptulose7-phosphate. Unlike wild-type, the tkl1/tkl2 strain did not accumulate S7P and SBP upon carbon starvation  led to chronic S7P accumulation  into F6P and E4P. Indeed, genetic inactivation of both transaldolase isozymes  as sole carbon source. DHA can be transported into yeast cells and phosphorylated into DHAP, which then forms GAP. These reactions can support yeast growth, but only after several days of adaptation . In the The results from the above experiments present a conundrum regarding the source of SBP. Previous studies have shown that SBP is produced in yeast via a reversible reaction catalyzed by FBP aldolase, whose substrates are DHAP+E4P . HoweverE. coli phosphofructokinase can phosphorylate S7P to SBP . Moreover, many degradation enzymes have promiscuous activity against a diversity of substrates, rendering their functions difficult to determine from biochemistry alone . For exaotidases  and nuclotidases , but whiotidases .PHM8 deletion occurred in S7P and SBP levels, which are more sensitive to flux through the ribose salvage pathway than are Phm8’s direct substrates and products. Measurement of these more distal metabolites was a key benefit of metabolomics over a more targeted analytical approach.To analyze the physiological function of nucleotide degradation enzymes in yeast, we employed metabolomic analysis of targeted deletion strains , and exabcy1 and snf1) exhibited a distinct pattern of PPP metabolites , an essential activator of the PEP-consuming enzyme pyruvate kinase. The elevated PEP provides a readily accessible reserve of high-energy phosphate bonds, which facilitate fast uptake of glucose if it becomes re-available , 2012b. phm8 deletion strain, however, show that nucleotide salvage plays an indispensable role. This can be rationalized based on the abundance of ribosomes, which are needed in large amounts only during rapid growth . In organisms where Phm8 orthologs are present, our results may directly facilitate mapping of their nucleotide degradation pathways. In other organisms, the approach laid out here may translate even though the gene product does not. For example, although mammalian cells are not normally subject to acute starvation, autophagy is essential for survival of the neonatal period  deletion set . Double Saccharomyces cerevisiae was characterized as described previously  coupled by electrospray ionization (ESI) (negative mode) to a high-resolution, high-accuracy mass spectrometer  operated in full scan mode at 1 s scan time, 10standard . Isomerseviously . Metaboleviously . Energy eviously .S. cerevisiae genomic DNA. The amplified fragments were cloned into a modified pET15b vector  and overexpressed in the E. coli BL21(DE3) Gold strain  as previously described (p-nitrophenyl phosphate (pNPP) and 90 phosphorylated metabolites as described previously (Km and kcat), phosphatase activity was determined in the presence of 5 mM MgCl2 over the range of substrate concentrations (0.001–9.5 mM), and the kinetic parameters were calculated by nonlinear regression analysis of raw data to fit to the Michaelis–Menten function using the GraphPad Prism Software .The genes encoding Phm8 (Yer037w) and Sdt1 (Ygl224c) were amplified by PCR using escribed . The receviously . For theSupplementary Figures S1–4, Supplementary Tables S1–3