Our key observation is that a minimal consistent reconstruction can be defined via a set of sparse modes of the global network, and fastcore iteratively computes such a set via a series of linear programs. Experiments on liver data demonstrate speedups of several orders of magnitude, and significantly more compact reconstructions, over a rival method. Given its simplicity and its excellent performance, fastcore can form the backbone of many future metabolic network reconstruction algorithms.Systemic approaches to the study of a biological cell or tissue rely increasingly on the use of context-specific metabolic network models. The reconstruction of such a model from high-throughput data can routinely involve large numbers of tests under different conditions and extensive parameter tuning, which calls for fast algorithms. We present  fastcore, a fast algorithm for the reconstruction of compact context-specific metabolic network models. The algorithm takes as input a global metabolic model and a set of reactions that are known to be active in a given context, and it produces a context-specific model. fastcore is significantly faster than other algorithms, typically obtaining a genome-wide reconstruction in a few seconds. High-throughput model building will soon become a common procedure for the integration and analysis of omics data, and we foresee many future applications of fastcore in disease and patient specific metabolic modeling.Metabolism comprises all life-sustaining biochemical processes. It plays an essential role in various aspects of biology, including the development and progression of many diseases. As the metabolism of a living cell involves several thousands of small molecules and their conversion, a full analysis of such a metabolic network is only feasible using computational approaches. In addition, metabolism differs significantly from cell to cell and over different contexts. Therefore, the efficient generation of context-specific mathematical models is of high interest. We present  PLOS Computational BiologyThis is a Cell metabolism is known to play a key role in the pathogenesis of various diseases context-specific metabolic models To maximize the predictive power of a metabolic model when conditioning on a specific context, for instance the energy metabolism of a neuron or the metabolism of liver, recent efforts go into the development of Most algorithms for context-specific metabolic network reconstruction (see ‘Related work’ section for a short overview) first identify a relevant subset of reactions according to some ‘omics’ information , and then search for a subnetwork of the global network that satisfies some mathematical requirements and contains all (or most of) these reactions fastcore, a generic algorithm for context-specific metabolic network reconstruction. fastcore takes as input a core set of reactions that are supported by strong evidence to be active in the context of interest. Then it searches for a flux consistent subnetwork of the global network that contains all reactions from the core set and a minimal set of additional reactions. Flux consistency implies that each reaction of the network is active  in at least one feasible flux distribution fastcore is its generality: As it only relies on a preselected set of reactions and a simple mathematical objective (flux consistency), it can be applied in different contexts and it allows the integration of different pieces of evidence (‘multi-omics’) into a single model.We present sparse modes of the global network, and fastcore is designed to compute a minimal such set. Every iteration of the algorithm computes a new sparse mode via two linear programs that aim at maximizing the support of the mode inside the core set while minimizing that quantity outside the core set. fastcore's search strategy is in marked contrast to related approaches, in which the search for a minimal consistent reconstruction involves, for instance, incremental network pruning fastcore is simple, devoid of free parameters, and its performance is excellent in practice: As we demonstrate on experiments with liver data, fastcore is several orders of magnitude faster, and produces much more compact reconstructions, than the main competing algorithm MBA Computing a minimal consistent reconstruction from a subset of reactions of a global network is, however, an NP-hard problem m metabolites and n reactions is represented by an m×n stoichiometric matrix S, where each entry ijS contains the stoichiometric coefficient of metabolite i in reaction j. A flux vector i in the network. Reactions are grouped into reversible ones . A metabolic network model that contains no blocked reactions is called (flux) consistentA metabolic network of S, a problem of interest is to test whether the network is consistent or not. Additionally, if the network is inconsistent, it would be desirable to have a method that detects all blocked reactions.Given a metabolic network model with stoichiometric matrix ε). This is equivalent to testing if the following LP is feasible:It has been suggested that network consistency can be detected by a single linear program (LP) reduceModel function of the COBRA toolbox S corresponding to the reversible reactions in A straightforward solution to the problem would involve iterating through all reactions, computing the maximum and minimum feasible flux of each reaction via an LP that satisfies the constraints in (1). Reactions with minimum and maximum flux zero would then be blocked. This is the idea behind the FVA  algorithm and the In most problems of interest there will be no single mode that renders the whole network consistent, and an iterative algorithm like the one described in the previous section must be used. For performance reasons it would therefore be desirable to be able to establish the consistency of as many reactions as possible in each iteration of the algorithm.cardinality—denoted by card(v) and defined as card(v) = #supp(v), i.e., the number of nonzero entries of card(v) is, however, not straightforward, for the following reasons: First, the card function is quasiconcave only for S), it is not obvious how to efficiently maximize the quasiconcave card(v). Third, in practice consistency implies fluxes that are ε-distant from zero, in which case some adaptation of the card function is in order.Since consistency implies nonzero fluxes, it is sufficient to optimize a function that just ‘pushes’ all fluxes away from zero. Formally, this amounts to searching for modes card(v) over a nonnegative flux subspace indexed by a set of reactions θ by a concave function that is the minimum of a linear function and a constant function:ε is the flux threshold. The problem of approximately maximizing card(v) can then be cast as an LP: We introduce an auxiliary variable card(v)ε, this simplifies toε (contrast this with LP-2).Here we propose an approach to approximately maximize irreversible reactions of Returning to the network of fastcc (for fast consistency check). Since fastcc is just a variant of fastcore, we defer its detailed description until the next section.By construction, the above approximation of the cardinality function applies only to nonnegative fluxes. In order to deal with reversible reactions that can also take negative fluxes, we can embed LP-7 in an iterative algorithm (as in the previous section), in which reversible reactions are first considered for positive flux via LP-7, and then they are considered for negative flux. The latter is possible by flipping the signs of the columns of the stoichiometric matrix that correspond to the reversible reactions under testing, in which case the fluxes of the transformed model are again all nonnegative, and the above approximation of the cardinality function can be used. This gives rise to an algorithm for detecting the consistent part of a network that we call ε = 1. However, such an approach is prone to the same drawback as LP-2, namely, that the two irreversible copies of a blocked reaction can carry equal positive flux at the solution of LP-7 due to the presence of cycles introduced by the transformation. The authors acknowledge this problem but they do not fully resolve it. In our case, we avoid this problem by working with the original reactions and a series of LPs with appropriate sign flips of the stoichiometric matrix, thereby guaranteeing the completeness of the algorithm.Independently to this work, a similar approach to network consistency testing was recently proposed, called OnePrune consistent global network The reconstruction problem involves computing a minimal consistent network from a global network and a ‘core’ set of reactions that are known to be active in a given context. Formally, given (i) a Our approach hinges on the observation that a consistent induced subnetwork of the global network can be defined via a set of modes of the latter:Theorem 1.Let  be a set of modes of the global network , and let supp(v) be the union of the supports of these modes. The induced subnetwork  is consistent.Proof. For each fastcore.This simple result allows one to cast the reconstruction problem as a search problem over sets of modes of the global network:elementary modes of the global network, since the union of their supports covers the whole set r be the number of elementary modes, and n binary vectors, where each vector jm captures the support of elementary mode j . Also, let n binary vector with i is included in the core set n binary vector r real vector Note that, without loss of generality, in NLP-8 we can restrict the search for Theorem 2.When all elementary modes are available, the following MILP-9 solves NLP-8 exactly.Proof. By definition, i will be included in the reconstruction j is selected when n, which can be prohibitive for large n. Nonetheless, it is reassuring to know that an exact solution to the context-specific network reconstruction problem is possible, albeit with high complexity. Next we describe fastcore, an approximate greedy algorithm that scales much better to large networks, and we compare it to MILP-9 in the Note, however, that MILP-9 does not scale to large networks, for the following reasons: First, it requires computing all elementary modes of the global network, which can be a very large number set covering problemfastcore algorithm: We build up the set card(A), each added mode is constrained to have sparse support outside L1-norm minimization, which is a standard approach to computing sparse solutions to (convex) optimization problems An alternative search strategy for computing fastcore algorithm is shown in indSparseMode  in the second constraint of LP-10, with an equal scaling of all flux bounds in The overall arseMode . This fuInput: A consistent metabolic network model Output: A consistent induced subnetwork functionfastcore. The flipped variable ensures that a reversible reaction is tested in both the forward and negative direction. The algorithm terminates when all reactions in fastcore has no free parameters besides the flux threshold ε.The fastcc algorithm for detecting the consistent part of an input network (see previous section) can be viewed as a variant of fastcoreindSparseMode are omitted , the reconstructions obtained by GIMME and fastcore can differ significantly: Running the createTissueSpecific function of the COBRA toolbox on a set of liver core reactions  on the liver problem  Both fastcore and MBA involve a search for a minimal consistent subnetwork, however the search strategy of fastcore is very different to MBA: Whereas fastcore iteratively expands the active set fastcore's search strategy differs to MBA in two key aspects: First, consistency testing in fastcore involves the maximization of flux cardinality (LP-7) instead of sum of fluxes (LP-3), which results in fewer LP iterations. Second, the search for compact solutions in fastcore involves L1-norm minimization instead of pruning. The advantage of the former is that it can be encoded by a single LP, resulting in significant overall speedups . The consistent global model serves then as input for the context-specific reconstruction with fastcore. In Generic metabolic reconstructions like Recon 2 are inconsistent models as they contain reactions that are not able to carry nonzero flux due to gaps in the network (see next section). The first step towards obtaining a consistent context-specific reconstruction is therefore to extract the consistent part of a global generic model. This can be achieved by fastcore algorithm was implemented in the COBRA toolbox ε = 1e-4. The software is available from bio.uni.lu/systems_biology/softwareWe report results on two sets of problems, the first involving consistency verification of an input model, and the second involving the reconstruction of a context-specific model from an input model and a core set of reactions. The fastcc, the consistency testing variant of fastcore, for consistency verification of four input models, and compared it against the FastFVA algorithm of Gudmundsson and Thiele fastcc but with LP-3 replacing LP-7) of the CMC algorithm of Jerby et al. reduceModel function of the COBRA toolbox In the first set of experiments we applied c-Yeast  as a metric for network consistency testing, in agreement with the theoretical analysis and the discussions above.The results are shown in fastcore algorithm to reconstruct a liver specific metabolic network model from the consistent part of Recon 1  of the fastcore reconstruction appear also in the MBA reconstruction, whereas for the strict liver model the common reactions are 1739 out of 1818 (95%). The two algorithms turned out to use alternative transporters to connect the core reactions: In the standard liver model, 46 out of 59 reactions that are present exclusively in the fastcore reconstruction are transporter reactions or other reactions which are not associated to a specific gene and thus are not sufficiently supported in the core set, whereas in MBA the corresponding numbers are 116 out of 139 reactions. . If not yet included, transporters from the extracellular medium to the cytosol were added to the model . This was necessary as the transport reactions were not sufficiently supported in the core set. This ‘extended’ liver model was able to convert 17/21 metabolites (vs 12/21 metabolites of the non-extended model). The extended liver model was then used to simulate the liver disorders hyperammonemia and hyperglutamenia, which affect the capacity to metabolize dietary amino acids into urea fastcore model faithfully match the experimentally observed ones fastcore can indeed give rise to functionally relevant models.As argued above, the reconstructions obtained by fastcore algorithm to build a cell-type specific murine macrophage model from the consistent part of Recon1bio  a consistent network model of 953 reactions, 831 of which are intracellular reactions. This is a much more compact model than the one obtained with GIMMEp.We also used the fastcore is a generic algorithm for context-specific metabolic network reconstruction from genome-wide metabolic models, and it was motivated by requirements of fast computation and compactness of the output model.fastcore can perform this analysis in a few minutes, whereas for the same problem other algorithms would need hours or days.  Another example where fast computation is imperative is cross-validation. In the current study .(PDF)Click here for additional data file.


Yersinia pestis is a gram-negative bacterium that causes plague, a disease linked historically to the Black Death in Europe during the Middle Ages and to several outbreaks during the modern era. Metabolism in Y. pestis displays remarkable flexibility and robustness, allowing the bacterium to proliferate in both warm-blooded mammalian hosts and cold-blooded insect vectors such as fleas.Y. pestis CO92 and supporting experimental growth and metabolite measurements. The model contains 815 genes, 678 proteins, 963 unique metabolites and 1678 reactions, accurately simulates growth on a range of carbon sources both qualitatively and quantitatively, and identifies gaps in several key biosynthetic pathways and suggests how those gaps might be filled. Furthermore, our model presents hypotheses to explain certain known nutritional requirements characteristic of this strain.Here we report a genome-scale reconstruction and mathematical model of metabolism for Y. pestis continues to be a dangerous threat to human health during modern times. The Y. pestis genome-scale metabolic reconstruction presented here, which has been benchmarked against experimental data and correctly reproduces known phenotypes, provides an in silico platform with which to investigate the metabolism of this important human pathogen. Yersinia pestis is a gram-negative bacterium within the family Enterobacteriaceae that, along with Yersinia pseudotuberculosis and Yersinia enterocolitica, is one of three members of its genus that can cause disease in humans. Y. pestis diverged from Y. pseudotuberculosis only 1,500 - 20,000 years ago, but Y. pestis and Y. pseudotuberculosis diverged from Y. enterocolitica in the more distant past , reasoning that the unidentified gene will be located near other genes involved in fatty acid biosynthesis  through YPO1601 (fabF)), show correlated expression with the genes in this cluster, and be annotated as hypothetical. The best match based on these criteria is the hypothetical gene YPO1594. Consequently, we propose that YPO1594 might possess the ability to carry out the same catalytic function as FabI. Other genes showing correlated expression but located farther away from YPO1597-YPO1601 are YPO3732 and YPO2055.The two gaps in lysine and fatty acid biosynthesis highlighted in this work are significant because model simulations cannot occur unless both gaps are filled. The gap in lysine biosynthesis is noteworthy in that the disrupted gene, YPO0170, encodes a bifunctional enzyme, ArgD, that is involved in arginine biosynthesis as well : specifimelB). The former is the homolog of the putative melibiose symporter YP1470 from Y. pestis 91001, a strain that can utilize melibiose .Pathway analysis and model simulations led to the hypothesis that YP CO92 cannot utilize rhamnose and melibiose due to a missing sink reaction and perturbed gene regulation, respectively, but other possible mechanisms have been advanced. A disruption in gene regulation might contribute to the rhamnose-negative phenotype as well. Specifically, a recent study that compared the sequences of rhamnose fermentation genes in rhamnose-positive and rhamnose-negative strains suggested that a point mutation in the transcriptional activator RhaS might be responsible for the rhamnose-negative phenotype . Experimelibiose , but theglpD that might account for this phenotype: glpD encodes aerobic glycerol 3-phosphate dehydrogenase, an enzyme that is essential for glycerol utilization [glpD [gpsA, but the gpsA homolog in E. coli can only catalyze the transformation from dihydroxyacetone phosphate to glycerol 3-phosphate in an irreversible manner  and, more importantly, the glycerol kinase glpK (YPO0090) have also been disrupted by large deletions and are presumed to be pseudogenes. As with glpD, there is a second annotated glycerol kinase in the YP CO92 genome, YPO3312, but it is unknown whether YPO3312 can duplicate the function of YPO0090.Like rhamnose and melibiose, several hypotheses have been advanced to explain why YP CO92 cannot metabolize glycerol. Analysis of the YP CO92 genome sequence revealed the presence of a 93 bp in-frame deletion in lization , and thion [glpD . There i4Cl; therefore, YP CO92 most likely obtains elemental nitrogen through catabolism of one or more amino acids. Glycine, threonine, and serine can all interconvert. In turn, the breakdown of L-serine by L-serine dehydratase (YPO1771) or L-threonine by L-threonine dehydratase (YPO3896) leads to the direct formation of NH3. Simulations that exclude glycine and threonine from the in silico growth medium (serine is not a component of BCS medium) force nitrogen acquisition to occur through multi-step pathways that are less efficient, leading to slower growth. Providing supplemental nitrogen through sources such as NH4Cl, in contrast, leads to a faster in silico growth rate that varies with the uptake rate of the supplemental source.We saw slow growth for YP CO92 in both experimental measurements and model simulations in the absence of glycine and threonine, and the model predicts that this phenotype stems from insufficient supply of nitrogen. BCS medium does not contain an explicit source of nitrogen such as NHY. pestis strains such as CO92 display methionine auxotrophy [Y. pestis strains such as Pestoides F and Angola, suggesting that it is present in YP CO92 as well but that the associated genes remain to be identified. For these reasons, the model includes a set of non-gene-associated reactions that recycles MTA back into methionine via the methionine salvage pathway, and predicts that these reactions are essential in YP CO92.It is well known that certain xotrophy ,26, and Yersinia genus and to integrate and interrogate -omics data sets generated for these organisms. Integrated models for other pathogens have already provided insight into important phenomena such as drug-target networks [The analyses presented here concerning lysine, fatty acid, amino acid, rhamnose, melibiose, and glycerol metabolism help to illustrate how flux-balance analysis (FBA) of well-curated metabolic models can provide a context for interpreting experimental data. The crucial information provided by FBA is pathway utilization: whereas visual inspection of static pathway diagrams alone can indicate whether a certain pathway is present or absent in an organism, visual inspection cannot indicate whether a certain pathway carries flux and is therefore utilized. In contrast, FBA can provide this insight. For example, YP CO92 appears to have the ability to metabolize rhamnose because a complete set of genes and reactions connects imported rhamnose to central metabolism, but FBA analysis suggests that the absence of L-lactaldehyde degradation prevents this pathway from being utilized. Similarly, the gaps in lysine and fatty acid biosynthesis are readily apparent when genome annotation data is overlaid on static diagrams for the two pathways, but the model highlights the importance of these gaps - that they are essential reactions - since growth simulations cannot take place unless the gaps are filled. Looking forward, we anticipate that this reconstruction will serve as a platform with which to reconstruct the metabolism of other strains within the networks ,35 and hnetworks . SimilarE. coli K12 MG1655 and between YP CO92 and Salmonella enterica serovar Typhimurium LT2. The three bacteria are all closely-related enterobacteria and published reconstructions for both E. coli [S. Typhimurium LT2 [E. coli and S. Typhimurium were carried over to form the initial YP CO92 reconstruction. Homology was determined through one of the following: (1) a Smith-Waterman protein search [Y. pestis CO92 genome using FASTA [E. coli [S. Typhimurium [E. coli as the reference and S. Typhimurium as the query, these cutoffs led to approximately 75% overlap between the two models and a 2.5% false positive rate, defined here as the number of E. coli genes predicted to have homologs in S. Typhimurium but that did not carry over after manual curation.The YP CO92 model iPC815 was reconstructed via a four-step process ,38. The n search  with a qn search ; (2) a Dng FASTA ; and (3)ng FASTA . A gene E. coli or S. Typhimurium models catalyzed by gene 1 AND gene 2 was ported to the YP CO92 model only if YP CO92 was deemed to have homologs for both gene 1 and gene 2. If neither or only one of the two genes was present, the reaction was not considered shared and was not ported.With the final list of shared metabolic genes, we returned to the previously published metabolic reconstructions, this time focusing on the potential for shared reactions instead of shared genes. A reaction was considered shared if it had a complete gene-protein-reaction association (GPR) in the YP CO92 model. A complete GPR is one in which all genes required to catalyze a particular reaction are present. For example, a GPR in the E. coli and Salmonella models were also added to the YP CO92 model, completing the draft YP CO92 metabolic reconstruction. Reactions without gene-protein associations ("orphan" reactions) were not ported.Reactions known to be spontaneous in both the Yersinia genus. We used the PATRIC [The second step was model refinement. We searched approximately 2700 publications in PubMed using the keywords "Yersinia" and "metab*" to collect experimental data for as many genes in the draft reconstruction as possible. Our search focused on the YP CO92 strain in particular, but we also noted any relevant data from any species within the e PATRIC , KEGG [1e PATRIC , and othY. pestis 91001 metabolic model [Y. pestis at 27-28°C [Y. pestis at 37°C, but we assume that this distribution also holds at 37°C based on data from Y. enterocolitica at 37°C [Y. pestis KIM218, another biovar Orientalis strain, galactose is present as one of the monomer units in the core oligosaccharide at 25°C but not 37°C [Y. pestis CO92 LPS does not contain O-antigen at either temperature [The third step was to convert the refined reconstruction into a mathematical format suitable for computation, the stoichiometric matrix (S-matrix), and to develop explicit mathematical equations for the biomass objective functions (BOF). The model contains two BOFs that simulate biomass formation at 25-28°C and 37°C. Both are derived from similar BOFs constructed for the published  27-28°C ,42. We c at 37°C . Accordinot 37°C . Moreovenot 37°C ,17. The perature .in silico production of biomass precursor metabolites were filled by identifying and adding to the model enzymes with the potential to catalyze the missing reaction(s). These candidates were gleaned from primary literature, genome annotation, and database sources such as KEGG and PATRIC. A similar pathway analysis procedure was used to ensure that the model reproduced known YP CO92 amino acid auxotrophies [The fourth step was model evaluation and debugging. Critical gaps preventing trophies .m by n matrix containing m metabolites and n reactions. The relationship between reactions and the concentration time derivatives is:The model (S-matrix) was implemented in Matlab and flux balance analysis (FBA) performed using the COBRA Toolbox and glpk solver . The S-mx and v denote the vector of metabolite concentrations and reaction fluxes, respectively. Steady-state FBA is performed by solving the following linear optimization problem:where c) is a zero-vector except for one element that has a value of one and corresponds to the reaction to be optimized, which in the model is one of the two BOFs. Model constraints during simulations were set by either experimental data collected as part of this study  and upper (ub) bounds. The optimization vector  of 0.1. Both the first and second cultures contained 0.2% potassium gluconate as a carbon source [600 of ~3.0. The third culture was obtained from bacteria grown overnight, washed twice with 33 mM potassium phosphate buffer pH 7.0, and inoculated into fresh media containing one of the eleven tested carbon sources to an initial OD600 of 0.05. Aliquots from cultures were taken at 0, 2, 4, 6, 8 and 10 hours time points to measure OD600 and to prepare samples for metabolite identification and uptake/secretion measurements. These samples were obtained by centrifugation of 1.5 ml of bacterial culture at 10,000 rpm for 2 minutes at 4°C followed by filtration of the supernatants through a 0.2 μm low binding polyethersulfone membrane filter . Samples were then immediately frozen and stored at -80°C.S medium  in whichS medium . The medn source , and the2O) in 5-mm NMR tubes. DSS is used as an internal standard and to provide a 1H chemical shift reference at δ 0.00 ppm. 1H NMR spectra were acquired on a Varian INOVA-600 MHz NMR spectrometer  at 298 K, using a triple resonance 5-mm HCN salt-tolerant cold probe. A one-dimensional NOE pulse sequence adapted from the two-dimensional Varian tnnoesy was used. For each sample, 96 transients were collected into 64 K data points using a spectral width of 7225.4 Hz with a relaxation delay of 1.0 s, an acquisition time of 4.00 s, and a mixing time of 100 ms. Spectra were processed using Chenomx 6.1. A 0.5-Hz line-broadening function was applied to all spectra prior to Fourier Transformation (FT) and baseline correction. The profiler module of Chenomx was used to identify and quantify metabolites.540 μL of spent media extracts were added to 60 μL of 5 mM 2,2-dimethyl-2-silapentane-5-sulfonate (DSS) in 99.9% deuterium oxide . E. Biomass objective functions. F. Comparison between iPC815 and the YP 91001 model of Navid, et al. G. Growth simulations on different carbon sources. H. Growth simulations on different nitrogen sources. I. Growth simulations on different phosphorus sources. J. Growth simulations on different sulfur sources. K. Individual components in BCS growth medium. L. Substrate uptake and secretion rates used to constrain model simulations.Click here for fileE. coli and Salmonella Typhimurium LT2 that were predicted to be essential by the E. coli iAF1260 model [Salmonella Typhimurium LT2 consensus model [E. coli only . C. LisClick here for fileThe iPC815 model in SBML format.Click here for file


Mycobacterium tuberculosis, the causative agent of tuberculosis (TB), to successfully infect human hosts. Adaptations allow the organism to evade the host immune responses during acute infections and persist for an extended period of time during the latent infectious stage. In latently infected individuals, estimated to include one-third of the human population, the organism exists in a variety of metabolic states, which impedes the development of a simple strategy for controlling or eradicating this disease. Direct knowledge of the metabolic states of M. tuberculosis in patients would aid in the management of the disease as well as in forming the basis for developing new drugs and designing more efficacious drug cocktails. Here, we propose an in silico approach to create state-specific models based on readily available gene expression data. The coupling of differential gene expression data with a metabolic network model allowed us to characterize the metabolic adaptations of M. tuberculosis H37Rv to hypoxia. Given the microarray data for the alterations in gene expression, our model predicted reduced oxygen uptake, ATP production changes, and a global change from an oxidative to a reductive tricarboxylic acid (TCA) program. Alterations in the biomass composition indicated an increase in the cell wall metabolites required for cell-wall growth, as well as heightened accumulation of triacylglycerol in preparation for a low-nutrient, low metabolic activity life style. In contrast, the gene expression program in the deletion mutant of dosR, which encodes the immediate hypoxic response regulator, failed to adapt to low-oxygen stress. Our predictions were compatible with recent experimental observations of M. tuberculosis activity under hypoxic and anaerobic conditions. Importantly, alterations in the flow and accumulation of a particular metabolite were not necessarily directly linked to differential gene expression of the enzymes catalyzing the related metabolic reactions.The ability to adapt to different conditions is key for  Mycobacterium tuberculosis latently infects one-third of the human population and is responsible for millions of deaths worldwide every year. The ability of the pathogen to persist in the human population stems from its capacity to adapt to host-induced stresses and adjust its metabolism to different host environments. We have developed a novel model to interpret M. tuberculosis H37Rv metabolic adjustment by combining gene transcription data with a genome-scale metabolic network model. Using our model, we were able to identify the changes in the metabolic program associated with hypoxia, predict phenotypic change, and determine the critical metabolic enzymes and pathways that are required for pathogen survival. In particular, we predicted the switch in the tricarboxylic acid cycle from an oxidative to a reductive path. The altered importance of different metabolites and pathways under hypoxic conditions may provide guidance for designing novel, adjuvant drug therapies for clearing persistent and latent infections. Mycobacterium tuberculosis, the causative agent of tuberculosis (TB), caused 8.8 million new TB cases and resulted in the death of 1.5 million people worldwide in 2010 M. tuberculosisin vitro persister models can be created based on acid stress, hypoxic stress, and carbon starvation in silico approach to create state-specific models based on readily available gene expression data. The coupling of differential gene expression data with a metabolic network model allows us to metabolically characterize any TB disease state, provided the corresponding microarray data are available. We applied this technique to characterize the metabolic adaptations of M. tuberculosis in response to hypoxia.Targeting different aspects of metabolism in the latent state is a viable therapeutic strategy that is supported by evidence of differential metabolic activity among several dormant and latent states of M. tuberculosisin vitro persistence models dosR gene, which encodes a transcription factor essential for the hypoxic persistence of mycobacteria M. tuberculosis H37Rv and its ΔdosR deletion mutant compared to normoxia dosR regulator to the hypoxic response, reviewing the list of differentially expressed genes provides a limited view of what the dosR-initiated gene expression pattern entails in terms of M. tuberculosis metabolic adaptation to hypoxia.Similar to the introduction of nitric oxide M. tuberculosis are composed of hundreds of distinct but interconnected chemical reactions, each processing particular metabolites that, taken together, ultimately allow the cell to function and grow M. tuberculosis have been used to identify genes essential for growth in vitro, ex vivo, and in vivo host conditions A systems-level understanding of metabolism requires the identification and reassembly of the constituent components  and methods to analyze metabolic phenotypes Gene expression data captures the transcriptional state of a cell in a particular biological state and it is challenging to interpret this partial information with respect to an altered metabolic program. The strength of a transcriptional approach is that we can capture a specific snapshot of the cell without elaborating the underlying signaling and gene regulatory networks. The weakness is that the transcriptional state is not a direct readout of the metabolic enzyme concentrations that perform metabolic reactions. Efforts to connect transcriptional levels to metabolic activity in network models of metabolism have focused on correlating absolute expression levels to metabolite flows M. tuberculosis H37Rv under hypoxic conditions dosR deletion mutant, indicating that the presence of the dosR gene was essential for the pathogen to adapt to hypoxia M. tuberculosisM. tuberculosis to hypoxia Thus, based only on the differential gene expression data from 13C flux changes upon removal of the gcn4 global regulator gene under histidine starvation conditions M. tuberculosis in human granulomas is partly due to its ability to adapt to a condition of low oxygen availability dosRM. tuberculosis in response to moving from the reference state of normoxia to an altered hypoxic state as defined by its transcriptional state. We used the iNJ661m metabolic network of M. tuberculosis H37Rv iNJ661 network iNJ661, e.g., in the methylcitrate cycle pathway. We integrated this network with microarray data that included gene expression ratios for both induced and repressed mRNA gene transcription for wild type M. tuberculosis H37Rv, as well as for the ΔdosR deletion mutant, associated with the transfer from normoxic air to hypoxic nitrogen gas with 0.2% oxygen (1.5 mm Hg) dosR gene does not directly encode an enzyme in the metabolic network, we assumed that the normoxic metabolic state was equivalent between the two strains, and thus we used the same network for the normoxic simulation. Using the metabolic network/gene-expression integration model, we predicted hypoxia-induced changes in important phenotypes , biomass composition, and fluxes through the central carbon metabolism for both wild type M. tuberculosis H37Rv and its ΔdosR deletion mutant. We used the observed changes in experimental phenotypes to qualitatively validate and indicate the utility of the proposed method The persistence of M. tuberculosis H37Rv and the corresponding ΔdosR mutant under normoxia and hypoxia 2 hours after switching to a condition of 0.2% oxygen. The oxygen uptake rates in dosR strain differed substantially from the wild type predictions, suggesting that the deletion mutant was not able to modulate its metabolism to adapt to hypoxic conditions. In particular, the wild type normalized oxygen uptake rate was considerably lower than in the ΔdosR strain under hypoxic conditions, indicating that the deletion mutant was less able to adapt to the low-oxygen stress than the wild type per unit biomass. Because the deletion mutant is not able to grow efficiently under hypoxia, its overall ATP production rate is relatively lower than that for the wild type . M. tuberculosis cell concentrations during a 200-day growth period in which oxygen was depleted around day five, marking the onset of hypoxic growth in silico-modeled cell concentrations of the two strains in the normoxic (days 0–5) and early hypoxic (days 5–60) stages of growth, and allows us, by inspection, to qualitatively estimate the time periods during which our model could capture the growth pattern of M. tuberculosis. The results for the wild type strain indicated that the model successfully reproduced the growth of this strain up to day 60. After this period, additional cellular reprogramming in response to extended hypoxia occurs dosR and represents further biological and metabolic adaptations not modeled here. The model results for the ΔdosR mutant provided relatively accurate prediction for the first 12 days. After this initial period, the model begins to break down, presumably due to additional biological and metabolic factors not modeled by the initial dosR gene reprogramming response.The inability of the Δin silico experiments to gauge the influence of fluctuations in the gene expression data and determine whether the metabolic predictions were specific to the expression data or the metabolic network per se.To ascertain the robustness and specificity of our approach, we conducted To address fluctuations in the data, we created simulated gene expression data sets where all differential gene expression values were sampled from their corresponding normal distribution defined by their observed means and standard deviations M. tuberculosis H37Rv and the ΔdosR mutant. The prediction qualitatively indicated whether hypoxia induced an increase, decrease, or no change in each metabolite's biomass composition. dosR mutant, they were similar to the wild type strain. However, the number of metabolites that were predicted to change for ΔdosR was slightly smaller than that for the wild type one (42 vs. 51), and the biomass compositions of two MYC-related metabolites that increased under hypoxia in the wild type strain actually decreased in ΔdosR. These results implied that the dosR gene played a role in the modulation of biomass composition, but not as a sole regulator of biomass accumulation. To further test the ability of our approach to alter biomass composition, we qualitatively predicted the biomass changes of Mycobacterium bovis upon transfer from a fast chemostat growth condition Through the model interpretation of altered gene expression via the metabolic network, we predicted hypoxia-induced changes in biomass composition in both wild type M. tuberculosis H37Rv and its ΔdosR deletion mutant in more detail. dosR strain indicated only a slight overall decrease in these fluxes. Thus, as captured by our integrated metabolic network model, without the dosR gene the organism fails to adapt its metabolism to cope with low-oxygen stress. Boshoff and coworkers recently confirmed the importance of fermentation in latent hypoxic M. tuberculosis by analyzing metabolite isotopes in the central carbon metabolism to identify the usage of the reductive TCA cycle under anaerobic conditions Given that the metabolic network model provides detailed information of all metabolic fluxes, we examined the resulting hypoxia-induced changes associated with the carbon central metabolism of wild type + efflux was six times larger than the normoxic value of 9.1 millimoles per gram of dry weight of the organism (mmol/gDW). This was in qualitative agreement with experimentally observed succinate accumulation and acidification in the medium in which M. tuberculosis H37Rv is cultured under hypoxia The altered flux distribution in the TCA cycle was also accompanied by altered extracellular secretion rates. In particular, the increased flux associated with succinate production at the bottom of the TCA cycle in M. tuberculosis. We further noted that due to the increased secretion of succinate mentioned above, the dctA gene that encodes for the succinate transporter was also predicted to become essential under hypoxia. This suggests that disruption of these pathways could prevent hypoxic adaptation and render the pathogen more susceptible to alternative antibiotic treatments.We further characterized the altered metabolic state of the wild type strain associated with hypoxia by calculating which metabolic genes were essential for adaptation to hypoxic conditions. We defined these genes as those predicted to be nonessential under normoxia, i.e., removing them from the metabolic network did not prevent the organism from accumulating biomass, but became essential under hypoxia. 2-fixating microbes utilize the reductive TCA cycle M. tuberculosis grown in glucose-supplemented Middlebrook 7H9 M. tuberculosis oxidizes glucose and glycerol to carbon dioxide via glycolysis and the TCA cycle. At the same time, the oxidized forms of the redox intermediaries are converted to reduced forms in order to maintain chemical balance. Thus, the cell converts nicotinamide adenine dinucleotide (NAD), nicotinamide adenine dinucleotide phosphate (NADP), and flavin adenine dinucleotide (FAD) to the reduced forms of NADH, NADPH, and FADH2, respectively. Under normoxia, the cell maintains this balance by utilizing the constant supply of oxygen from the environment. Under hypoxia, to maintain balance of the redox intermediaries M. tuberculosis must decrease the reduction of NAD, NADP, or FAD and preferentially select pathways that convert the reduced forms back to the oxidized forms. Thus, in our model, hypoxic M. tuberculosis preferred glucose utilization because it reduces less NAD to NADH as compared to glycerol utilization and, as shown in Many COM. tuberculosis and calculate its metabolic adaptations based only on differential gene expression data. Importantly, we derived our condition-specific metabolic states from gene expression data, which are widely available, and not protein abundances, which are rarely available.We developed a novel approach to interpret changes in gene expressions in terms of an altered metabolic program. Given a known reference state, we used changes in gene expression associated with a new state to construct a corresponding condition-specific metabolic state. This state captured the metabolic adaptations that the organism executed through an altered gene expression program. We modeled this adaptation via a metabolic network that characterizes nutrient uptake adjustments, alterations in preference of metabolic pathways, and changes in biomass composition. We implemented this approach to model the immediate change from aerobic to anaerobic conditions for There are a number of related methods that use gene expression data to modify the flow of metabolites in a metabolic network. These methods differ in their implementation of how transcription levels of different genes are connected to the reaction fluxes associated with the corresponding translated protein enzymes catalyzing the reactions. All methods deal differently with the general lack of a perfect correlation between transcriptional levels and protein concentrations and, hence, the lack of a direct one-to-one correspondence between expression values and reaction fluxes Our approach combined different aspects of the above methods by using the concepts of a reference and a treatment condition. For a treatment condition, our assumption was that an existing metabolic network could generate a set of reference fluxes characteristic of the reference condition and that the mRNA transcription data was reflective of the differential gene expression between the reference and treatment conditions. We used the relative expression changes to introduce soft constraints and limits on the relative flux changes, avoiding the introduction of arbitrary thresholds at the price of a more complex optimization problem. Regardless of whether an enzyme functions in either parallel or serial reaction paths in the metabolic network, we captured the notion that if there was a significant change in the expression level of a metabolic gene, it was very likely associated with an attempt to change the related reaction flux, although such a change is not required. In addition, we allowed the biomass composition to change in response to the treatment condition.The advantage of this procedure was the general ability to account for all individual gene expression alterations and provide a detailed interpretation of the metabolic adjustments that capture gradual flux increases or decreases, without using any arbitrary threshold or assuming any correlation between absolute gene expression data and the upper limits of reaction fluxes across different genes under each condition. The disadvantages were in the formulation of a more complex optimization problem and the requirement of the availability of an existing metabolic network for the reference condition and the corresponding differential gene expression data between this reference condition and the treatment condition of interest.Saccharomyces cerevisiae (yeast) and prokaryotic bacteria. In yeast, the observed correlations between changes in mRNA level and protein abundance ranged from modest correlations between 0.2 and 0.5 S. cerevisiae growing under steady state conditions shows a higher correlation between mRNA levels and protein abundance than under transient conditions Escherichia coli with a mutation in the pgi gene, transcription levels and corresponding protein abundance of the central metabolism genes changed in a correlated manner, with a coefficient of 0.81 S. cerevisiae and Haemophilus influenzae, respectively.In our approach, we made use of differential gene expression data of the changes in the transcriptional program between a well-defined reference condition and a perturbed state. Because both mRNAs and proteins are under control of several different, but possibly correlated, processes, such as transcriptional and post-transcriptional control, degradation, ribosomal capacity, availability of the appropriate metabolites, and energy levels, the relative mRNA level of a gene is not necessarily directly proportional to the concentration of its corresponding protein ref to an altered condition new, the limit of the corresponding normalized reaction flux catalyzed by the corresponding protein was bound by the ratio of [protein]new/[protein]ref. We approximated this ratio by [mRNA]new/[mRNA]ref+L, where the mRNA levels are taken from microarray experiments and L indicates a slack variable that allows for possible violation of the assumption. The method further assumes that the reference state is associated with a functioning metabolic network description that allows for steady state flux through its metabolite reactions and biomass accumulation. In addition, we assumed that the new state captured by the altered gene expression levels could also be described by a steady state approximation. This makes our model suitable for interpreting gene expression data that describes a transition from one stable condition to another one. In the case studied here, the immediate response of M. tuberculosis H37Rv to hypoxia, the model adaptations appear to be reliable for at least seven days after the insult. Longer-term adaptations that are dependent upon different gene expression programs, e.g., as in the extended hypoxic response, would have to be modeled by data directly associated with that state.Thus, a formulation that uses a relative change correlation from one steady state to another could provide a practical approach under certain circumstances without requiring full knowledge of all possible regulatory mechanisms that govern the relationship between mRNA level and protein abundance. Our approach was based on the assumption that if the transcriptional mRNA level for a gene changes from a reference in vitro environment, where careful characterization of metabolism is possible, to an in vivo environment, where experimental data on metabolism would be more difficult to obtain, could be modeled based solely on differential gene expression measurements. Conversely, the metabolic model interpretation would not be suitable for creating tissue- or cell-specific metabolic networks based on the current overall human metabolic network reconstruction Metabolic adaptations associated with changing from an M. tuberculosis H37Rv to hypoxia based on an existing metabolic network for normoxic conditions and relative gene expression changes under hypoxic conditions highlighted the type and amount of information that could be extracted from our modeling approach. Phenotypic effects of the hypoxia-induced gene expression program due to low-oxygen stress included adjusting the metabolism to a lower rate of oxygen uptake, lowering ATP utilization, altering biomass composition, increasing cell wall production, engaging the glucose-processing glycolysis pathway, and accommodating anaerobic respiration by using the reductive side of the TCA cycle. The dosR gene controlled this gene program and the gene expression profile of the deletion mutant ΔdosR revealed that it did not accommodate these metabolic adaptations. The mutant was less fit and displayed a substantially reduced growth rate under these conditions compared to the wild type strain. These predictions are supported by observations from previous experimental studies in vitro-based work presented here, our approach is ideally suited to elucidate the metabolic responses of M. tuberculosis to other stressors, such as nitric oxide The case study of modeling the immediate metabolic adaptation of in vitro iNJ661m metabolic network of M. tuberculosis H37Rv iNJ661 network iNJ661 model was augmented with reactions and metabolites involved in biotin synthesis, fumarate and succinate synthesis, and the methylcitrate cycle and minor changes to the biomass function were made. The iNJ661m network contains 663 genes, 838 metabolites, and 1,049 reactions and correctly predicts growth rates of normoxic H37Rv in different media. We used microarray data measured in triplicate from Park et al. M. tuberculosis H37Rv and the ΔdosR deletion mutant We used the i under an FBA-predicted optimal biomass production rate. Further, we solved an optimization problem to obtain a set of reference fluxes i,refx for each reaction i normalized by the optimal biomass production rate  i, the expression ratio of this gene was assigned to the reaction ratio iR. If several genes were jointly required for a reaction i to take place, the reaction ratio iR was assigned to the geometric mean of the expression ratios of the genes. This formulation captured the condition that all reaction ratios were required. If any one of several genes was sufficient for a reaction i to occur, the reaction ratio iR was assigned to the arithmetic mean of the expression ratios of the genes. This formulation captured the condition that, at a minimum, any one reaction ratio was required. If a gene (or genes) was associated with several reactions, we used the above rules to construct a reaction ratio and assign this ratio to the overall normalized flux of these reactions.We associated gene expression ratios with reaction ratios according to the gene-protein-reaction relations in the metabolic network. If only one gene was associated with a metabolic reaction i,refx and iR obtained above, we developed a set of constraints to incorporate the effects of altered gene expression on the metabolic network . We summarized these constraints in Given the values for i was down-regulated (iR<1), we attempted to decrease the absolute value for ix, the normalized flux through the reaction, to the level of iR|i,refx| (the converse holds for up-regulated genes). To allow for possible violations of the corresponding constraints, we introduced non-negative slack variables iL to modulate the flux level constraints.Constraints 1 and 2 describe how gene expression changes could affect reaction fluxes in our model, with the special cases of reversible and irreversible reaction fluxes treated more fully in Supplemental m,newc. Constraint 3 represents the mass balance of each metabolite, where miS denotes the stoichiometric coefficient for metabolite m in reaction i, m,refc represents the original coefficient of this metabolite in the biomass objective function, and the non-negative variables minc for each metabolite  and then minimized the modifications in the biomass objective function  using the COBRA toolbox We performed 500 Monte Carlo simulations to calculate the distribution of normalized oxygen uptake rates of the wild type strain based on experimentally determined gene expression fluctuations. In each simulation, we randomly generated an expression value for each gene based on its assumed normal distribution with mean and standard deviation corresponding to the experimental wild type values We also performed another set of 500 simulations to calculate the oxygen uptake rates for randomized gene expression data sets. In these simulations, we assigned an expression value for each gene by randomly selecting a value from the experimental data set M. tuberculosis H37Rv and the ΔdosR deletion mutant under normoxic (days 0–5) and early hypoxic (days 5–60) conditions to compare the model predictions with experimentally determined growth characteristics X indicates the cell concentration of M. tuberculosis, t denotes time in days, and μ and d represent biomass production rate and lysis rate, respectively, in units of h−1. The value for μ differed between the strains of M. tuberculosis (wild type and ΔdosR) under the two growth conditions (normoxic and hypoxic), while we assigned d one uniform value and assumed that this value was the same for both strains. The parameters of this equation were determined from matching the calculated growth of the wild type strain to the experimental values. We first performed an FBA of the iNJ661m network wt strain's normoxic n biomass production rate wt,nμ and then determined the value of d by reproducing the experimental normoxic cell concentrations. Given d, we further matched the calculated cell concentrations under hypoxia of the wild type to determine the hypoxic h biomass production rate wt,hμ. To estimate the growth rate of the ΔdosR mutant, we assumed an inverse proportionality between normalized oxygen uptake rate and biomass production rate. Thus, we set the normoxic biomass production rate μdosR,nΔ to be equal to that of the wild type strain wt,nμ, and obtained the hypoxic rate of the mutant μdosR,hΔ via the following equation:wt,hO and OdosR,hΔ denote the calculated normalized oxygen uptakes of the wild type and ΔdosR strains under hypoxia, respectively. Supplemental μ and lysis rate d.We calculated the cell concentrations of wild type We identified a metabolic gene as being essential for adaptation to hypoxia if we predicted that this gene was nonessential under normoxia but essential under hypoxia. To determine gene essentiality under normoxia, we performed an FBA to predict the biomass production rate for the wild type strain and for each individual metabolic gene deletion mutant. We modeled deletion mutants by removing all reaction(s) related to the deleted gene. If the ratio for the biomass production rate of a single-gene deletion mutant to wild type was greater than a threshold (0.10), we categorized the metabolic gene as nonessential under normoxia. Similarly, if the ratio for the biomass production rate calculated under hypoxia (as approximated in Protocol S1MATLAB-formatted models of metabolism for M. tuberculosis HR37v and its ΔdosR deletion mutant.(ZIP)Click here for additional data file.Table S1Biomass production and cellular lysis rates for simulating growth of wild type M. tuberculosis H37Rv and the ΔdosR deletion mutant under normoxia and hypoxia.(PDF)Click here for additional data file.Table S2Predictions of the hypoxia-induced changes in biomass composition of wild type M. tuberculosis H37Rv and the ΔdosR deletion mutant. Normoxic coefficients were set to be the same as the original coefficients of the corresponding metabolites in the biomass function of the iNJ661m metabolic network dosR deletion mutant strain) of Mycobacterium tuberculosis H37Rv under hypoxia M. tuberculosis H37Rv upon exposure to hypoxia. “Increase” (or “Decrease”) indicated that a predicted hypoxic coefficient was greater  than the corresponding normoxic coefficient.(PDF)Click here for additional data file.Text S1Predicting metabolic fluxes in yeast.(PDF)Click here for additional data file.Text S2Biomass change of M. bovis under slow growth conditions.(PDF)Click here for additional data file.Text S3Generation of a reference flux distribution in Step I.(PDF)Click here for additional data file.Text S4Additional implementation details for the constraints given in Step III.(PDF)Click here for additional data file.Text S5Detailed descriptions for solving the optimization problems outlined in Step IV.(PDF)Click here for additional data file.


Constraint-based computational approaches, such as flux balance analysis (FBA), have proven successful in modeling genome-level metabolic behavior for conditions where a set of simple cellular objectives can be clearly articulated. Recently, the necessity to expand the current range of constraint-based methods to incorporate high-throughput experimental data has been acknowledged by the proposal of several methods. However, these methods have rarely been used to address cellular metabolic responses to some relevant perturbations such as antimicrobial or temperature-induced stress. Here, we present a new method for combining gene-expression data with FBA (GX-FBA) that allows modeling of genome-level metabolic response to a broad range of environmental perturbations within a constraint-based framework. The method uses mRNA expression data to guide hierarchical regulation of cellular metabolism subject to the interconnectivity of the metabolic network.Yersinia pestis and analyzed its metabolic response to (i) variations in temperature known to induce virulence, and (ii) antibiotic stress. Without imposition of any a priori behavioral constraints, our results show strong agreement with reported phenotypes. Our analyses also lead to novel insights into how Y. pestis uses metabolic adjustments to counter different forms of stress.We applied GX-FBA to a genome-scale model of metabolism in the gram negative bacterium in silico evaluation of cellular goals under different conditions and can be used for a variety of analyses such as identification of potential drug targets and their action.Comparisons of GX-FBA predicted metabolic states with fluxomic measurements and different reported post-stress phenotypes suggest that mass conservation constraints and network connectivity can be an effective representative of metabolic flux regulation in constraint-based models. We believe that our approach will be of aid in the  The recent progress in genome sequencing techniques has led to the development of genome-level models of metabolism that have been analyzed using constraint-based approaches, such as flux-balance analysis (FBA) ,2. The sAccording to the central dogma of biology, information flows from DNA to mRNA and ultimately to enzymes which catalyze and regulate various cellular functions. Hence, one might envision a fully “hierarchical” regulation of metabolism where expression levels of mRNA correlate directly with the amount of enzymes and thus with the flux through associated reactions. For some conditions, this simplified assumption can be used for the purpose of modeling metabolic activity . HoweverThe varying role of hierarchical regulation for network reactions has limited the utilization of gene-expression data to improve predictions of genome-scale metabolic models. The earliest attempt at imposing transcriptional regulation on constraint-based models was conducted by Palsson and coworkers who developed regulatory flux-balance analysis (rFBA) -25 whereLater, Nielsen and coworkers  further Another method dubbed E-Flux  uses gena priori user-defined objective function and also do not fully make use of the predictions of FBA models; thus, a significant portion of the available data is not fully utilized.The introduction of steady-state regulatory flux balance analysis (SR-FBA)  which utH), moderately expressed or lowly expressed (RL). iMAT utilizes MILP to identify a possible steady-state flux distribution among those that maximize the number of reactions with predicted flux consistent with the gene-expression data as well as the model’s stoichiometric and thermodynamic constraints. Thus, the goal of iMAT is to maximize the sum of the number of reactions in RL that carry a flux of zero, and the number of reactions in RH that carry a flux greater than an arbitrarily chosen threshold , we consider dr a percentage flux change from condition 1 to condition 2. For conditions where both x and y are zero, we define dr=0. Thus, we may calculate the average (per reaction) percentage error in GX-FBA predicted flux by calculatingwhere where the sum is over the N reactions for which there is experimental flux data.To gauge the effect of degeneracy in the FBA optimal flux state (condition (1) above) on the set of GX-FBA solutions, we used the following approach which is a variation on an effective random sampling method previously suggested :*FBA.(1) Identify the optimal value of the FBA objective function, Zi, use flux variability analysis .(4) Randomly select a reaction from νi = νi*.(5) Calculate the FBA optimal flux state subject to GX-FBA, the maximum and minimum biomass production flux, as well as agreement with fluxomic measurements.(6) Calculate the GX-FBA optimal flux state using the FBA optimal state in (5). From the resulting flux profile, we determine the value of Z(7) Repeat from step (4).For each of our simulations we sampled 25000 different FBA optimal flux states.We argue that to properly analyze mRNA experiments for their systems-level impact on cellular metabolism, it is necessary to couple these experimental data with a theoretical framework that takes metabolic network connectivity and mass conservation into account. In contrast to the expression activity of a single gene, the metabolic activity of a reaction not only depends on the expression of the enzyme, but also on the abundance of its substrates and products. Thus, the activity of a single reaction is conditional on the structure of the metabolic network as well as the network’s global activity pattern.It has previously been observed experimentally that gene-expression profiles provide qualitative descriptions of metabolic flux activity ,54. HoweBy maximizing the qualitative and quantitative agreement between flux profile and gene-expression pattern subject to metabolic feasibility, we allow the relationship between transcription level and flux to span the full range of possible coupling strengths. To this end, we have developed a new constraint-based approach for combining gene-expression data and metabolic flux analysis, GX-FBA, which explicitly takes mass conservation and the connectivity of a metabolic network into account (see Methods). A simple example of how GX-FBA implements regulation via gene-expression is presented in Figure In Figure 2. Figure As shown in Figure 2 and malate. Figure In Figure not controlling the final flux activity pattern. Overall, the predicted GX-FBA solution for this sample problem agrees with expected metabolic behavior when oxygen concentration in the medium is reduced.Finally, a direct consequence of the network connectivity is that down-regulation of reaction 3 is incommensurate with up-regulation of reaction 7. Since the GX-FBA flux solution corresponds to the activity pattern maximizing its objective function and reaction 7 has a greater shadow price (positive contribution to the objective function) than reaction 3, reaction 7 is up-regulated while the flux for reaction 3 remains the same. This serves as an example of hierarchical regulation through the gene-expression dictum the number of up and down regulated reactions, not taking into account the magnitude of change in expression level. Instead, GX-FBA aims to maximize the correlation between differential changes in gene-expression and reaction fluxes, explicitly taking the level of differential gene-expression into account. Second, GX-FBA does not use a binary criterion for pattern maximization whereby the metabolic flux of reactions corresponding to highly expressed genes must exceed an arbitrarily chosen threshold value and that of lowly expressed genes should be zero [pattern of either a single experiment or the consensus pattern from a compendium of experiments, thus forgoing the introduction of an objective function for any of the activity states.It is immediately evident that GX-FBA shares certain features with the iMAT method, in particular, the use of gene-expression data to constrain the overall metabolic activity pattern and absence of a need to predetermine required cellular functionalities. However, in the following we will point out three significant differences between the two approaches. First, iMAT maximizes  be zero . Third, S. cerevisiae under different nutritional environments. The experimental flux measurements and microarray data are from Daran-Lapujade et al. [In order to validate GX-FBA’s utility for predicting changes in flux activity based on gene-expression data, we used the method to examine the metabolic behavior of e et al. . The mete et al.  that wase et al. .d) in each reaction’s flux activity as the eukaryote transitions between different growth conditions (see Methods). This calculation was repeated for the GX-FBA predicted results using wild-type FBA flux values as reference state. The average percentage error (e) (see Methods) between measured and predicted flux magnitude changes was calculated, finding on average that e = 21%. Furthermore, to assess the capability of GX-FBA to accurately identify metabolically active reactions after a perturbation, we compared the results of our predictions with experimental measurements and calculated the average precision (0.88) and recall (0.99) values , making it necessary to evaluate the possible impact of degenerate optimal FBA flux states  on the GA Figure b. We fouYP is one of the most prolific killer organisms of all time. Conservative estimates stipulate that 200 million people have been victims of bubonic plague in various pandemics throughout human history . There iWe used two available mRNA expression data sets for YP’s response to temperature change, one for strain 201  and one 2+ cation in the medium. Gene-expression data for Strain 201 were derived from bacteria grown in a calcium-poor environment while the data for strain KIM5 are from samples grown in a Ca2+-rich (4mM) medium. This single difference results in phenotypic variations that can explain the observed dissimilarities between the gene-expression results. The cellular behavior dubbed ‘low-calcium response’ (LCR) refers to the observation that following the transition from 26 to 37°C and in the absence of Ca2+ , viruleronments . Start oUsing the available gene-expression data and GX-FBA, we analyzed the metabolic underpinnings for the observed phenotypic behaviors. Computational simulations for strain 201 predict a significant decrease in flux for biomass production upon transition from 26°C to 37°C, while simulations of strain KIM5 find the flux of biomass production at 37°C is nearly equal to that of 26°C . In case of arginine, the up regulated pathways point to subsequent conversion of this amino acid to the metabolically more tractable compounds succinate and glutamate, and thus the process is clearly linked to the global carbon and nitrogen metabolism.In addition to being used as a carbon source, another possible reason for increased production of arginine could be the need to boost production of ornithine, which is a precursor for production of polyamines. Polyamines are cationic organic compounds which modulate DNA, RNA and protein synthesis and are essential for cellular growth -74: in YoxyR and katG genes in E. coli, which are responsible for the induction of catalase and peroxidase detoxifying enzymes [Furthermore, it is known that polyamines up-regulate the  enzymes . GX-FBA  enzymes . The cat enzymes . Thus th enzymes . Thus, iIn order to determine the primary causes for the reduced flux of biomass production in strain 201, we systematically analyzed the effect of the mRNA expression value of each individual gene. Although we observe reduced activity in energy metabolism, particularly oxidative phosphorylation . Interestingly, GX-FBA predicts that after treatment with Streptomycin, production of another set of essential amino acids  is increased. Given the reduced growth yield of the bacteria, these amino acids must serve an alternate purpose than inclusion in microbial biomass. Elucidating this role might aid in enhancing the bactericidal capacity of Streptomycin.Upon interaction with Chloramphenicol, the activities of nearly all of YP pathways that are crucial for synthesis of biomass, including glycolysis, urea cycle, and pathways for production of fatty acids and lipopolysaccharides, are reduced.Interestingly, our simulations show that following interaction with both antibiotics, pathways of riboflavin metabolism in YP are enhanced. Some early studies -86 have As can be seen from Figures de novo purine biosynthesis has been attributed to the lowered rate of growth [de novo biosynthesis of purines consumes significant amounts of energy. Down-regulation of this pathway could be part of a cell-wide energy-saving strategy.In YP, it has been shown that following a transition from ambient temperature to 37°C and a calcium-deficient medium, the adenylate energy charge of the cells decreases . The resf growth ,63. HoweTo date, implementations of FBA have been incapable of addressing states of metabolic activity resulting from perturbations other than gene losses/additions, incorporation of genetic expression data based on Boolean logic -23,26 orY. pestis to a number of environmental perturbations which are known to cause phenotypic changes, ranging from induction of virulence to cellular death.CSR is a system-level response, and hence, any study of such phenomena that only focuses on the altered activity of a handful of enzymes will overlook the cascading effects of gene-expression changes on the entire cellular metabolism. In order to expand the utility of FBA genome-scale models toward solving such state transitions, we developed GX-FBA, which combines hierarchical regulation imposed by gene-expression with the rigid constraint of metabolic reaction connectivity. We have applied our methodology toward studying the metabolic response of bacterium soft internal constraints  on a network by GX-FBA (see Methods), the behavior of a reaction can oppose hierarchical directives.One of the first questions about the utility of GX-FBA that has to be answered involves verification that the constraints imposed by network connectivity alone have the ability to partially mimic metabolic regulation, and if need be, oppose the dictum of hierarchical regulation. Through imposition of S. cerevisiae[e = 21%.This flexibility of GX-FBA is a strength and can be used to aid in identifying reactions in a pathway that might be least susceptible to hierarchical regulation in response to a given environmental condition. In order to illustrate this capability of GX-FBA, we used available flux measurements for erevisiae to examiA number of studies have shown that in some cases, there is not a strong correlation between mRNA expression levels and protein abundance -91. SuchGiven that our GX-FBA methodology can predict some of these differences, we surmise that network connectivity can serve as an appropriate constraint for ensuring that GX-FBA does not summarily impose hierarchical regulation on the network, since network connectivity is a critical component of metabolic flux regulation.Environmental perturbations usually cause a cellular response that is characterized by adjustments in genetic expression levels and cellular physiology. This rearrangement, if successful, permits the cell to adapt to the new environment. Study of cellular response mechanisms to external changes provides the basis for addressing questions related to cellular robustness and opens the possibility to identify drug targets. To date, studies on cellular stress response have primarily focused on the identification of expression patterns (either in transcriptome or proteome) and how these translate into system-wide effects on the metabolome, fluxome, and ultimately, realized cellular phenotypes.The flea/host/flea life cycle of YP forces the bacteria to adapt to two environments that differ in temperature and nutrient levels. Analysis of YP's acclimation from ambient temperature in the flea gut to 37°C in the mammalian host can provide us with information about how the cell prepares for inducing virulence and combating the host’s defenses.2+); the YP cell's primary metabolic response involves reducing the activity of most prominent producers of ROS, most notably oxidative phosphorylation. The reduced rate of ATP production via ATP synthase coupled with increased energy demand associated with CSR can explain the observed depletion of the ATP pool in stressed cells [Our analyses suggest that immediately following introduction into the host and encapsulation within a phagocyte  are significantly downregulated. This suggests that an examination of metabolism of hydroxyl radicals in YP could highlight either exceptions to the reported mechanism of cellular death by bactericidal antibiotics or could find alternate means for generation of this ROS.Finally, for both Streptomycin and Chloramphenicol, the activities of a majority of the TCA cycle reactions do not change drastically. In contrast, a majority of the reactions associated with oxidative phosphorylation are downregulated. This is unexpected because recent work by Kohanski et al.  have shoWe grouped the metabolic reactions that behave similarly under the four stress conditions based on function and pathway affiliation to look for a possible global stress-response strategy in YP. Overall the metabolic activity of only a handful of pathways was similarly altered among all 4 conditions. GX-FBA predicts that for all examined perturbations, the metabolic activity of pathways of metabolism for purines, pyrimidines as well as amino acids alanine, aspartate, glutamate, and tyrosine were constantly reduced.The likely consequence of these motifs is conservation of energy. This is in agreement with the observation that CSR is usually accompanied by exhaustion of cellular ATP pool ,92-94, ade novo purine biosynthesis consumes considerable energy. Production of Inosine 5'-monophosphate starting from ribose 5-phosphate demands five molecules of ATP. Hence, reduced de novo production of purines could be part of the cellular energy conservation efforts.The reduced production of purines after stress has previously been ascribed to lowered growth rates ,63 and aYersinia pestis to study CSR and metabolism of this pathogen as it transitions between host and vector environments and combats deleterious effects of antibiotic treatment, we find that the cell primarily tries to conserve energy while maximizing import of needed metabolites. Our efforts also show that by using this methodology that successfully couples gene-expression data to system-level models of metabolism, we can glean new insights that might not be readily discernible through other means.In summary, we have developed a new method to combine microarray data with a constraint-based formalism to gain deeper understanding of the system-level metabolic behavior of cells following a wide range of perturbations. Applying our framework to a large-scale model of metabolism in the gram-negative bacterium The authors declare that they do not have any competing interests.AN and EA conceived the idea and designed the experiments. AN performed the computations and analyzed the results. EA led the project and programmed the COBRA GX-FBA program. AN and EA wrote the paper and approve of its final version.Matlab script of GX-FBA algorithm for use with the COBRA toolbox.Click here for fileComplete description of the sample model  in SBML format.Click here for file