Due to the growing amount of biological knowledge that is incorporated into metabolic network models, their analysis has become more and more challenging. Here, we examine the capabilities of the recently introduced chemical organization theory (OT) to ease this task. Considering only network stoichiometry, the theory allows the prediction of all potentially persistent species sets and therewith rigorously relates the structure of a network to its potential dynamics. By this, the phenotypes implied by a metabolic network can be predicted without the need for explicit knowledge of the detailed reaction kinetics.E. coli that incorporates the regulation of all involved genes. Our method correctly predicts the known growth phenotypes on 16 different substrates. Without specific assumptions, organization theory correctly predicts the lethality of knockout experiments in 101 out of 116 cases. Taking into account the same model specific assumptions as in the regulatory flux balance analysis (rFBA) by Covert and Palsson, the same performance is achieved (106 correctly predicted cases). Two model specific assumptions had to be considered: first, we have to assume that secreted molecules do not influence the regulatory system, and second, that metabolites with increasing concentrations indicate a lethal state.We propose an approach to deal with regulation – and especially inhibitory interactions – in chemical organization theory. One advantage of this approach is that the metabolic network and its regulation are represented in an integrated way as one reaction network. To demonstrate the feasibility of this approach we examine a model by Covert and Palsson , 2002) of the central metabolism of The introduced approach to model a metabolic network and its regulation in an integrated way as one reaction network makes organization analysis a universal technique to study the potential behavior of biological network models. Applying multiple methods like OT and rFBA is shown to be valuable to uncover critical assumptions and helps to improve model coherence. The analysis of metabolic networks aims at the understanding of metabolic capabilities of organisms to adapt to, and to maintain growth under different external and internal conditions. Various tools exist today to analyze and predict behavior of organisms solely based on metabolic network structure.E. coli [E. coli under different growth conditions. The growth on each of the carbon sources glucose, lactose, and glycerol could be matched to a specific organization. However, as negative regulation for some genes was ignored because the down-regulation of genes cannot push gene expression levels below the basal level, some organizations represented biologically infeasible system states, for example the simultaneous uptake of all carbon sources.Important results have been obtained by applying methods like flux balance analysis , modelinE. coli . It was E. coli to predict growth phenotypes. Finally, the method is applied to the complete network model to predict the lethality of gene knockouts.In this paper, we present an approach to explicitly consider inhibitory regulatory interactions within the analysis of chemical organizations. This allows the more faithful and more precise consideration of biological network models, making the identification of all potential phenotypes of regulated metabolic networks possible. First, the basic concepts of the theory of chemical organizations are presented in the next section. Then, the approach to deal with inhibitory interactions is introduced. The method is then first applied to a subnetwork of a network model of the central metabolism of The theory of chemical organizations  providesreaction network.Let closed, if for all reactions A set of species m = |n = |S =  be its m × n stoichiometric matrix, where mi, j is the number of molecules of species i that is produced in reaction j . A set of species self-maintaining if a flux vector v =  ∈ Given a reaction system (1) For every reaction (2) For every reaction i ∈ Sv)i ≥ 0.(3) For every species In other words: if we consider only the sub-network made up by the species of organization.A set of species balanced organization, if a flux vector conforming to the self-maintenance condition can still be found, if in requirement 3 of the self-maintenance definition, the greater equal condition is replaced by equality:An organization i ∈ Sv)i = 0.(3') For every species dx(t)/dt = Sv(x(t)), then all steady states of the system are instances of organizations. In other words, the species with concentration levels greater than zero in a particular steady state are exactly those species contained in a corresponding organization. Note that organizations do not necessarily contain a steady state, as they can also embody growth in which species have increasing concentrations. The only assumption made for this theorem is that molecules that are present and can react will react sooner or later . Note that this assumption differs fundamentally from the assumption made by methods like elementary mode analysis, which assume that each reaction can be switched off independently even if the reactants are present in large concentrations [A rigorous link between organizations and the potential dynamics of a reaction system is provided by Theorem 1 from Ref. : Assume trations .n + m inequalities v ≥ 0 and S · v ≥ 0 in the flux space To compute organizations, the convex polyhedral cone Regulation has not yet been explicitly considered in the analysis using the theory of chemical organizations. The aim of this section is to elaborate a concept that allows us to also account for regulation. This concept makes it possible to also study regulated metabolic networks using organization theory. The basic idea is to map regulatory rules to normal chemical reaction rules. For inhibitory rules and rules using the direction of a reversible flux we introduce pseudo species representing the absence of a species and the direction of a flux, respectively.To examine the effects of regulation on chemical organizations we first need to discuss the general types of regulatory interactions that occur in biological systems in more detail.e.g., small molecules, proteins, RNA) acting on further biological target entities. As we are considered with reaction networks, we focus here on the regulation of reactions. Two different types of regulation have to be considered. The first type of regulation only changes the flux of the regulated reaction slightly. Certain types of autoregulation fall into this category. This kind of regulation does not change the structure of the reaction network and hence does not affect its organizational hierarchy. The second type of regulation is more drastic: it turns a reaction completely off or enables a formerly unavailable reaction. This is the case, for example, when the expression of a protein that catalyzes a reaction is suddenly repressed. As a consequence, the catalyzed reaction is not available to the network anymore once the protein is completely degraded. The induction of uptake pathways is an example for enabling novel reactions. New reaction pathways become suddenly available.Regulation appears on different levels in the cell, being carried out by a variety of biological entities  and minpression ). Howeveon or off is assigned to a regulated reaction [Several approaches exist to represent and model regulatory interactions , for exareaction . We willactivation, in which a species is required in order to perform a certain reaction, and inhibition, in which a species inhibits a certain reaction and makes it unavailable. To model this kind of regulation we make use of the properties of reactions being similar to rewriting rules, where the left hand side is being replaced by the right hand side. Taking this approach, the molecules on the left hand side need to be present for the reaction to proceed. Additionally, regulatory events can be triggered not only by the presence or absence of a species, but also by a species being available in excess or not.Two types of regulatory events have to be considered: Activation or turning on a reaction by a specific species can be simply modelled by considering this species as a kind of a catalyst. In terms of rewriting rules this approach can be considered as an additional constraint on the presence of certain species for the reaction to proceed. By this, the reaction can only take place when the activating species is present. Being a catalyst, the activating species is not consumed within the reaction it catalyzes.E activates a reaction that transforms a reactant A into product B. In the absence of E, the reaction shall have a zero flux, while the flux shall become positive in the presence of E and A. A reaction A → B activated by E becomes:Let us consider the general case in which species E as a catalyst on the reactant and product side of the reaction equation does not change the stoichiometric matrix S. Still, one unit of A is being consumed to produce one unit of B. Therefore any flux vector that guarantees self-maintenance for a set of metabolites including E but without considering E as an activator, will also guarantee self-maintenance when E is added as a catalyst to model activation.Note that adding I inhibits a reaction, we could add an if-statement to each reaction that guarantees that the reaction is only available when I is absent. But since we intend to model regulation within the language of reactions, such if-statements would not fulfill our requirements. An alternative way to model inhibition is to understand it as another type of activation, that is, as the activation of a reaction by the absence of an inhibitor. For achieving this we have to introduce a pseudo species Ī that represents the absence of inhibitor I. In terms of rewriting rules, such species is just a constraint on the presence of a certain species for a reaction to take place. A reaction A → B inhibited by I becomes:Handling inhibition is more diffcult. If inhibitor I, represented by pseudo species Ī, educt A can react to form product B.Only in the absence of direction at which one or more reversible reactions operate. Two examples can be found in Covert and Palsson [pdhR) and the rule for the catabolite activator protein (gene cra). Given a reversible reaction r: A ↔ B and the following flux-direction dependent regulatory rule:Sometimes it can make sense to define regulatory rules that depend on the  Palsson , the rulr is positive (forward), then activate protein E.","If the flux of reaction fr and its inverse counterpart we map this regulatory rule to the following conventional reaction rules by introducing a pseudo species fr or rf or the backward reaction rule rb can be active. Here, in Eq. (3), we use the presence of the molecular species A and fr as an indicator for the activity of reaction rf . Conversely, we can use the presence of the molecular species B and rb.Because in consistent organizations (see below) either fr to every reversible reaction rule r in order to obtain an indicator for the direction in which it operates. Then, these indicators can even be combined to represent a more complex rule. Note that in Covert and Palsson [e.g., PYR for the regulation of pdhR; and FDP or F6P for the regulation of cra).If necessary, we can add a pseudo species like  Palsson , differeIntroducing pseudo species causes a problem, as now two network species represent the same molecular entity. When computing the organizations of such a network, some organizations might exist that contain both or neither of the two species. In both cases, the presence of the species is not clearly defined. Either the presence and absence is indicated simultaneously, or no statement is made at all. Consequently, we only consider those organizations in the remaining of this paper, in which for all species it is clearly defined whether they are present or not. We call such organizations consistent.consistent organization, if for all species S ∈ S or An organization In passing we note that this approach allows one to model more than two states of a molecule, for example different phosphorylation states.There are few cases where a reaction is regulated by a single molecule alone. In most cases regulation is more complex, for example if the availability of a reaction is being determined by the interaction of a set of proteins. In such cases we need to model regulation by a set of boolean functions. This section presents an approach to account for such functions on the level of regulation .AND or OR, and the negation NOT. The construction of a negation has been outlined above. In principle, it would be suffcient to present a method to implement AND or OR. However, we present methods for both to ease the process of converting regulation logics to chemical reactions.All binary boolean functions can be reduced to either AND function. A typical regulation incorporating an AND function is the required presence of two activators to perform a reaction. If we consider activator E1 and activator E2 to be necessary for a reaction converting educt A into product B we can write:First we consider the OR function is considered. An example for this case is a reaction transforming educt A into product B that can alternatively be activated by two activators E1 and E2. The presence of one of these activators is suffcient to perform the reaction. In this case, the reaction is split into two parts; one that accounts for the presence of activator E1, and one that accounts for the presence of activator E2:Next, the Taking these two basic functions, it is possible to model all regulatory relationships that can be represented by boolean rules in metabolic networks .I can shut down both reactions. Thus, we have a simple AND function that requires for both reactions that both I and P1, respectively P2, are absent. A model without regulation would contain only reactions transforming A to P1 and P2, the influx to A and the outflux from the products: A, A → P1, A → P2, P1 → ∅, P2 → ∅}.As an example for the presented procedure, we analyze a simple reaction network comprising – apart from inflow and outflow – two reactions forming a switch as depicted in Figure The boolean expressions describing the regulation are:Applying the presented procedure, these expressions are transformed into chemical reactions. The resulting reaction network contains the following reactions:The network contains 16 organizations as listed in Table O10 = {A, I, O11 = {A, Ī, P1, O12 = {A, Ī, P2}. In the remaining organizations it is at least for one species not clearly defined whether it is present or not. Taking Organization 2 for example, the presence of A and I is determined with A present and I absent, but there is no information concerning species P1 and P2. In Organization 6, inhibitor I is present and absent at the same time. Figure I is present and shuts down reactions (2) and (3), turning the switch off. In the other two consistent organizations I is not present and there is either a flux through reaction (2) (Organization 11) or through reaction (3) (Organization 12). They represent the two other states of the switch.Three organizations are consistent: E. coli by Covert and Palsson [core network to study wildtype growth phenotypes on different carbon sources, and the complete network for predicting knockout experiments. Both networks are listed in the Supplement  and 168 reactions. The complete list of network reactions can be found in the Supplement.E. coli by Covert and Palsson [For predicting the lethality of gene knockouts we use the complete network model of the regulated central metabolism of  Palsson . DependiThe core network model contains 16 consistent organizations. They are listed in Table In Organization 2, external oxygen is available. Consequently, the aerobic response regulators ArcA and Fnr are absent here. This is the only difference between Organizations 1 and 2.lac gene, LacI, is absent in the organization, no uptake reactions for external lactose are contained in the organization. The lactose permease LacY, a product of the lac genes, is missing. As glucose is available in the medium, the lactose uptake system is not induced by the presence of external lactose. This effect is known as inducer exclusion. The metabolite required for upregulation of the lac genes is not taken up by the cell. Organization 5 represents a similar case in which glycerol is available in the growth medium but not taken up. All external carbon sources and oxygen are available in Organization 10, but the cell is still exclusively utilizing glucose. Organizations 6 to 9 represent further input combinations defining growth conditions with external glucose available. The availability of oxygen does not change the reactions in the part of the central metabolism that is considered in the core model.The first organization that utilizes an external carbon source is Organization 3, which contains the reactions for glucose uptake. Consequently, the metabolites of the central metabolism are present in this organization. When examining the proteins of the organization, we find that the glucose response regulator Mlc is absent. The organization next in size is Organization 4. Here, lactose is additionally in the medium. Although the repressor of the In Organization 13, lactose is the exclusive external carbon source. Consequently, LacI is absent as it is bound by allolactose, a derivative of lactose. Hence, it cannot repress the genes necessary for lactose uptake and utilization. We find the corresponding gene products present in this organization, namely LacZ and LacY. Additionally, derivatives of lactose, for example galactose, are contained in this organization. These metabolites are created in the pathway leading from lactose to the central metabolism. Another diauxic shift effect can be observed in Organization 14. Here, external lactose and glycerol are present as carbon sources, but as in the case with glucose and lactose, only lactose is taken up. Organizations 15 and 16 represent further growth conditions in which lactose is taken up. Once again, the availability of oxygen does not change the reactions in the modeled part of the central metabolism.Glycerol is the exclusive external carbon source in Organization 11. As all proteins necessary for glycerol uptake are present, glycerol is taken up. For glycerol uptake, three different enzymes catalyze the reaction from glycerol-3-phosphate to dihydroxyacetone-phospate, a metabolite of glycolysis. One of these enzymes, glycerol-3-phosphate-dehydrogenase, is constitutively expressed in the model. The other two proteins, glycerol-3-phosphate kinases GlpABC and GlpD are specific for anaerobic, respectively aerobic growth conditions. Therefore, GlpABC is present and GlpD absent in Organization 11, where no oxygen is available. When oxygen is available as in Organization 12, GlpD is present and GlpABC absent.in vivo data and predictions by flux balance analysis (FBA) and rFBA. The results are summarized in Table Knockout experiments are performed using the complete network model. Gene knockouts are modeled by deleting all reactions in which the corresponding protein takes part as educt or product. The set of consistent organizations is determined for each knockout experiment using a heuristic approach detailed in the Supplement. The lethality of a knockout can be predicted by the existence of organizations containing all biomass precursor metabolites. If such an organizations is not found, the knockout is predicted to be lethal. We use organization theory (OT) and an adapted version of organization theory  to predict the same gene knockouts as Covert and Palsson , who userpiA, and rpiA + rpiB on glucose). The self-maintenance property allows for the accumulation of internal metabolites, while in rFBA, only steady states are considered, and any accumulation of metabolites is regarded as lethal. In these two cases, the organizations containing all biomass precursors contain metabolites with positive productions.  Hence, OT predicts the knockout to be nonlethal while rFBA predicts it to be lethal as no steady state exists. In aOT we restrict our analysis to organizations that are balanced . With this model specific assumption aOT classifies the two knockout experiments correctly.In two cases, OT predicts a lethal knockout to be nonlethal  yield deeper insights into the differences between chemical organization theory and regulatory flux balance analysis, namely in the treatment of by the cell secreted molecules.Further three incorrect predictions by OT (acs). According to the model, the corresponding gene is only transcribed if no carbon source is available or at most acetate or formate, or both. The second pathway is catalyzed by acetate kinase A (gene ackA) and phosphotransacetylase (gene pta). If one of these genes is knocked out, the first pathway can still support the central metabolism, given that acetate is the exclusive external carbon source. In this case, chemical organization theory predicts both knockouts as lethal, which is not the case in vivo and correctly predicted by rFBA. The reason for this discrepancy is that in any network containing the biomass precursor metabolite pyruvate, this metabolite will be secreted by the cell. Therefore, such a network also comprises the external form of pyruvate which is an inhibitor for the only remaining uptake reaction for acetate. Consequently, there exists no organization containing all biomass precursor metabolites when acetate is the exclusive carbon source in the growth medium and the second pathway is knocked out. Because the presence of metabolites is not explicitly considered in rFBA, this inhibition is not detected by rFBA. However, because the knockout is nonlethal in in vivo experiments, the levels of secreted pyruvate might not be suffcient to have an effect on the expression of acs. Or, the cell switches its uptake from acetate to pyruvate until it is depleted and then switches back to acetate again.In the case of acetate uptake, there are two pathways that enable the utilization of this carbon source as depicted in Figure ppc on glycerol as nonlethal can be explained by the same argument. Gene ppc codes for the phosphoenolpyruvate carboxylase, which supplies the citric acid cycle with oxaloacetate (OA). When ppc is knocked out, the only alternative for OA production is the glyoxylate shunt, consisting of the isocitrate lyase (gene aceA) and the malate synthase A (gene aceB). However, the glyoxylate shunt is only active if E. coli grows on acetate or fatty acids as the sole carbon source [ppc on a glycerol growth medium is lethal in vivo, as the glyoxylate shunt is not activated. In the model, the glyoxylate shunt is regulated by the fatty acid and acetate response regulators IclR and FadR as depicted in Figure fadR is only expressed if external glucose, or no acetate is available in the growth media. If activated, FadR leads to an upregulation of iclR, which then leads to a downregulation of aceA and aceB, inactivating the glyoxylate shunt. If acetate is available in the growth medium, fadR is not expressed, and thus aceA and aceB are expressed at high levels, activating the glyoxylate shunt. Any organization containing the biomass precursor metabolite acetyl-CoA also contains acetate, which is secreted. Hence, any organization containing the biomass precursors also contains the external form of acetate, which activates the glyoxylate shunt.The incorrect prediction of the knockout of n source . Hence, E. coli to grow on glycerol if ppc is knocked out. Our result suggests that the activation of the glyoxylate shunt would be enough. There have been reports of E. coli strains growing on glucose media that were also able to grow with ppc knocked out, which is usually lethal. This was facilitated by a mutation that lead to an upregulation of the glyoxylate shunt [Even though considerable amounts of acetate secretion on glycerol media has only been reported in high density cultures , OT indite shunt . Thus, te.g., when externally supplied), the other species represents the metabolite at low concentration . These modifications allow aOT to correctly predict the three cases discussed above. Note that the underlying assumption of this modification is also made by Covert and Palsson [The problems encountered in the regulation by secreted species can be resolved by introducing a pseudo species representing the secreted version of a species. Therefore, in aOT, a metabolite that can be secreted is represented by two species: one represents the metabolite at high concentration .By transforming the boolean formalism that represents the regulation of a metabolic network into reaction rules, we were able to demonstrate how chemical organization theory can be applied to regulated metabolic networks. Using a model of the central metabolism of E. coli , each ofe.g., [Without specific assumptions, organization theory (OT) was able to predict the lethality of knockout experiments correctly in 101 out of 116 cases (87.1%). With model specific assumptions, "adapted" organization theory (aOT) was able to predict the lethality of knockout experiments correctly in 106 cases (91.4%), achieving the same performance as rFBA . When coe.g., ). In thiMoreover, there are cases in other models in which predictions by OT are more accurate than those by FBA. This occurs, for example, due to the fact that FBA only incompletely takes co-factors into account. These co-factors are molecules that are necessary for some reactions to proceed. They can interact through various means with the substrates and products of a reaction. In the (unregulated) metabolic model by Reed et al. , we idenIn our analysis of the model by Covert and Palsson , we founFirst, (r)FBA only considers steady states. A system state with accumulating metabolites is regarded as lethal. In OT, accumulating metabolites are explicitly allowed to also cover system states related to growth. To adopt the steady state assumption in OT however, one simply can restrict the analysis to balanced organizations in aOT. However, only considering steady states is not necessarily the best "natural" choice. As models usually are not complete, the biological system might contain pathways that are not modeled but can take care of overproduced metabolites. Also, certain molecular species accumulate in the cell at certain time points, for example in different phases of the cell cycle. Hence, states with positive productions of certain species are not necessarily lethal.in vivo lethality of a knockout in one case.Second, in OT only the presence or absence of metabolites is considered. Hence, even smallest concentrations of species will potentially trigger further responses. When secreted metabolites have much lower concentrations than external metabolites supplied by the growth medium, this can lead to wrong predictions as secreted metabolites shall not trigger further regulation : if theA related issue has been raised by Shlomi et al. : The choThe largest organization does not necessarily encompass the whole system. Thus when analyzing larger models, OT allows the exact prediction of those parts of a model that can give rise to a steady state. Parts missing in such a state can then be refined. For example in the case of knockout experiments, we can determine which part of a network is still available. Such knowledge is important when trying to reduce a metabolic model for a specific purpose, for example to increase the production of a certain metabolite. Even though the presented method can also be used for genome scale networks, it remains to be seen if all of the regulated organization in such a system could still be found. The bottleneck in the computation is the determination of all organizations of a regulated network before checking if they are consistent. Their number can grow exponentially with network size, in which case computation is primarily constrained by the available memory. This problem might be circumvented by an approach that partitions the solution space of the self-maintainance condition and searches those partitions in parallel for organizations . However, such an approach has not yet been implemented. Currently, the analysis of a pure (non-regulated) metabolic network of genome scale by  is possiIn recent years other approaches for the integration of regulatory networks into stoichiometric analysis have been proposed: Steady-state regulatory flux balance analysis (SR-FBA)  builds oi.e., the state when all external inputs are defined, resembles the organizations we found. However, those states are restricted to the regulatory part of the network, since the closure of the participating molecules is not taken into account. Another aspect of this concept that has not yet been analyzed is to which extent this method can also be applied to larger networks, for example those we analyzed in this work. The integration of the regulatory network into a metabolic network using a flux through the network might further increase the combinatorial explosion of the number of extreme pathways. Nonetheless, this approach is valuable for identifying underlying pathways in a regulatory network, a prospect which has not yet been analyzed in connection with OT.Another approach, a matrix formalism to analyze regulatory systems, has been proposed by Gianchandani et al. . Similarin silico network models. All phenotypes of interest observed in vivo should have corresponding organizations in the network model.Because OT does not rely on kinetics, it can serve as a first step to analyze the potential behavior of regulated systems. The analysis delivers all potential network phenotypes described by the sets of molecular species that can coexist over a long time (cf. Theorem 1 in Ref. ). The fuWhen regulation is considered in metabolic networks, the presented approach offers the advantage that both the metabolism and its regulation are modeled within one single framework: chemical reaction rules forming a network. The unification comes at the expense of introducing a set of pseudo species to represent the absence of species. This allows one to model and consider inhibitory interactions within the framework of organization theory. Using an appropriate user interface, the pseudo species can be easily hidden.CK and PD introduced the idea of pseudo species indicating the absence of metabolites. All authors contributed to the presented new concepts and procedures building on the framework of organization theory. Software implementation, data preparation, and analysis was done by CK and FC. All authors read and approved the final manuscript.Supplement including the analyzed network models and a descritption of the employed algorithms to compute organizations.Click here for fileThe analyzed core model in SBML format.Click here for fileThe analyzed complete model in SBML format.Click here for file


Metabolomics has emerged as a powerful tool in the quantitative identification of physiological and disease-induced biological states. Extracellular metabolome or metabolic profiling data, in particular, can provide an insightful view of intracellular physiological states in a noninvasive manner.iMM904, to investigate how changes in the extracellular metabolome can be used to study systemic changes in intracellular metabolic states. The iMM904 metabolic network was reconstructed based on an existing genome-scale network, iND750, and includes 904 genes and 1,412 reactions. The network model was first validated by comparing 2,888 in silico single-gene deletion strain growth phenotype predictions to published experimental data. Extracellular metabolome data measured in response to environmental and genetic perturbations of ammonium assimilation pathways was then integrated with the iMM904 network in the form of relative overflow secretion constraints and a flux sampling approach was used to characterize candidate flux distributions allowed by these constraints. Predicted intracellular flux changes were consistent with published measurements on intracellular metabolite levels and fluxes. Patterns of predicted intracellular flux changes could also be used to correctly identify the regions of the metabolic network that were perturbed.We used an updated genome-scale metabolic network model of Saccharomyces cerevisiae, Our results indicate that integrating quantitative extracellular metabolomic profiles in a constraint-based framework enables inferring changes in intracellular metabolic flux states. Similar methods could potentially be applied towards analyzing biofluid metabolome variations related to human physiological and disease states. In addition, there is a rapidly growing literature and accompanying databases that compile this information. This has provided the basis for the assembly of genome-scale metabolic networks for various microbial and eukaryotic organisms -11. Thesin silico simulations of allowable network states based on governing physico-chemical and genetic constraints [E. coli metabolism [A genome-scale network reconstruction is a structured collection of genes, proteins, biochemical reactions, and metabolites determined to exist and operate within a particular organism. This network can be converted into a predictive model that enables straints ,13. A wistraints -16. Moststraints . Insteadtabolism  as well tabolism .Network reconstructions provide a structured framework to systematically integrate and analyze disparate datasets including transcriptomic, proteomic, metabolomic, and fluxomic data. Metabolomic data is one of the more relevant data types for this type of analysis as network reconstructions define the biochemical links between metabolites, and recent advancements in analytical technologies have allowed increasingly comprehensive intracellular and extracellular metabolite level measurements ,21. The Metabolite secretion by a cell reflects its internal metabolic state, and its composition varies in response to genetic or experimental perturbations due to changes in intracellular pathway activities involved in the production and utilization of extracellular metabolites . VariatiSince metabolic networks describe mechanistic, biochemical links between metabolites, integration of such data can allow a systematic approach to identifying altered pathways linked to observed quantitative changes in secretion profiles. Measured secretion rates of major byproduct metabolites can be applied as additional exchange flux constraints that define observed metabolic behavior. For example, a recent study integrating small-scale EM data with a genome-scale yeast model correctly predicted oxygen consumption and ethanol production capacities in mutant strains with respiratory deficiencies . The resIn this study, we implemented a constraint-based sampling approach on an updated genome-scale network of yeast metabolism to systematically determine how EM level variations are linked to global changes in intracellular metabolic flux states. By using a sampling-based network approach and statistical methods Figure , EM chanS. cerevisiae metabolic network, iMM904; and (ii) the systematic inference of intracellular metabolic states from two yeast EM data sets using a constraint-based sampling approach. The first EM data set compares wild type yeast to the gdh1/GDH2 (glutamate dehydrogenase) strain [This study was divided into two parts and describes: (i) the reconstruction and validation of an expanded ) strain , which i) strain ,32. The ) strain . We analiND750, a fully compartmentalized and elementally-balanced S. cerevisiae metabolic network, was used as the basis for reconstructing the iMM904 network [iND750 network were also re-evaluated to update the model based on existing literature. The iMM904 network was reconstructed using the SimPheny® modeling software . Existing gene-protein-reaction (GPR) associations from iND750 were also reviewed and several were modified to include additional genes and proteins. GPR associations are Boolean representations of the logical relationship between ORFs and their corresponding transcripts, proteins, and reactions to enable mapping of genes to their respective functions. The included model text files [see Additional file The previously reconstructed  network . The net network . The detS containing the stoichiometric coefficients of the reactions in the network. The steady-state solution space containing possible flux distributions is determined by calculating the null space of S: S . v = 0, where v is the reaction flux vector. Minimal media conditions were set through constraints on exchange fluxes corresponding to the experimental measured substrate uptake rates. All the model-based calculations were done using the Matlab COBRA Toolbox [The network reconstruction was converted to a constraint-based model using established procedures . Network Toolbox  utiliziniMM904 model was initially validated by simulating wild type yeast growth in aerobic and anaerobic carbon-limited chemostat conditions and comparing the simulation results to published experimental data on substrate uptake and byproduct secretion in these conditions [iFF708 model in a previous study [in silico growth rate to the measured dilution rate, which are equivalent under continuous culture growth, and minimizing the glucose uptake rate. The accuracy of in silico predictions of substrate uptake and byproduct secretion by the iMM904 model was similar to the accuracy obtained using the iFF708 model and results are shown in Figure S1 [see Additional file The nditions . The stuus study . The preiMM904 network was further validated by performing genome-scale gene lethality computations following established procedures to determine growth phenotypes under minimal medium conditions and compared to published data. A modified version of the biomass function used in previous iND750 studies was set as the objective to be maximized and gene deletions were simulated by setting the flux through the corresponding reaction(s) to zero. The biomass function was based on the experimentally measured composition of major cellular constituents during exponential growth of yeast cells and was reformulated to include trace amounts of additional cofactors and metabolites with the assumed fractional contribution of 10-6. These additional biomass compounds were included according to the biomass formulation used in the iLL672 study to improve lethality predictions through the inclusion of additional essential biomass components [in silico strain with the appropriate supplements at non-limiting, but low levels. Furthermore, trace amounts of essential nutrients that are present in the experimental minimal media formulation  were supplied in the simulations [The mponents . The modulations .Three distinct methods to simulate the outcome of gene deletions were utilized: Flux-balance analysis (FBA) -38, Miniin silico deletion phenotypes involved choosing a threshold for the predicted relative growth rate of a deletion strain that is considered to be viable. We used standard ROC curve analysis to assess the accuracy of different prediction methods and models across the full range of the viability threshold parameter, with results shown in Figure S2 [see Additional file a priori [The comparison between experimental and a priori . The opta priori . The MCCThe method implemented in this study is shown schematically in Figures Relative levels of quantitative EM data were incorporated into the constraint-based framework as overflow secretion exchange fluxes to simulate the required low-level production of experimentally observed excreted metabolites. The primary objective of this study is to associate relative metabolite levels that are generally measured for metabonomic or biofluid analyses to the quantitative ranges of intracellular reaction fluxes required to produce them. However, without detailed kinetic information or dynamic metabolite measurements available, we approximated EM datasets of relative quantitative metabolite levels to be proportional to the rate in which they are secreted and detected (at a steady state) into the extracellular media. This approach is analogous to approximating uptake rates based on metabolite concentrations from a previous study performing sampling analysis on a cardiomyocyte mitochondrial network to identify differential flux distribution ranges for various environmental (i.e. substrate uptake) conditions .gdh1/GDH2 strains were flask cultured under minimal glucose media conditions; thus, glucose and oxygen uptake rates were set at 15 and 2 mmol/hr/gDW, respectively, for the gdh1/GDH2 strain study. In the anaerobic case the oxygen uptake rate was set to zero, and sterols and fatty acids were provided as in silico supplements as described in [The raw data was normalized by the raw maximum value of the dataset (thus the maximum secretion flux was 1 mmol/hr/gDW) with an assumed error of 10% to set the lower and upper bounds and thus inherently accounting for sampling calculation sensitivity. The ribed in . For theA modified FBA method with minimization of the 1-norm objective function between two optimal flux distributions was used to determine optimal intracellular fluxes based on the EM-constrained metabolic models. This method determines two optimal flux distributions simultaneously for two differently constrained models (e.g. wild type vs. mutant) – these flux distributions maximize biomass production in each case and the 1-norm distance between the distributions is as small as possible given the two sets of constraints. This approach avoids problems with alternative optimal solutions when comparing two FBA-computed flux distributions by assuming minimal rerouting of flux distibution between a perturbed network and its reference network. Reaction flux changes from the FBA optimization results were determined by computing the relative percentage fold change for each reaction between the mutant and wild-type flux distributions.We utilized artificial centering hit-and-run (ACHR) Monte Carlo sampling ,41 to unDue to the overall shape of the metabolic flux solution space, most of the sampled flux distributions resided close to the minimally allowed growth rate (i.e. biomass production) and corresponded to various futile cycles that utilized substrates but did not produce significant biomass. In order to study more physiologically relevant portions of the flux space we restricted the sampling to the part of the solution space where the growth rate was at least 50% of the maximum growth rate for the condition as determined by FBA. This assumes that cellular growth remains an important overall objective by the yeast cells even in batch cultivation conditions, but that the intracellular flux distributions may not correspond to maximum biomass production .Z-scores (see below) are not significantly affected by either the portion of the solution space sampled or the exact scaling of secretion rates. The final overall sample used was created by combining the samples for all minimum growth rate thresholds for the highest extracellular metabolite secretion rate (maximum 1 mmol/hr/gDW). This approach allowed biasing the sampling towards physiologically relevant parts of the solution space without imposing the requirement of strictly maximizing a predetermined objective function. The samples obtained with no EM data were used as control samples to filter reporter metabolites/subsystems whose scores were significantly high due to only random differences between sampling runs.To test the sensitivity of the results to the minimum growth rate threshold, separate Monte Carlo samples were created for each minimum threshold ranging from 50% to 100% at 5% increments. We also tested the sensitivity of the results to the relative magnitude of the extracellular metabolite secretion rates by performing the sampling at three different relative levels . For each minimum growth rate threshold and extracellular metabolite secretion rate, the ACHR sampler was run for 5 million steps and a flux distribution was stored every 5000 steps. The sensitivity analysis results are presented in Figures S3 and S4 [see Additional File Since the experimental data used in this study was generated in chemostat conditions, and previous studies have indicated that chemostat flux patterns predicted by FBA are close to the experimentally measured ones , we assuZ-score based approach was implemented to quantify differences in flux samples between two conditions  flux difference vectors for each pair of conditions considered (e.g. mutant or perturbed environment vs. wild type). Based on this flux difference sample, the sample mean  and standard deviation  between the two conditions was calculated for each reaction i. The reaction Z-score was calculated as:A s Figure . First, which describes the sampled mean difference deviation from a population mean change of zero (i.e. no flux difference between perturbation and wild type). Note that this approach allows accounting for uncertainty in the flux distributions inferred based on the extracellular metabolite secretion constraints. This is in contrast to approaches such as FBA or MoMA that would predict a single flux distribution for each condition and thus potentially overestimate differences between conditions.Z-scores can then be further used in analysis to identify significantly perturbed regions of the metabolic network based on reporter metabolite [ Z-scores. These reporter regions indicate, or "report", dominant perturbation features at the metabolite and pathway levels for a particular condition. The reporter metabolite Z-score for any metabolite j can be derived from the reaction Z-scores of the reactions consuming or producing j (set of reactions denoted as Rj) as:The reaction tabolite  or subsytabolite  Z-scoresNj is the number of reactions in Rj and mmet,j is calculated aswhere Z-score was normalized by computing μmet,Nj and σmet,,Nj corresponding to the mean mmet and its standard deviation for 1,000 randomly generated reaction sets of size Nj. Z-scores for subsystems were calculated similarly by considering the set of reactions Rk that belongs to each subsystem k. Hence, positive metabolite and subsystem scores indicate a significantly perturbed metabolic region relative to other regions, whereas a negative score indicate regions that are not perturbed more significantly than what is expected by random chance. Perturbation subnetworks of reactions and connecting metabolites were visualized using Cytoscape [To account and correct for background distribution, the metabolite ytoscape .S. cerevisiae network, iND750, was used as the basis for the construction of the expanded iMM904 network. Prior to its presentation here, the iMM904 network content was the basis for a consensus jamboree network that was recently published but has not yet been adapted for FBA calculations [iND750 content was carried over and further expanded on to construct iMM904, which accounts for 904 genes, 1,228 individual metabolites, and 1,412 reactions of which 395 are transport reactions. Both the number of gene-associated reactions and the number of metabolites increased in iMM904 compared with the iND750 network. Additional genes and reactions included in the network primarily expanded the lipid, transport, and carbohydrate subsystems. The lipid subsystem includes new genes and reactions involving the degradation of sphingolipids and glycerolipids. Sterol metabolism was also expanded to include the formation and degradation of steryl esters, the storage form of sterols. The majority of the new transport reactions were added to connect network gaps between intracellular compartments to enable the completion of known physiological functions. We also added a number of new secretion pathways based on experimentally observed secreted metabolites [A previously reconstructed ulations . The majabolites .iND750 reactions, but the genes encoding these proteins were not associated with their corresponding GPRs. Other examples include glycogenin and NADPH cytochrome p450 reductases (CPRs), which are required in the assembly of glycogen and to sustain catalytic activity in cytochromes p450, respectively. These additional proteins were included in iMM904 as part of protein complexes to provide a more complete representation of the genes and their corresponding products necessary for a catalytic activity to occur.A number of gene-protein-reaction (GPR) relationships were modified to include additional gene products that are required to catalyze a reaction. For example, the protein compounds thioredoxin and ferricytochrome C were explicitly represented as compounds in S. cerevisiae networks associated with quinone, beta-alanine, and riboflavin biosynthetic pathways were essentially inferred from known reaction mechanisms based on reactions in previous network reconstructions of E. coli [iMM904 network contents as well as a detailed list of changes between iND750 and iMM904 is included [see Additional file Major modifications to existing reactions were in cofactor biosynthesis, namely in quinone, beta-alanine, and riboflavin biosynthetic pathways. Reactions from previous  E. coli ,47. ThesiMM904 metabolic network was validated by comparing in silico single-gene deletion predictions to in vivo results from a previous study used to analyze another S. cerevisiae metabolic model, iLL672 [iFF708 network [iND750 network [iLL672 model consisted of 3,360 single-gene knockout strain phenotypes evaluated under minimal media growth conditions with glucose, galactose, glycerol, and ethanol as sole carbon sources. Growth phenotypes for the iMM904 network were predicted using FBA [The updated genome-scale , iLL672 . This ne network , which wsing FBA -34, MoMAsing FBA , and liniMM904 has 212 more genes than iLL672 with experimental data, we also present results for the subset of iMM904 predictions with genes included in iLL672 (reduced iMM904 set). When the same gene sets are compared, iMM904 improves gene lethality predictions under glucose, galactose, and glycerol conditions over iLL672 somewhat, but is less accurate at predicting growth phenotypes under the ethanol condition. It should be noted that the iLL672 predictions were obtained directly from [iMM904 predictions. Overall, when viability cutoff is chosen as indicated above for each method separately, the three prediction methods  perform similarly.Since tly from  and thusiMM904 greatly increased the number of true viable predictions, the full model also made significantly more false viable predictions compared with reduced iMM904 and iLL672 predictions. However, it is important to note that 143 reactions involved in dead-end biosynthetic pathways were actually removed from iFF708 to build the iLL672 reconstruction [While the full gene complement in truction . As moretruction .gdh1/GDH2 mutant strain was previously developed [Gdh1, was deleted and the NADH-dependent form of the enzyme, Gdh2, was overexpressed. The net effect is to allow efficient assimilation of ammonia into glutamate using NADH instead of NADPH as a cofactor. While growth characteristics remained unaffected, relative quantities of secreted metabolites differed between the wild-type and mutant strain under aerobic and anaerobic conditions.The eveloped ,50 in orgdh1/GDH2 and wild-type strains reported in [iMM904 network [see Additional file Z-scores were calculated from the sampling analysis to quantify flux changes between the mutant and wild-type strains, with Zreaction > 1.96 corresponding to a two-tailed p-value < 0.05 and considered to be significantly perturbed [see Additional file We analyzed EM data for the orted in  under aeorted in , primarip < 0.05) between mutant and wild-type. Statistical measures of recall, accuracy, and precision were calculated and represent the predictive sensitivity, exactness, and reproducibility respectively. From the sampling analysis, a considerably larger number of significantly perturbed reactions are predicted in the anaerobic case  than in aerobic . The top percentile of FBA flux changes equivalent to the percentage of significantly perturbed sampling reactions were compared to the intracellular data. Results from both analyses are summarized in Table To validate the predicted results, reaction flux changes from both FBA and sampling methods were compared to differential intracellular metabolite level data measured from the same study. Intracellular metabolites involved in highly perturbed reactions (i.e. reactants and products) predicted from FBA and sampling analyses were identified and compared to metabolites that were experimentally identified as significantly changed  and subsystem (oxidative phosphorylation), is certainly feasible as NADH is a primary reducing agent for ATP production. Pentose phosphate pathway and NAD biosynthesis also appears among the most perturbed anaerobic subsystems, further suggesting perturbed cofactor balance as a common, dominant effect under both conditions.Perturbations under aerobic conditions largely consisted of pathways involved in mediating the NADH and NADPH balance. Among the highest scoring aerobic subsystems are TCA cycle and pentose phosphate pathway – key pathways directly involved in the generation of NADH and NADPH. Reporter metabolites involved in these subsystems – glyceraldehyde-3-phosphate, ribulose-5-phosphate, and alpha-ketoglutarate – were also identified. These results are consistent with flux and enzyme activity measurements of the nditions , which rgdh1/GDH2 modification in both aerobic and anaerobic conditions. For example, the proline biosynthesis pathway that uses glutamate as a precursor was significantly perturbed in both conditions, as supported by significantly changed intracellular and extracellular levels. There were differences, however, in that more amino acid related subsystems were significantly affected in the anaerobic case  significantly perturbed amino acid subsystems, 2) a broad perturbation subnetwork converging on glutamate  e Figure .A recent study reported that potassium limitation resulted in significant growth retardation effect in yeast due to excess ammonium uptake when ammonium was provided as the sole nitrogen source . The proiMM904 model and the EM profile analysis method to analyze amino acid secretion profiles for a range of low potassium and high ammonia conditions reported in [iMM904 model, sampled the allowable solution space, computed reaction Z-scores for changes from a reference condition , and finally summarized the resulting changes using reporter metabolites. Figure In order to elucidate the differences in internal metabolic states, we utilized the orted in . As befogdh1/GDH2 strain data. Taken together with the anaerobic gdh1/GDH2 data, the results consistently suggest highly perturbed threonine and folate metabolism when amino acid-related pathways are broadly affected.In addition to perturbed amino acids, a secondary effect notably appears at high ammonia levels in which metabolic regions related to folate metabolism are significantly affected. As highlighted in green in Figure In both ammonium-toxic and potassium-limited environments, impaired cellular growth was observed, which can be attributed to high energetic costs of increased ammonium assimilation to synthesize and excrete amino acids. However, under high ammonium environments, reporter metabolites related to threonine and folate metabolism indicated that their perturbation, and thus purine supply, may be an additional factor in decreasing cellular viability as there is a direct relationship between intracellular folate levels and growth rate . Based ogdh1/GD2 mutant) and environmental (excess ammonium and limited potassium) perturbations, and the predicted intracellular metabolic changes were consistent with previously published experimental data including measurements of intracellular metabolite levels and metabolic fluxes. Our reanalysis of previously published EM data on ammonium assimilation-related genetic and environmental perturbations also resulted in testable hypotheses about the role of threonine and folate pathways in mediating broad responses to changes in ammonium utilization. These studies also demonstrated that the sampling-based method can be readily applied when only partial secreted metabolite profiles (e.g. only amino acids) are available.The method presented in this study presents an approach to connecting intracellular flux states to metabolites that are excreted under various physiological conditions. We showed that well-curated genome-scale metabolic networks can be used to integrate and analyze quantitative EM data by systematically identifying altered intracellular pathways related to measured changes in the extracellular metabolome. We were able to identify statistically significant metabolic regions that were altered as a result of genetic (With the emergence of metabolite biofluid biomarkers as a diagnostic tool in human disease ,56 and tConceived and designed the experiments: MLM MJH BOP. Performed experiments: MLM MJH. Analyzed the data: MLM MJH. Wrote the paper: MLM MJH BOP. All authors have read and approved the final manuscript.iMM904 network content. The data provided represent the content description of the iMM904 metabolic network and detailed information on the expanded content.Click here for fileiMM904 model files. The data provided are the model text files of the iMM904 metabolic network that is compatible with the available COBRA Toolbox [ Toolbox . The modClick here for fileSupplemental figures. The file provides the supplemental figures and descriptions of S1, S2, S3, and S4.Click here for fileGdh mutant aerobic and anaerobic analysis results. The data provided are the full results for the exometabolomic analysis of aerobic and anerobic gdh1/GDH2 mutant.Click here for file


It is based on a comprehensive approach combining (i) tracer cultivation on 13C substrates, (ii) 13C labelling analysis by mass spectrometry and (iii) mathematical modelling for experimental design, data processing, flux calculation and statistics. Whereas the cultivation and the analytical part is fairly advanced, a lack of appropriate modelling software solutions for all modelling aspects in flux studies is limiting the application of metabolic flux analysis.The quantitative analysis of metabolic fluxes, i.e., 13C metabolic flux analysis. The application is based on the new Elementary Metabolite Unit (EMU) framework, significantly enhancing computation speed for flux calculation. From simple notation of metabolic reaction networks defined in a spreadsheet, the OpenFLUX parser automatically generates MATLAB-readable metabolite and isotopomer balances, thus strongly facilitating model creation. The model can be used to perform experimental design, parameter estimation and sensitivity analysis either using the built-in gradient-based search or Monte Carlo algorithms or in user-defined algorithms. Exemplified for a microbial flux study with 71 reactions, 8 free flux parameters and mass isotopomer distribution of 10 metabolites, OpenFLUX allowed to automatically compile the EMU-based model from an Excel file containing metabolic reactions and carbon transfer mechanisms, showing it's user-friendliness. It reliably reproduced the published data and optimum flux distributions for the network under study were found quickly (<20 sec).We have developed OpenFLUX as a user friendly, yet flexible software application for small and large scale 13C metabolic flux analysis. OpenFLUX will strongly facilitate and enhance the design, calculation and interpretation of metabolic flux studies. By providing the software open source, we hope it will evolve with the rapidly growing field of fluxomics.We have developed a fast, accurate application to perform steady-state  Metabolic flux analysis (MFA) plays a central role in metabolic engineering and systems biology . Metabolx/ATP) or P/O ratio which are inherently linked to the purely stoichiometric approaches - and [U-13C]-glucose experiments and GC-MS analysis of proteinogenic amino acids for several microorganisms. Recent developments allow to generate equation systems automatically -glucose (with 99% enrichment purity), and all fluxes were normalized with respect to the glucose uptake rate . As the published MIDs are uncorrected, all the simulated EMU variables were modified for mass interference from non-carbon backbone isotopes using the molecular formula of the amino acids fragments . The first n+1 signal elements were normalized (n indicates number of backbone carbon), and then truncated to the correct vector length  before performing weighted least-square analysis. The inferred metabolic model consisted of a total of 71 reactions and 42 balanceable metabolites. The metabolite model yielded a total of 26 degrees-of-freedom and 18 fluxes were determined experimentally: anabolic precursor yields (11), biomass yield (1), secreted product yields (5), and glucose uptake rate (1). To reduce the number of unknown parameters, these 18 fluxes were chosen as free fluxes, and the associated flux values were used deterministically as no redundant data exist in the measurement set. Note that if one suspects gross measurement errors in the flux measurement set, then these fluxes should be set free and the flux values subjected to the least-square analysis together with the MIDs. Five (5) of the remaining 8 free fluxes are associated with the reversibility of non-oxidative pentose-phosphate pathway enzymes (3), glucose-6P isomerase (1) and intercellular CO2 exchange (1). The other 3 free fluxes were assigned (by the software) to the irreversible fluxes of glucose-6P dehydrogenase, pyruvate carboxylase, and glycine synthesis via the serine route.We reconstructed the metabolic network of lysine producing ormation  and addiormation . The inpThe MID of 9 amino acids and trehalose were reported. Three "S" type reactions were included in the metabolite network to directly map label distribution of alanine, aspartate and glutamate to pyruvate, oxaloacetate and α-ketoglutarate, respectively. This was not necessary for all other amino acids and trehalose because these metabolites were already described in the isotopomer balances.-4, and the optimizations were terminated when the magnitude of directional derivative in search direction is less than 2 × 10-4. 13C-FLUX was implemented in Ubuntu Linux 7.1 operating system.All computational work was performed on a Pentium D 3.00 GHz computer. OpenFLUX was implemented in MATLAB 7.3.0.267 (R2006b) . Numerical optimization was carried out using FMINCON function from MATLAB's Optimization Toolbox. Since we used numerical gradient, FMINCON automatically used the active-set algorithm . Termination tolerance on the function value was set to 1 × 10NS structure (Eq. 3) is automatically produced  involved in the optimization is significantly less than a complete isotopomer model (262 variables).The model created by OpenFLUX was validated for the TCA cycle test case by comparing the labelling data simulated for a given set of fluxes with cumomer based simulation  . ForwardThe labelling patterns obtained for the test case were next corrupted with 1% Gaussian noise, and subjected to least-square analysis using 13C-FLUX  and OpenThe introduction of "X" type metabolites and "S" type reactions in OpenFLUX' flagging system for metabolites and reactions has several advantages. In this example, OpenFLUX automatically calculated the cofactor balances and the required oxygen uptake rate based on a given P/O ratio of 3 Figure . OpenFLUC. glutamicum [13C]-glucose, GC-MS 13C enrichment analysis of proteinogenic amino acids -Glucose and CO2 EMUs. A total of 20 balancing matrix equation sets were used to calculate the unknown EMUs, 9 of which are single equation balances that are easily calculated. The 108 unknown EMU variables correspond to 360 scalar MID variables, which is a substantial reduction from the 8380 unknown scalar variables expected in the full isotopomer model.The isotopomer model for A total of 50 cycles of optimization were performed for both wild type and engineered strain datasets. The total computation time for each cycle was about 16 seconds. The calculated MIDs shown in Table 13C MFA. We have shown that the front-end model setup is relatively simple and intuitive, and the back-end optimization is stream-lined and is significantly faster than 13C-FLUX. Overall, this means that studying large-scale metabolic models becomes more tractable, especially for problems that have large number of unknown free fluxes and/or demand more stringent statistical evaluation. The underlying metabolic models are transparent to the user, and could be adapted for other purposes. In addition, the definition of the simulated output vector is flexible, thus various experimental data types can be applied. Finally, the inclusion of two different but complementary confidence interval determination algorithms  enables a more robust evaluation of flux solutions.OpenFLUX is a generic and efficient novel software tool for C. glutamicum metabolic model as an example problem, and were able to reproduce the calculated MIDs, the optimized flux parameters and the corresponding confidence intervals. We also showed that OpenFLUX is computationally fast.OpenFLUX performed well on real metabolic problems. We have applied the 13C MFA could be used to validate soft assumptions regarding P/O ratio and cofactor balances H).OpenFLUX is useful for exploring different network topology, flux distribution and modelling assumptions. The application grants the user the ability to control the underlying metabolic models and data inputs via a simple textual interface. Experimental design is critical to justify choice of substrates and analytical techniques. One can troubleshoot potential observability and sensitivity issues by simulating hypothetical MIDs data on a typical range of flux distributions, and subsequently explore the resolution of different flux parameters. OpenFLUX supports testing of various labelled substrates. For incomplete metabolic models, 13C tracer studies for flux analysis in newly arising systems approaches. Providing it open source aims on further development of the software as a general platform for 13C fluxomics. 13C MFA requires significant upfront investment to construct the isotopomer balance model and to establish the numerical optimization for flux analysis. Users who are already familiar with MFA will find that 13C MFA is readily implemented once the atom transitions are included into the metabolic model. Lastly, the text-based spreadsheet interface is an effective means of disseminating the metabolic model because the network topology and modelling assumptions are readily found in a single model definition file.Overall, the purpose of OpenFLUX is to encourage the adoption of I: Identity matrix; NS: null space matrix; P: compactification scaling factor; S: stoichiometric matrix; WSSR: weighted sum of squared residuals; vnet: net flux; vxch: exchange flux; v←, v→, vnet→, : net forward flux; UB: flux upper boundary; AAV: atom activity vector; EMU: elementary metabolite unit; GC: gas chromatography; IDV: isotopomer distribution vector; MFA: metabolic flux analysis; MID: mass isotopomer distribution; MS: mass spectrometry; NMR: nuclear magnetic resonance; TCA: tricarboxylic acid; OpenFLUX is optimized for MATLAB 7.3 (R2006b)  and Java 6  on a Microsoft Windows XP platform. It requires the MATLAB Optimization Toolbox. The software is also available for MacOS 10.4.11 (and later) and Ubuntu linux 7.1 operating systems. Microsoft Excel 2003 was used to generate the model input for the Java parser, alternative spreadsheet programs are also useable..OpenFLUX is released as open source and is available upon request, both compiled and as source code. Supplementary information is available online The authors declare that they have no competing interests.13C fluxomics and coordinated the writing of the paper. All authors have approved the final manuscriptLEQ programmed the JAVA parser, implemented OpenFLUX in MATLAB and performed the EMU based simulations. He also performed 13C-FLUX simulations and contributed to writing the paper. CWI performed the simulations based on isotopomer mapping, provided data and modelling details on the real test case scenario, contributed expertise for development of OpenFLUX and contributed to writing of the paper. LKN provided his expertise in mathematical modelling of fluxes and contributed to writing the paper. JOK designed and supervised the study. He contributed expertise in vnet) and exchange flux (vxch) are used as flux coordinates, where vxch is mapped to reverse flux (v←) if vnet is positive, otherwise vxch is mapped to the forward flux (v→)  Figure .vnet and vxch coordinate system was created for compactification purposes. As vxch can range from 0 to infinity, which represents either irreversible or fully reversible reactions, vxch is compactified using (12). This has been shown to reduce the response curvature of the 13C label with respect to the reaction's reversibility and improve linearization of the model [The he model . Howeverl [ from .v→ is expressed as v← plus a net forward flux , which can be positive or negative , which is readily created using Gauss-Jordan elimination. According to (5), we find that v→, net of a given reversible reaction is a linear combination of vxch and vnet into v→ and v←. NS with the required structure can be reproduced for all metabolic network configurations.Here, we introduce a straightforward linear coordinate system to describe bi-directional flux: e Figure . This liv→, net and v← coordinate system still allows the compactification of v← to the same effect as compactification of vxch; since v←, like vxch, is mapped equally to the forward and reverse fluxes .The new s Figure . HoweverIn OpenFLUX, the metabolic model is organized into a table consisting of seven columns, three metabolite lists and two experimental data columns Figure  see Add. The metth element of the product is obtained fromThe setup of the reactions relevant to isotopomer balance must obey the following rules: (1) reactant stoichiometry is always one; (2) same stoichiometric coefficients in both the reaction and atom transition equation; (3) only uni- or bi-molecular reactions. Within these rules, both normal and scrambling reactions can be adequately described. These rules imply that scrambling occurs on the product side of the reaction equation . The limitation of reaction order to bi-molecular reaction is because the parser is not capable of generating a nested Cauchy-product for higher order condensation reactions. Nonetheless, higher order reactions can be decomposed into bi-molecular reactions. The Cauchy-product is the convolution of 2 sequences A and B, where the n13C tracer context, these sequences relate to the MID of 2 EMUs involved in a condensation reaction  and reactions that do not contribute to the tracer distribution  are classified as type "B" reactions. The atom transition equation for this reaction type is not required. Type "S" reaction is a convenient approach to map a product's MID to their respective precursor(s) without incurring additional degrees-of-freedom in the metabolite balance model, such as R21 for production of aspartate from oxaloacetate. This is especially useful when the labelling for a metabolite can be measured, but its production rate is unknown. Aspartate production rate is typically incorporated into the oxaloacetate biomass drain flux (R18).The fifth column contains the definition of each reaction type. There are 5 reaction types, namely "F", "FR", "R", "B" and "S". Reversible reactions are decoupled into the forward ("FR") and reverse ("R") flux. This scheme ensures that "R" type reactions (R8) are always assigned as free fluxes. "B", "S" and "F" are used to identify the relevance of a reaction to metabolite balance, isotopomer balance or both respectively. For "F" type reactions, metabolites that are to be excluded from the isotopomer balance are marked with "X" (case insensitive) in the atom transition equation. This is typically used for cofactors, such as NAD(P)H, FADHThe sixth column contains the allocation of free fluxes for the metabolite balance model. It allows the user to specify an invariant value for a known free flux, or to allocate the preference for a reaction to be used as a free flux. For example, the drains of pyruvate, α-ketoglutarate and oxaloacetate to biomass were given the values of 0.07, 0.23 and 0.12 respectively. Additional drains for valine and lysine were added to enable subsequent model validation in 13C-FLUX. Also, the activity of pyruvate uptake flux is 1 because all fluxes are normalized to this reaction. "X" is assigned to R2 as a preferred free parameter as the reaction represents the glutamate uptake flux. By convention, "X" is assigned to any "R" type reaction.The seventh column carries the experimental standard deviations associated with each of the known fluxes. This allows a known flux value to be used either deterministically, where the flux value is fixed, or as an experimental measurement, where the flux is set free and the flux value is included in the least-square analysis. Using flux values deterministically may lead to gross-measurement error, but can reduce computation time.13C isotopomer distribution in metabolites. The 13C enrichment of these metabolites must be known.Metabolites that are considered external to the system must be identified in order to generate a balanceable stoichiometric matrix. The list comprises the reactants of the system inputs and products of the system outputs. The EMU variables to be simulated were chosen to be the full carbon backbone of valine, lysine, aspartate and succinate. They are written in the form "metabolite name#binary number". "1" and "0" are used to indicate whether the carbon atom at a given position is to be included or omitted respectively. For example, the simulated valine EMU variable is written as "VALX#11111". The experimental measurements and the associated errors are listed in the same order used to list the simulated EMU variables in the model definition file. The input substrates are pyruvate and glutamate, and are placed into another list. Generically, an input substrate is any exo-metabolite that enters the system boundary and can contribute to Before the metabolite and isotopomer models are generated, OpenFLUX inspects the model definition file for potential inconsistencies. Mainly, OpenFLUX checks for consistency in metabolite naming, stoichiometry, carbon atom length for a given metabolite, and for presence of higher order reactions or unbalanced atom transition equation. The inconsistencies are reported to the user, and must be resolved before the metabolic models are successfully generated.Parameter estimation and sensitivity analysis is executed from MATLAB's command line. OpenFLUX is initialized by typing "start13OF". The user then chooses the various optimization tasks to be performed. After choosing the task, a series of command line prompts are given to the user to specify the parameters required by the optimization program. Once completed, the optimization begins.TCA cycle metabolic model. Contains the hypothetical TCA cycle metabolic network, produced in the format that is readable by OpenFLUX. Information on how to set up the input substrates and the simulated output EMU vector are included. The EMU balance model used for flux calculation is also included.Click here for fileC. glutamicum metabolic model. Contains the C. glutamicum metabolic network for both wild-type and mutant strains. Model and data are reproduced from Becker et al. [r et al. . File inClick here for fileAtom transition equations. Contains typical reaction and atom transition equations encountered in the central metabolism. Pathways included are glycolysis (Embden-Meyerhof and Entner-Doudoroff pathways), TCA cycle (including glyoxylate shunt and anaplerotic reactions), pentose-phosphate pathway and amino acid biosynthesis from central metabolite precursors.Click here for file