Aspergillus nidulans is a member of a diverse group of filamentous fungi, sharing many of the properties of its close relatives with significance in the fields of medicine, agriculture and industry. Furthermore, A. nidulans has been a classical model organism for studies of development biology and gene regulation, and thus it has become one of the best-characterized filamentous fungi. It was the first Aspergillus species to have its genome sequenced, and automated gene prediction tools predicted 9,451 open reading frames (ORFs) in the genome, of which less than 10% were assigned a function.A. nidulans, by using a pathway-driven approach and by employing comparative genomics tools based on sequence similarity. The central metabolism of A. nidulans, as well as biosynthetic pathways of relevant secondary metabolites, was reconstructed based on detailed metabolic reconstructions available for A. niger and Saccharomyces cerevisiae, and information on the genetics, biochemistry and physiology of A. nidulans. Thereby, it was possible to identify metabolic functions without a gene associated, and to look for candidate ORFs in the genome of A. nidulans by comparing its sequence to sequences of well-characterized genes in other species encoding the function of interest. A classification system, based on defined criteria, was developed for evaluating and selecting the ORFs among the candidates, in an objective and systematic manner. The functional assignments served as a basis to develop a mathematical model, linking 666 genes (both previously and newly annotated) to metabolic roles. The model was used to simulate metabolic behavior and additionally to integrate, analyze and interpret large-scale gene expression data concerning a study on glucose repression, thereby providing a means of upgrading the information content of experimental data and getting further insight into this phenomenon in A. nidulans.In this work, we have manually assigned functions to 472 orphan genes in the metabolism of A. nidulans can be used as an approach to improve the functional annotation of the genome of this organism. Furthermore we show how the metabolic model establishes functional links between genes, enabling the upgrade of the information content of transcriptome data.We demonstrate how pathway modeling of  Aspergillus nidulans, also known as Emericella nidulans, as it can undergo sexual reproduction in its life cycle in addition to the non-perfect  form that characterizes aspergilli, is an important member of the filamentous fungal genus Aspergillus. This genus encompasses a large diversity of species of great medical and economical relevance. In the medical and agricultural fields, A. flavus and A. parasiticus represent major producers of mycotoxins (e.g. aflatoxins) that can contaminate important food and feed crops, while A. fumigatus may cause serious diseases in immuno-compromised animals and humans (e.g. invasive pulmonary aspergillosis). From a biotechnological viewpoint, Aspergillus species represent important industrial producers of diverse products, such as industrial enzymes (e.g. amylases by A. niger and A. oryzae), bulk chemicals (e.g. citric acid by A. niger), and pharmaceuticals .A. nidulans has become one of the model organisms of choice for filamentous fungal genome research as it is a representative of the important group of aspergilli, but also because this fungus has served as a model organism for studies of cell development and gene regulation [Whereas the first efforts made in fungal genome research have focused on yeasts, there has been an increasing focus on filamentous fungi due to their medical, agricultural and biotechnological importance. There are quite large differences between yeast and most filamentous fungal genomes, with the latter exhibiting larger genomes owing to larger centromers and lower gene density per nucleotide length as well as the presence of far more genes. Furthermore, many of the filamentous fungal genes have a more complex structure due to the presence of multiple introns . A. nidugulation . It is oAspergillus species have recently been completed  or are nearing completion  [A. nidulans (strain FGSC A4) was released by the Broad Institute of MIT and Harvard, with a13-fold coverage, in Spring 2003 [Genome-sequencing projects of several terreus) ,4. In paing 2003 . The sizing 2003  matches In order to improve the predictions and improve the annotation, automatically assigned genes should be subjected to manual curation. Herein, integration of different types of data and combination of diverse genomic tools play a major role. Functional assignments of genes based on genomic data may be complemented with information providing biochemical and physiological evidence. Of special importance in functional genomics are high-throughput data generated by post-genomic techniques (e.g. transcriptome data using hybridization arrays ), which Thiobacillus ferrooxidans [A. nidulans.Metabolic reconstructions can give a valuable contribution to functional genomics, by uncovering missing metabolic functions  and hence putting forward the identification of the corresponding genes ,17. The ooxidans ) and eukooxidans ), and heA. nidulans, based on detailed metabolic reconstructions of other eukaryotes, namely A. niger [Saccharomyces cerevisiae [Mus musculus [Penicillium chrysogenum [Aspergillus [A. nidulans. Our analysis assigned functions to 472 orphan ORFs in the metabolism of A. nidulans, by employing similarity-based tools of comparative genomic analysis (BLAST) and using public (non-redundant) databases of genes and proteins of established function [A. nidulans. Furthermore, the information contained in the metabolic reconstruction can be exploited for the analysis of large-scale transcription data. To illustrate this, the reconstructed metabolic network of A. nidulans was used in connection with an algorithm developed by Patil and Nielsen [A. nidulans (deletion of the regulatory gene creA) [A. nidulans [In particular, we focused on the functional annotation of the genes involved in the central metabolism of this fungus, as well as on the biosynthetic pathways of relevant secondary metabolites. For the purpose, we reconstructed the central metabolic network of A. niger , Saccharrevisiae , and Musmusculus . In whatysogenum  and aflaergillus  were usefunction . These f Nielsen  for the ne creA) . In a prnidulans .A. nidulans, as well as those involved in the biosynthesis of secondary metabolites of interest, are listed in Tables A. nidulans that had not been annotated earlier  is presented in Additional file The reliability of the functional assignments was evaluated according to the criteria described in Materials and Methods, and the candidate ORFs were classified into categories, as shown in Additional file A. nidulans still remained without a link to a specific ORF in the genome. These metabolic functions corresponded to biochemical conversions for which no ORFs (hits) were identified by homology-based comparative analysis, or to those candidate ORFs that were subsequently neglected for not complying with the criteria considered . Nevertheless, 33 of these metabolic functions  were considered to be part of the metabolic network, since they were essential for growth .After employing the algorithm described above, some of the metabolic functions predicted to occur in A. nidulans. The model comprised 1213 metabolic reactions, of which 1095 were biochemical transformations and 118 were transport processes. In addition, the model included 732 metabolites that could be balanced, i.e. metabolites whose net rate of their formation could be balanced with their net rate of consumption. Out of the 1213 reactions, there were 794 unique reactions , i.e. 419 of the reactions in the metabolic network were redundant. All the reactions in the metabolic network are listed in Additional file A. niger and S. cerevisiae. Besides catabolic and biosynthetic pathways, the model also included polymerization reactions and a reaction describing the formation of biomass, which was considered as a drain of building blocks or macromolecules in appropriate ratios to produce 1 mmol of monomers in the macromolecule or 1 g dry-weight (DW), respectively. These ratios were calculated based on the composition of the macromolecules in terms of building blocks  and on nidulans  for lipi. oryzae  for the on rates . The valA. nidulans on each of the four different substrates studied , along with a list of the essential genes. The results from these studies were used to further refine the metabolic model. In fact, these investigations provided evidence for the existence of some metabolic steps for which no assignments were made based on homology searches. Therefore, these "missing functions" were considered to be part of the metabolic network for the sake of having an operative metabolic model.Single gene deletions were simulated and the capability of the corresponding mutants to grow on several carbon sources was determined . Table A. nidulans on different carbon sources. Fig. A. niger [A. oryzae in carbon-limited chemostat cultures [The model was simulated to predict the maximum theoretical growth yields of A. niger  and expecultures . All comA. nidulans, in order to detect overall metabolic responses to specific genetic and environmental perturbations, using an algorithm developed by Patil and Nielsen [highly regulated or reporter metabolites (i.e. metabolites around which the most significant changes in transcription occur) and highly correlated subnetworks , which enable to uncover metabolic responses to perturbations from transcriptional profiles.The reconstructed metabolic network was used in combination with data from large-scale transcriptional studies conducted with  Nielsen . This alA. nidulans  and concerned a reference strain grown on media containing different carbon sources (either glucose or ethanol), as well as a mutant strain that was impaired in the carbon repression system due to deletion of the carbon catabolite repressor gene creA [creA mutant strain grown on glucose, and the creA mutant strain grown on ethanol. Differentially expressed genes were identified by using a two-way ANOVA, resulting in the calculation of two p-values for each ORF: a p-value concerning the effect of the growth medium, which was independent of the genotype of the strain, and a p-value concerning the effect of the genotype, which was independent of the medium used. Of the 3,278 ORFs included in the expression data sets, 571 ORFs were represented in the metabolic model developed in this study and thus the corresponding transcription profiles were considered for the analysis of reporter metabolites and metabolic subnetworks. The top 30 reporter metabolites, ranked according to p-values concerning the effect of the medium and genotype, are listed in Table The expression data sets used in this study represented the transcription levels of approximately one third of all predicted ORFs in ene creA . Transcr+ and NADH as reporter metabolites. Moreover, L-xylulose and D-sorbitol, which are involved in the metabolism of polyols, were ranked second and third, respectively, in the list of reporter metabolites concerning the effect of the genotype. Furthermore, it was observed that metabolites participating in the formation of secondary metabolites (e.g. sterigmatocystin) were among the 30 most highly regulated metabolites.Methanol, ethanol, and acetaldehyde were also found as very highly ranked reporter metabolites in the list concerning the effect of the medium, which is an indication of the differential regulation of a whole set of dehydrogenases, and is also suggested by the emergence of NADA. nidulans and S. cerevisiae, which enabled to transfer specific tools for the analysis of -omics data in yeast to A. nidulans. Thus, all the enzymes associated to the top 30 reporter metabolites . In this way, we aimed at identifying all ORFs that were associated to a given function , even though, by not being so stringent, we may have run into the problem of also finding false positives. Furthermore, assignment of ORFs to these categories may be valuable in future annotation studies.The selection of ORFs among the candidates encoding each function involved the specification of certain criteria and the development of a classification system. Hereby the reliability of the assignment of specific metabolic functions to candidate ORFs could be evaluated objectively and systematically, and furthermore it was possible to classify each annotation into categories according to the criteria defined. These criteria were essentially based on the E-values of BLAST searches and on the consistency between the function of interest and the function of the BLAST hits. All ORFs that were classified into at least one of the categories defined  were considered in the metabolic model, whereas the ORFs that did not fall into any of the categories were not incorporated in the model. The categories A*, Y*, and O* were included to take into account also those ORFs for which the results from the comparative analysis were not conclusive, but did not contradict the function in question  in BLAST searches, because the probability of finding them by chance in the database is higher. Moreover, in order to have an idea on the order of magnitude of reasonable E-values for the different BLAST searches, previously annotated ORFs were used as positive controls. However, universal criteria may not apply, since the proteins' sequences may have diverse properties in the different parts of the metabolism . Therefore, a sensitivity analysis was performed, in which different cut-off values in the E-values were considered in the BLAST searches. The stringency of this criterion determined the number of metabolic functions assigned to ORFs, as well as the number of ORFs considered for each function . It wouA. nidulans or this could not be directly extrapolated from other organisms. For example, even though in S. cerevisiae there are two genes (YDR341C and YHR091C) encoding the enzyme arginyl tRNA synthetase (EC 6.1.1.19), only a single ORF (AN6368.2) was identified in A. nidulans, through BLASTP searches. Similarly, a single ORF was found in A. nidulans (AN5610.2) for L-aminoadipate-semialdehyde dehydrogenase (EC 1.2.1.31), which is a complex enzyme in yeast containing two subunits , encoded by two different genes .As mentioned above, all BLAST hits for a given function whose E-values were below the cut-off and that were classified into at least one of the categories described were considered to encode that function. However, in some cases, the discrimination between ORFs encoding isoenzymes and subunits of enzyme complexes was difficult, particularly for those cases in which there was no information available for This study therefore shows clearly that the outcome of comparative genomics is highly dependent on the criteria chosen, and also highlights the importance of the application of a systematic evaluation to the obtained annotations.A. nidulans was again illustrated in this work with a study concerning transcriptional responses to changes in the growth medium composition (glucose and ethanol) of a wild type strain and a mutant strain with deletion of the regulatory protein CreA [A. nidulans, the reporter metabolites identified after applying the method from Patil and Nielsen [Transcriptomics has become a cornerstone of functional genomics over the last decade and the analysis and interpretation of microarray data has proven to be a new challenge. Even for well-studied model organisms, the analysis and interpretation of transcriptome data is often hampered by the numerous genes that have no function assigned. This becomes even more evident when transcriptomics moves on to genomes whose annotation barely relies on automated gene prediction. In these cases, basically any additional information can be very helpful for the analysis and interpretation of data. As shown previously by our group, the metabolic network reconstructed in this work can be valuable for upgrading the information content in transcriptome data , i.e. toein CreA . The ini Nielsen , still pFor both categories , the highest ranked reporter metabolites were involved in the biosynthesis of amino acids  Table , which wA. nidulans, in particular in the metabolism of ethanol . However, tracing back the underlying perturbations from the topology of the network and observed transcriptional responses is still a challenging task, even for well-studied organisms.On the other hand, this approach may play an important role in functional genomics, by giving insight into the perturbations that lead to specific transcriptional responses . In fact, from the list of reporter metabolites presented in Table A. nidulans allows the utilization of tools that have been developed by the yeast community for the analysis of -omics data. This represents an advantage, because one can rely on the linkage of the expression data to a specific reaction rather than to a specific gene. After identification of the reporter metabolites and the reactions in which they participate, the reconstructed metabolic network of S. cerevisiae can be used to identify ORFs in yeast that are involved in the same reactions and use these for further analysis. As an example, the "GO term finder" available at Saccharomyces Genome Database was used to identify specific parts of the metabolism related to the reporter metabolites. The results (reporter metabolites) obtained based on the differential expression according to the medium revealed many GO categories that could be directly linked to the change of the carbon source from glucose to ethanol, and therefore again showed that by using this approach one can obtain a birds-eye view on the major metabolic changes. The results based on the changes in the genotype of the strains, i.e. deletion of the carbon repression mediator CreA, showed that the highest ranked reporter metabolite, as well as other lower ranking ones, was involved in the amino acid biosynthesis, which was also confirmed by the GO term analysis. This linkage between glucose repression and amino acid biosynthesis was further substantiated by the finding that a defined set of genes that is regulated via CreA also has binding sites for CpcA (homologue of GNC4 from S. cerevisiae) that is a major regulator of the amino acid metabolism [Furthermore, the reconstructed metabolic network for tabolism . This shtabolism ,37, and A. nidulans. Moreover, we showed how the metabolic reconstruction establishes functional links between genes, enabling the upgrade of the information content of transcriptome data.In this work, we illustrated the use of a pathway-driven approach to improve the functional annotation of the genome of A. nidulans was based on the method previously described by Osterman and Overbeek [The approach employed in this work for the annotation of the metabolic genes within the genome of Overbeek . The difA. nidulans, as well as selected pathways from its secondary metabolism, was reconstructed using as templates detailed metabolic reconstructions of other organisms. For the reconstruction of the metabolism of carbon compounds in A. nidulans, a detailed metabolic reconstruction for A. niger [S. cerevisiae [S. cerevisiae is simpler than for many other eukaryotic cells, the energy metabolism of A. nidulans was reconstructed using as references the corresponding pathways from both yeast [P. chrysogenum [Aspergillus [A. nidulans was in part supported by available genomic data, such as previously annotated ORFs [A. nidulans were also predicted based on biochemical evidence given by reports on isolation and characterization of enzymes in this fungus [A. nidulans was supported solely by physiological evidence (e.g. the ability to grow on a certain sugar as the sole carbon and energy sources require a transporter and a complete pathway for metabolism of this sugar).The central metabolism of A. niger  was usedrevisiae , for whith yeast  and mousth yeast . The bioysogenum  and in dergillus , respectted ORFs , sequencted ORFs , Expressted ORFs  and Tentted ORFs . The mets fungus ,42. FurtA. nidulans were based on those in the metabolic networks of other organisms that served as templates for the reconstruction.The directionality and reversibility of the reactions included in the metabolic network of A. nidulans was reconstructed and the missing functional roles identified, the genome of A. nidulans was surveyed for the genes encoding the corresponding enzymes, by employing comparative genomics tools based on sequence similarity. This approach was also applied for the identification of ORFs encoding metabolic functions that had been previously assigned to genes in A. nidulans, aiming at identifying isogenes. The sequences of a set of proteins with the designated enzymatic activity in other organisms (queries) were compared with the set of all predicted proteins in A. nidulans [A. nidulans (e.g. fungi or eukaryota). BLASTP (blosum62) was used for comparative analysis and assigning metabolic functions to ORFs in the genome of A. nidulans. The selection of the best candidate ORFs for a given function relied on the cut-off in the expectation values  considered, as well as on the score-to-sequence length ratio. Protein sequences or translated nucleotide sequences were used in the comparisons, rather than nucleotide sequences, due to the presence of introns, which characterizes eukaryota, and thus filamentous fungi. For the cases in which no hits were generated in this way, the translated nucleotide sequences of genes encoding the specific enzymes (obtained from the (non-redundant) NCBI nucleotides database [Once the metabolic network of nidulans . The pronidulans  (searchedatabase ) were usOnce candidate ORFs were identified for the metabolic functions, the reliability of the functional assignments was assessed and the ORFs were classified into different categories, according to several criteria, as shown in Fig. Aspergillus nidulans Database [Aspergillus nidulans Linkage Map [Previous annotations of the candidate ORFs (if available in the Database  or in Thkage Map ) were coThe protein domains originally predicted for the candidate ORFs  were comS. cerevisiae [A. nidulans [A. nidulans generated in this way were used to evaluate the reliability of the candidate ORFs. This was accomplished by comparing the functions assigned to the ORFs in yeast with those assigned to the candidate ORFs. The candidate ORFs were then classified into the following classes Y, Y*, Y-X or Y-NA  protein database at NCBI [Potential homologs of the candidate ORFs encoding the metabolic functions in  at NCBI . The corA. nidulans was supported by information concerning this fungus available in the literature. Otherwise, information was extrapolated from A. niger or S. cerevisiae.The BLAST searches often yielded several hits (or candidate ORFs) with E-values lower than the cut-off value (or with similar score-to-length ratios) for a given function. These hits could potentially correspond to ORFs encoding isoenzymes or subunits of enzyme complexes. In these situations, all candidate ORFs were considered and classified according to the criteria described above. In some cases, the existence of these hypothetical isoenzymes or subunits in +- and a NADP+-dependent reaction, respectively. Reactions catalysed by multi-enzyme complexes were included, if at least one of the subunits was identified.Multi-enzyme complexes and isoenzymes were represented in a different way in the metabolic reconstruction. All subunits considered to belong to a same multi-enzyme complex were associated to a single reaction in the metabolic network, whereas isoenzymes were represented as independent reactions. For example, in the metabolic network of A. nidulans, the pyruvate dehydrogenase complex is represented by two subunits (AN5162.2/AN9403.2), which are associated to a single reaction (EC 1.2.4.1). On the other hand, two isoenzymes of glutamate dehydrogenase (AN7451.2 and AN4376.2) were associated to two different reactions in the metabolic network, a NADAnother issue that was addressed was related to the assignment of different functions to the same ORF. These ORFs could possibly encode multifunctional proteins, and hence these were surveyed for the existence of multiple protein domains to verify the hypotheses.A. nidulans, including reactions encoded by previously annotated genes as well as metabolic functions initially missing, served as a basis to develop a stoichiometric model. The model was subsequently used for simulating microbial growth and for gene deletion analysis, by employing flux balance analysis and linear programming methods [The reconstructed metabolic network of  methods ,43.A. nidulans. This method enables the identification of so-called reporter metabolites and metabolic subnetworks, based on their interconnectedness within the metabolic network through common metabolites and on information about changes in the expression level of the genes.The reconstructed metabolic network was used in combination with a computational method published by Patil and Nielsen  for analcreA deleted strain of A. nidulans, grown on different carbon sources, specifically glucose and ethanol [versus ethanol) or genotype of the strains (reference versus creA deletion mutant) were used in combination with information on the topology of the metabolic network of S. cerevisiae [Saccharomyces Genome Database [This approach was applied to analyze expression data concerning a reference strain and a  ethanol . Furtherrevisiae  for furtDatabase .HD performed the annotation work and drafted the manuscript. ISO carried out the annotation work. GH participated in the design of the study and helped to draft the manuscript. JN participated in the design and coordination of the study and helped to draft the manuscript. All authors read and approved the final manuscript.A. nidulansList of the reactions comprising the metabolic model developed for . List of the reactions comprising the metabolic model developed for A. nidulans. Each reaction is associated to an ORF within the genome of A. nidulans (when available), and to the EC number of the corresponding enzyme (when available). The classification of the ORFs into categories is also presented. The functional assignments were based on a cut-off in the E-values of BLAST searches of 1E-50. The reactions that are common to the metabolic networks of A. nidulans and S. cerevisiae are represented by AN and SC, respectively.Click here for fileA. nidulansList of metabolites (abbreviations and full names) included in the metabolic model for . In the abbreviations, the suffixes 'm', 'g', 'e' stand for metabolites localized in the mitochondria, glyoxysomes and extracellular medium, respectively. No suffix was added to cytosolic metabolites.Click here for fileList of the ORFs associated to each biochemical reaction for different cut-off values in the E-value of BLASTP searchesClick here for file


Despite enormous efforts to combat malaria the disease still afflicts up to half a billion people each year of which more than one million die. Currently no approved vaccine is available and resistances to antimalarials are widely spread. Hence, new antimalarial drugs are urgently needed.Plasmodium falciparum, the deadliest malaria pathogen. We assembled a compartmentalized metabolic model and predicted life cycle stage specific metabolism with the help of a flux balance approach that integrates gene expression data. Predicted metabolite exchanges between parasite and host were found to be in good accordance with experimental findings when the parasite's metabolic network was embedded into that of its host (erythrocyte). Knock-out simulations identified 307 indispensable metabolic reactions within the parasite. 35 out of 57 experimentally demonstrated essential enzymes were recovered and another 16 enzymes, if additionally the assumption was made that nutrient uptake from the host cell is limited and all reactions catalyzed by the inhibited enzyme are blocked. This predicted set of putative drug targets, shown to be enriched with true targets by a factor of at least 2.75, was further analyzed with respect to homology to human enzymes, functional similarity to therapeutic targets in other organisms and their predicted potency for prophylaxis and disease treatment.Here, we present a computational analysis of the metabolism of The results suggest that the set of essential enzymes predicted by our flux balance approach represents a promising starting point for further drug development. Malaria represents one of the major health issues worldwide. According to WHO estimations there were around 250 million clinical cases and about 1 million disease related deaths in 2006  and reaction fluxes v being constant, since bio-chemical reactions are typically much faster than changes in the phenotype of a cell during growth or differentiation:Flux balance analysis (FBA) is a commonly used method to investigate the metabolic capabilities of cellular systems, since it allows to estimate unknown fluxes in metabolic networks with respect to cellular constraints ,112-115.The solution space of the resultant linear equation system is a high dimensional flux cone, containing all flux configurations that are feasible at steady state. Constraints derived from thermodynamics and cellular environment conditions further restrict the solution space. Organisms are thought to be optimized in the course of evolution. Therefore, a biologically meaningful objective function, which is a linear function of fluxes, is applied to the set of possible solutions to identify a flux distribution that is optimal with respect to the cellular objective. Maximization of biomass is one such target function that is assumed to be suitable especially for microorganisms . For eukS is the stoichiometric matrix of the cellular system, v are internal fluxes as well as exchange fluxes, and min vand max vare the lower and upper bounds on fluxes.where E > 10 and likelihood of gene absence calculated by the match-only integral distribution algorithm logP < -0.5. Genes covered by the Bozdech and Tarun data sets were considered to be expressed if the corresponding signal-to-noise ratio  - mean)/std, with Foreground signal being the signal resulting from specific hybridization and Background signal being the noise caused by non-specific binding), is greater or equal to a threshold. Signal-to-noise ratios were extracted from the raw data, averaged over all replicates and normalized using quantile normalization [t was chosen for the Bozdech data set in such a way that the average Euclidean distance between the binary expression values (expr (g | t) = 0: gene g is silent given threshold t, expr (g | t) = 1: gene g is expressed given threshold t) is maximal for non-consecutive pairs of samples of the same data set and minimal for consecutive pairs:The expression status was determined for each gene of every expression sample. For the Le Roch data set the same parameter cutoffs were applied as mentioned in   and ring stage expression samples of the Le Roch set and was therefore used to determine expression in Daily samples.et al. [yp 1(forward direction), yn 1(backward direction), y0 (no flux)) is set to 1. The sum of these binary variables composes the objective function that is sought to be maximized to obtain flux distributions that are consistent with corresponding expression profiles. However, the Shlomi method has several limitations: synthesis of metabolites needed for growth is not guaranteed, reactions of low confidence are treated the same as those with annotated genes, in order to maximize the objective function all reactions catalyzed by the same gene product are sought to be active simultaneously in case the gene is expressed and furthermore no limits are set on available nutrients. To cope with these issues we extended the method as follows. (a) Additional constraints force the network to produce a set of target metabolites that are assumed to be essential during the life cycle stage of interest  and constraints were introduced that keep these reactions inactive if the respective variable is set to 1. (c) For each expressed gene a boolean variable  and constraints were added, making sure that at least one of the reactions associated to an expressed gene has to carry a non-zero flux in case the respective variable is set to 1. Replacing variables yp 1and yn 1in the objective function with this variable type avoids that all reactions catalyzed by the same expressed enzyme are sought to be active at the same time to further optimize the objective function value. (d) With respect to the restrained access of the parasite to nutrients of the host the network is forced to fulfill its tasks with a minimum amount of externally supplied metabolites by subtracting the absolute flux values through the parasite's plasma membrane transporters from the objective function value. (e) To simulate the parasites environment the uptake of certain metabolites was constrained in accordance with knowledge about the blood stage. The corresponding mixed integer linear program reads as follows:Flux distributions were predicted for the different life cycle stages of the malaria pathogen with an extended version of the method proposed by Shlomi et al. . This meα denotes the reward for setting the fluxes of reactions to zero that correspond to unexpressed genes (NER), β represents the reward for assigning a zero flux to such reactions that are not associated with any gene (NGR), γ denotes the reward for having a non-zero flux through any reaction assigned to an expressed gene (EG), while δ is the penalty for forward fluxes v+ through parasitic plasma membrane transporters (T) importing external metabolites. In our calculations the variables were set as follows: α = 2, β = 0.1, γ = 1, and δ = 0.5. Inequalities (5)-(7) are the same as in [y3 is set to 1, at least one of the corresponding variables of type y1 have to equal 1 as well. Matching variables y1 and y3 are identified via function r(i) that maps a gene onto a set of reactions that are catalyzed by the gene product. Biomass production is ensured by (4), which requires e fluxes of at least one molecule of the respective target metabolites through system boundaries.Within the solution space, which is defined by equations and inequalities (2)-(14), a flux distribution is sought that maximizes the objective function described by (1). me as in  and (8) P. falciparum such a linear program was formulated. In case the solution space of the problem was empty, the knocked-out reaction was considered to be indispensable and thus a putative drug target, since no path exists converting external nutrients into all target metabolites, which presumably results in impaired parsite development. In contrast to the previously conducted flux balance analysis no gene expression is considered for the identification of essential reactions.FBA methods can be used to determine reactions of a metabolic network that are essential for the synthesis of certain target metabolites such as biomass precursors by simulating the effects of knocked-out genes ,126,127.FBA: flux balance analysis; IDC: intraerythrocytic developmental cycleCH developed the original idea, carried out all computational analyses and drafted the manuscript. AH provided tools for the knock-out simulations and together with HGH and SB participated in the design and evaluation of the analyses. All authors contributed to and approved the final manuscript.Assembled metabolic network of P. falciparum in SBML format.Click here for fileAssembled metabolic network of the human erythrocyte in SBML format.Click here for fileGene expression samples. In order to calculate a stage-specific flux distributions our flux balance approach requires a gene expression profile of the stage of interest. We obtained gene expression samples from different publications, including Bozdech et al., Le Roch et al., Sacci et al., and Tarun et al.Click here for fileNormalized Hamming distance matrix for gene expression samples. In order to compare the gene expression profiles of the different time points normalized Hamming distances (see text for formula) have been calculated as described in the text for each pair of gene expression samples. The darker the color of a matrix entry, the lower is the corresponding Hamming distance. Sample labels are composed of the sample abbreviation and the number of expressed genes.Click here for fileBozdech gene expression samples mapped onto metabolic pathways. Mapping gene expression data onto metabolic networks may uncover active pathways for each stage and metabolic differences between the individual life cycle stages. For this purpose, we calculated the ratio of expressed genes per KEGG pathway (# expressed genes/# genes with available expression data for pathway) for each Bozdech gene expression sample. The darker the color of a matrix entry, the lower is the ratio. Clusters of pathways with similar patterns of expressed genes during the individual life cycle time points were calculated with the built-in function hclust ('average' method) of the statistics software R (colored bars).Click here for fileLe Roch gene expression samples mapped onto metabolic pathways. See caption of Additional file Click here for fileTarun gene expression samples mapped onto metabolic pathways. See caption of Additional file Click here for fileDaily gene expression samples mapped onto metabolic pathways. See caption of Additional file Click here for fileMetabolites essential for parasite development. Metabolites listed in this table are assumed to be essential during those developmental stages of the parasite that are specified in the third column. Some entries represent pseudo-metabolites that do not correspond to actual metabolites. These have been added as products in the equations of certain important reactions such as glutathione reductase. Requiring the production of these pseudo-metabolite ensures that the respective reaction is active.Click here for fileNormalized Hamming distance matrix for calculated flux distributions. Flux distributions have been predicted with our flux balance approach (see Figure Click here for filePredicted host parasite metabolite exchanges. Flux distributions have been predicted with our flux balance approach (see Figure Click here for fileNormalized Hamming distance matrix for calculated flux distributions using improved approach. Flux distributions have been predicted with our improved flux balance approach (see Figure Click here for fileReaction distribution among stage-specific fluxes. Flux distributions have been predicted with our improved flux balance approach (see Figure Click here for filePredicted metabolic fluxes consistent with Bozdech gene expression data mapped onto metabolic pathways. Flux distributions have been predicted with our improved flux balance approach (see Figure Click here for filePredicted metabolic fluxes consistent with Le Roch gene expression data mapped onto metabolic pathways. Same as Additional file Click here for filePredicted metabolic fluxes consistent with Daily gene expression data mapped onto metabolic pathways. Same as Additional file Click here for fileOverview of pathway specific consensus reactions for different time points of intraerythrocytic cycle. Flux distributions have been predicted with our improved flux balance approach (see Figure Click here for fileRanked predicted essential reactions. Knock-outs were simulated with a simple FBA approach neglecting gene expression information. No assumptions were made about the cellular environment and nutrient uptake was not restricted, since such information is not available for all stages. Successively reactions were constrained to carry no flux, while the network was forced to produce all metabolites that are assumed to be essential during any developmental stage (all metabolites listed in Additional file Click here for file


In silico genome-scale metabolic models enable the analysis of the characteristics of metabolic systems of organisms. In this study, we reconstructed a genome-scale metabolic model of Corynebacterium glutamicum on the basis of genome sequence annotation and physiological data. The metabolic characteristics were analyzed using flux balance analysis (FBA), and the results of FBA were validated using data from culture experiments performed at different oxygen uptake rates.C. glutamicum contains 502 reactions and 423 metabolites. We collected the reactions and biomass components from the database and literatures, and made the model available for the flux balance analysis by filling gaps in the reaction networks and removing inadequate loop reactions. Using the framework of FBA and our genome-scale metabolic model, we first simulated the changes in the metabolic flux profiles that occur on changing the oxygen uptake rate. The predicted production yields of carbon dioxide and organic acids agreed well with the experimental data. The metabolic profiles of amino acid production phases were also investigated. A comprehensive gene deletion study was performed in which the effects of gene deletions on metabolic fluxes were simulated; this helped in the identification of several genes whose deletion resulted in an improvement in organic acid production.The reconstructed genome-scale metabolic model of C. glutamicum. This can form a basis for the in silico design of C. glutamicum metabolic networks for improved bioproduction of desirable metabolites.The genome-scale metabolic model provides useful information for the evaluation of the metabolic capabilities and prediction of the metabolic characteristics of  Corynebacterium glutamicum is a facultatively aerobic, gram-positive bacterium that can grow on various sugars or organic acids [C. glutamicum under oxygen deprivation conditions has recently been proposed [C. glutamicum has been chosen as one of the effective hosts for metabolic engineering purposes [in silico metabolic models, which help predict the cellular behavior and production of useful chemicals, are highly desired.A coryneform bacterium, ic acids ,2. This ic acids ,2 and lyic acids  with higic acids ,5. Furthproposed ,7. Owingpurposes -10. ThusRecently, on the basis of whole-genome information, the genome-scale metabolic networks of cells have been reconstructed and applied to metabolic flux balance analysis (FBA) ,12 for mC. glutamicum. Metabolic reactions and other parameters for biomass were collected using databases and literatures. After reconstruction of the genome-scale metabolic model, we performed FBA simulations with the maximization of biomass production and evaluated the results of the simulations by using experimental data of C. glutamicum cultures grown at different oxygen uptake rates (OURs). Our results revealed that the production rates of biomass and organic acids predicted using our model agreed well with the experimental rates; this result suggests that this model well represents the intracellular metabolic profiles of C. glutamicum. It should be noted that the representation of such changes in the metabolic profiles that occur on changing the oxygen uptake is difficult for another genome-scale model of C. glutamicum reported recently [C. glutamicum.In this study, we present the reconstruction of a genome-scale metabolic model of recently . FurtherC. glutamicum metabolic network were collected by a search of public databases and scientific publications. The genome-scale metabolic network was based on the pathways in the BioCyc database collection [ for C. glutamicum. We also referred to the information on C. glutamicum in the Kyoto Encyclopedia of Genes and Genomes database . In general, the genome-scale model constructed using only public databases contains incorrect and insufficient metabolic pathways owing to the incompleteness of database information. The most frequently observed incorrectness was missing enzymes in metabolic pathways. Thus, the resulting network was then subjected to the gap-filling process to allow biomass formation. For gap filling, we referred to published cell-specific data available in the literatures, such as Ref. [The known metabolic reactions in the llection  for C. g as Ref. ,28 and r as Ref. ,30.C. glutamicum cells have a characteristic cell membrane termed as MAPc [The reaction "biomass synthesis" is a hypothetical metabolite in the metabolic network, which represents the requirement of precursors and coenzymes for the biomass formation. Biomass synthesis consists of a linear combination of 43 components, including amino acids, DNA, RNA, lipids, and cell envelope components. In our model, the biomass composition was determined from various reported data. The demands of precursors such as pyruvate, acetyl-CoA, and oxaloacetate for biomass production were based on the data in Ref. . For the as MAPc , which c as MAPc ; the com as MAPc . The bio as MAPc .C. glutamicum metabolic network were calculated by using flux balance analysis (FBA), in which constrains are imposed by the stoichiometry in a metabolic network [Metabolic fluxes of the  network . A pseudS is the stoichiometric matrix representing the stoichiometry of metabolic reactions in the network and v is a vector of all metabolic fluxes. vmin and vmax indicate the minimum and maximum constraints on the fluxes and are used to define the constraints for maximal enzymatic rate, irreversibility of reaction, or constant uptake from the environment. cT is a vector representing the objective function to be maximized, as a linear combination of metabolic fluxes. In general, the biomass production rate mentioned above is used as the objective function to be maximized. In this study, we followed this method to calculate the metabolic flux profile under the assumption that organisms have been evolved toward growth maximization. For all simulations in this paper, glucose was chosen as the sole carbon source and the following external metabolites were allowed to freely transport through the cell membrane: CO2, H2O, SO3, NH3, and PO4. All calculations, including the linear programming problems, were performed using the commercially available software Lindo  and Matlab .where C. glutamicum strain ATCC 13032 was used in the culture experiments. The composition of the synthetic medium used for the preculture of the microorganism was the same as that employed in our previous study [4)2SO4, 3.0 g of Na2HPO4, 6.0 g of KH2PO4, 2.0 g of NaCl, 84 mg of CaCl2, 3.9 mg of FeCl3, 0.9 mg of ZnSO4.7H2O, 0.1 mg of (NH4)6Mo7O21.4H2O, 0.3 mg of Na2B4O7.10H2O, 0.4 mg of MgSO4.7H2O, 40 mg of FeSO4.7H2O, 500 μg of vitamin B1·HCl, 0.1 g of EDTA, and 10 μg of biotin. The medium composition for the main culture was the same as that for the preculture except the initial glucose concentration was changed to 80 g/L for batch cultivation and 20 g/L for continuous cultivation.us study   with a liquid working volume of 200 mL. In the batch cultures, the cells were first allowed to grow aerobically at a high aeration rate  and high agitation speed (800 rpm) until the cell concentration, as measured by the optical density at 660 nm (OD660), reached 5~15. Then, for experiment 1, the culture conditions were changed to no aeration and gentle agitation (100 rpm) and for experiment 2, the aeration rate was altered to 0.5 vvm and the OUR was maintained at a constant value (0.5 mmol/gDW/h) by changing the agitation speed. For the aerobic cultures , chemostat cultivations were carried out using a 500-mL jar fermenter with a liquid working volume of 200 mL. The aeration rate was fixed at 1 vvm and the dilution rate, at 0.2 h-1 for all chemostat culture experiments. In order to change the OUR in these chemostat cultures, the agitation speed was set to 800, 1000, and 1100 rpm for experiments 3, 4, and 5, respectively.For microaerobic culture conditions  and a pH controller .660. The dry cell weight (DCW) was calculated using the measured OD660 according to the following formula:Cell growth was monitored by measuring the OD2SO4 in an ion-exclusion column TSKgel Oapak-P  at 40°C. The flow rate was set to 0.8 ml/min. The concentration of dissolved oxygen (DO) in the culture was monitored by using an oxygen electrode , and the concentrations of exhaust oxygen and carbon dioxide were monitored by using an exhaust gas analyzer .The culture supernatant was used for measuring the concentration of glucose and organic acids. Glucose was measured using an enzymatic assay kit, the Glucose CII test Wako  according to the manufacturer's protocol. Organic acids were quantified using a HPLC system, Hitachi L-6200 equipped with a L-4000H UV detector . Samples were eluted with 0.75 mM HC. glutamicum ATCC 13032, whose genomic DNA sequence was determined by 2 independent research groups [C. glutamicum were obtained from Ref.[) and by inference from physiological considerations and genome annotations [We reconstructed a genome-scale metabolic network for h groups ,36; the h groups ,28. The from Ref.. From thotations .C. glutamicum has several characteristics that distinguish it from the networks of other microorganisms. The cell envelopes of coryneform bacteria and mycobacteria have a unique structure consisting of a covalently linked complex comprising mycolic acid, arabinogalactan, and peptidoglycan (MAPc) [C. glutamicum. In the central metabolic pathway, the reconstructed model of C. glutamicum has pyruvate carboxylase in the anaplerotic pathway and lacks pyruvate formate lyase. In addition, C. glutamicum has 2 pathways for the biosynthesis of diaminopimelate, which is a precursor for lysine biosynthesis. One pathway involves the direct conversion of Δ1-piperideine-2,6-dicarboxylate to diaminopimelate, which is catalyzed by diaminopimelate dehydrogenase; the other pathway involves an indirect conversion, which is catalyzed by 4 independent enzymes [C. glutamicum does not have glycine C-acetyltransferase, which is involved in the conversion of threonine to glycine. These distinguishing characteristics of the metabolic pathways are necessary to represent the flux profile of C. glutamicum.The reconstructed metabolic network of n (MAPc) . In orden (MAPc) ,30 and t enzymes . AdditioC. glutamicum, we compared the growth and metabolic profiles obtained by FBA simulations with those obtained by experiments performed at various oxygen levels. Here, we focused on the OUR as a parameter to change the metabolic profiles of C. glutamicum; this is because OUR is known to alter the metabolic profile drastically and is a key factor for controlling the productivity of several materials by this microorganism, such as organic acids. We performed a series of experiments involving the culture of C. glutamicum ATCC 13032 at various oxygen levels. The results of these experiments are summarized in Fig. -1; in these cultures, the oxygen supply was changed by altering the agitation speed to 800, 1000, and 1100 rpm  is less than 10% over 10 hours. The production rates of CO2 and organic acids were measured in the steady states of the continuous cultures. We also confirmed that, for GUR, OUR, and production rates of organic acids, the ranges of deviation from the means were less than 5% during the steady state. In microaerobic and oxygen anaerobic conditions, C. glutamicum exhibited low specific growth rate , and maintaining a steady state in the continuous cultures was difficult. Thus, we used batch cultures in this study and altered the oxygen supply conditions during the culture. In the batch cultures, cells were first grown under aerobic conditions with aeration and a high agitation speed; during the exponential growth phase, nitrogen gas started to be supplied instead of air for maintaining the anaerobic condition (experiment 1) and the agitation speed was controlled to maintain a constant OUR for the microaerobic condition (experiment 2). After changing the oxygen supply conditions, the production rates of CO2 and organic acids were measured  cycle was activated (experiment 4 and 5).In order to verify the results of the FBA using our genome-scale model of 2, and biomass using experimentally observed OUR and GUR values. The predicted yields are presented in Fig. Using the experimental data summarized in Fig. 13C-tracer experiment [C. glutamicum exponentially grown with glucose as the sole carbon source under aerobic conditions. The GUR and OUR were set to those measured experimentally. As presented in Fig. 13C-tracer experiment and our simulation. For example, in our simulation result of aerobic condition, 14.7% of total carbon flux was consumed from acetyl-CoA to synthesis biomass components, such as lipid. In contrast, to obtain fluxes in the 13C-tracer experiment shown in Fig. In order to evaluate the accuracy of the predictions by the FBA simulations in more details, we compared the results of the FBA simulations with the intracellular metabolic flux profile obtained by using a periment . Here, w2, and organic acids agreed well between experimental results and FBA simulations, we further analyzed the changes in the intracellular metabolic profiles on changing the oxygen supply by using FBA simulations of our genome-scale model. In Fig. 2 in the TCA cycle and the residual glucose is converted to acetate to produce ATP. Further decrease in the oxygen supply results in the production of lactate instead of acetate (phase III). In this phase, the carbon flux to the TCA cycle is almost stopped (except for fluxes to supply metabolites required for the production of biomass such as amino acids). The oxygen uptake is not enough to oxidize all the NADH produced in glycolysis; thus, lactate production is utilized as a mechanism to oxidize NADH in order to maintain the intracellular redox balance. In phase IV, succinate is produced instead of lactate. This is because the capacity of NADH oxidation is greater in the succinate production process than in the lactate production process. Two moles of NADH can be oxidized during the production of 1 mole of succinate from 1 mole of pyruvate, while only 1 mole of NADH can be oxidized during the production of 1 mole of lactate from 1 mole of pyruvate (see the profile (c) and (d) in additional file Since the production yields of biomass, COAs shown in Fig. C. glutamicum [The difference between the previously proposed genome-scale model of utamicum  and our utamicum  consistsutamicum  lacks thC. glutamicum is widely used for the industrial production of various amino acids such as lysine and glutamate, the prediction of metabolic profiles in the production phase of such amino acids is desirable for the improvement of the productivity. Thus, we validated the results of FBA simulation for lysine production by comparing the results with those of 13C-tracer experiment presented in Ref. [Since  in Ref. . In orde in Ref. ). These  in Ref. . In the  in Ref. . It shou in Ref.  exhibiteC. glutamicum is also widely used for glutamate production. However, the flux profile of the glutamate production phase cannot be represented by using the genome-scale model so far. Glutamate production by C. glutamicum can be induced by several triggers such as biotin depletion [13C-tracer experiments has revealed the changes in the metabolic flux profiles, indicating that a large fraction of carbon derived from glucose is converted to glutamate with the activation of the phosphoenol-pyruvate carboxylase pathway, which provides carbon flux to the TCA cycle [epletion , Tween 4epletion , and penepletion . After rCA cycle . HoweverCA cycle ,44. AddiCA cycle . The incC. glutamicum under oxygen deprivation conditions was proposed for increasing the productivity [C. glutamicum to improve organic acid productivity is desirable. Using FBA of our C. glutamicum metabolic model, we determined candidate genes for target deletion to improve the organic acid productivity under oxygen deprivation conditions. Table Recently, the production of organic acids by uctivity . For theC. glutamicum, which is commercially important for the production of amino acids and useful chemicals. This model includes hundreds of metabolites and reactions among them, and also includes that the hypothetical reaction representing synthesis of biomass to calculate the requirement of metabolites for cell growth. It should be stressed that, this model is not just a collection of all the public available data about the metabolic reaction of C. glutamicum. Instead, we constructed the model by adding and deleting metabolic reactions to/from those on the databases, to make this model available for the flux balance analysis. For example, based on some literatures, we added some reactions to the metabolic model to fill gaps in the network to allow biomass formation. Also, we removed some reactions to avoid the formation of inadequate loop reactions, which makes impossible to calculate balance of metabolic fluxes due to the arbitrary generation of metabolites by this loop reaction as discussed above. Only after fixing these problems, we could use the metabolic model for FBA and predict the metabolic profiles. Using the genome-scale model, we performed FBA to understand the characteristics of the metabolic network and to identify candidates of the target metabolic pathways that can be manipulated to improve organic acid production by C. glutamicum. The results revealed that the FBA agreed well with the experimental results; this suggests that when the cells grow exponentially, the metabolic profiles can be predicted by our genome-scale model with maximization of the biomass production rate. We also performed simulations to predict the metabolic profiles in amino acid production phases, and succeeded in representing the metabolic profiles in the lysine production phase. However, the glutamate production phase, in which the cells stop growing, could not be represented by the genome-scale model. Further improvements in the model, such as inclusion of some gene regulatory machinery, should be considered. Furthermore, we performed in silico screening to identify candidates of the target metabolic pathways that can be manipulated to improve organic acid production by C. glutamicum. Our results revealed that the disruption of H+-ATPase activity is the most effective in improving lactate production under oxygen deprivation conditions. In fact, recent studies showed that the disruption of H+-ATPase results in significant changes of metabolic flux profiles in C. glutamicum [in silico screening remains as future works. We expect that further extensive studies using our genome-scale model with experimental verifications will enable us to understand in detail the characteristics of the metabolic networks of C. glutamicum.In this study, we developed a genome-scale metabolic model of utamicum , althougThe authors declare that they have no competing interests.YS and MS performed the model construction and simulations. NS performed the culture experiments. CF participated in the design of the study and drafted the manuscript. TH rewrote the manuscript. HS conceived and supervised the study. All authors revised and approved the final manuscript.C. glutamicum genome-scale modelList of metabolic reactions in the . The sheet "reactions" contains all the reactions in the C. glutamicum genome-scale model categorized by their metabolic pathway and the sheet "abbreviated metabolites" enlists the abbreviations of the metabolites.Click here for fileGrowth and organic acid production by C. glutamicum under the anaerobic condition (experiment 1). The culture was initiated under aerobic conditions with air aeration and a high agitation speed, and 9 h after inoculation (indicated by a black arrow) the culture conditions were changed to no aeration and gentle agitation (100 rpm). The GUR, OUR, and production rates of organic acids, biomass, and carbon dioxide were calculated using the data obtained from 9 to 15 h after inoculation.Click here for fileC. glutamicum under microaerobic conditions (experiment 2)Growth and organic acid production by . The culture was initiated under aerobic conditions with air aeration and a high agitation speed, and 9 h after inoculation (indicated by a black arrow) the aeration rate was changed to 0.5 vvm and the OUR was maintained at a constant value (0.5 mmol/gDW/h) by changing the agitation speed. The GUR, OUR, and production rates of organic acids, biomass, and carbon dioxide were calculated using the data obtained 9 to 15 h after inoculation.Click here for fileC. glutamicum in the different phasesMetabolic flux profiles of . Figures (a) ~(e) show the schematic representations of the metabolic profiles in phases I ~ V, respectively. The thickness of the green arrows roughly corresponds to the metabolic fluxes; the gray arrows represent reactions with zero flux. The following abbreviations are used: Re_Mq, reduced form of menaquinone; Ox_Mq, oxidized form of menaquinone.Click here for fileSummary of differences between the genome-scale models of C. glutamicum in Ref.[ and present study. The essential differences between the previous study [m in Ref. and presus study  and our Click here for file


A more refined analysis not assuming extremization remains an elusive task for large metabolic systems due to algorithmic limitations.Cellular metabolism is one of the most investigated system of biological interactions. While the topological nature of individual reactions and pathways in the network is quite well understood there is still a lack of comprehension regarding the global functional behavior of the system. In the last few years flux-balance analysis (FBA) has been the most successful and widely used technique for studying metabolism at system level. This method strongly relies on the hypothesis that the organism maximizes an objective function. However only under very specific biological conditions  being still efficient on the analysis of large biological systems, where exact deterministic methods experience an explosion in algorithmic time. The algorithm we propose can be considered as an alternative to Monte Carlo sampling methods. It can be viewed as a chemical engine that transforms available raw materials into energy or into the building blocks needed for the biological function of the cells. In more specific terms a metabolic network is indeed a processing system transforming Although the general topological properties of these networks are well characterized -3, and nE. coli behave optimizing their growth performance [It is well known that under evolutionary pressure, prokaryote cells like formance . Flux Baformance . On the formance  has showhit and run have mixing times that scale only polynomially with system size [So far, apart from exact algorithms evaluating the volume of the space of possible solutions, that are unsuitable for analyzing metabolic networks larger than some dozens metabolites ,9, the btem size . HoweverAs a concrete step toward an efficient characterization of the set of fluxes compatible with the stoichiometric constraints, we propose a novel message-passing technique derived from the field of statistical physics and information theory.As already mentioned, a metabolic network is an engine that converts metabolites into other metabolites through a series of intra-cellular intermediate steps. The fundamental equation characterizing all functional states of a reconstructed biochemical reaction network is a mass conservation law that imposes simple linear constraints between the incoming and outcoming fluxes at any chemical reaction:ρ is the vector of the M metabolite concentrations in the network. i (o) is the input (output) vector of fluxes, and ν are the reaction fluxes governed by the M × N stoichiometric linear operator M intra-cellular relations among the N fluxes.where lhs of 1 can be set to zero. Under these hypotheses the problem of finding the metabolic fluxes compatible with flux-balance is mathematically described by the linear system of equationsAs long as just steady-state cellular properties are concerned one can assume that a variation in the concentration of metabolites in a cell can be ignored and considered as constant. Therefore in case of fixed external conditions one can assume metabolites (quasi) stationarity and consequently the b is the net metabolite uptake by the cell. Without loss of generality we can assume that the stoichiometric matrix i.e. that rank-dimensional manifold embedded in the N-dimensional space of fluxes. In addition, the positivity of fluxes, together with the experimentally accessible values for the maximal fluxes, limit further the space of feasible solutions. This fact may be expressed by the following inequalities:where in such a way that together, 2 and 3, define the convex set of all the allowed time-independent phenotipic states of a given metabolic network.V ⊂ ℝN of dimension N - M. The set of inequalities 3 then defines a convex polytope Π ⊂ V that, from the metabolic point of view, may be considered as the allowed configuration space for the cell states. The main goal of this work is computation of the volume of this space of solutions and of certain subspaces of it. Although conceptually simple, the notion of sub-dimensional volume like that of Π requires some new definitions.Mathematically speaking, the space of feasible solutions consistent with the Equations 2 is an affine space ϕ : ℝN-M → V ⊂ ℝN  × N Jacobian matrix ϕ in the canonical bases. Denoting λ = det N induces a measure on V (which does not depend on ϕ):Consider any linear parameterization allowing to compute the volume of our polytope1Π (·) is the indicator function of the set Π. It is worth pointing out that given the linear structure of the metabolic equations, the determinant of the mapping is a  constant. Although the coefficient λ could be explicitly calculated, it turns out that as far as only relative volume quantities are concerned, as in the case of the in silico flux knock-outs introduced below, this term factors out and therefore we will drop it from the rest of the computation.where The problem of describing the polytope Π can be cast into a probabilistic framework. We define the probability density W = V ∩ {νi = Marginal flux probabilities over a given set of fluxes are obtained by integrating out all remaining degrees of freedom. In particular we can define single flux marginal probability densities as integrals on the affine subspace volW (Π ∩ W) is the  volume of the intersection between the polytope Π and the hyperplane {νi = νi = νi = where the normalization term P-hard [e.g. N - M around 10 or so). To overcome such severe limitations we will introduce a very efficient approximate computational strategy that will allow us to compute the volume and the shape of the space of solutions for real-world metabolic networks.¿From a computational point of view, the problem of the exact computation of the volume of a polytope with current methods requires the enumeration of all its vertexes. The vertex enumeration problem is #P-hard ,17, but P-hard ), and maWe will adopt the following three steps strategy:a la Riemann considering an a N-dimensional square lattice whose elementary cell is of size εN. The approximated volume is then proportional to the number of cells intersecting the polytope Π. Of course the smaller ε the better is the approximation.• We discretize the problem • We consider an integer constraint satisfaction problem where each of the mass-balance equations set a hard constraint over the involved discretized fluxes.• We solve the constraint satisfaction problem using a message-passing algorithm called Belief Propagation.ε of side ε partitioning ℝN as in the simple sketch of Figure ϕ-1 into a partition Γε of ϕ-1(Π). The number of cells ε of Λε intersecting Π is proportional to the numbers of cells of Γε intersecting ϕ-1(Π). Finally, the volume in Eq. 5 is proportional to limε → 0εN-Mε . For any given ε one we have then defined discrete variables νi ∈ {0,1,..., qmax is the granularity of the approximation.Consider the regular orthogonal grid Λsi, a, as the ones appearing in normal stoichiometric relations, the discrete version of Eqs. 2 close in the set of positive integers defining a constraint satisfaction problem. The ε-approximation of the volume is then the number of elementary cells that are solution to the discretized mass-balance equations. It is interesting to note that in the case of fractional stoichiometric relations one can multiply all terms for the minimum common multiple of all denominators, getting an equivalent mass-balance equation with integer coefficients.When dealing with integer coefficients The integer constraint satisfaction is solved using Belief Propagation (BP), a local iterative algorithm that allows for the computations of marginal probability distributions. BP is exact on trees, and perform reasonably well on locally tree-like structures -22. Thisreverse search algorithm presented by Avis and Fukuda in [In this section we will analyze the performance of our algorithm against an exact algorithm on low dimensional polytopes. Among the different packages available in the Internet, we have chosen LRS , a progrukuda in  that canα = M/N and fixed number of terms different from zero K in each of the reactions. All fluxes were constrained inside the hypercube 0 ≤ νi ≤ 1. As a general strategy we have calculated several random instances of the problem and measured the volume (entropy) of the polytope using the LRS and BP algorithm. In particular, we have first generated 1000 realizations of random stoichiometric matrices with N = 12, M = 4. Note that N = 12 is around the maximum that allows simulations with LRS in reasonable time (around one hour per instance). For each polytope then we have computed the two entropies SLRS and SBP with both algorithms, fixing the same maximum value for the discretization qmax = 1024 for all fluxes.We have devised a specific benchmark generating random diluted stoichiometric matrices at a given ratio qmax = 16 , 64, 256, 1024. One can see how a finer binning of messages improves the quality of the approximation, seemingly converging to a single distribution of errors. It is expected that for larger N the histograms would peak around the true value: upon increasing the number of fluxes, loops become larger and the overall topology of the graph becomes more locally tree-like, validating the hypothesis behind the Bethe approximation. Unfortunately, the huge increase of computer time experimented in the calculation of the volumes using LRS made impossible to test systems large enough to make any reasonable scaling analysis.In Figure N ~12 where the running time of LRS explodes exponentially while BP maintains a modest almost-linear behavior.Finally we address the issue of the computational complexity of the algorithm which is a crucial one if one is interested in approaching real world metabolic networks whose size typically is at least 50 times the size of the largest network that can be analyzed with exact algorithms. In Figure qmax = 2048. As it can be seen in the two cases, the predictions of both methods compare rather well. Assuming the accuracy of MCS, differences are probably due to small loops structures in the graph. We leave for a future work the issue of a more detailed comparison of both methods. However we really think that the emerging scenario of RBC metabolism captured by BP is analogous to that obtained by MCS both quantitatively and qualitatively.We used our BP algorithm and MCS  to obtai used in  (resultsGHz). Of course, no stringent statement can be done at this level about the comparative performance of the two algorithms. This positive result encourages us to face the problem of metabolism at organism-wide scale.The MCS method appears to be quite efficient . The partial knock-out effect on flux i is then obtained reducing repeatedly SKOνdν in the unperturbed network. At 75% knock-out, two kinds of regimes are divided by a clear threshold at ν ~ 0.6: (i) for ⟨νi⟩ < 0.6, S0 - SKO at larger average fluxes, correlations increase rapidly but with larger fluctuations. The presence of this threshold can be understood noting that reactions belonging to the linear (glycolysis) an circular (Krebs cycle) pathways are, in the wild cell, fast flux reactions, with average flux values larger than 0.5. An analogous scenario emerges in the case of a 100% knock-outs, but now fluctuation are wider, and also fluxes with intermediate average value start becoming important. This is the case for instance of the 6 large impact fluxes having average flux around 0.3. A closer inspection reveals that among them there is an exchange fluxes (glycogen) and 5 internal fluxes . The first three  are the first steps of glycolysis, while PDH is the input of the Krebs cycle, and CS is a segment of the cycle strictly related to PDH. It is interesting that this peculiar behavior  are related to key check-points of central metabolism.Finally in Figure E. coli. The network used contains, in its original format, 1035 reactions and 626 metabolites [νi = νj is present we eliminate variable νi using elementary row operations. Doing so new trivial mass balance equations appear, an then we iterate the eliminations until all trivial mass-balance equations disappear. During Gaussian elimination, some mass balance equations become effective dead-end metabolite (i.e metabolites that are only consumed or produced). Fluxes participating to dead-end metabolites are set to zero at the beginning and removed from the system. The new set of equations is equivalent to the original one but with a lower number of fluxes. Reversible reactions have been considered using bidirectional signed fluxes. Using BP we are able to compute the marginal flux distributions in around 40 minutes, using qmax = 64.Finally we analyze the average fluxes distribution function in the metabolic network of abolites . The netP(ν) ∠ (ν + ν0)γ-. The fit gives an exponent γ around 1.5, a result that compares very well with previous simulations found in: (i) [γ is a signature of universality in cell's metabolism.We ran our algorithm on this network and computed the average fluxes in each reaction. We have performed a statistical analysis of these averages in the spirit of ,24,25. T in: (i)  where FB in: (i)  that theν ≈ 0.5, and smaller ones for ν ≈ 0.4 and μ ≈ 0.6. At present we do not know whether these jumps are just due to statistical fluctuations  or they reflect relevant biological or structural information about the network.A more careful analysis of the data may reveals however that the distribution of averages fluxes has a richer structure. In Figure α = M/N and fixed number of terms different from zero K, in each of the reactions, with results that compare very well with those of exact algorithms. Moreover, we show that while the running time of exact algorithms increases more than exponentially for already moderate sizes, our algorithm is polynomial. The program was run on the Red Blood Cell metabolism producing with shorter computational time results that are in both quantitatively and qualitatively in good agreement with those obtained by MCS presented in [We proposed a novel algorithm to estimate the size and shape of the affine space of a non full-dimensional convex polytope in high dimensions. The algorithm was tested in specific benchmark, i.e. random diluted stoichiometric matrices at a given ratio ented in ,11.E. coli central metabolism, and as expected, reactions with little redundancy turned out to be the ones with larger impact in the size of the space of the metabolic solutions. Specifically, most of the reactions associated with the transformation of glucose in pyruvate, belong to this set, as well as some reactions in the citric cycle. In addition we show strong correlations between the characteristics of the flux distributions of the wild type network and the changes in size of the space of solutions after reaction knock-outs. Finally, we calculate the distribution of the average values of the fluxes in the metabolism of the E. coli and present results that are consistent with those of the literature. In the present approach we have mainly followed a discretization strategy that although polynomial, becomes computationally rather heavy for mass balance equation containing a large number of fluxes. We are currently investigating other representation schemes for the messages. The final hope is to obtain an algorithm that allows for on-line analysis of organism-wide metabolic networks.Then, our program was used to study the Let us conclude by noting that in principle the presented approach can be extended to deal with constraints whose functional form is more general than linear, provided that the number of variables involved in each of the constraints remains small, as in the case of inequalities enforcing the second law of thermodynamics for the considered reactions . Work isM mass-balance equations imposes a constraint onto a subset of the metabolic fluxes. Let A be the set of equations and I the set of fluxes. Consider the a-th row of i ∈ a} ≡ {i1, ..., I be the labels of the fluxes involved in the considered equation having stoichiometric coefficients different from zero. Let also {a ∈ i} ≡ {a1, ..., A be the labels of the equations in which flux i participates. The emerging structure is a bipartite graph, with two types of nodes: variable nodes representing the fluxes of the reactions and factor nodes imposing mass conservation. In this case marginals become q-modal probability densities that for large values of In the previous section we have seen how the metabolic problem can be cast into a constraint satisfaction framework where each of ν satisfying all flux-balance constraints can be expressed as a product of flux and reaction marginals [Under the hypothesis that the factor graph is a tree it can be shown ,27 that arginals -21:di is the number of equations in which flux νi participates (i.e. the degree of site i). The marginal probabilities are defined as:where ε-cells intersecting the polytope Π  the number of elementary real-world situation where the graph is not a tree. One can hope that typical loop length are large enough to ensure weak statistical dependence of neighboring sites which lay at the heart of the Bethe approximation [One may wonder how such an approach could be useful in a ximation ,29. It iximation  used in ximation , binary ximation , and in ximation ,34. In aThe algorithm is based on two type of messages exchanged from variable nodes to functional nodes, and vice versa:μi → a(ν): the probability that flux i takes value ν in the absence of reaction a.• ma → i(ν): the non-normalized probability that the balance in reaction a is fulfilled given that flux i takes value ν.• The two quantities satisfy the following set of functional equations:a but i, b ∈ i\a, is the set of metabolites in reaction i but a, Ci → a is a constant enforcing the normalization of the probability μi → a(ν), and δ  is the Kronecker delta function  is 1 if a = b and 0 otherwise). The set of Equations 11 can be solved iteratively and upon convergence of the algorithm one can compute the marginal flux distributions as:where μj → a messages except one, an expression of the form na - 1 convolutions for each outputting message, i.e. na (na - 1) convolutions in total for constraint a. In the case of the complete E. coli network we have mass-balance equations with na as large as 500, then reducing the computational complexity of the iteration has a cogent practical implication on the performance of the proposed algorithm. There is a way to reduce this quadratic load to just O (na) convolutions. The method we propose is not confined to convolutions and works generally for any associative operation. Note that for operations that are efficiently invertible and commutative, one could just operate all na terms  and then for each outputting message operate with the inverse of the undesired element  i.e. a and let us assume that na is a power of two, say 2n (this assumption can be easily relaxed). We will iteratively build a n × na auxiliary matrix d = 1, ..., n - 1. This is equivalent to operate consecutive pairs of fluxes over metabolite a, then consecutive quadruples and so on. One needs just 2na operations for computing the full matrix at this stage.A brute force integration of the discrete set of equation would be much too inefficient for analyzing large networks, due to the multiple dimensional sum over Ca → i one needs additionally n = log2 na operations: we just have to operate the complement of i in its pair with the complement of this pair in its quartet and so on on all levels, i.e. in a compact form na + nalog2 na. Moreover, if all messages are to be computed sequentially this number can be further reduced to O (na).To compute Authors equally contributed to this work. All authors read and approved the final manuscript.Human red blood cell metabolism supplementary files. The archive contains 4 text files: rbc.sto (stoichiometric matrix where each column is a reaction and each line is a metabolite), rbc.flu , rbc.names (contains the name of both reactions and metabolites), and rbc.max .Click here for fileE. coli central metabolism supplementary files. The archive contains 3 text files: central.sto (stoichiometric matrix where each column is a reaction and each line is a metabolite), central.flu , central.names (contains the name of both reactions and metabolites).Click here for file