Several formal approaches have been developed to support the investigation of such networks. One of the relevant problems in this context is the comprehension of possible causal dependencies. Keeping in mind both expressiveness and ease of use, we aimed at providing: i) a minimal notation to represent causality in biochemical interactions, and ii) an automated tool allowing human experts to easily vary conditions of in silico experiments. We exploit a reading of chemical reactions in terms of logical implications: starting from a description of a metabolic network in terms of reaction rules and initial conditions, chains of reactions, causally depending one from the another, can be automatically deduced. Both the components of the initial state and the clauses ruling reactions can be easily varied and a new trial of the experiment started, according to a what-if investigation strategy. Our approach aims at exploiting computational logic as a formal modeling framework, amongst the several available, that is naturally close to human reasoning. It directly leads to executable implementations and may support, in perspective, various reasoning schemata. Indeed, our abstractions are supported by a computational counterpart, based on a Prolog implementation, which allows for a representation language closely correspondent to the adopted chemical abstract notation. The proposed approach has been validated by results regarding gene knock-out and essentiality for a model of the metabolic network of Escherichia coli K12, which show a relevant coherence with available wet-lab experimental data.We apply techniques from formal methods and computational logic to develop an abstract qualitative model of metabolic networks in order to determine in vitro experiments by effectively pruning non promising directions.Starting from the presented work, our goal is to provide an effective analysis toolkit, supported by an efficient full-fledged computational counterpart, with the aim of fruitfully driving  Under this regard, causality can play an important role in finding chains of reactions that connect the parts of the system of interest, e.g. for determining causal correlations among molecules that are not apparently correlated. In general, the proposed models of complex systems code a lot of information and determining possible correlations and causal dependencies may be not straightforward or computationally expensive.Understanding the relationships amongst the elements involved in biologic interaction networks, such as the functioning of cellular metabolism, is a relevant problem in Systems Biology. In the words of , “diagraWe focus here on metabolic networks, i.e. the set of the cellular biochemical pathways involved in energy management and in the synthesis of structural components. Biochemical pathways are typically composed of chains of enzymatically catalyzed chemical reactions and are interconnected in a complex way. Starting from the composition of local, well understood behaviour, the study of the overall emerging behaviour of metabolic networks appears difficult.i) a minimal notation to represent causality in biochemical interactions, and ii) an automated tool allowing the human expert to easily vary conditions of the in silico experiment. We introduce a simple and skeletal notation, inspired by biochemical reactions, to emphasize the causality aspects we are concerned with. The choice of relying on computational logic, which “provides a straightforward and intuitive representation of human reasoning” ,b] for c. However, it is important to have considered convergence over reactants rather than over explanations. It is easy to observe that at the fourth step we would have the explanation a[b[a[b]]] due to the cycle between a and b. This amounts to say that – in the presence of cycles – explanations can growth indefinitely, i.e. convergence occurs at infinity. Hence, we have restricted ourselves to compute the reactants that can be produced, which is a finite process. However, the following correspondence between computational results and the potentially infinite model of explanations can be drawn.As standard, one would like to relate the computational construction provided with the original model, i.e. our adopted formalisation of biochemical reactions, introduced in section Results and Discussion. Let us start to observe that keeping track of the rule used when applying R be a set of rules, a a reactant, I a set of reactants and Let (Outline).a in the bottom-up process .(⇒) By induction on the number of steps needed to firstly cause I,RE(a). .(⇐) By induction on structural complexity of To address the problem of causality in metabolic networks, as seen above, we developed a software tool based on an implementation of a standard bottom-up semantics, running on top of SICTUS Prolog Interpreter (see ).The authors declare that they have no competing interests.in silico experiments, while they jointly develop the formalisation of the metabolic causality and the analysis of the experimental results.All the authors equally contributed to the present work and wrote the paper. More precisely, CB and AB taken care of the computational framework and DC carried out the


Well-curated and validated network reconstructions are extremely valuable tools in systems biology. Detailed metabolic reconstructions of mammals have recently emerged, including human reconstructions. They raise the question if the various successful applications of microbial reconstructions can be replicated in complex organisms.We mapped the published, detailed reconstruction of human metabolism (Recon 1) to other mammals. By searching for genes homologous to Recon 1 genes within mammalian genomes, we were able to create draft metabolic reconstructions of five mammals, including the mouse. Each draft reconstruction was created in compartmentalized and non-compartmentalized version via two different approaches. Using gap-filling algorithms, we were able to produce all cellular components with three out of four versions of the mouse metabolic reconstruction. We finalized a functional model by iterative testing until it passed a predefined set of 260 validation tests. The reconstruction is the largest, most comprehensive mouse reconstruction to-date, accounting for 1,415 genes coding for 2,212 gene-associated reactions and 1,514 non-gene-associated reactions.We tested the mouse model for phenotype prediction capabilities. The majority of predicted essential genes were also essential in vivo. However, our non-tissue specific model was unable to predict gene essentiality for many of the metabolic genes shown to be essential in vivo. Our knockout simulation of the lipoprotein lipase gene correlated well with experimental results, suggesting that softer phenotypes can also be simulated.Mus Musculus, 1415 genes). We demonstrate that the mouse model can be used to perform phenotype simulations, similar to models of microbe metabolism. Since the mouse is an important experimental organism, this model should become an essential tool for studying metabolic phenotypes in mice, including outcomes from drug screening.We have created a high-quality mouse genome-scale metabolic reconstruction, iMM1415 ( The first genome-scale reconstruction of metabolic networks emerged eleven years ago , four yein silico model can be converted into a functional model of human metabolism, which was validated by applying 288 flux balance analysis (FBA) based tests of core functionality of human metabolism [The release of the human genome  and its tabolism . A recentabolism . Also, etabolism . Furthertabolism .Bos taurus) [Mus musculus) reconstructions [Metabolic networks have been reconstructed for two further mammals, a central metabolic reconstruction of cattle ( taurus)  and fourructions -25.Two oructions ,25, whilructions ,23. The ructions . In addiructions .The mouse serves as a fundamental experimental animal for human biomedical applications. Furthermore, the availability of phenotyped inbred knockout mouse strains  make it Given the high sequence homology between most mammalian genomes, an obvious starting point for metabolic reconstruction of mammals is the comprehensive human metabolic reconstruction, Recon 1. We therefore sought to create draft mammalian metabolic reconstructions based on Recon 1. The mouse reconstruction was then manually completed and validated. We also present simulation results using a functional model of mouse metabolism to test its phenotype prediction capabilities.Mus musculus) . The non-mammalian organism with the highest number of genes homologous to Recon 1 genes was the zebra-fish (Danio rerio)   had the lowest ratio of both mapped genes (84%) and reactions (91%). Furthermore, we created for each mammalian modelA and modelB a compartmentalized and non-compartmentalized version. The more complex, compartmentalized versions had more metabolic dead ends (321 vs. 150) and therefore more reactions with zero fluxes. The number of reactions with non-zero fluxes for both compartmentalized and non-compartmentalized versions of all draft mammalian models created using approach A and B are summarized in Table The ratio of Recon 1 genes with a homologous gene as well as the ratio of reactions from Recon 1 included in the draft reconstructions for each mammal is shown in Figure Given the high number of reactions mapped to the draft mouse reconstruction, and the high number of reactions with non-zero fluxes resulting in the corresponding metabolic modelA and modelB, we sought to finalize the mouse reconstruction by gap analysis/filling. First, we aimed to understand the metabolic differences between human and mouse to ensure that the mouse reconstruction is not merely a modified version of human metabolism. This implies that also genes and pathways unique to mouse metabolism needed to be identified. Therefore, we employed the Comparative Pathway Analyzer 1.0  relying . Using the SMILEY algorithm, we searched for the minimal number of reactions within the entire KEGG database necessary to add to the non-compartmentalized mouse modelB in order to enable the production of biomass.First, we decided to test which of the four mouse metabolic models were able to produce biomass by optimizing for the corresponding reaction accounting for all known biomass precursors required for cell replication. The compartmentalized and non-compartmentalized draft mouse models from approach A produced biomass without any modifications. In contrast, both versions of modelB were unable to produce biomass. Therefore, we sought to gap fill the draft non-compartmentalized modelB to identify reactions that needed to be added to the model for production of all biomass components. The SMILEY gap filling algorithm identifies reactions from a database that need to be added to a model to fulfill the optimality condition (e.g. production of biomass) .. Using The results from 40 iterations of the algorithm were checked manually for two criteria: i) the result did not suggest a reversible reaction for a known irreversible reaction and ii) the added reaction(s) are known to occur in mouse. Of the 40 iterations, 30 suggested adding the same reaction either alone or in addition to some other metabolic reactions. This reaction (KEGG ID R06522) exists in mouse and humans (according to KEGG and Entrez gene ) but wasTo validate the mouse reconstruction and to ensure mouse-characteristic metabolic properties of the resulting models, we manually tested each of the 288 FBA validation tests that were developed for Recon 1  using boWe ran the validation tests on the compartmentalized mouse draft modelA in an iterative manner and evaluated particularly the failed tests. This process revealed that out of the 131 reactions initially removed due to missing homologous genes in the HomoloGene database, 36 had sequence and physiological evidence of existence in the mouse (according to KEGG and EntrezGene databases) . The observed discrepancy in lethality can be explained by either, i) growth environment simulations, ii) incomplete biomass reaction, iii) missing regulation, iv) wrongly included reactions, or v) any combination of the aforementioned possibilities. Wrongly included reactions could be identified by systematically eliminating non-gene-associated reactions from iMM1415  to impr. For five of those, a gene deletion had no effect in the model, since isozymes existed within the reconstruction. For the three remaining genes , the deletion led to elimination of corresponding reactions. The effect of these deletions on growth depends on i) the presence of alternative reactions/pathways or ii) importance of reactions for biomass precursor synthesis. We investigated the effect of these three gene deletions on the overall network by performing a FVA. We then compared the FVA results of essential gene knockout (DHCR7) to the FVA results of wild type  [LPL survive until adulthood but with elevated triglyceride levels [Finally, we sought to simulate knockouts of genes with softer phenotypes. The .1.1.34) , an enzy.1.1.34) . Mutatio.1.1.34) . Mice wie levels .-16 against even probability of decreased and increased flux capacity); and ii) lipid metabolism, where 100 reactions with decreased and 253 reactions with increased flux capacity (p < 10-15 against even probability of decreased and increased flux capacity). Additionally, the flux capacity changed significantly within the triacylglycerol metabolism  the glycan metabolism, where 31 reactions had decreased and 312 reactions increased flux capacity  using the COBRA toolbox  and the Given a reconstructed metabolic network on a mathematical form with appropriate constraints on each reaction  and a biological objective Z (such as biomass), flux balance analysis (FBA) calculates a set of network fluxes that maximize Z. It has several derived applications used to further analyze the flow of metabolites through a metabolic model . One sucmin, metabolite ≥ -1000 mmol/gdw hr). FVA was performed on the draft models to determine number of reactions with a non-zero flux. Following FVA on each draft model, we drew phylogenetic trees of the results and compared to phylogenetic tree based on all transcripts of protein domain sequence from the SuperFamily database [The entire HomoloGene build 52 was downloaded on 11/17/2008 . We extrdatabase .Gap filling was done using the SMILEY algorithm, as described elsewhere . We downFor validation of the mouse reconstruction, we used a modification of the validation process used in the creation of the human Recon 1 network. Each of the 288 validation tests used for Recon 1 was manually checked for applicability in the mouse. This was done by manually reviewing each validation test using Comparative Pathway Analyzer 1.0 . If all http://www.informatics.jax.org, accessed on 1/12/2010) [max,i), no change or increased flux capacity. For an unbiased selection of interesting metabolic subsystems, we counted number of reactions with increased and decreased flux ranges and calculated a single value Chi-Square test with 1 degree of freedom comparing the observation against even probability of increased and decreased flux capacity. Since independent tests were done for each of the 10 major subsystems, a p-value of 0.05/10 was considered statistically significant to correct for multiple testing.Information on mouse knockout phenotypes were gained from the Mouse Genome Informatics site (12/2010) . For eac12/2010) ,66, we p12/2010)  to estimMIS, NJ, ES, IT and BOP conceived of the study. MIS, NJ and IT created and validated the models. MIS performed phenotype simulations. MIS drafted the manuscript. MIS, ES, IT and BOP revised the manuscript. All authors read and approved the final manuscript.Supplemental file S1: Absolute number and percentage of Recon 1 genes found in all species within the HomoloGene database.Click here for fileSupplemental file S2: Details of KEGG search for unique reactions in mouse and human using Comparative Pathway Analyzer 1.0.Click here for fileSupplemental file S3: List of 260 flux balance analysis tests used for validation of the mouse reconstruction.Click here for fileSupplemental file S4: List of genes added again during the validation process and the corresponding metabolic subgroups.Click here for fileSupplemental file S5: The iMM1415 model of mouse metabolism in a SMBL format.Click here for fileSupplemental file S6: A detailed reaction list of all reactions in the iMM1415, including the biomass reaction.Click here for fileSupplemental file S7: Uptake rates for exchange reactions in the mouse reconstruction under minimal medium conditions.Click here for fileSupplemental file S8: A list of genes predicted to be essential in the mouse metabolic network, along with bibliographic information if available.Click here for file


A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments. in silico evolved networks is underlined by an increased number of multifunctional enzymes and independent paths leading from initial metabolites to biomass. These findings provide evidence that fluctuating environments can be a major evolutionary force leading to the emergence of robustness as a side effect. A direct prediction resulting from this study is that organisms living in stable and fluctuating environments should display differing levels of robustness against gene loss.One of the most surprising recent biological findings is the high level of tolerance organisms show towards loss of single genes. This observation suggests that there are certain features of biological systems that give them a high tolerance (i.e. robustness) towards gene loss. We still lack an exact understanding of what these features might be and how they could have been acquired during evolution. Here, we offer a possible answer for these questions in the context of metabolic networks. Using mathematical models capturing the structure and dynamics of metabolic networks, we simulate their evolution under stable and fluctuating environments . We find that the latter scenario leads to evolution of metabolic networks that display high robustness against gene loss. This robustness of  High-throughput single gene deletion studies in several organisms revealed that a large fraction of genes have little or no detectable fitness effects when compromised Direct selection for robustness against gene loss is expected to be weak Escherichia coli and Saccharomyces cerevisiae finds that, when the effect of deletion is tested in all possible environments, only half of all reactions determined to be dispensable under rich media could be considered dispensable for “real” It is possible that biomass production and adaptation to multiple environments act as similarly realistic selective pressures on metabolic networks that could lead to the emergence of robustness as a byproduct. The former can drive the emergence of isoenzymes for increased dosage Taken together, the above described studies suggest that observed robustness against gene deletion in metabolic networks is a byproduct of their evolutionary dynamics under changing environmental conditions. Early studies on the effects of changing environments in evolution have shown that it can facilitate polygenic variation To study the effect of selection under fluctuating environments on metabolic network properties, we relied on a proposed evolutionary scenario Here, we implement this scenario using a computational model of metabolic networks. In brief, the model consists of metabolites, enzymes that catalyze the transfer of biochemical groups between metabolites, and transporters that can allow intake and release of metabolites see Methods.Using this model we have run evolutionary simulations under different environmental scenarios see Methods.To test that these results are robust against the main assumptions of the model and the simulation scheme, we have analyzed an alternative model. In this model, enzymes were allowed to maintain broader activity by introducing a small background rate for all reactions an enzyme can catalyze see Methods.To understand the basis of such robustness we have analyzed the structure of networks resulting from evolution under stable and fluctuating media. As mentioned above, all evolutionary simulations resulted in enzymes that are specialized and in networks with faster biomass production compared to the ancestral ones. However, networks evolved under fluctuating media displayed two important features that distinguished them from networks evolved under stable media. Firstly, fluctuating environments resulted in networks that contain more redundant paths. The average number of independent fluxes see Methods These clear differences in the global properties of networks evolved under fluctuating and stable media suggest that both the number of independent fluxes and the number of multifunctional enzymes in a network contribute to its robustness. To better understand the relation between these properties and robustness, we performed a detailed analysis of the fitness effects of single gene deletions . In netwDeletion of multifunctional enzymes might result in lower fitness effects either because these enzymes behave as isoenzymes (i.e. back up the function of another enzyme) or catalyze reactions that are non-essential but beneficial. We find evidence for both of these possibilities. Firstly, almost all multifunctional enzymes have low dosage, suggesting that the reactions they catalyze are non-essential but beneficial when they occur at low rate. Because these reactions are beneficial when occurring at low rate, there is no selective pressure for the multifunctional enzymes to duplicate (so to increase dosage) and potentially specialize. Secondly, most multifunctional enzymes have functions that overlap with other enzymes in the network. This finding results from a structural analysis of all networks evolved under one of the stable environments (M1-networks) and under fluctuating environments (V-networks) and that contain a multifunctional enzyme: We find that among the 36 M1-networks with multifunctional enzymes, 19 contain at least one multifunctional enzyme that behaves as an isoenzyme. Among the 72 V-networks with multifunctional enzymes, 42 contain at least one multifunctional enzyme that behaves as an isoenzyme. In both M1- and V-networks, multifunctional enzymes in the remaining networks catalyze at least one reaction that is not directly involved in biomass production, further supporting their non-essential role.Interestingly, the difference in fitness effects of deleting multi- vs. mono-functional enzymes were significantly reduced in networks evolved under fluctuating environments. Considering fitness effects in different media, deleting monofunctional enzymes in these networks had, on average, only 1–2 fold larger effect compared with deleting multifunctional enzymes. Similarly, networks containing multifunctional enzymes were only 1 to 3 fold more robust than those without any such enzymes. These analyses suggest that while multifunctional enzymes can contribute significantly to robustness against gene deletion, evolution under fluctuating media increased robustness of networks mostly through generation of independent fluxes.If evolution under fluctuating environments is the driving force behind emergence of robustness against gene deletion, would it be possible that robustness is lost as the environment stabilizes? Indeed, redundant paths (i.e. independent fluxes) might infer a cost on the organism due to increased number of enzymes that are not always required, or because some of the paths are in fact disadvantageous in some environments. This is the case in our simulations as we find certain gene deletions to increase fitness above wild type levels in networks evolved in fluctuating media . To furts in a given environment could be maintained even if that environment is seen only once every s/u generations, where u is the mutation rate The finding that a switch in the environment towards stability leads to reduction in robustness fits nicely with the observation that prokaryotes specializing on one mode of energy generation has much reduced fraction of dispensable genes compared to generalists Here we have provided evidence that fluctuating environments can lead to emergence of robustness against gene loss in metabolic networks. Using computer simulations that embed a plausible scenario of metabolic network evolution, we found that selection for biomass production rate in a fluctuating media leads to emergence of networks, which can tolerate single gene deletions more readily. This robustness against gene loss is highest when fitness is measured under rich media, where all metabolites seen during evolution are considered to be available, and diminishes as fitness is measured separately under each media. We find that the molecular basis of such robustness in evolved networks is an increase in the number of independent fluxes and multifunctional enzymes.E. coli and S. cerevisiae finds that most of the observed robustness in rich media is apparent, strongly diminishing as different environments are considered separately These findings are perfectly in line with observations made in natural, current-day metabolic networks. Computational analysis of metabolic networks from Mycoplasma genitaliumInterestingly, we find that robustness and its underlying features would be lost entirely as the environment stabilizes and network evolution continues. This leads to the prediction that robustness of the metabolic network in an organism should be directly correlated with environmental conditions it experiences; organisms whose metabolism depends on stable resources should display lower robustness. This prediction is supported both from a specific gene deletion study in in silico evolution as presented here or alternatively by considering the space of possible metabolic networks and how evolution could move in this space. The two approaches are complementary; recent modeling studies using the latter approach are providing us with important insight on common design principles that can result in evolution E. coliAny attempt to fully distill design principles of biological systems has to consider evolutionary dynamics Methods have been described in detail previously The details of different modeling choices we made are as follows.g denotes the presence of group g, whereas “0” denotes the absence of that group. Metabolites are associated with a random free energy that is taken from a uniform distribution between zero and one, and that is required to specify thermodynamic properties of the biochemical reactions. For the production of biomass, it is necessary to have at least one donor and acceptor of each group as external metabolites. Thus, a minimal medium contains two randomly chosen metabolites as a donor-acceptor pair. Rich medium consists of two different random donor-acceptor pairs. Four randomly chosen metabolites are involved in biomass formation. All of these random choices are made independently for each evolutionary simulation.Metabolites are assumed to consist of five different biochemical groups. Each biochemical group is either present once or is absent, resulting in a total of 32 possible metabolites. Each metabolite can be represented by a binary string of length 5, where “1” at position iE(1) and iE(0), with iE(1) + iE(0) = iE. Here, iE is the total dosage of enzyme i, iE(0) is the concentration of the enzyme without its group being bound to it, and iE(1) is the concentration of enzyme with its group being bound to it. The free energy difference between both states of an enzyme is assumed to be a random value taken from a uniform distribution ranging from zero to one. We further assume that in principle all metabolites that contain a specific biochemical group  can serve as a donor for the transfer reaction involving that group, whereas all metabolites that do not contain that group can in principle serve as an acceptor. We assume linear kinetics for the transfer of a group to an enzyme, given by v = ijk(iE(0)(ij)X(1)−iE(1)(ij)X(0)/ijq), where ijk is the rate constant of the reaction j of an enzyme i, (ij)X(1) is the concentration of the donor of the reaction, (ij)X(0) is the concentration of the corresponding acceptor, and ijq is the equilibrium constant of the reaction resulting from the free energies of the reactants. For the transfer of a group from a donor to an acceptor, two half-reactions need to be coupled. This results in Michaelis-Menten–like kinetics and implies that functional enzymes need to maintain nonzero rate constants for at least two reactions that are coupled. Enzymes that maintain nonzero rate constants for more than two reactions are defined as multifunctional. We assume that in the initial network there are 5 enzymes that are unspecific and transform groups from each donor to each acceptor with the same rate constant. The initial dosage of enzymes is iE = 1.Enzymes catalyze the transfer of a specific biochemical group. We assume that groups are transferred by a “ping-pong mechanism”: A donor of a group transfers the group to the appropriate enzyme and is thereby transformed into its corresponding acceptor. The enzyme then transfers the group to an acceptor, thereby transforming it into its corresponding donor. Thus an enzyme can be in two possible states, v = itijT(jX−jextX), where iT is the dosage of the transporter i, ijt is the rate constant for the transport of metabolite j, jX is the metabolite concentration in the cell, and jextX is the metabolite concentration in the environment. We assume that in the initial network there is a single transporter that transports all metabolites with the same rate constant. The initial dosage of the transporter is 0T = 1.We assume that transporters transport metabolites passively across the cell membrane. The rate of transport is given by BMv = BMkΠiXi over all metabolites iX that are involved in biomass formation. The rate constant is set to BMk = 1 in all simulations. We assume that the formation of biomass leads to growth. The growth rate is given by W = 1/V*dV/dt = BMv/(0C+EEC+TTC), where 0C is the amount of biomass that is required for structural compounds , EC is the amount of biomass per enzyme, TC is the amount of biomass per transporter, E is the total dosage of enzymes, and T is the total dosage of transporters. The parameters 0C, EC, and TC are set to 10, 1, and 1, respectively. Note that due to cell growth, metabolites are constantly diluted at a rate equal to the growth rate. The fitness of a network in a given medium is assumed to be proportional to the steady-state growth rate. The fitness in an environment that fluctuates between different media is given by the geometric mean over the fitness values a network has on each of the media.Biomass is formed by the condensation of specific metabolites. The rate of biomass formation follows linear kinetics given by the product j kijα1/ and Σj tijα1/ over all rate constants ijk or ijt of an enzyme or transporter, i, respectively, is constant. For values of α>1, increasing the rate constant for a single reaction has an over-proportional effect on all other rate constants. In our simulations we use Σj kijα1/ = 1, Σj tijα1/ = 1, and α = 2. This implies, for example, that a transporter catalyzing the transport of a single metabolite has a four times higher rate constant for this reaction than a transporter that is specialized on the transport of two metabolites.We assume that enzymes can either catalyze a large number of reactions with low activity, or a lower number or reactions with improved catalytic activities. Specifically, we assume that the sum ΣThe resulting trade-off between enzyme specificity and activity in the model is inline with the general findings from protein engineering and directed evolution experiments In an alternative model, we further relax the assumption of a strong tradeoff between specificity and catalytic activity and allow enzymes to specifically maintain a background activity for all possible reactions. This alternative model allows us to use any network for the starting point of evolutionary simulations. Using this model, we have analyzed whether forcing specialization of enzymes towards specific reactions (which in some extent decreases complexity in the system) has any effect on our conclusions. As shown in ijkα1/ or ijtα1/, respectively, for a single reaction is either increased or decreased by a small value of m = 0.05, while the rate constants of the other reactions are decreased, or increased appropriately. Gene deletions and duplications decrease and increase the dosage of an enzyme respectively. To simulate evolution, we first calculate the effect of all possible mutations in the current network on the steady-state growth rate to obtain the mutant with maximal increase in fitness. This mutation is then assumed to become fixed and the resulting network is used to search for the next mutations. Details on the calculation of the steady states are as described in We assume that there are two types of mutations: (1) mutations that change the kinetic properties of an enzyme and (2) mutations that change the number of copies of an enzyme, i.e., gene deletions and duplications. For the first type of mutation we assume that the value of For each set of independent simulations, we randomly chose nutrients, metabolites involved in biomass formation, and the free energies of the metabolites. Changing free energies of the metabolites alters the energetic landscape of the initial network and might favor different pathways even if the topology of the network remains the same.Note that, while changing the many parameters of the model could easily alter the properties of individual evolved networks, the qualitative nature of the results presented here would be maintained. This is because our analysis is a comparative one among networks that evolve under different evolutionary scenarios. While model details would change the outcome of evolution in specific simulation, they would do so in similar ways under the different scenarios considered.Specific parameter choices in this study differ from a previous study using the same model The evolved networks contain many enzymes in multiple copies. These multiple copies of a single enzyme could be seen as isoenzymes. As one would expect for isoenzymes, the knockout of a single copy would have a relatively small effect. We here determine robustness by knocking out all enzymes of the same type. This gives a measure for how essential the reaction catalyzed by an enzyme is.BMv, see above) in the face of enzyme knockouts. To measure it, we delete each enzyme existing in a given network one by one and calculate the rate of biomass formation for each mutant. This allows us to characterize the full dynamical effect of a gene deletion on biomass formation, rather than just viability (i.e. non-zero vs. zero biomass production rate) and effects on yields.More specifically, we calculate robustness as network's rate of biomass production . See legend of Distribution of relative fitness for single knockouts in networks resulting from different evolutionary scenarios and using a model version where duplications are introduced as frequently as small mutations. Each distribution contains measurements from 100 networks and is shown as a boxplot, as implemented in the statistical package “R” ((2.58 MB TIF)Click here for additional data file.Figure S2www.r-project.org). See legend of Distribution of relative fitness for single knockouts in networks resulting from different evolutionary scenarios and using a model version where enzymes are forced to maintain a non-zero rate for all possible reactions. The simulation scheme is also changed from the original analysis; for the fluctuating environment scenario, we have used networks evolved under stable environments as the starting network. This corresponds to modelling a shift in the environment from stable source to fluctuating sources of metabolites. Each distribution contains measurements from 20 networks and is shown as a boxplot, as implemented in the statistical package “R” ((2.55 MB TIF)Click here for additional data file.


With such a model at hand it is also possible to detect reactions having a large effect on a certain variable such as a substance concentration.During the stages of the development of a potent drug candidate compounds can fail for several reasons. One of them, the efficacy of a candidate, can be estimated Trypanosoma brucei.We show an algorithm that systematically tests the influence of activators and inhibitors of different type and strength acting at different positions in the network. The effect on a quantity to be selected (e.g. a steady state flux or concentration) is calculated. Moreover, combinations of two inhibitors or one inhibitor and one activator targeting different network positions are analysed. Furthermore, we present TIde (Target Identification), an open source, platform independent tool to investigate ordinary differential equation models in the common systems biology markup language format. It automatically assigns the respectively altered kinetics to the inhibited or activated reactions, performs the necessary calculations, and provides a graphical output of the analysis results. For illustration, TIde is used to detect optimal inhibitor positions in simple branched networks, a signalling pathway, and a well studied model of glycolysis in Using TIde, we show in the branched models under which conditions inhibitions in a certain pathway can affect a molecule concentrations in a different. In the signalling pathway we illuminate which inhibitions have an effect on the signalling characteristics of the last active kinase. Finally, we compare our set of best targets in the glycolysis model with a similar analysis showing the applicability of our tool. In the current pharmaceutic development new drugs are often found by screening a library of small molecular entities (SME) against so-called 'blockbuster targets' which are supposed to play a relevant role in the onset of a certain disease. The development of drugs for new targets is in most cases less interesting for a pharmaceutical company due to the fact that the research is more expensive, they fail pre-clinical trials more often and are in most cases financially less successful ,2. In orOne problem that drugs against novel targets can cause is their possible lack of efficacy. During the development, possible targets are validated via knock-out experiments which work in a totally different way than medication with competitive inhibitors against the corresponding enzymes. While in the first case the flux through a certain pathway can be completely shut down, in the second case it will only be partially decreased which the system can overcome, e.g. by substrate accumulation or feedback regulation. Therefore quantitative modelling should be incorporated into drug research.A systematic approach to the identification of possible drug targets in a reaction network renders possible with the established tools and methods used in systems biology. Over the last years more and more mathematical models for chemical reaction networks have proven to be successful in predicting an microorganism's response to changes in its environment and to perturbations in its gene expression -6. TheseSuch a kind of analysis has already been applied manually to different kinds of small example models -14 and lOther approaches to determine modified enzyme activities in order to achieve a certain change in a systems behaviour already exist (e.g.  and 18]18]), but) works in three steps  single reactions and investigating the results in a given ODE model, we have developed a platform independent tool written in Python  which peIn the following, these three steps of the tool's functionality will be explained.Starting from an SBML model, TIde is supposed to simulate the effects of different modifications of single reactions and combinations thereof. Therefore, the first step of the tool is the identification of the present kinetic formulas for each reaction by numerically comparing them to known kinetic types collected in an internal database. The identity of two formulas is judged by testing all possible parameter matchings of those formulas, repeatedly replacing the parameters by random values, and checking whether the results are similar except for numerical inaccuracy. Using the information about the present kinetics, the database can be searched for known modifier formulas. The identification of the kinetic parameters makes it possible to automatically replace a kinetic by a formula representing a certain kind of modification mechanism acting on the corresponding enzyme.Then, a set of new models is created in which systematically every reaction is replaced by a modification. During this step up to five new models per reaction can be created since four types of modifications are known to the database. These types are competitive, uncompetitive, and noncompetitive inhibition and nonessential activation. Additionally, a competitive inhibition for cofactors is available.vi with reaction velocity vi which is dependent on substance concentrations S and parameters p) will automatically be added to the internal database. Also a standard noncompetitive inhibition (I and its dissociation constant Ki) and a standard nonessential activation (A and its dissociation constant Ka) will be created. Because of that the number of new models created during this step will be at least twice as large as the number of reactions included in the original model.Unknown formulas  as discussed in the following. The first two models were simple metabolic pathways including a branch, the third was a simple signalling cascade, and the fourth one was a biologically relevant example of aerobic metabolism in a brucei .The first two models . Such lethal modifications should be considered in order to identify possible side effects of the potential drug.In the future we plan to extend our tool to handle constraints which have to be fulfilled during simulation. The idea behind this is that certain modifications and effective modifier concentrations could lead to the death of the simulated organism (Project name: TIde• Project home page: • Operating systems: Cross platform• Programming language: Python, C• Other requirements: Python 2.5 or higher, SciPy 0.5 or higher, NumPy 1.1 or higher, PyX 0.9 or higher, semanticSBML 1.0 or higher, libSBML 3.3• License: GNU GPL• Any restrictions to use by non-academics: None• Furthermore, we have attached a walkthrough for our tool (see Additional file MS wrote the tool, conducted the computational experiments, and drafted the manuscript. BMB participated in the design of the tool. EK designed the tool and the numerical experiments and helped to draft the manuscript. All authors read and approved the final manuscript.Walkthrough. Shows how the tool is used from the command line.Click here for fileTIde-1.2.1 source code. Contains the packed python source code of our tool.Click here for fileTIde-1.2.1 prerequisites installer. A Windows installer for all programs and libraries required by TIde.Click here for file


Small-molecular metabolic autocatalytic regulators, which are crucial to metabolic pathways, are identified in a novel systems-wide study in different organisms, revealing that in the enzymatic reactions of conserved autocatalytic cycles, the autocatalytic behavior of replicators varies. If chemical A is necessary for the synthesis of more chemical A, then A has the power of replication . We provide the first systems-level analysis searching for small-molecular autocatalytic components in the metabolisms of diverse organisms, including an inferred minimal metabolism.+, coenzyme A, tetrahydrofolate, quinones) and sugars. Although the enzymatic reactions of a number of autocatalytic cycles are present in most of the studied organisms, they display obligatorily autocatalytic behavior in a few networks only, hence demonstrating the need for a systems-level approach to identify metabolic replicators embedded in large networks.We find that intermediary metabolism is invariably autocatalytic for ATP. Furthermore, we provide evidence for the existence of additional, organism-specific autocatalytic metabolites in the forms of coenzymes (NADMetabolic replicators are apparently common and potentially both universal and ancestral: without their presence, kick-starting metabolic networks is impossible, even if all enzymes and genes are present in the same cell. Identification of metabolic replicators is also important for attempts to create synthetic cells, as some of these autocatalytic molecules will presumably be needed to be added to the system as, by definition, the system cannot synthesize them without their initial presence. Two fundamental features of living systems are heredity and metabolism, the latter being controlled by the former -3. AlthoIn a trivial sense the cytoplasm is autocatalytic in that just the membrane and DNA alone are incapable of replication. DNA may code for the constituents of cytoplasm, but without these constituents there is no machinery to do anything. Enzymes would need to be added to the system. Enzymes catalyze the synthesis of more enzymes, so the enzymatic machinery can be regarded as autocatalytic. However, according to Gánti's theory ,8,9, met2, one molecule of 3-phospho-glycerate is still not sufficient for autocatalytic growth: one needs three molecules of 3-phospho-glycerate to produce a fourth one, and, ultimately, three new molecules in addition to the three with which the system was successfully launched. But since we are dealing with a network, alternative starting compound sets are possible, such as (xylulose-5-P AND erythrose-4-P), OR . The more complex the autocatalytic network, the more alternative sets we can expect to be identified, but this expectation is reduced by the also increasing number of interconversions due to alternative reaction pathways in large systems. But in general a few alternative obligatorily autocatalytic sets can be expected to be present.As Gánti  pointed The relevance of these cycles is not clear, however, as these are embedded in larger networks of reactions, through which the cycle intermediates could potentially be reconstructed. Thus, the existence of an autocatalytic sub-network does not guarantee that the whole network is autocatalytic Figure . ConversEscherichia coli metabolism by Romero and Karp [E. coli, thus it is a bootstrapping molecule sensu Romero and Karp, but is clearly not an autocatalytic metabolite by our definition. Moreover, the authors identified the set of bootstrap molecules with the preconception that certain compounds should necessarily be bootstrapping. Thus, it remains to be investigated in an unbiased way whether large metabolic networks contain autocatalytic components.Another intellectual source behind the present study is an earlier nutrient-related analysis of and Karp  aiming aIn the present study we test the idea that intermediary metabolisms of extant organisms are autocatalytic and we attempt to systematically identify autocatalytic sub-networks in different species using recently published high-quality metabolic network reconstructions. Our analysis not only shows that ATP is a universal obligatory autocatalytic compound, but also reveals species-specific differences in the set of autocatalytic molecules and variations in the structure of some autocatalytic sub-networks. These findings lend strong support to the view that replication in living systems is not restricted to macromolecules, but also involves small-molecule metabolism ,8,9, albSynechocystis sp. PCC 6803 and the hypothetical minimal metabolism where such reconstructions were not available). In contrast to high-throughput automated reconstructions, these published networks were manually reconstructed from diverse information sources and contain accurate information on reaction reversibility, cofactor usage and also include transport processes and reactions without assigned open reading frames [Synechocystis sp. PCC 6803 we attempted to reconstruct a genome-scale metabolic network from the publicly available automatic reconstruction of MetaCyc [We investigated numerous metabolic networks capable of uptaking different sets of nutrients, including the network of an autotrophic species (a cyanobacterium) and also a hypothetical minimal network Table . Since ag frames . In the  MetaCyc  as a tem MetaCyc .Synechocystis, we also defined a food set comprising only inorganic compounds required for autotrophic growth. Generally, an analysis starting from the richest medium (as defined by the full complement of transportable nutrients) would identify the minimum set of autocatalytic metabolites, whereas an investigation starting from a minimal medium would identify the largest set of autocatalytic molecules for a given organism. As biosynthetic pathways leading to certain compounds are still not completely characterized in the available metabolic reconstructions, we cannot expect the scope of the initial molecules to span all metabolites, even if otherwise no autocatalytic metabolite is present in the network. To circumvent this difficulty, we identified the sets of molecules that can be produced by each metabolic network . If the scope of the external molecules did not extend to all producible molecules, then we searched for the internal molecule whose addition to the initial seed increased the scope the most. Next, this molecule was added to the initial seed and the scope analysis was repeated. We continued to add molecules until the scope of the seed matched the set of producible compounds. Finally, we inferred the smallest set of autocatalytic compounds for each network based on the results of the scope analysis .We performed computational analyses of the metabolic networks to identify autocatalytic compounds, that is, intermediate metabolites that are required for their own biosynthesis and, therefore, cannot be accessed from the food set. Given an initial set of metabolites (seed set), the method of scope analysis ,18 allowSaccharomyces cerevisiae) suggest that eukaryotic cells bear at least two autocatalytic compounds: cytoplasmic and mitochondrial ATP. This finding is entirely consistent with the endosymbiotic origin of mitochondria and demonstrates that the mitochondrion retained not only its genetic membranes [Chlamydia psittaci [E. coli network  and adding external (ext) ATP and ADP to the food set. Notwithstanding these modifications, we still identified ATP as an autocatalytic molecule, which can be explained by the fact that ADP/ATP must be simultaneously present on both sides of the membrane for the transport reaction to run. In summary, our results show that, to our present knowledge of metabolisms, the autocatalytic synthesis of ATP is unlikely to be bypassed by other reactions in a larger network.Our systematic analysis reveals that in none of the 11 investigated metabolic networks did the scope of the externally available molecules include all producible compounds . AlthouSynechocystis sp., which requires only a limited set of inorganic food molecules for autotrophic growth. Analysis of the metabolic network of Synechocystis sp. strain PCC6803 reveals four additional autocatalytic sub-networks . Furthermore, the biosynthesis of NAD+, coenzyme A (CoA) and tetrahydrofolate (THF) was also found to be autocatalytic in Synechocystis, irrespective of the food set  are present in most of the studied organisms . We found that in addition to ATP, NAD+, CoA and quinones also behave as autocatalytic compounds under this condition , demonstrating that uptake of certain intermediates from the environment can kick-start the corresponding autocatalytic sub-networks. For example, uptake of cysteine renders biosynthesis of CoA non-autocatalytic in E. coli. On the other hand, the fact that we did not identify THF as an autocatalytic metabolite in this species can best be explained by structural differences between the Synechocystis and E. coli networks: the possibility to convert AMP to GMP via IMP in the nucleotide salvage pathway of E. coli renders THF synthesis non-autocatalytic, even when folate is absent from the medium.Apparently, the reactions of the autocatalytic cycles identified in ms Table : for insSynechocystis, however, remain autocatalytic in certain heterotrophic organisms, despite the fact that all transportable nutrients are included in the food sets  is required for its own synthesis in different biochemical reactions in the two organisms , hence providing evidence for the existence of alternative forms of metabolic replicators, where the whole relevant cycle or network constitutes the autocatalyst.Some autocatalytic compounds of +, acetyl-CoA:CoA, ATP:ADP pairs). Consider the following imaginary biosynthesis of this coenzyme  for different compound families and different organisms in Additional data file 1.In line with the general considerations on autocatalytic cycles, we find that ADP and ATP are both autocatalysts since they are intermediates of the same autocatalytic cycle . Howevere Figure . SupposeE. coli metabolic network containing 660, 904 and 1,260 genes, respectively [E. coli. However, in organisms with less-studied metabolism, the set of identified autocatalytic molecules might change if novel metabolic routes and bypasses will be discovered. For example, we found that THF biosynthesis would not be autocatalytic in G. sulfurreducens if a route from adenine to IMP were present, as can be inferred from the genome sequence of Geobacter metallireducens . In a sE. coli metabolic network could also use GTP as a cofactor. In this case, GTP (besides ATP) was also identified as an autocatalytic compound; however, this finding does not alter our main conclusion that a nucleotide triphosphate is indispensable to kick-start the metabolism.In addition to network completeness, we also investigated how the accuracy of reconstruction affects our results. First, biochemical studies show that some ATP utilizing enzymes can also accept GTP , albMycobacterium tuberculosis where AMP can be accessed from the food set. Moreover, because at least one of these reactions is always a hydrolysis, and water would be abundant in an 'empty' system, we conclude that, for all practical purposes, these routes can be considered irreversible and production of ATP would be highly unlikely. However, even if a small amount of ATP emerged via slow backward reactions, this would not be sufficient to leave that trivial, non-physiological steady state according to theoretical studies of the dynamics of energy metabolism [Second, we asked how the assignment of reaction reversibility could affect our results. In high-quality metabolic reconstructions, reaction reversibility reflects the direction(s) of the reactions under physiological conditions. On the other hand, any chemical reaction is, in principle, reversible. Thus, one might argue that a very small amount of ATP  could be synthesized by ATP consuming reactions, which could kick-start the metabolism even if ATP was initially absent from the cell. However, we found that two or more 'irreversible' reactions should operate in the reverse direction to produce ATP from food molecules, even in tabolism ,32. Thus+ biosynthesis in two different organisms  demonstrates that alternative forms of metabolic replicators is not a mere hypothetical possibility [We performed systems-level analysis of diverse metabolic networks to demonstrate that intermediary metabolisms contain obligatory autocatalytic biochemical cycles and, hence, qualify as replicators . We founsibility . Howeversibility ,35 . In contrast, the presence of metabolic replicators in heterotrophs may seem less obvious, since they consume organic compounds in the food set - yet we find at least ATP to be always such a replicator, and occasionally other coenzymes also.The result that even heterotrophs contain metabolic replicators deserves special attention. For autotrophs the presence of clearly autocatalytic sub-networks as the Calvin cycle or the reductive citric acid cycle suggested that at least one of its intermediates, or some related compound, would be in the set of autocatalytic metabolites, given that there are no alternative synthetic routes, which is an empirical issue. We have settled this issue for + are needed in CoA synthesis  and sugars or sugar-containing compounds (in the autotrophic metabolism of a photosynthetic bacterium). Importantly, the metabolic pathways associated with these autocatalytic nucleotide cofactors are present in many organisms, but they do not necessarily operate in an autocatalytic manner, as the autocatalytic compounds can be synthesized from food molecules or with the help of alternative pathways. This finding clearly underlines the need for a systems-level approach to identify obligate replicators embedded in large metabolic networks. Our work also has relevance for attempts to create synthetic cells, as some of these autocatalytic molecules will presumably be needed to be added to the system as the system cannot synthesize them without their initial presence.The current study constitutes, to our knowledge, the first systematic search for replicators embedded in large biochemical networks. Although parts of metabolism that are autocatalytic in isolation  have been put forward previously, it remained unknown whether these cycles operate in an obligatorily autocatalytic manner when embedded in larger networks. Our analysis of the small molecule metabolism of 10 living organisms and an inferred minimal metabolism suggests that all metabolic networks have at least one universal autocatalytic molecule, ATP . Conceptually, this finding supports the view that a small but important part of inheritance is provided by the set of autocatalytic compounds of intermediary metabolism. Although ATP appears to be the only universal autocatalytic metabolite, other, organism-specific autocatalytic molecules have been identified in the forms of nucleotide cofactors . Note that those compounds, which cannot be synthesized from the food molecules in steady state would always be identified as inaccessible by the scope analysis (a non-steady-state approach), but the reverse is not necessarily true. Because flux balance analysis is widely used to assess the production capabilities of metabolic networks, we performed a series of flux balance analyses on each network to identify the set of producible metabolites in each organism. As the principles of flux balance analysis have been described elsewhere , here weSecond, some biosynthetic pathways leading to producible metabolites involve reaction steps in which a non-producible cofactor participates . As certain intermediates of these pathways would appear inaccessible in the scope analysis, we excluded them from the set of producible metabolites (even though they could be synthesized in steady state).In the first step of scope analysis , metabolIf the scope of the input set did not include all metabolites that can be otherwise produced by the network, then we identified the smallest set of internal molecules that had to be added to the input set, so that the scope of this combined input included all required metabolites. To find the smallest set of such internal molecules, we searched for the metabolite that increased the scope to the highest extent . Next, we added this metabolite to the set of input molecules and performed the scope analysis again. The above steps were iterated until we arrived at an input set whose scope included all required metabolites.Synechocystis .Those molecules increasing the scope the most at various steps of the above procedure are either autocatalytic molecules  or intermediates in the biosynthetic pathways leading to such molecules . In other cases, the identity of the autocatalytic molecule is not self-evident from those compounds found to give the highest increase in the scope . In such cases, we analyzed the set of molecules, which became accessible after the addition of the identified molecule to the seed. These cases are further discussed in the description of the analysis of CoA, coenzyme A; THF, tetrahydrofolate.ESz conceived the idea for the study. All authors contributed to the design and planning of the research. BP performed the Flux Balance Analyses, and ÁK performed the scope analyses and network curations. All authors were involved in writing the manuscript. All authors approved the final version of the manuscript.Synechocystis network. The figures (S1-S9) show the autocatalytic production of the identified metabolites. The table (S2) lists the relevant statistics for each metabolic network analyzed. Additional data file Synechocystis sp PCC 6803. The separate worksheets lists are: 1, the metabolites involved in the metabolic reconstruction, with their abbreviations and identifier used in the MetaCyc database; 2, the reactions with reaction ID, pathway, EC number and references; 3, the metabolites that cannot be produced in the network (dead end metabolites); 4, the reactions that were left out from the metabolic network, and the reason for the exclusion; and 5, the references and notes for the worksheets.The following additional data are available. Additional data file e table S lists thThe figures (S1-S9) show the autocatalytic production of the identified metabolites. The table (S2) lists the relevant statistics for each metabolic network analyzed.Click here for fileIf the network reconstruction used abbreviated names for the metabolites, then the abbreviations are also included for ease of comparisons with the reconstruction.Click here for fileThe separate worksheets lists are: 1, the metabolites involved in the metabolic reconstruction, with their abbreviations and identifier used in the MetaCyc database; 2, the reactions with reaction ID, pathway, EC number and references; 3, the metabolites that cannot be produced in the network (dead end metabolites); 4, the reactions that were left out from the metabolic network, and the reason for the exclusion; and 5, the references and notes for the worksheets.Click here for file


Mycobacterium tuberculosis, the bacterium that causes tuberculosis (TB). Key components of mycobacterial cell walls are mycolic acids which are targets for several first-line TB drugs. We used E-Flux to predict the impact of 75 different drugs, drug combinations, and nutrient conditions on mycolic acid biosynthesis capacity in M. tuberculosis, using a public compendium of over 400 expression arrays. We tested our method using a model of mycolic acid biosynthesis as well as on a genome-scale model of M. tuberculosis metabolism. Our method correctly predicts seven of the eight known fatty acid inhibitors in this compendium and makes accurate predictions regarding the specificity of these compounds for fatty acid biosynthesis. Our method also predicts a number of additional potential modulators of TB mycolic acid biosynthesis. E-Flux thus provides a promising new approach for algorithmically predicting metabolic state from gene expression data.Metabolism is central to cell physiology, and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. We present a novel method for modeling metabolic states using whole cell measurements of gene expression. Our method, which we call E-Flux (as a combination of flux and expression), extends the technique of Flux Balance Analysis by modeling maximum flux constraints as a function of measured gene expression. In contrast to previous methods for metabolically interpreting gene expression data, E-Flux utilizes a model of the underlying metabolic network to directly predict changes in metabolic flux capacity. We applied E-Flux to  Mycobacterium tuberculosis (M. tb). Virulence, growth in human hosts, and drug resistance are all related to changes in M. tb's metabolism. We predict the effects of a variety of conditions on the production of mycolic acids, essential cell wall components. Our method successfully identifies seven of the eight known mycolic acid inhibitors in a compendium of 235 conditions, and identifies the top anti-TB drugs in this dataset. We anticipate that the method will have a range of applications in metabolic engineering, the characterization of disease states, and drug discovery.The ability of cells to survive and grow depends on their ability to metabolize nutrients and create products vital for cell function. This is done through a complex network of reactions controlled by many genes. Changes in cellular metabolism play a role in a wide variety of diseases. However, despite the availability of genome sequences and of genome-scale expression data, which give information about which genes are present and how active they are, our ability to use these data to understand changes in cellular metabolism has been limited. We present a new approach to this problem, linking gene expression data with models of cellular metabolism. We apply the method to predict the effects of drugs and agents on  Metabolism is central to cell physiology and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. Gene expression data provide global insight into the regulation of metabolic reactions, but methods for inferring the behaviour of metabolic networks, and particularly metabolic flux, from these data are limited. There is thus a need to develop computational approaches that utilize available genomic data to make inferences about metabolism at the level of large scale metabolic networks.One approach to computationally studying metabolism is to develop detailed models based on coupled differential equations describing the dynamics of enzyme action. Such models, however, require measuring numerous kinetic parameters that can be prohibitively difficult for large systems and for organisms – such as infectious disease agents – that are difficult to work with experimentally.Flux balance analysis (FBA) is an alternative approach to modeling metabolism without developing detailed simulation models that include enzyme kinetics Briefly, FBA represents a metabolic network by capturing the stoichiometries of constituent reactions in a stoichiometric matrix, S, and describing a flux configuration as a set of rates at which the reactions in a network are moving (ie the set of reaction fluxes). FBA requires that constraints for some reactions be known, reflecting their maximum or minimum rates. These constraints can either be measured (e.g. uptake reactions) or calculated from physical parameters (e.g. oxygen diffusion) or thermodynamic constraints. In many cases, the constraints can be related to the degree of enzymatic activity for the given reaction. The matrix S and the set of reaction constraints define the set of all possible flux configurations at steady state. A flux configuration can be visualized as a vector in flux space, and all flux configurations that are feasible at steady state lie within a cone in this space, called the flux cone. The core approach of FBA is to choose a metabolic objective which is a linear function of fluxes, and then use linear programming to optimize this objective subject to the constraints. The algorithm results in one or more flux configurations that are optimal for the chosen metabolic goal, and the optimal production capacity of that objective.Escherichia coli and Mycobacterium tuberculosis using a pseudo-steady-state dynamic modeling approach FBA provides a method for exploring capabilities and states of a metabolic system at steady state, and genome scale metabolic models can be reconstructed based on annotated genome sequences coupled with literature curation While powerful, FBA is limited in that it does not take into account the gene regulatory state, as described for example by gene expression data. In effect, the basic approach predicts metabolic capabilities assuming all reactions have the same maximum capacity. Indeed, many of the errors in the prediction of gene knockout phenotype were traced back to the lack of gene regulation in standard FBA models M. tuberculosis (M. tb), the pathogen that causes tuberculosis (TB). An estimated one third of the world's population has been exposed to this disease, which is estimated to kill 1.6–1.8 million annually worldwide. Multiple drug resistant (MDR) and extensively drug resistant (XDR) strains of tuberculosis are emerging worldwide, so the development of new drugs is of the essence. Bacterial metabolism plays an important role in TB pathology, both in terms of metabolic alterations associated with intracellular growth M. tb's slow growth rate, the hazards of experimenting directly with this infectious organism, and limitations in measuring all metabolites simultaneously, there is considerable motivation to augment experimental approaches with computational methods for predicting M. tb metabolism.We have developed a method, which we call “E-Flux”, to predict metabolic capacity based on expression data. E-Flux extends FBA by incorporating gene expression data into the metabolic flux constraints. We applied E-Flux to M. tb, based on a compendium of expression measurements from these conditions. Our method successfully identifies seven of the eight known inhibitors of mycolic acid or fatty acid production that were present in the compendium. E-Flux also correctly predicts whether conditions are directly inhibiting mycolic acid production, or inhibiting production indirectly through other mechanisms. Our method thus provides a promising approach to modeling metabolic state from whole cell measurements of gene regulation.We used E-Flux to predict the impact of drugs and environmental conditions on mycolic acid biosynthesis capacity in The key innovation underlying the E-Flux approach is that we use expression data to model the maximum possible flux through metabolic reactions. When the expression for a particular enzyme-coding gene is low (relative to some reference), we place a tight constraint on the maximum flux through the corresponding reaction(s). When expression is high we place a looser constraint on the flux through the reaction(s). We then use FBA with the applied constraints and an appropriate objective function to determine a corresponding metabolic state or optimal metabolic capacity.1 is poorly expressed. Our method models this conceptually as a thin pipe around reaction 1, limiting the maximum flux through this reaction. Conversely, in the bottom panel, G1 is highly expressed corresponding to more possible flux (a wider pipe). Under conditions in which substrate is not limited, we would predict more flux through reactions 3 and 4, and less through reactions 1 and 2 in the top panel. Conversely, we might predict more flux through reactions 1 and 2, and less through 3 and 4, in the bottom panel.Conceptually, our method can be understood as setting the width of “pipes” around particular reactions as a function of expression state. Geometrically, setting maximum flux constraints according to gene expression reshapes the flux cone. Different gene expression states result in different flux cone geometries, which can lead to different solutions for the same metabolic objective. Reshaping the flux cone and thus generating different flux configurations is similar to the approach used to predict phenotypes from gene knockouts using FBA Our method does not assume that enzyme concentrations, enzyme activities, or realized reaction fluxes are determined by mRNA expression values. Indeed, the true flux for a reaction depends on the enzyme kinetics and concentration, as well as the concentration of metabolites. The effective enzyme concentration in turn depends on gene expression, transcription and translation, post-translational modification and degradation. It would be prohibitive to determine these values for many reactions in an organism.However, the biological rationale behind our method is that expression data provide measurements on the level of mRNA for each gene. If there were limited accumulation of enzyme over the time course considered, and given a particular level of translational efficiency, the level of mRNA can be used as an approximate upper bound on the maximum available protein and hence as an upper bound on reaction rates to some level of approximation. This allows us to extend flux balance analysis from an algorithm that assumes that all reactions have the same constraint, as has been done previously, to an approach making use of condition-dependent, empirical data. E-Flux allows us to link such data directly to changes in metabolic capability. We discuss rationale behind our method further in the Tv, and aj and bj are the minimum and maximum fluxes through reaction j. We assume that we have a set of expression measurements for some or all of the genes associated with the reactions in S.Mathematically, our approach modifies FBA as follows. FBA involves solving the following optimization problem:j, for the jth reaction according to a function of the expression of gene j and associated genes:The core E-Flux method chooses the maximum flux, bj = −bj, otherwise aj = 0. For the results presented here, “associated genes” refers both to genes that are components of the same enzyme complex, and genes associated with separate isozymes of the reaction. In the latter case, we choose f to be a monotonically increasing function of the expression of the corresponding genes. In general bj can also depend on genes that modulate the activity of the enzyme for reaction j and f can thus take on a more general form. In the f.If the reaction catalyzed by the corresponding enzyme is reversible then aM. tb. The first model consisted of just those reactions underlying mycolic acid production. Mycolic acids are cell wall components characteristic of mycobacteria and essential for the survival of the bacterium We tested E-Flux on two metabolic models that include the biosynthesis of mycolic acids in M. tuberculosis to 75 different substances and conditions, including known anti-tubercular drugs, growth conditions and unknown compounds. Specifically, this set also included eight known inhibitors of mycolic acid production. Our goal was to use E-Flux to predict the impact of each of these compounds or conditions on mycolic acid biosynthetic production in M. tuberculosis.We analyzed the microarray data from the Boshoff TB gene expression compendium M. tb's dormancy phase.To explore the method's relevance to data from diverse groups and for a variety of experimental conditions, we also analyzed a set of expression data of Karakousis et al. M. tuberculosis metabolism of Beste et al. Two genome-scale metabolic models are available for M. tuberculosis, namely those of Beste et al. Beste et al.'s model As with the model of mycolic acid production, we applied E-Flux to the genome scale model to predict the impact of each of the compounds or conditions in the Boshoff TB gene expression compendium on mycolic acid biosynthetic production Our computational approach is shown in Following pre-processing, we separated the drug or condition (cy5) and control channels (cy3). For each experiment we first applied expression data from the control channel to set constraints on maximum fluxes of reactions in the model. We then used FBA to find a flux configuration that maximized overall mycolic acid biosynthesis  and ethionamide. Isoniazid, a first-line drug for TB, is a prodrug that is activated by the bacterial catalase-peroxidase enzyme KatG Nocardia and Streptomyces and is a potent and highly selective inhibitor of the type II dissociated fatty acid synthase of plants and bacteria E-Flux also predicts thiolactomycin and ethambutol as strong selective inhibitors. Thiolactomycin is a natural product produced by both M. tbtbIn addition, E-Flux predicts a number of weaker inhibitors, including two drugs known to impact mycolic acid. Cerulenin is a fungal mycotoxin that is known to inhibit both FAS-I and FAS-II cycles in mycolic acid synthesis in E-Flux also predicts several novel compounds not previously associated with inhibition of mycolic acid biosynthesis. These include predictions of weak effects for the protein synthesis inhibitor streptomycin and the ionophore valinomycin. These compounds are predicted as non-specific inhibitors consistent with an overall impact on metabolism. PA-21 was also predicted to be a weak and marginally specific inhibitor, although the mechanism of this compound has not been reported. Of the novel predicted inhibitors, only ZnSO4 was predicted to have a strong effect with marginal specificity. However, only a single replicate for ZnSO4 is present in the Boshoff data set, and preliminary experimental data suggest that this prediction is likely a false positive.Interestingly, E-Flux also predicted a small number of compounds that may enhance fatty acid biosynthesis. Menadione and chlorpromazine are predicted to be weak non-specific enhancers, although these results are convolved with GSNO and one instance of GSNO in isolation was predicted as a strong and specific enhancer. However, it is noteworthy that menadione has been reported to increase fatty acid production in human fat cells, in addition to a number of other metabolic effects Curiously, triclosan was also predicted as an enhancer. Triclosan is known to inhibit the enoyl-ACP reductase of FASII M. tb to isoniazid provide the opportunity to examine the predictions of E-Flux for dormant tuberculosis. Though it is a strong inhibitor of mycolic acid biosynthesis, isoniazid has little activity against M. tb under oxygen deprivation or nutrient starvation M. tb under a range of treatment conditions, when such data become available.The data of Karakousis et al. M. tb genes as reported by Boshoff et al. To rule out that our predictions reflect similarities in gene expression independent of metabolic modeling, we clustered the expression of the 29 genes used in the mycolic acid biosynthetic model across all 437 experiments in the Boshoff data set. As can be seen in In this paper, we have presented a novel method for predicting metabolic capacity from gene expression data. E-Flux extends flux balance analysis to predict characteristics of steady state metabolism that correspond to specific empirically-measured gene expression states. The key innovation of our method is that we use gene expression data to model the maximum flux through individual metabolic reactions.M. tuberculosis, based on microarray data from the Boshoff TB expression compendium. E-Flux correctly predicts seven of eight inhibitors of mycolic acid biosynthesis within this compendium, and correctly predicts the specificity of this inhibition for mycolic acid biosynthesis in all but one case. E-Flux also predicts a small number of additional potential inhibitors, as well as potential enhancers of mycolic acid production. We also tested E-Flux on data for dormant M. tb treated with isoniazid, and it correctly predicts the difference in effect of this agent in several dormancy models.We have used E-Flux to predict the impact of drugs, drug combinations, and environmental conditions on mycolic acid biosynthetic capacity in M. tb, the availability of many microarray experiments for this organism (www.tdbd.org), and the essential role of metabolism in the pathogenesis of M. tb.E-Flux thus provides a potentially powerful tool for exploring metabolic state (which is relatively difficult to measure) from gene expression state (which is relatively simple to measure in many circumstances). This is particularly significant for tuberculosis given the difficulty of working with upper bound on the potential flux through the corresponding metabolic reactions, i.e. for a particular level of translation and degradation, the amount of mRNA sets an upper bound on the amount of available enzyme. The amount of available enzyme is in turn proportional to maximum flux (e.g. Vmax) through a particular reaction.The key principle underlying the E-Flux method is that mRNA levels for enzymes approximate an Saccharomyces cerevisiae, for example, reported a correlation of 0.61 after correcting for methodological issues Staphylococcus aureus biofilm and planktonic cells showed qualitative agreement between transcriptomic and proteomic expression differences Desulfovibrio vulgaris reported correlations between 0.45–0.53 S. cerevisiae and D. vulgaris genes associated with central intermediary and energy metabolism display higher levels of correlation than other groups E. coli DF11and a pgi mutant found a correlation of .81 between the log ratio of transcripts and the log ratio of enzyme activities E. coliWe acknowledge that mRNA expression is not sufficient to determine fluxes or, in many cases, true upper bounds on fluxes, but nonetheless argue that including mRNA expression data into flux balance models provides a new and useful way to connect expression data with models cellular metabolism, and is an improvement upon effectively assuming that all reactions that are present have the same maximum flux. The degree of correlation between mRNA and protein levels is an area of ongoing research Although the total amount of available enzyme sets an upper limit on the maximum flux through a particular reaction, many regulatory processes may modulate the effective levels of enzyme activity. Metabolite feedback regulation, allosteric interactions, and various covalent modifications may alter the activity of enzymes already synthesized. These modulations, however, cannot lead to more activity than is possible if all available enzyme were maximally active. For example, in the extreme case where an enzyme is completely deactivated by covalent modification (e.g. inactivation through phosphorylation), the true flux through a reaction is zero whereas mRNA levels might suggest a higher bound. With respect to E-Flux, this means that the upper bound on enzyme activity set by mRNA levels is an upper bound, but not always a tight one. In such a case, the accuracy of predictions made by E-Flux may depend on the difference between the approximate and true bounds.It would be possible to generalize the E-Flux framework to take modulation of enzyme activity into account. In our application to mycolic acid production, we model maximum flux for a reaction as a function of all genes that are components of the corresponding enzymes or enzyme complexes. However, we could incorporate the expression of all genes whose products modulate the activity of a given enzyme into this function. For example, if an enzyme is inactivated through phosphorylation by a kinase, we may choose to model the corresponding maximum flux as a function of the expression of the genes for both the enzyme and kinase. This approach is conceptually similar to the coupling of metabolic models with Boolean regulatory models taken by Covert et al. A number of previous methods have been developed to gain insight into metabolism from expression data. The most common method is to identify genes or sets of genes from particular pathways that are differentially expressed under different conditions M. tb genes Other methods have been based on classifying gene expression by similarity to expression patterns corresponding to known metabolic or cellular states More fundamentally, our method does not require a set of training data whose effect on the pathway is known in advance. Traditional classification methods require exemplars from the categories to be classified Since the initial development of E-Flux, two other methods for combining expression data with flux balance analysis have been described. The method of Becker and Palsson E-Flux provides a general approach for modeling metabolism from expression data. This approach has a number of potential applications, beyond the application to tuberculosis presented here. E-Flux can also be used to investigate and model other disease states where expression data are available and for which metabolic alterations are associated. For example, many cancer cells are known to grow glycolytically in the presence of oxygen and to develop a lipogenic phenotype E-Flux could in principle also be used as a tool for drug discovery. For example, if a drug were sought that decreased production of a particular metabolite, then genome-scale expression profiles of a large number of small molecules could be analyzed with E-Flux and subsequent study could focus on those for which E-Flux predicted the desired inhibition. This would be a valuable approach in settings where screening directly for the effect of interest is expensive relative to microarray analysis. In addition, since E-Flux can predict unanticipated effects, the approach could be used to predict possible undesirable effects including the production of toxic metabolites. Furthermore, if a set of objective functions were developed, each corresponding to a different subsystem or pathway in the metabolic network, then E-Flux could be used separately for each objective to help identify a molecule's mechanism of action.Finally, E-Flux provides a new tool for efforts to engineer metabolic systems. Flux analyses have been previously used to guide the design of metabolic networks. E-Flux enhances this approach by enabling the prediction of metabolic characteristics for specific empirically determined gene expression states.M. tuberculosisWe used two metabolic models: a model of the mycolic acid biosynthesis subsystem et al.'s representation of mycolic acids with that of Raman et al., as the latter is more detailed and as this allows direct comparison of the results of E-Flux in the two models. The model is available as The genome-scale model we used was closely based on that published by Beste et al. http://www.ncbi.nlm.nih.gov/geo/ under accession number GSE9776 and are also two-channel data of H37Rv M. tb; the dataset contains 17 arrays for 6 unique conditions, comparing M. tb's response to isoniazid in dormancy models.The expression data published by Boshoff et al. ijkgy denote the log-transformed measurement from the ith channel, jth chip, kth variety , and gth gene. Then we fit the modelijμ is the average measurement for channel j of chip i, gG represents the effect of gene g, jg(AG) represents effects specific to chip j and gene g, ig(DG) represents effects specific to channel i and gene g, k and gene g , and ijkgε is error. Thus we fit for, and subtract out, systematic, non-biological effects such as overall brightness and spot effects. We fit the model such as to minimize the residual sum of squares (RSS) given byWe processed the expression data using MAANOVA 2.0 j for the j'th chip), and found the maximum of these, Mmax. We then added (Mmax-Mj) to both channels of the j'th chip, for each j. The resulting values had the same median for the Cy3 channels, and different medians for the Cy5 channels, while the difference between Cy3 and Cy5 channel medians on each chip was the same as in the raw data. We also performed E-Flux using log-transformed values; predictions using log-transformed and raw values were correlated with R = 0.99 after the control-channel median adjustment described here.We compared the results of our method using ANOVA-processed data with those using the published values without statistical filtering. In this approach, the published data (log format) were exponentiated to obtain raw values. To remove noise resulting from variation in overall brightness from chip to chip while preserving median differences between condition and control channels, we adjusted the medians of each chip according to the median of that chip's Cy3 channel. We set the median of all control channels to the maximum of the control channel medians across the dataset  to avoid obtaining negative flux constraint inputs. In other words, we computed the median of each chip's Cy3 channel (denoted MComparing predictions based on ANOVA-processed and raw expression data (with median adjustment), our results for the top mycolic acid inhibitors  are preserved, as are the inhibitory predictions for cerulenin, PA-824 and valinomycin. Ethambutal was also a predicted inhibitor from the unprocessed data, but not so strongly, along with streptomycin. The enhancing effect of triclosan was more strongly predicted from the raw data than the ANOVA-processed data. ZnSO4 was inhibitory but not as strongly, and GSNO was not as strongly enhancing. Overall, results from the two data sets were positively correlated with R = 0.62 at a significance level p = 2.11e-48.For the data on isoniazid and dormancy from Karakousis et al. a and b from expression data for control and condition channels, using these as constraints for flux balance analysis with a given objective, and comparing the maximum production capacity of that objective between the control and condition.The E-Flux method consists of creating constraint vectors a and b for the control and condition channels for each condition in the compendium of expression data as follows. For each reaction that is catalyzed by only one gene, we set the upper bound bj to the expression value for the gene whose product catalyzes reaction j, taking the value from the relevant data. For example, reaction 2 in the mycolic acid sub-model is catalyzed by gene Rv3279c corresponding to birA 2b is initially set to 15. For each reaction catalyzed by a complex requiring two genes we set bj to the minimum of the expression of the two genes, and for reactions which can be catalyzed by either gene we set bj to the sum of their expression values. We then normalized the bj values to 1 by dividing each component of bj by M = maxj (bj). For each exchange reaction, we set aj = −1 and bj = 1; in other words, these reactions were not constrained by gene expression. Changing the constraint  on exchange reactions to another value does not change the results presented here, as the relative production capacity from control to condition is a log ratio and is not dependent on the overall scale. Following Raman et al., all internal reactions in the model were modeled to be irreversible, so that aj = 0 for these (j = 1 to 219). For the reactions catalyzed by the remaining unknown gene in Raman's model we set bj = 1 and aj = 0.We constructed constraint vectors acontrol and bcontrol taken from the cy3 channel of the chip, and acondition and bcondition taken from the condition channel. Linear optimization was then performed with each set of constraints and the same objective function, namely a weighted production of mycolic acids. The objective function for the mycolic acid subsystem model wasi represents the vector  with a 1 in the i'th component and 0 in all other components. Since the linear programming tool linprog in matlab minimizes cTv, the coefficients of c were chosen to be negative so that the optimization maximizes (−cTv), namely the weighted flux creating mycolic acids. The reactions included in c produce alpha, cis- and trans- methoxy mycolate and cis- and trans- keto mycolate respectively. This is the same as objective function c1 in Raman et al. Our results are insensitive to the particular balance between the α-, keto- and methoxy- mycolates in the objective function. In the genome-scale model our objective function was the same but the reactions are numbered differently. We also performed E-Flux with two alternative objective functions: biomass as given in Beste et al., and the mycolic acid objective function with the same weights as given in All of these steps were performed for the control channel expression data and then separately for the condition channel. This yields 4 vectors: control = max(cTv) using constraints taken from the control channel, and Pcondition = max(cTv) using constraints taken from the condition channel. The relative production, namely the results shown in condition/Pcontrol).This procedure, with either objective function, yields two results for the maximal production capacity: Pbj equal to the expression value for the gene catalyzing the j'th reaction, we explored using sigmoidal, exponential and polynomial increasing functions to create the constraint b, so that rather than bj = expression(j), we used bj = f(expression(j)) where f is sigmoidal, exponential or polynomial. The results presented in In addition to setting To determine whether predictions were significant we resampled the control channel of each chip, adding noise sampled from the noise distribution given by the Anova model as described above. We compared the mycolic acid production capacity from one such resampled control dataset to another, and repeated the procedure 800 times. We then found the “null” interval in which 95% of the values lie. The interval is denoted by the dotted lines in To make a distinction between predictions that are specific to the mycolic acid pathway and those that may result from the conditions' effects on a large number of genes in M. tuberculosis, we used two approaches. For the first, we computed predictions using randomly chosen genes from each chip in place of the genes in the metabolic model. To do this, we chose a random permutation of all genes on each chip, and these randomly chosen genes  to form the constraint vectors a and b. This was done for both control and condition channels of each chip, using the same gene permutation for the two channels. We then applied E-Flux to recompute the predicted inhibition or enhancement using constraints from expression of the randomly selected genes. After repeating this procedure, we found the range in which 95% of the resulting predictions lie, for each experiment Click here for additional data file.Figure S2Predictions of E-flux applied to mycolic acid biosynthesis in M. tuberculosis. Second set in alphabetical order from the Boshoff expression data compendium.(3.16 MB TIF)Click here for additional data file.Figure S3Predictions of E-flux applied to mycolic acid biosynthesis in M. tuberculosis. Third set in alphabetical order from the Boshoff expression data compendium.(3.16 MB TIF)Click here for additional data file.Figure S4Predictions of E-flux applied to mycolic acid biosynthesis in M. tuberculosis. Fourth set in alphabetical order from the Boshoff expression data compendium.(3.16 MB TIF)Click here for additional data file.Figure S5Predictions of E-flux applied to mycolic acid biosynthesis in M. tuberculosis. Fifth set in alphabetical order from the Boshoff expression data compendium.(3.16 MB TIF)Click here for additional data file.Dataset S1Integrated genome-scale model in XML format(1.13 MB XML)Click here for additional data file.