Scheffersomyces stipitis exhibits great potential for the efficient lignocellulosic biomass fermentation. Therefore, a comprehensive understanding of its unique physiological and metabolic characteristics is required to further improve its performance on cellulosic ethanol production.As one of the best xylose utilization microorganisms, S. stipitis CBS 6054 was developed on the basis of its genomic, transcriptomic and literature information. The model iTL885 consists of 885 genes, 870 metabolites, and 1240 reactions. During the reconstruction process, 36 putative sugar transporters were reannotated and the metabolisms of 7 sugars were illuminated. Essentiality study was conducted to predict essential genes on different growth media. Key factors affecting cell growth and ethanol formation were investigated by the use of constraint-based analysis. Furthermore, the uptake systems and metabolic routes of xylose were elucidated, and the optimization strategies for the overproduction of ethanol were proposed from both genetic and environmental perspectives.A constraint-based genome-scale metabolic model for S. stipitis could be used as a starting point for future experiment designs aimed at identifying the metabolic bottlenecks of this important yeast.Systems biology modelling has proven to be a powerful tool for targeting metabolic changes. Thus, this systematic investigation of the metabolism of  Saccharomyces cerevisiae is considered as the most suitable biocatalyst for industrial ethanol production from sugars or starch feedstocks for its well-characterized genetics, ample genetic tools, high ethanol productivity and so on [Zymomonas mobilis. It was reported that for Z. mobilis the maximum yield of ethanol could reach 97% of the theoretical yield and the tolerance of ethanol was up to 120 g/l [Z. mobilis and S. cerevisiae, have been carried out to develop more efficient ethanol producers, the success is not very satisfactory [Along with the increasing stress on the shortage of oil reserves and the negative ecological impacts of greenhouse gas emissions, there is a trend for searching of the renewable clean fuels to substitute the traditional fossil fuels worldwide -3. Currend so on . Anothersfactory ,11.Scheffersomyces stipitis, formerly known as Pichia stiptis[S. stipitis were unclear, such as the slow sugar consumption rate [S. stipitis were poorly characterized, which hinders the effective gene manipulation for strain improvement. Hence, a systematic understanding of physiological features and metabolic capacities of S. stipitis is in great need and genome-scale metabolic model (GSMM) could provide such a platform.A naturally occurring xylose-fermenting yeast a stiptis, was proa stiptis. Other aa stiptis, simple a stiptis. Howeverion rate  and the ion rate . Besideshttp://systemsbiology.ucsd.edu/InSilicoOrganisms/OtherOrganisms) and the number is still growing owing to the high-throughput genome sequence technologies. GSMMs have been successfully applied to many aspects, such as the design of the metabolic engineering strategies, the understanding of microbial physiology, the contextualization of various omics data, etc. [S. stipitis has been reconstructed to investigate some key metabolic traits [iTL885 is presented. Compared with the previous model, our model captured more metabolic genes for the adoption of an integrated genome annotation way. In addition, many carbohydrate metabolic pathways were included to represent the unique characteristic of S. stipitis. Aside from the study of the physiological changes of ethanol production, the new model was mainly used to make predictions in prior to experiment validation, which is one of the most important applications of constraint-based models. In this research, the proposed model was used to predict the essentiality of the genes and evaluate the capacity of ethanol production with xylose as carbon source.Up to now, there are more than 80 published genome-scale metabolic models . Meanwhile, a ‘KO list.xlsx’ with KEGG ORTHOLOGY (KO) identifiers corresponding to the assigned genes was obtained by KEGG Automatic Annotation Server (KAAS). By the integration of the two genome annotation results, a draft model including 1139 reactions and 850 genes was achieved. Then, the draft model was curated with the biochemical information from databases and literature . Following the main reconstruction steps described in Figure S. stipitis. By the combination of information from the sequenced genome, transcriptional expression [S. cerevisiae, but not the remaining 28 monosaccharide transporters for some of which were unique to S. stipitis, such as the arabinose-proton symporter (AUT) and xylose transporters (XUT), reflecting the capabilities of pentose utilization [S. stipitis. A map illustrating the central carbohydrate metabolism is provided  and rhamnose metabolism encoded by four genes (LRA1-4) were also added to the model by extensive literature mining [During model reconstruction, various sugar transport reactions and metabolic pathways were manually checked and added to the draft model for a better understanding of the carbohydrate metabolism in pression  and expepression , 36 putalization . The newe mining -25.iTL885 comprises 885 metabolic genes, 1240 reactions, and 870 metabolites. The 1240 metabolic reactions were distributed over 61 metabolic pathways and located into three cellular compartments. Compared with iMM904 (13.9%) and iBB814 (13.7%), the gene coverage of iTL885 is the highest, about 15.2%  and metabolism of glycerolipid and sphingolipid. In addition, nearly 92% of the metabolic reactions were associated with certain genes and the carbohydrate metabolism contained the largest percentage of metabolic genes, which was consistent with the physiological property of S. stipitis to use most of the sugars present in biomass substrates [The resulting genome-scale metabolic model  iMM904 1.9% and is Figure , and thebstrates . MeanwhiiTL885, 130 genes  were predicted to be essential on a minimal medium with glucose as carbon source. This percentage was close to that of S. cerevisiae (12.9%) [XYL1 (PICST_89614), XYL2 (PICST_86924), PGI1 (PICST_84923), and TAL1 (PICST_74289). Of them, XYL1 (xylose reductase) and XYL2 (xylitol dehydrogenase) encode the two initial enzymes of xylose metabolic pathway, which has been introduced to S. cerevisiae for the production of lignocellulosic ethanol [PGI1 (glucose-6-phosphate isomerase) and TAL1  link the pentose phosphate pathway to glycolysis by the formation of key glycolysis intermediate D-fructose 6-phosphate  were predicted to be nonessential on the xylose medium. Actually, two independent ethanol synthesis pathways were identified. One is the common cytoplasmic ethanol pathway, the other is the mitochondrial pathway encoded by ADH3 (PICST_88760), a mitochondrial alcohol dehydrogenase (absented in iBB814). However, the latter pathway functioned only when the cytoplasmic pathway was eliminated, which had been experimentally validated [The essentiality of each gene to cell growth was evaluated by removing each individual reaction from the stoichiometry matrix (see Method section). In the model  12.9%) . As illu PICST_749. Of the.9% . As alidated . The lisS. stipitis[Oxygen is a key factor that affects the production of ethanol in  stipitis,30,31. H stipitis. However stipitis. The resPDC, ALD and ADH) for ethanol production were greatly improved under the oxygen-limited condition [S. stipitis has spurred numerous studies on the overexpression of non-oxidative PPP genes  to improve the utilization of xylose in the recombinant S. cerevisiae[S. stipitis[More specifically, the distributions of carbon flux under different oxygen levels (aerobic and semiaerobic) were investigated by flux balance analysis (FBA) Figure . It was ondition . Meanwhierevisiae as well  stipitis. However stipitis.S. stipitis was mainly focused on the illustration of transport mechanism and metabolic pathway [iTL885, seven putative high-affinity xylose transporters (XUT1-7) were annotated, and one of them (XUT1) has been biochemically characterized from S. stipitis[S. stipitis genome, which ensures the quick cellular response to the change of xylose in the environment, as the transcriptional data showed that the transcription of RGT2 with xylose could increase 65-fold [Previous study of xylose utilization in  pathway ,37. In t stipitis. However stipitis,38. As a 65-fold .XYL1 (PICST_89614), XYL2 (PICST_86924), and XKS (PICST_68734), respectively [AAD1), D-ribulose reductase (ARD2) and D-ribulokinase (RKS1), which was found due to the fact that xylose still can be metabolised in the XKS disruption strain [The assimilated xylose can be metabolised via two catabolic routes: xylulokinase pathway and D-arabinose utilization pathway Figure . Xylulokectively . Based on strain . This paS. stipitis[ALA2 (PICST_70108), which led to a considerable increase of ethanol accumulation rate. The third effective strategy was to augment the supply of NADPH by deleting the NADP-dependent glutamate dehydrogenase gene GDH3 (PICST_82969). This optimization approach not only increased ethanol production rate about 3.4%, but had a negligible influence on cell growth (with the maximum growth rate remain at 0.07 mmol/gDCW/h).Efficient production of xylose-derived ethanol is of particular interest for  stipitis,42. To gALA2 deletion strain could improve ethanol production rate up to 1.29 fold of the control  and one fungus (A. niger). The thresholds of the bidirectional BLAST (BLASTp) for a functional sequence were set to have an e-value less than 1 × 10-30, an amino acid sequence identity above 40%, and a matching length at least 70% of the query sequence. To obtain a original reactions list, also called in-house model, GSMMs of S. cerevisiae iMM904 [P. pastoris iPP668 [A. niger iMA871[S. cerevisiae. As a result, a draft model was developed and used as a start point for subsequent network refinements. With the biochemical information acquired from public databases such as KEGG [The availability of whole genome of  stipitis enables  stipitis,46. Firsdatabase . Then, te iMM904 , P. pasts iPP668  and A. ner iMA871 were seler iMA871 was useder iMA871 and assi as KEGG , MetaCyc as KEGG , BRENDA  as KEGG , and TCD as KEGG . A detaiAll computational simulations were performed using COBRA toolbox  on Matla-1) to predict the maximum ethanol production rate at each controlled oxygen uptake rate. The aerobic condition was simulated by uncostraining the oxygen uptake rate, and the semiaerobic condition by constraining the exchange reaction of oxygen to −5 mmol/gDW/h. To modelling the amino acids addition, each of amino acid was constrained to have a maximum consumption rate of 0.1 mmol/gDCW/h.All the simulations were performed on a minimal medium with limited carbon source. The uptake rates of ammonia, sulphate, phosphate, sodium, kalium, and ferrite were unconstrained with the lower and upper flux bounds of −1000 and 1000 mmol/gDW/h respectively. Xylose or glucose was set as sole carbon source with a uptake rate of 3 mmol/gDCW/h . The robin silico knockout was performed by constraining the flux value of its corresponding reaction to zero when maximizing the growth rate. This method also works for the complex GPRs such as isoenzymes and multiplex enzymes. If the maximum growth rate of the gene knockout strain is less than 1 x 10-6 of the wild type, the deleted gene is defined as essential. Otherwise, it’s a nonessential gene. The OptKnock algorithm in COBRA toolbox identifies candidate genes that lead to the overproduction of desired metabolite [The computational single gene deletion was conducted to predict the important genes for the synthesis of building blocks of cellular biomass . For a gtabolite ,60. WithGSMM: Genome-scale Metabolic Model; BLAST: Basic Local Alignment Search Tool; KO: KEGG ORTHOLOGY; KEGG: Automatic Annotation Server (KAAS); COBRA: Constraint-Based Reconsruction and Analysis; PPP: Pentose Phosphate Pathway; TCA cycle: Tricarboxylic Acid Cycle; GPR: Gene-Protein-Reaction; XYL1: Xylose reductase; XYL2: Xylitol dehydrogenase; XKS: D-xylulokinase; PGI1: Glucose-6-phosphate isomerise; TAL1: Transaldolase; ADH: Ethanol Dehydrogenase; PDC: Pyruvate Decarboxylase; ALD: Aldehyde Dehydrogenase; RPE1: D-ribulose-5-phosphate 3- epimerase; RKI1: Ribose-5-phosphate Ketol-isomerase; SNF3: High-affinity glucose transporter; RGT2: Glucose sensor; XUT: Xylose Transporters; SUT: Hexose Transporter; AAD1: D-arabinitol Dehydrogenase; ARD2: D-ribulose reductase; RKS1: D-ribulokinase; GLY: Threonine aldolase; ALA2: Alanine transaminase; GDH3: NADP-dependent glutamate dehydrogenase.The authors declare that they have no competing interests.TL constructed the model and drafted the manuscript. WZ provided suggestions for model analysis and simulations. LML designed the experiments and JC revised the manuscript. All authors read and approved the final manuscript.Genome reannotation. This Excel workbook contains the detailed gene annotation results by BLAST and KAAS, as well as the 36 reannotated sugar transporters. Click here for fileModel structure. This Excel workbook contains detailed information of S. stipitis iTL885, including all the reactions, metabolites, and GPRs. Click here for fileEssential genes. This Excel workbook is a list of the predicted essential genes with glucose as sole carbon source and the original reactions corresponding to the abbreviations in Figure Click here for file


Geobacter sulfurreducens is capable of coupling the complete oxidation of organic compounds to iron reduction. The metabolic response of G. sulfurreducens towards variations in electron donors  and acceptors (Fe(III), fumarate) was investigated via 13C-based metabolic flux analysis. We examined the 13C-labeling patterns of proteinogenic amino acids obtained from G. sulfurreducens cultured with 13C-acetate.13C-based metabolic flux analysis, we observed that donor and acceptor variations gave rise to differences in gluconeogenetic initiation, tricarboxylic acid cycle activity, and amino acid biosynthesis pathways. Culturing G. sulfurreducens cells with Fe(III) as the electron acceptor and acetate as the electron donor resulted in pyruvate as the primary carbon source for gluconeogenesis. When fumarate was provided as the electron acceptor and acetate as the electron donor, the flux analysis suggested that fumarate served as both an electron acceptor and, in conjunction with acetate, a carbon source. Growth on fumarate and acetate resulted in the initiation of gluconeogenesis by phosphoenolpyruvate carboxykinase and a slightly elevated flux through the oxidative tricarboxylic acid cycle as compared to growth with Fe(III) as the electron acceptor. In addition, the direction of net flux between acetyl-CoA and pyruvate was reversed during growth on fumarate relative to Fe(III), while growth in the presence of Fe(III) and acetate which provided hydrogen as an electron donor, resulted in decreased flux through the tricarboxylic acid cycle.Using G. sulfurreducens cells under various electron donor/acceptor conditions using 13C-based metabolic flux analysis. Our results can be used for the development of G. sulfurreducens as a chassis for a variety of applications including bioremediation and renewable biofuel production.We gained detailed insight into the metabolism of  Geobacter species conserve energy for growth by coupling the complete oxidation of organic compounds to the reduction of Fe(III) and a variety of toxic and radioactive metals Fe(III)citrate) and 10 mM non-labeled acetate with 27.5 mM fumarate , respectively. The carbon mass isotopomer distributions (MIDAA) of alanine, glycine, valine, leucine, isoleucine, phenylalanine, serine, aspartate, and glutamate were compared to those obtained from an identical culture containing only non-labeled compounds.In order to assess metabolic flux distributions in n source ,33,35,37AA measured in the acetate/Fe(III)citrate culture gave a slope of 1.003 with R2 of 1.000 and an intercept of 0.000. In addition, the root mean square (RMS) /dt = 0) as well as biomass (d[x]/dt = 0).To investigate the metabolic response of 13C-tracer containing minimal medium at least once prior to the initiation of an experiment to extremely minimize the fraction of non-labeled cells. The main cultures with the identical medium were inoculated with the mid-exponential phase 13C-precultures.In addition, one batch experiment (E2) was performed in which both acetate and hydrogen were provided as electron donors and Fe(III)citrate served as the electron acceptor. This experiment consisted of four replicate cultures, which were harvested and pooled when the concentration of Fe(II) approached 50 mM. All the batch cultures were transferred (1 vol/vol-%) into 13C-tracer carbon source for 13CMFA. A summary of the cultivation conditions is provided in Table All cultures contained a mixture of 70% non-labeled and 30% uniformly labeled acetate  as a Cell growth was monitored by determining total protein by the bicinchoninic acid method with bovine serum albumin as a standard  and assuN-methyl-N-tert-butyldimethylsilyl trifluoroacetamide as previously described , , 13CMFA 13C-based MFA.In this metabolic network, the conversion from phosphoenolpyruvate to pyruvate is catalyzed by pyruvate kinase, whereas the reverse reaction from pyruvate to phosphoenolpyruvate by phosphoenolpyruvate synthase and/or pyruvate phosphate dikinase. Also, the conversion of pyruvate to acetyl-CoA is catalyzed by the irreversible pyruvate dehydrogenase, and the bidirectional pyruvate synthase. Enzyme reactions catalyzing the identical substrate/product pairs in the same direction cannot be discriminated by the G. sulfurreducens applied to the present study is listed in Table The precursor demand of Overview of in vivo Fluxes' and 'Fumarate Utilization' are the rates normalized to acetate uptake and fumarate uptake, respectively. They can be understood as molar yield coefficients on a particular substrate or the rates of enzyme reactions associated with the uptake of a unit substrate in unit time.In the present work, we utilized two different flux quantities. The relative fluxes utilized in sections 'Specific Metabolic Fluxes' are the specific fluxes scaled by cell growth. We defined these specific fluxes as the relative flux i v(rate of a metabolite processed idc/dt [mmolL-1h-1] per acetate uptake rate [mmolL-1h-1]) normalized by XSY. Thus, the specific flux i q[(mmol/h) (gbiomass/h)-1] of the ith enzyme reaction equalsAnother flux quantity introduced in section 'The specific flux can be understood as the rate of a metabolic enzyme reaction associated with the synthesis of a unit biomass in unit time.13CMFA were implemented using MATLAB . Numerical optimization was carried out using the Optimization Toolbox (Version 4.2) of MATLAB.All computations involved in carbon mass isotopomer analysis and in vivo metabolic fluxes were computed stochastically by starting the numerical optimization runs from arbitrary points and by using normal random numbers of measurement data. Hereby, 13C labeling patterns of amino acids were computed directly if specified in the stoichiometric network model  of MATLAB.The l Figure . OtherwiStatistical data analysis such as random number generation, confidence interval, analysis of variance (ANOVA) and multiple comparison procedure were conducted using the Statistics Toolbox (Version 7.1) of MATLAB. One-way ANOVA was implemented to test the hypothesis that the means of the flux estimates given for the different culture conditions were identical, against the general alternative that they were not. In addition to this, multiple comparisons were performed to obtain information about which pairs of flux mean estimates are significantly different or not.13C2] acetate was applied to 13CMFA in all the four experiments (Table 13C6] citrate was utilized.U-3C2 acetaThe authors declare that they have no competing interests.13C metabolic flux analysis, and drafted the manuscript. MVC conceived the experimental design, conducted the experiments including analytics, and participated in the manuscript draft. DRL and JS co-supervised the work and were involved in writing the manuscript. All authors read and approved the final manuscript.THY constructed the metabolic model, implemented data analysis such as GC/MS carbon labeling analysis and Anabolic precursor demand. Precursor stoichiometry given for the anabolic demand of G. sulfurreducens are listed.Click here for fileGC/MS mass isotopomer distributions. Carbon mass isotopomer distributions of different amino acid fragments computed from GC/MS measurements of TBDMS-amino acid derivatives are listed.Click here for file


Graph-based modularity analysis has emerged as an important tool to study the functional organization of biological networks. However, few methods are available to study state-dependent changes in network modularity using biological activity data. We develop a weighting scheme, based on metabolic flux data, to adjust the interaction distances in a reaction-centric graph model of a metabolic network. The weighting scheme was combined with a hierarchical module assignment algorithm featuring the preservation of metabolic cycles to examine the effects of cellular differentiation and enzyme inhibitions on the functional organization of adipocyte metabolism.Our analysis found that the differences between various metabolic states primarily involved the assignment of two specific reactions in fatty acid synthesis and glycerogenesis. Our analysis also identified cyclical interactions between reactions that are robust with respect to metabolic state, suggesting possible co-regulation. Comparisons based on cyclical interaction distances between reaction pairs suggest that the modular organization of adipocyte metabolism is stable with respect to the inhibition of an enzyme, whereas a major physiological change such as cellular differentiation leads to a more substantial reorganization.Taken together, our results support the notion that network modularity is influenced by both the connectivity of the network’s components as well as the relative engagements of the connections. The topology of interactions in a biological network is often studied by modeling the network as a graph, which allows the use of established algorithms and metrics such as shortest path analysis and betwDespite the important insights obtained from topological analysis, almost all of the graph-based studies to date have examined a biological network under a single static condition. For insIn the case of a metabolic reaction network, gene or even protein expression data may not best capture the interactions between the network’s components, as mRNA levels or enzyme concentrations do not necessarily correlate with reaction rate or metabolite turnover. A more comprehensive snapshot of the physiological state may be provided by a metabolic network’s reaction flux distribution, which directly reflects the relative engagements of enzymes, integrating the various layers of regulatory processes active in the cell. Intuitively, the flux of a reaction can be used to weight the interaction mediated by the reaction. For example, Yoon and coworkers applied flux-based weights to adjust the edge distances in a graph model of murine adipocyte metabolism, and thereby reflect metabolic state-dependent variations in the interactions between metabolite pools,15. Whil13C) labeling, metabolic flux analysis (MFA), and flux balance analysis (FBA), Generally, mathematical model-based analysis of isotopic enrichment of multiple metabolite pools offers the greatest resolution. Flux balance analysis is a constrained optimization based approach typically used to estimate fluxes in conjunction with a metabolic objective function. The problem is usually severely underdetermined in FBA. In the present study, we used a constrained optimization based approach to estimate metabolic fluxes, but without assuming a metabolic objective. Rather, we minimized the sum of squared differences between the measured and estimated exchange fluxes, as the problems were well constrained. Applied to a model of adipocyte metabolism, ShReD-based modules obtained using flux weights more consistently reflected recognizable functions of established pathways compared to the modules obtained without the weights. Comparisons of modules obtained using several different flux sets representing distinct metabolic states identified robust reaction pairs that repeatedly partitioned into the same module across many levels of modular hierarchy, suggesting possible co-regulation.Recently, we defined a new metric, termed Shortest Retroactive Distance (ShReD), to capture feedback and other cyclical interactions in a metabolic network. Based oV, which ranks the ShReD between two reaction nodes relative to the distribution of all ShReDs involving either one of the two reaction nodes.Weighting the edges that define the interactions between the reaction nodes substantially impacted the overall distribution of ShReDs. In the un-weighted case, when all edges have the same unit distance, the ShReDs are close to normally distributed, with a skewness of −0.048 Figure A. In the2=0.35, p<0.01) between the un-weighted ShReD and the corresponding weighted ShReD. The correlation analysis was performed on reaction pairs with ShReD < 100, since the maximal ShReD value was capped at 100 (see Methods). The positive correlation suggests that the topology of the metabolic network as defined by the stoichiometry has some influence on the closeness of cyclical interactions between enzymes as defined by the fluxes of the reactions connecting the enzymes . A scatter plot of the partition score and the modularity score for the Day 12 flux-weighted model shows a significant positive correlation  for reaction pairs with a positive modularity score . Forty reaction pairs, or roughly 1.5% of the possible 2556 reaction pairs, satisfied the criterion for at least one of the four models. A heat map displaying the number of models (of the four adipocyte models) for which a given reaction pair meets the criterion shows that 17 of the 40 reaction pairs robustly partition together across the different metabolic states . Only 5 of the 17 robust reaction pairs identified in Figure We next investigated whether the modularity score Vn R2 = 0.5, p<0.01n R2 = 0.5, p<0.01n R2 = 0.5, p<0.01n R2 = 0.5, p<0.01The partitions of the four flux-weighted models show clear differences in hierarchical modularity. The differences are mainly due to the placement of the reactions catalyzed by phosphoenolpyruvate carboxykinase (PEPCK) and pyruvate carboxylase (PCX). For the Day 4 model, the first partition of the initial network isolates both enzymes from the main network along with transport reactions that do not have any cyclical interactions . A large distance implies that the reaction pair’s partition and modularity scores (the coordinates of the H-V space) are substantially influenced by the change in metabolic state, whereas a short distance suggests that the change in metabolic state has little impact on the reaction pair’s placement in the module hierarchy. These distances are shown as heat maps for the changes in flux distribution between Day 4 and Day 12 Figure A and DayIn this paper, we present a novel methodology for investigating the impact of different metabolic states on the functional organization of metabolic networks. The methodology utilizes metabolic flux data as weights for a graph-based partitioning method that conserves cyclical interactions. Previously, we assessed the cyclical interactions based on ShReDs calculated by assuming static interactions, and thus a uniform graph distance, between each connected reaction pair. In the present study, we allow the interactions, and thus the graph distances, to vary with the metabolic state.+. However, in the weighted network, the directional interaction from R28 to R63 is very weak, since only a very small fraction of the NADH produced by glycolysis is used for proline synthesis. The corresponding edge distance is 1251, which is approximately 50-times the average of non-infinite ShReDs in the network (25). As a result, the weighted ShReD between these two reactions traverses an alternate sequence of reaction nodes, comprising 10 reactions spanning parts of glycolysis and the TCA cycle, 2-oxoglutarate synthesis, and glutamate synthesis  models shows that the weighted model yields greater functional homogeneity of modules based on the canonical pathway assignments of the constituent reactions  reductase, requires NADPH as a cofactor for activity, while bWhile the partitions of the four flux-weighted models share similar modules as exemplified by the robust reaction pairs, they also exhibit notable differences. For the Day 4 partition, reactions catalyzed by PCX and PEPCK both split off immediately from the parent network at depth one of the hierarchy. This split is due to the very low flux carried by these reactions at Day 4, which excludes them from significant cyclical interactions with any of the other reaction nodes. Day 4 represents an early stage of differentiation when an immature adipocyte phenotype is expected. While lipogenic genes are activated, the fluxes of lipid synthesis and triglyceride accumulation remain low at this stage relative to other parts of central carbon metabolism. Our results suggest that PCX and PEPCK, which catalyze upstream steps in glycerogenesis and fatty acid synthesis from glucose, are not yet integral to any major functional modules in the immature adipocyte. However, at Day 12 , whereas a weaker influence is modeled as a larger edge weight (longer path distance). Formally, we define the edge distance between a connected pair of reaction nodes as the inverse of the fraction of the intermediate metabolite production flux that is directed towards the destination reaction node. In the example of Figure 1,2 between R1 and R2 is given by:Previously, we defined a metric, termed ShReD, to characterize the connectivity between two biochemical network components that interact retroactively. Connect1 and R3 is given by:The edge distance between R0 is 100 mol/min, of which 70 and 30 mol/min is directed towards R3 and R4, respectively. Based on the assumption that the metabolite pool is homogeneous and the contributions of the upstream reactions to this pool are indistinguishable, the directed interaction from R1 to R3 is the same as the interaction from R2 to R3. The weighting would be the same if v1 and v2 are each 50, or if v1 is several orders of magnitude smaller than v2. Even if v1 = 0.01, it has to be assumed that 70% of that small flux is directed towards R3, because the source of the intermediary metabolite flux cannot be distinguished by the downstream enzymes. Similarly, the interaction from R1 and R4 is the same as the interaction from R2 to R4. Generalizing for a pair of reactions Ri and Rj connected through an intermediary metabolite M produced by an arbitrary number reactions N, the edge distance from node Ri to Rj is given by:The above definition can be extended in a straightforward manner to cases when more than one reaction produces the metabolite that mediates the interaction between two reactions Figure B. These k that produce the intermediary metabolite M, vk is the flux of Rk, and vj is the flux of the reaction Rj. When vj is close to zero, the corresponding edge distance is very large, as is any ShReD that includes this edge. In such cases, allowing a ShReD to reach an arbitrarily large value could exaggerate the numerical difference between reactions whose fluxes are not statistically different from zero. Therefore, the value of a flux-weighted ShReD was capped with an upper bound. For numerical convenience, the cap was set at 100, as fewer than 5% of all ShReDs calculated in this study exceeded this value. The calculation of ShReDs based on flux weights is illustrated in Figure In equation 3, the index k refers to the set of reactions RPartitions of flux-weighted and unweighted network models were generated using Newman’s community detection algorithm similar V has a positive entry Vij if the corresponding ShReD between a pair of reaction nodes is small relative to the expected ShReD, whereas it has a negative entry if the corresponding ShReD is large. Due to the skewing effect of the flux weights on the ShReD distribution, the determination of whether a weighted ShReD is small or large relative to expectation was based on a log ratio. Formally, we define an entry Vij in the modularity matrix V as follows.In our previous work, we computed a modularity score based on the difference between the actual and expected ShReD assuming that each edge in the graph model has equal length, or weight. In this study, we modify the modularity matrix from which the modularity score is calculated to account for the skewness of weighted ShReD distributions. The desired modularity matrix ij is the fraction of all weighted ShReDs involving reaction Ri or Rj that is longer than the ShReD between Ri and Rj (ShReDij). If exactly half of all ShReDs involving Ri or Rj are longer (or shorter) than ShReDij, then Vij is zero. Otherwise, Vij is positive or negative depending on the rank of ShReDij relative to all other ShReDs involving Ri or Rj. As an example, consider the subnetwork shown in Figure 24,31). Of these, ShReD24,31 ranks 11th in terms of length. Applying equation 4, p24,31 = 10/25 = 0.4, and V24,31 = −0.41. If pij = 0, pij is arbitrarily set to 0.01. The smallest Vij value is thus −4.60, which is on the same order of magnitude as the other entries in the modularity matrix.In equation 4, ps, that maximizes the modularity score[V:To generate a partition, we assign each reaction in a subnetwork into one of two daughter subnetworks. The goal is to find a set of assignments, represented by a binary vector ty score. The sumi or sj of vector s has a value of either −1 or 1. An increase in Q is obtained in two cases: if Vij is positive and reactions i and j are assigned to the same subnetwork (si = sj = 1 or si = sj = −1), or if Vij is negative and the two reactions are assigned to different subnetworks (si = 1 and sj = −1 or vice versa). A solution to the maximization problem can be found using a number of different optimization methods. For example, an approximate solution can be obtained using eigenvalue decomposition[s vectors) with larger Q scores. The GA was implemented using custom code written in MATLAB with the following parameters. The initial population of solutions comprised 100 randomly generated s vectors. The population size was kept constant. A fixed fraction (60%) of the solutions was selected for reproduction based on fitness (Q score). New individuals were bred through crossover and mutation. During crossover, an element in the offspring s vector was assigned the same value as the corresponding elements in the parent s vectors if the values were the same in both parents. Otherwise, the element was randomly assigned either −1 or 1. The mutation (sign change) rate was set to 20%. The GA terminated when the average Q score of the population reached a plateau with an absolute slope < 0.05 with respect to generation number. The fittest solution (s vector with the largest Q score) generated over the course of the GA was used for the partition. For the subnetworks encountered in this study, termination was reached generally within 200 generations. For the example subnetwork of Figure Each element sposition. In thisThe partitioning results are reported in the form of a hierarchical tree annotated with several properties. Each module is represented as a pie chart, where the size of each slice is proportional to the fraction of reactions that belong to the corresponding, pre-assigned canonical (textbook) grouping. The homogeneity index of a module corresponds to the fraction occupied by the largest slice in the pie chart. The homogeneity index therefore ranges from 0 to 1, where a larger number indicates greater homogeneity in terms of composition based on the canonical group assignments. The black lines connecting the nodes in the hierarchical tree represent ShReD-based partitions, whereas the red lines represent the formation of components from partitions that include disconnected components. The depth of a module is determined as the number of black edges traversed from the root node to the module. The height of a module is determined as the largest possible number of black edges traversed from the module to a terminal leaf node.To determine the correlation between modularity and flux weighted ShReD-based partitioning, we define a partition score H for a pair of reaction nodes by scaling the number of shared modules in the partition tree with respect to the partition depth of the terminal modules for the reaction nodes:Shared is the number of modules in the partition hierarchy that include both reactions i and j, and mi and mj are, respectively, the maximal depth of reactions i and j. The numerical range of H is thus from 0 to 1. A value of zero indicates that the two reactions are immediately separated after the first partition operation, whereas a value close to one indicates that the two reactions remain together in the same module through many rounds of partition operations.where To assess the impact of metabolic state and its corresponding flux distribution on the hierarchical partition of reaction modules, a Euclidean distance is computed for each reaction pair in the H-V (partition score – modularity score) coordinate space from its original location corresponding to the first metabolic state to its new location corresponding to the second state. All coordinates are normalized to the mean partition score and modularity score of the corresponding flux-weighted partition.The authors do not report any financial or other commercial conflict of interest.Conceived and designed the experiments: GVS SH KL. Performed the experiments: GVS MY SH. Analyzed the data: GVS MY SH KL. Contributed reagents/materials/analysis tools: GVS SH KL. Wrote the paper: GVS MY SH KL. Wrote the program code used in the analysis: GVS SH. All authors read and approved the final manuscript.Reaction definitions and composition of each module in Figures 2 and 5.Click here for fileIncludes Tables S1-S2 and Figures S1-S5. The tables and figures are referenced in the text.Click here for file


With the advent of high-throughput technologies, the field of systems biology has amassed an abundance of “omics” data, quantifying thousands of cellular components across a variety of scales, ranging from mRNA transcript levels to metabolite quantities. Methods are needed to not only integrate this omics data but to also use this data to heighten the predictive capabilities of computational models. Several recent studies have successfully demonstrated how flux balance analysis (FBA), a constraint-based modeling approach, can be used to integrate transcriptomic data into genome-scale metabolic network reconstructions to generate predictive computational models. In this review, we summarize such FBA-based methods for integrating expression data into genome-scale metabolic network reconstructions, highlighting their advantages as well as their limitations. A central challenge in the development of systems biology is the integration of high-throughput data to generate predictive computational models. With the advent of high-throughput technologies, “omics” data types have provided quantitative data for thousands of cellular components across a variety of scales. Genomics provides data on a cell's DNA sequence, transcriptomics on the mRNA expression of cells, proteomics on a cell's protein composition, and metabolomics on a cell's metabolite abundance. Computational methods are needed to reduce this dimensionality across the wide spectrum of omics data to improve understanding of the underlying biological processes , a constraint-based modeling approach, can be used to probe these network reconstructions by predicting physiologically relevant growth rates as a function of the underlying biochemical networks  algorithm  and sets of lowly expressed reactions (RL). The algorithm then solves a mixed integer linear programming (MILP) problem according to stoichiometric and thermodynamic constraints while also maximizing RH and minimizing RL. Mirroring GIMME, the presence of reactions is allowed to deviate from the expression data in order for the algorithm to result in a functioning model. Thus, like GIMME, iMAT returns a functioning metabolic model that integrates expression data with a genome-scale metabolic network reconstruction by maximizing the number of highly expressed reactions and minimizing the number of lowly expressed reactions; however, unlike GIMME, this method does not demand that the user supply functionalities that the model is assumed to meet. Instead, iMAT requires that reactions catalyzed by the products of highly expressed genes are able to carry a minimum flux. By removing this need for user-specified objective functions, iMAT bypasses assumptions about metabolic functionalities of a particular network, which proves advantageous for models where there is no clear objective function, as in models of mammalian cells.Similar to GIMME, the Integrative Metabolic Analysis Tool (iMAT) results in a functioning model in which the fluxes of reactions correlated with high mRNA levels are maximized and the fluxes of reactions associated with low mRNA levels are minimized  uses statistically significant changes in gene expression measurements to determine sequences of highly and lowly expressed reactions  aims to fuse together metabolic networks and transcription regulatory networks with expression data (Chandrasekaran and Price, Each of the methods discussed hinges on the assumption that mRNA transcript levels are a strong indicator for the level of protein activity. For instance, GIMME and iMAT assume that mRNA levels below a certain threshold suggest that the corresponding reactions are inactive. MADE follows a similar logic, turning reactions on and off depending on the changes in mRNA transcript levels. E-Flux and PROM assume that transcript levels indicate the degree to which reactions are active, evident in the constraining of the upper bounds in the FBA optimization problems associated with these methods.However, recent studies have called into question the validity of this assumption which correlates mRNA transcript levels to protein levels. In one of the first large-scale screens to assess the correlation between mRNA and protein expression, the Pearson product moment correlation coefficient, a measure of the linear dependence between two variables ranging from −1 to 1, was calculated to be 0.356 for yeast data (Gygi et al., Acknowledging this questionable association between transcriptomic and proteomic data, the discussed methods claim to treat the assumption that mRNA levels serve as a strong indicator for protein activity as a “soft constraint.” Rather than requiring that the reconstruction mirror the expression data exactly, the methods allow for deviations in the FBA flux solution space in order to generate a functioning model that adheres to the specified constraints. In the case of GIMME, highly expressed reactions are prioritized relative to lowly expressed reactions; however, in the event that an optimal, functioning solution cannot be found, the assumption can be violated and lowly expressed reactions can be added back into the reconstruction. Thus, this assumption that mRNA transcript levels correlate to protein levels serves as a cue rather than a mandate.Mycobacterium tuberculosis (Colijn et al., The above methods have been used to not only integrate expression data from a variety of sources but to also make progress toward overcoming key challenges in the field of systems biology. For instance, iMAT, highlighting its applicability in multi-cellular organisms, was used to curate the human metabolic network reconstruction and predict tissue-specific gene activity levels in ten human tissues (Duarte et al., Given the recent success with using genome-scale metabolic network reconstructions as a platform for integrating expression data, efforts should focus on multi-omics data integration. A handful of methods have already been introduced that integrate two or more types of omics data into genome-scale metabolic network reconstructions. For example, despite the current dearth of quantitative metabolomics data, a method has been developed that demonstrates how semi-quantitative metabolomics data can be used with transcriptomic data to curate genome-scale metabolic network reconstructions and identify key reactions involved in the production of certain metabolites (Cakir et al., The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


With the continued proliferation of high-throughput biological experiments, there is a pressing need for tools to integrate the data produced in ways that produce biologically meaningful conclusions. Many microarray studies have analysed transcriptomic data from a pathway perspective, for instance by testing for KEGG pathway enrichment in sets of upregulated genes. However, the increasing availability of species-specific metabolic models provides the opportunity to analyse these data in a more objective, system-wide manner.ambient (Active Modules for Bipartite Networks), a simulated annealing approach to the discovery of metabolic subnetworks (modules) that are significantly affected by a given genetic or environmental change. The metabolic modules returned by ambient are connected parts of the bipartite network that change coherently between conditions, providing a more detailed view of metabolic changes than standard approaches based on pathway enrichment.Here we introduce ambient is an effective and flexible tool for the analysis of high-throughput data in a metabolic context. The same approach can be applied to any system in which reactions (or metabolites) can be assigned a score based on some biological observation, without the limitation of predefined pathways. A Python implementation of ambient is available at http://www.theosysbio.bio.ic.ac.uk/ambient. The increasing availability of high-throughput biological data sets promises a deeper understanding of cellular processes than has ever previously been accessible. Many of these high-throughput experiments directly or indirectly measure metabolic changes within a cell, for example microarrays indirectly measure enzyme concentration and metabolomics experiments directly measure changing metabolite concentrations. The metabolism of any organism is a complex system with thousands of interacting entities, meaning that an integrated, network-based analysis is required in order to extract the maximum amount of knowledge from these data.Common methods for proteome and transcriptome analysis include GO or KEGG enrichment analysis using Fisher’s exact test or gene set enrichment analysis (GSEA ). These Other approaches have analysed such data using simple protein interaction graphs. Ideker et al.  have devIn order to find significantly changed pathways in metabolism, Breitling et al.  developeSeveral other recent methods have been developed to take explicit advantage of the underlying metabolic network structure controlled by transcriptional changes in order to determine network-based gene neighbourhoods. PathExpress  takes a a priori manual removal of these metabolites [Whilst GiGA and Active Modules can both find arbitrary modules in simple gene-gene interaction graphs, there are several problems in using such graphs to represent metabolic networks. Genes in these networks connect to all other genes associated with a particular metabolite, such that so-called currency metabolites  can link large swathes of metabolism to create large (complete) subnetworks. Currency metabolites can potentially falsely link unrelated parts of metabolism in pathway-building approaches and must therefore be accounted for. Usually this is done by abolites  or simplabolites . HoweverGenes encoding enzymes with the same function (isozymes) can also be problematic: often the quantity of real interest for a particular reaction is the net change in flux or flux capacity for that reaction, thus multiple gene changes related to a single reaction should be accounted for together rather than as separate nodes in a graph representation of metabolism. In contrast, multi-function enzymes can potentially erroneously link two separate parts of metabolism and cause inferred modules to consist of otherwise disconnected pathways within the metabolic network.ambient scoring system as detailed in the Methods section). Since reactions, rather than genes, are used for mapping data onto the network, isozymes and multifunctional enzymes can be amalgamated and separated respectively according to actual enzymatic function , eliminating the problems of gene-centric metabolic network representations.The bipartite metabolite-reaction representation of metabolism solves all of these problems by representing both metabolites and reactions as nodes and mapping data onto these entities separately. Figure The analysis of such a network representation requires that there is information mapping genes to reactions. Until recently this would have limited the use of this approach to organisms with published manually curated metabolic models (for example ) and orgambient, a new method for high-throughput data analysis in the context of metabolic models. ambient is an extension of the Active Modules approach such that it accommodates bipartite (reaction and metabolite) networks, allowing coordinated metabolic pathway changes to be discovered from transcriptomic or metabolomic data. Simulated annealing is used to find modules (i.e. connected components) containing reactions associated with genes that are highly changed in expression and metabolites that have low overall connectivity .ambient has several advantages over previous approaches to the discovery of metabolic modules. The bipartite representation of metabolism offers a systematic objective representation of metabolism which enables unbiased pathway finding. It also treats all metabolites equivalently, so information about the metabolic network is not lost through arbitrary decisions about which metabolites should be considered currency metabolites. In this paper we compare ambient to GiGA [ to GiGA  to show ambient is based on the Active Modules approach of Ideker et al. [ambient is provided at http://www.theosysbio.bio.ic.ac.uk/ambient.The algorithm implemented in r et al. , extendeambient requires as input a metabolic model and scores for those reactions for which data is available. By default, metabolite scores are calculated using their degree in the metabolic network (as described below) so their scores need not be specified by the user. For models with gene-protein-reaction (GPR) relationships, scores for genes can be provided, which are converted into scores for reactions. The metabolic model is represented by an undirected bipartite network, where an edge links a reaction node with a metabolite node when the metabolite is either a substrate or product of that reaction. Scores for reactions for which there are no data are by default set as the median score of the set of known reaction scores.ambient outputs three files: a ‘.tsv’ flatfile results table of all nodes from each significant module, a GraphML file for results visualisation and a ‘.dat’ file in the Python shelve format containing all input and output variables.The Python implementation of ambient with microarray data, so reactions have been scored according to the transcriptomic data for the enzymatic genes known to be involved in the catalysis of those reactions. The scores of each reaction have been assigned in the following way: where a reaction is linked to a single gene in its GPR the reaction is given the value of the fold-change of that gene’s transcript.Reaction nodes must each be assigned a score, according to the data being analysed. Although in principle this can be based on any dataset, in this work we have investigated the use of Where a reaction is catalysed by a single enzyme made up of multiple different gene products the mean of the fold-changes of those genes is assigned to the reaction. In this way error propagation from individual gene transcript measurements is reduced. Without any knowledge of relative activities of enzymes for each reaction, if a reaction is catalysed by multiple enzymes the mean of the inferred enzyme fold-changes is used. This takes into account all of the enzyme level changes affecting single reactions in a single fold-change score.m is defined as the union of a subset rm of reactions and a subset cm of metabolites that subtend a connected subgraph within the bipartite metabolic graph. The score S of a module is given by A module q = |rm| + |cm| is the number of nodes in the module m, ith reaction in the module, jth metabolite in the module and α is a constant given by  where α is defined here as the mean score of all reactions for which s > 0, divided by the mean value of w over the complete network. This formula for α is chosen to ensure that modules are not needlessly restricted by metabolite weights, but do not extend to cover large, biologically meaningless regions of the network. This algorithm tracks all module scores, the logarithmic term being added to bias exploration towards larger modules, without generating extremely large, biologically meaningless modules.As in the original Active Modules algorithm, the aim is to find the set of non-overlapping modules with the highest total score. Finding global maximum scoring modules is NP-Hard , so a siIn many cases, modules describing downregulated regions of the network are of as much interest as upregulated regions. These modules can be investigated by multiplying reaction scores by -1, which gives the most reduced reaction the highest score, and leaving the metabolite scores negative. With this transformation, downregulated modules can be found using the same algorithm as upregulated ones.The algorithm for finding high scoring modules is outlined here , accept the proposed move and set E = P,7. If 8. Repeat steps 4 to 7 until the temperature reduction criterion  and the empirical p-value is equal to the number of scores in this sample greater than the module score from annealing divided by P. This is determined for the top M modules. These M p-values are corrected for multiple testing using the Benjamini-Hochberg correction.The significance values of modules found by All network diagrams were created using Cytoscape v2.8.2 .ambient tool were taken from an experiment by DeRisi et al. [S. cerevisiae to glucose depletion. The gene scores used were the log fold-changes between the 0 hour timepoint (glucose rich) and 20.5 hour timepoint (glucose starved) of that experiment. The YEASTNET yeast model [ambient, and was also converted into a simple protein interaction network with edges induced by shared metabolites for input to GiGA [The data used to validate the i et al. , investist model  was take to GiGA .ambient modules may include reactions for which there is no data, as long as the scores from the surrounding reactions support such an inclusion.Overall the DeRisi dataset covers 6153 genes, of which 903 are present in the YEASTNET model, which through the gene-reaction relationships in that model provide scores for 1239 of the 1865 reactions in the model. Since the overall change in metabolism was being investigated, those reactions for which there were no data were assigned the median score of the reactions with known scores. Due to the formulation of the method, ambient was run with all parameters set as default except the maximum number of annealing steps N, which was set to 1,000,000. GiGA was run with all parameters at default values, ignoring metabolites with degree greater than 20 (currency metabolites) and restricting the number of genes per module to 40. Since GiGA does not make predictions about which metabolites are in particular modules, a simple rule was followed: where any non-currency metabolite was connected to more than one reaction in a GiGA module, it was included in that module. The analysis was run twice for each method, to find both up- and down-regulated modules; of particular interest was whether the main result of [esult of , of the ambient. The ambient analysis in both directions produced many positive scoring modules, of which four were significantly up-regulated and one was significantly down-regulated at the q < 0.05 level . The highest weight (connectivity) metabolite found to be in one of these modules is cytoplasmic L-glutamine, connected in the full metabolic network to 19 reactions. Figure ambient, along with their overlap with the GiGA modules found. The corresponding diagrams for GiGA are in Additional file ambient down-regulated module consisting of 333 reactions and metabolites. This large module indicates that the general downshift of metabolism between hour 0 and hour 20.5 in the experiment is captured in the ambient analysis. The module shows the reduction of lipid biosynthesis, amino acid production and also includes the biomass production reaction itself, as well as picking out the GLY/GNG pathway discussed below.Table ambient recapitulate the main conclusions of previous analyses [The yeast model used is compartmentalised, so mitochondrial and cytosolic reactions and metabolites are separated. Both GiGA and analyses ,13, nameambient analysis. Detailed results for these pathways can be found in Table ambient, GiGA and from expert manual inspection [S. cerevisiae. To assess the similarity between the two computational approaches and the DeRisi analysis, the recall, precision and F-measure were calculated, with the results as shown in Table ambient agrees somewhat better with expert interpretation of data for both the GLY/GNG top pathway and the TCA cycle results. Whilst recall is much better for the TCA connection pathway, ambient has a very poor precision. This reduced precision is because the down-regulated pathway found by ambient is very large, reflecting the general downshift in metabolism rather than just the most highly repressed enzymes. As seen in Additional file Each of the three parts of the central carbon metabolism show up in different modules in the spection . This taambient finds several linked but previously undiscovered pathways which add to our appreciation of the full metabolic response of S. cerevisiae to glucose depletion and diauxic shift. It is clear from the upregulated modules  which is present in GiGA module 3 encodes a multifunctional enzyme associated with 29 reactions in the yeast model. Using GiGA  will fail to distinguish between potentially very different reactions catalysed by such multifunctional proteins and will infer either all or none of them as parts of a metabolic module. This approach will therefore always lack the specificity inherent in the reaction-metabolite bipartite network representation of metabolism and results in unconnected ‘modules’, as seen in Additional file  which isambient over previous approaches to module-finding is that it encourages larger modules to form which might otherwise be hidden due to individual interconnecting low-scoring (or negative scoring) nodes or due to missing experimental data. This advantage, inherited from the simulated annealing approach, means that a fuller picture of how metabolic responses are coordinated can appear from the same data used in previous approaches, as can be seen in the good coverage of previously known and newly discovered affected parts of metabolism shown in Figure Another important advance in ambient in this case study, taking approximately 30 seconds on a 2.4 GHz chip, as opposed to ambient’s two hours.Against these advantages, it should be noted that the GiGA approach is much faster than ambient is not a deterministic algorithm, it arrives at slightly different solutions each time it is run. ambient was run ten times with the settings and data described above and the the consistency of the results was assessed. Each run produces what is in effect a partition of the set of all nodes, with each partition being a significant module, except the largest partition which consists of all nodes not in significant modules. The Adjusted Rand index [Since nd index  was usedambient is very effective for elucidating metabolic changes from transcriptomic datasets it does have several limitations that should be borne in mind. Firstly it does not in any way take into account regulation except in as much as the regulation is apparent in the changes of transcription levels of genes encoding enzymes. Secondly, as with all other current methods for mapping transcription onto metabolic networks, if genes with enzymatic products are not mapped onto the metabolic network then information about their changes cannot be used to investigate the changes in metabolism. Due to this inability, ambient does not extract all of the information possible from transcriptomic data, but just the information from genes with known functions. The elucidation of metabolic functions for uncharacterised genes would therefore require a different approach.While ambient. Also the best way in which transcript values are combined for each reaction is not known. If some knowledge of the relative activity of various enzymes for each reaction were integrated into this approach a more refined way of combining enzyme inferred changes could be used to score each reaction. Despite these potential limitations ambient has recapitulated the results produced by a very different computational approach and by expert curation of the same data used here, so some confidence can be drawn concerning the scoring system presented here.The best way to interpret transcriptomic changes in terms of their effect on reaction rates is an open question. With the approach to reaction scoring presented here, mismapping between mRNAs (transcripts) and reactions could impact on the effectiveness of ambient has been applied here to transcriptional data looking at yeast diauxic shift. This approach is of course applicable to any dataset containing two (or more) microarray measurements in differing conditions. However, due to the information now available in many metabolic models, and the use of a bipartite representation of metabolism, any information that can be mapped to genes, enzymes, reactions or metabolites can be included in an ambient analysis. The explicit links available between genes, proteins and reactions means that transcriptomic (as shown here), proteomic or fluxomic data could be mapped onto the metabolic network under study. Furthermore, metabolites were scored here purely by weight in the metabolic network, but if metabolomic information were available this could easily be incorporated into the scoring system.In order to look at the overall changes in yeast diauxic shift, the scores for reactions were left as mean log fold-changes of gene transcription. In order to further dissect any transcriptomic dataset, it would be possible to set the median reaction score to zero, therefore just search for especially up- and down-regulated pathways.Future developments will include methods for combining several different datasets into a single module-finding problem. Since the metabolic models used for this analysis can also be used in flux balance analysis (FBA), methods to combine computational flux estimates obtained from FBA with experimental data will be of particular interest in order to extend and refine our understanding of metabolic network function.ambient, a method for finding metabolic modules that represent coordinated metabolic differences between two environments or conditions. Using simulated annealing, ambient can go beyond previous approaches to the system level analysis of metabolic changes, as demonstrated here using transcriptomic data from a yeast glucose runout experiment. The bipartite representation of metabolism allows a much greater specificity of analysis and can incorporate information about metabolites, giving an objective view of the changes in cells during the diauxic shift.In this paper we have presented ambient will enable the analysis of disparate data that would otherwise be difficult to integrate, thus improving the biological understanding accessible using high-throughput experimental techniques.This approach has the potential to integrate many different types of high-throughput data obtained in a single experiment. It is hoped that The authors declare that they have no competing interests.JP and MS conceived the project, WB and JP developed the tool and WB wrote the manuscript. All authors read and approved the final manuscript.Supplementary Methods. Further details on the ambient algorithm and scoring system.Click here for fileSupplementary Figures. Figures S1-S4: diagrams of the positive and negative modules found by both ambient and GiGA.Click here for file


Saccharomyces genus have shown better adaptation at low temperature than Saccharomyces cerevisiae. This is the case of the cryotolerant yeasts Saccharomyces bayanus var. uvarum and Saccharomyces kudriavzevii. In an attempt to detect inter-specific metabolic differences, we characterized the metabolome of these species growing at 12°C, which we compared with the metabolome of S. cerevisiae (not well adapted at low temperature) at the same temperature. Our results show that the main differences between the metabolic profiling of S. cerevisiae growing at 12°C and 28°C were observed in lipid metabolism and redox homeostasis. Moreover, the global metabolic comparison among the three species revealed that the main differences between the two cryotolerant species and S. cerevisiae were in carbohydrate metabolism, mainly fructose metabolism. However, these two species have developed different strategies for cold resistance. S. bayanus var. uvarum presented elevated shikimate pathway activity, while S. kudriavzevii displayed increased NAD+ synthesis.Temperature is one of the most important parameters affecting the length and rate of alcoholic fermentation and final wine quality. Wine produced at low temperature is often considered to have improved sensory qualities. However, there are certain drawbacks to low temperature fermentations such as reduced growth rate, long lag phase, and sluggish or stuck fermentations. To investigate the effects of temperature on commercial wine yeast, we compared its metabolome growing at 12°C and 28°C in a synthetic must. Some species of the  Saccharomyces cerevisiae is around 32°C Temperature is one of the main relevant environmental variables that microorganisms have to cope with. The natural environment for the majority of microorganisms, including yeast species, exhibits temporal fluctuations in temperature on scales ranging from daily to seasonal. In addition, temperature is a key factor in some industrial processes involving microorganisms. Low temperatures (10–15°C) are used in wine fermentations to enhance production and to retain flavor volatiles. In this way, white and “rosé” wines of greater aromatic complexity can be achieved S. cerevisiae being primarily responsible for alcoholic fermentation, other species of the genus Saccharomyces, such as S. bayanus var. uvarum, have been isolated during wine and cider fermentation Saccharomyces hybrids have been isolated in wine fermentations S. cerevisiae and S. kudriavzevii, between S. cerevisiae and S. bayanus, as well as a triple hybrid S. bayanus x S. cerevisiae x S. kudriavzevii. However S. kudriavzevii has been isolated only from natural environments and was formally described from decaying leaves in Japan et al.et al.S. bayanus var. uvarum and S. kudriavzevii are considered the most psychrotrophic species of the Saccharomyces genus S. cerevisiae in terms of valuable organoleptic properties, such as greater glycerol production and lower ethanol production Despite S. cerevisiae using a variety of high-throughput methodologies. Some studies have analyzed the genome-wide transcriptional response of S. cerevisiae to low temperatures. These studies have mainly focused on cold shock et al. et al.S. cerevisiaeS. kudriavzevii and their natural hybrids In past years, some attempts have been made to elucidate the cold response in et al.In addition to transcriptomic, there are the other so-called “omics” currently available, such proteomics and metabolomics. In our group, we previously studied the proteome changes of a commercial wine yeast strain during the first hours of fermentation at low temperature S. bayanus var. uvarum and S. kudriavzevii species from S. cerevisiae, whose growth potential is limited at this temperature. To achieve these objectives, we analyzed the global metabolic profiling of S. cerevisiae growing in a steady-state chemostat at 12°C and 28°C at the same growth rate. Thus, for a better understanding of the low-temperature adaptation of S. bayanus var. uvarum and S. kudriavzevii, we characterized the metabolome of these species which we compared with the metabolome of commercial wine yeast QA23 at 12°C.The aim of this study is to improve the feasibility of low-temperature wine fermentation by identifying biomarkers and metabolic adaptations at low temperature in the industrial wine yeast strain QA23, and to detect differential metabolites that distinguish two cryotolerants S. cerevisiae (Sc) wine strain , a S. bayanus var. uvarum (Su) strain (CECT12600) and a S. kudriavzevii strain (Sk) (CR85) Sc strain was grown at a dilution rate (D) of 0.04 h−1 at 12°C and 28°C in 2 L chemostat  with a working volume of 0.75 L. The Su and Sk strains were grown under the same conditions, but only at 12°C. A temperature probe connected to a cryostat controlled the cultures grown at 12°C.A commercial et al.−1 of sugars (100 g L−1 glucose + 100 g L−1 fructose), 6 g L−1 malic acid, 6 g L−1 citric acid, 1.7 g L−1 YNB without ammonium and amino acids, anaerobic factors  and 60 mg L−1 potassium disulfite. The assimilable nitrogen source used was 300 mg N L−1 (120 mg N L−1 as ammonium and 180 mg N L−1 in an amino acid form). pH was measured online and kept constant at 3.6 by the automatic addition of 2 M NaOH and 1 M HCl. The stirrer was set at 100 rpm. Biomass and extracellular metabolites were constant for at least five volume changes before sampling. Sampling of cells from continuous cultures was carried out following the “general sample preparation recommendations for metabolon studies” of Metabolon, Inc. . When the steady state was reached, a volume of approximately 30 units of OD600 was centrifuged at 1000 g for 3 min at 4°C. After removing the supernatant, the cell suspension was washed with PBS, transferred to a 1.5–2.0 ml microcentrifuge tube and centrifuged again under the same conditions. The pellet was flash-frozen with liquid nitrogen and stored at −80°C.Cultures were grown in the synthetic grape must (SM) derived from that described by Bely 2SO4 with a flux of 0.6 mL min−1 and a column temperature of 50°C. The concentration of each was calculated using external standards. Each sample was analyzed in duplicate.Glucose, fructose, glycerol and ethanol were analyzed in all the supernatant samples. Analytical HPLC was carried out in a Surveyor Plus Chromatograph  equipped with a refraction index detector, autosampler and a UV-Visible detector. Prior to injection, samples were centrifuged at 13300 rpm for 5 min, and samples were diluted 10-fold and filtered through 0.22-µm pore size nylon filters . A total volume of 25 µL was injected into a HyperREZ XP Carbohydrate H+8 µm column (Thermo Fisher Scientific) assembled to its correspondent guard. The mobile phase used was 1.5 mM H−1.Ammonia concentration was measured with a kit following an enzymatic method . The concentration of free amino acid nitrogen was determined by the σ-phthaldehyde/N-acetyl-L-cysteine spectrophotometric assay (NOPA) procedure Frozen samples of cells, OD of approximately 30 units, were submitted to Metabolon, Inc.  for sample extraction and analysis. The sample preparation process was carried out using the automated MicroLab STAR® system from the Hamilton Company. Sample preparation was conducted using a proprietary series of organic and aqueous extractions. The resulting extract was divided into two fractions; one for analysis by liquid chromatography/mass spectrometry (LC/MS) and one for analysis by gas chromatography/mass spectrometry (GC/MS). Samples were placed briefly in a TurboVap® (Zymark) to remove the organic solvent. The LC/MS extracts reconstituted under acidic conditions were gradient-eluted using water and methanol, both containing 0.1% formic acid, while basic extracts, which also used water/methanol, contained 6.5 mM ammonium bicarbonate. The samples destined for the GC/MS analysis were re-dried under vacuum desiccation for a minimum of 24 h prior to being derivatized under dried nitrogen using bistrimethyl-silyl-triflouroacetamide (BSTFA).The LC/MS portion of the platform was based on a Waters ACQUITY UPLC and a Thermo-Finnigan LTQ mass spectrometer, which consisted of electrospray ionization (ISI) and a linear ion-trap (LIT) mass analyzer. The derivatized samples for GC/MS were analyzed in a Thermo-Finnigan Trace DSQ fast-scanning single-quadripole mass spectrometer using electron impact ionization. The GC column was 5% phenyl and the temperature ramp went from 40°C to 300°C in a 16-minute period. Accurate mass determination and MS/MS fragmentation (LC/MS), (LC/MS/MS) were carried out in a Thermo-Finnigan LTQ-FT mass spectrometer, which had an LIT front end and a fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer backend.Compounds were identified by comparison to Metabolon's library entries of purified standards or recurrent unknown entities. Data were normalized to the correct variation resulting from instrument inter-day tuning differences. Raw area counts for each compound were corrected in run-day blocks by registering the medians to equal one and by normalizing each data point proportionately.Sk, Su and Sc at both temperatures and the other two species were determined by t-tests. The statistical level of significance was set at P≤0.05.The metabolic data are the result of five replicates for each fermentation (temperature and strains). Significant differences between the supernatants of For the metabolic profiling data, two types of statistical analysis were performed. Following log transformation and imputation with minimum observed values for each compound, Welch's two sample t-tests were used to identify the metabolites that differed significantly between the experimental groups. An estimate of the false discovery rate  was calculated to take into account the multiple comparisons that normally occur in metabolomic-based studies. A low q-value (q<0.10) indicates high confidence in a result. For classification purposes, we mainly used random forest analyses. Random forests create a set of classification trees based on the continual sampling of experimental units and compounds. Statistical analyses were performed with the R program.vegan package (the rda function) of the R v.2.15 statistical software Principal component analysis (PCA) was done using the S. cerevisiae grown at a near-optimal temperature  versus a non optimal temperature , and to compare and contrast its profile to Saccharomyces genus members (S. bayanus var. uvarum and S. kudriavzevii) with greater tolerance at low temperature.This comparative biochemical study aimed to characterize the metabolic adaptations defining Sc at 12°C). When the steady state was reached (after five volume changes), the sampling of supernatants and cells was done. Saccharomyces strains and the concentration of the main compounds of oenological interest in the supernatant in the steady state. As seen, few sugars were consumed from the SM fed to the continuous cultures, and Sc at 28°C was the strain which more consumed sugars. Intriguingly, cryotolerant strains Su and Sk consumed less than 10% of the initial sugar content. These parameters clearly indicate that the metabolic study fitted the first wine fermentation stages . In accordance with this fermentation stage, residual nitrogen (both ammonium and amino acids) was hardly consumed, with high concentrations in the supernatant. The high concentrations of sugars and nitrogen indicated that these chemostat cultures were not carbon-limited or nitrogen-limited. As the steady state was reached in all the cultures, another nutrient, or group of nutrients, must limit growth. The physiological data showed remarkable differences between Sc and the cryotolerant species Su and Sk. Regardless of the growth temperature, the sugar consumption rate and the glycerol and ethanol production rate were higher for Sc than for Su and Sk. Conversely, Su and Sk presented higher biomass yields than Sc. Likewise, the cultures of Sc showed no significant differences in biomass yields, in the glucose and ammonium consumption rates, and in the ethanol production rate between both temperatures. Conversely, Sc at 12°C displayed greater amino acid consumption and lower glycerol production rates than Sc at 28°C.Our experimental design was based on continuous-culture fermentations. This system offers a stable and controlled environment for cells by maintaining constant biomass and concentrations of nutrients and products Sc−12°C versus the other continuous-cultures  resulted in 295 molecules identified from a total of 1700 molecules contained within the Metabolon library   . The twoompounds .Su and Sk , 2-palmitoylglycerophosphocholine, glycerol-3-phosphate and 1-oleoyglycerophosphocholine , and several more increased, such as linoleate (C18∶2) and linolenate (C18∶3) . We alsoocholine .Sc cells grown at 28°C, indicating that the cells grown at the higher temperature are better poised to deal with oxidative stress or that the Sc growing at 12°C undergo more oxidative stress  for the production of white and “rosé” wines because it improves the taste and aroma characteristics S. cerevisiae is the predominant species responsible for alcoholic fermentation, other species of the genus Saccharomyces, such as S. bayanus var. uvarumS. cerevisiae x S. kudriavzeviiSu and Sk growing at 12°C, which we compared with the metabolome of Sc (not well-adapted at low temperature) at 12°C. This comparison revealed that the inter-specific differences were even greater than the temperature-dependent metabolic changes. As we did not analyze the metabolic profiling of Su and Sk at 28°C, we cannot ascertain whether the changes observed in the metabolism of these species were due to low temperature. In a future study, the metabolic adaptation of these cryotolerant species at low temperature should be dealt with. The main differences between the metabolic profiling of Sc growing at 12°C and 28°C were observed in amino acid and lipid classes. These differences in the amino acid metabolism may be connected with the different consumption rate of organic nitrogen at both temperatures , such as glycerophosphorylcoline (GPC), 2-palmitoylglycerophosphocholine and 1-oleoyglycerophosphocholine, in the Sc grown at 12°C and 28°C were the metabolites belonging to the glutathione/glutaredoxin system, biochemicals that help cells detoxify reactive oxygen species (ROS). Cross-talk between signal transduction in response to the temperature downshift and oxidative stress has been previously reported by Zhang et al. SOD1, CTT1 and GSH1 significantly rose by a temperature downshift from 30°C to 10°C. Moreover, and consistent with this idea, Schade et al. et al. Another set of metabolites that distinguished the S. cerevisiae were in the carbohydrate metabolism. The Sk and Su strains had significantly higher levels of glucose and fructose, and most of the intermediates were of the higher part of glycolysis (C6 sugars), the pentose phosphate pathway and the trehalose metabolism. The easiest explanation is that these strains present a higher sugar uptake at low temperature. Yet when considering the residual sugars in the supernatant of steady-state cultures .The global metabolic comparison made of the three species revealed that the main differences between the two cryophilic species and cultures , Sk and u and Sk . Thus, tSu from Sc. Shikimate is an important precursor for aromatic amino acids tyrosine, phenylalanine and tryptophan. It is well-documented that tryptophan uptake is a limiting factor for yeast cell growth at low temperature Su can counteract the transport problem and improve its growth at low temperature.Despite the main differences among the three species lying in the carbohydrate metabolism, other important differences have been be detected. Shikimate, its metabolic intermediates, glucose-6-phosphate and phosphoenolpyruvate, which are shared with the glycolysis pathway, and a terminal product, tryptophan, were identified by the Random Forest analysis as factors separating Su and Sc strains. Apart from alpha-ketoglutarate, the initial substrate of the pathway, lysine and its pathway intermediates  significantly reduced in S. bayanus var. uvarum. Homocitrate synthase (HCS) catalyzes the conversion of alpha-ketoglutarate into homocitrate, and represents the rate-limiting step of lysine synthesis. The observed pattern of changes strongly suggests that HCS, a highly regulated enzyme, activity is inhibited in S. bayanus var. uvarum. Yet no obvious relationship to its ability to grow at 12°C has been identified in the scientific literature.Another amino acid biosynthesis route also showed differences in its intermediates and the final product separating the Sk, it is characterized by increased NAD+ synthesis and cell wall synthesis. NAD+ is a primary cofactor for the reductive reactions of energy metabolism and can serve as a marker of cellular energy status. Additionally, it is a co-substrate for certain NAD+-dependent histone deacetylases of the sirtuin family, which play a role in gene silencing and in regulating cellular metabolism + and NADH suggest that Sk has considerable nucleotide cofactor capacity to catalyze the reactions related to energy metabolism, as well as those reactions controlled by NAD+-dependent sirtuins. Furthermore, Sk has elevated several compounds relating to the synthesis of the cell wall polysaccharide chitin. It is known that many cold shock proteins in S. cerevisiae are serine/threonine-rich mannoproteins localized in the cell wall Regarding Saccharomyces. We have confirmed the importance of lipid metabolism in the cold adaptive response in S. cerevisiae, especially the lesser amount of phosphatidylcholine and its derivatives. We have also observed that two cryotolerant species, S. bayanus var. uvarum and S. kudriavzevii, differ from S. cerevisiae in terms of their capacity to use fructose at 12°C. Nevertheless, these two species have developed different strategies for cold resistance. S. bayanus var. uvarum showed great shikimate pathway activity, while S. kudriavzevii presented increased NAD+ synthesis. The differences in these metabolites of cold tolerance and the winemaking process suggest that it is possible to segregate the metabolism of S. cerevisiae from that of S. uvarum and S. kudriavzevi, and that it may provide a basis for understanding why S. cerevisiae performs better at 28°C, while its Saccharomyces counterparts do better at 12°C. This study advances our understanding of the cold response within the Saccharomyces genus at the metabolic level and can be used as a basis for future biotechnological applications for low-temperature wine fermentations.In summary, with this global metabolic profiling study, we have detected the main metabolites involved in low temperature response in three different yeast species from the genus Figure S1The homeostasis redox in S. cerevisiae. Metabolic differences in the Sc growing at 12°C and 28°C. Box legend: bar inside the box represents the median value, upper bar represents maximum of distribution, lower bar represents minimum of distribution and the circle represents extreme data points.(TIFF)Click here for additional data file.Figure S2Lysine synthesis. Differentially produced metabolites within Su and Sc. Box legend: bar inside the box represents the median value, upper bar represents maximum of distribution, lower bar represents minimum of distribution and the circle represents extreme data points.(TIFF)Click here for additional data file.Figure S3Cell wall synthesis. Differentially produced metabolites within Sk and Sc. Box legend: bar inside the box represents the median value, upper bar represents maximum of distribution, lower bar represents minimum of distribution and the circle represents extreme data points.(TIFF)Click here for additional data file.Table S1Metabolic comparison between Sc growing at 28°C, Su and Sk and Sc growing at 12°C (control condition). Green indicates difference (p≤0.05) between the groups shown, indicating a ratio <1. Light green indicates approaching significance (0.05≤p≤0.1) between the groups shown, indicating a ratio <1. Red indicates difference (p≤0.05) between the groups shown, indicating a ratio >1. Pink indicates approaching significance (0.05≤p≤0.1) between the groups shown, indicating a ratio >1. Non-coloured cell means values which are not significantly different for the comparison.(DOC)Click here for additional data file.


Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with Hebbian couplings, that is explicitly seen to correspond to the rate of decay of entropy production over time. Guided by this analogy, we show that reaction networks can be formally re-cast as systems of interacting reactions that optimize the use of the available compounds by competing for substrates, akin to agents competing for a limited resource in an optimal allocation problem. As an illustration, we analyze the scenario that emerges in two simple cases: that of toy (random) reaction networks and that of a metabolic network model of the human red blood cell. In specific, we obtain a variational principle that relates fluxes (i.e. the average number of microscopic transitions per time per volume for each process) in NESS to the minima of a global function where stoichiometric coefficients and steady-state concentrations appear as parameters. This function is reminiscent of the Hamiltonian of a Hopfield model with Hebbian couplings V , formed by M distinct chemical species  proportional to the substrate concentrations, which vary in time. At stationarity and for ideal systems, the Gibbs energy (GE) change per mole associated to each reaction i, i.e. R is the gas constant, i, i.e. the average number of transitions per time per volume, satisfies the relation i.We consider an open system enclosed in a volume We focus on the time evolution of the internal composition of such a chemical reactor. The dynamics of this system is driven essentially by two factors: (a) the fact that molecules can stochastically enter or leave the system, and (b) the fact that reactions events occur  inside the system. Reasonably, then, the NESS will depend (a) on the rate at which molecules can cross the system’s boundaries per unit volume  is easily linearized to yieldThis equation highlights the way in which concentrations affect the time evolution of the system and, in principle, one would now need to analyze the coupled system formed by (4) and (7). However, for simplicity, we replace i (the average net number of microscopic transitions per time per volume) while Note that H so that the NESS of (12) correspond to the solutions of the minimization problemi in a NESS) are generically of the form i will be characterized by unidirectional microscopic transitions for H is indeed minimized by solving H is achieved by taking Following i to other reactions in the network via shared compounds (the coupling coefficient i and j have a metabolite with finite concentration in common). Consider a species i and j such that j produces i). Then j will contribute to the increase of i between time t and time j will ultimately increase the probability of a concomitant advancement of reaction i. In other words, this situation favors the emergence of a positive correlation between reactions i and j. Likewise, if both i and j are either producing , the stoichiometry, the available nutrients, the production goals, etc. Whether for a given network the minimum of H is zero or not then depends on several factors, including the bounds on fluxes and the specific form of the uptakes. Note that ad hoc constraint usually represented by the maximization of a specific score function . The conditions (16) are instead reminiscent of Von Neumann’s model of reaction networks From a physical standpoint, H relates to standard quantities used to characterize non-equilibrium behavior in reaction networks, such as the entropy production. Indeed the entropy production per volume V is given byH is constant in NESS. It follows that for time scales shorter than A broader physical insight can be obtained by studying how H appears in the Gibbs theory of thermodynamic stability for ideal systems. Let us consider a system at equilibrium with vanishing net fluxes and evaluate the effect of a perturbation that drives the system away from equilibrium. Such a perturbation corresponds to a  change in the turnover i, which can be achieved e.g. by forcing a  non-zero flux i for a time G (i.e. H).It is noteworthy that this scenario essentially characterizes the Lyapunov condition described in N and M. Let M of which at most are independent  with initial conditions A simple algebraic argument allows to understand that, generically, a qualitative change in the solutions of (14) is expected to take place as one varies the ratio between the network parameters t the i, one can follow N and M. The result is the Langevin processSuch a transition can be fully investigated within the following, simple model: the stoichiometric coefficients where M species and N reactions in order to analyze the dependence of its steady state(s) on p and i and q and H vanishes; it only changes the value of H for this case is defined asTo illustrate the scenario underpinned by the above theory, we have simulated the dynamics defined byi one ends up in stationary states with i, instead, the system ends up in a different steady state for i, n, i.e. to chemical equilibrium. In other words, expectedly, boundary fluxes induce NESS.H is possible, namely the standard reduced model of the human red blood cell (hRBC) metabolism, which includes the glycolytic and the pentose phosphate pathway only  that the steady state of the hRBC metabolism is compatible with extracellular concentrations of GLC, LAC, K+, Na+ and CO2 due to the operation of a single hRBC is easily seen to be given byNow the variation of the In turn, for the extracellular medium one hasa and b are defined respectively asMinimizing this at fixed 2 is much larger than the others (implying 2). We can therefore define the fraction of GLC consumption through the PPP by re-scaling One sees that if the concentration of CO2, F varies between From this it is also immediately clear that, in general conditions for COH, see (13), in which stoichiometry, intakes, outtakes and concentrations appear as parameters. The cost function is closely related to Hopfield models of neural networks. This allows to rephrase such networks as systems of reactions interacting via Hebb-like rules and subject to an external forcing provided by the boundary fluxes. Furthermore H bears two simple physical interpretations. First, minimizing it amounts to finding the flux organizations that keep the overall “waste” of chemical species to a minimum, given the boundary conditions to be satisfied. Second, it equals (modulo a constant) the time derivative of the entropy production per volume: NESS thus correspond to flux configurations such that the entropy production decreases in time at the smallest allowed rate, in line with the ideas exposed in In this paper we have derived a variational principle for the NESS of chemical reaction networks, showing that, for time scales over which chemical potentials can be considered constant, stationary non-equilibrium fluxes minimize the function H rather than by taking Making contact with stoichiometric models of metabolic networks is relatively straightforward as long as boundary fluxes are taken to be fixed and one does not include additional objective functions that NESS are required to maximize. For instance, the maximization of biomass flux , it is possible to get rid of infeasible cycles by complementing the variational problem described here with the minimization of the square norm of the flux vector. This is a consequence of the Gordan theorem of alternatives An important property that NESS should possess is thermodynamic feasibility, i.e. they should not contain infeasible loops i in (7)), the situation is completely equivalent to the Minority Game with anti-correlated strategies studied in i, i.e. the system asymptotically reaches chemical equilibrium. As it should be, NESS are induced by non-zero boundary fluxes, i.e. by non-zero fields Perhaps not too surprisingly, the formal aspects of this theory present many common traits with those developed over the past decade for the analysis of large games with heterogeneous interacting agents, specifically with Minority Games Besides a possible theoretical interest in deepening the analogy just described  appearing in the reduced model of hRBC metabolism.(PDF)Click here for additional data file.Table S2Reactions  appearing in the reduced model of hRBC metabolism.(PDF)Click here for additional data file.