Metagenomics yields enormous numbers of microbial sequences that can be assigned a metabolic function. Using such data to infer community-level metabolic divergence is hindered by the lack of a suitable statistical framework. Here, we describe a novel hierarchical Bayesian model, called BiomeNet (Bayesian inference of metabolic networks), for inferring differential prevalence of metabolic subnetworks among microbial communities. To infer the structure of community-level metabolic interactions, BiomeNet applies a mixed-membership modelling framework to enzyme abundance information. The basic idea is that the mixture components of the model  are shared across all groups (microbiome samples), but the mixture proportions vary from group to group. Through this framework, the model can capture nested structures within the data. BiomeNet is unique in modeling each metagenome sample as a mixture of complex metabolic systems (metabosystems). The metabosystems are composed of mixtures of tightly connected metabolic subnetworks. BiomeNet differs from other unsupervised methods by allowing researchers to discriminate groups of samples through the metabolic patterns it discovers in the data, and by providing a framework for interpreting them. We describe a collapsed Gibbs sampler for inference of the mixture weights under BiomeNet, and we use simulation to validate the inference algorithm. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among inflammatory bowel disease (IBD) patients. Based on the discriminatory subnetworks for this metabosystem, we inferred that the community is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an antioxidant connected to IBD. Because this metabosystem has a greater capacity to exploit host-associated glycans, we speculate that IBD-associated communities might arise from opportunist growth of bacteria that can circumvent the host's nutrient-based mechanism for bacterial partner selection. Metagenomic studies of microbial communities yield enormous numbers of gene sequences that have a known enzymatic function, and thus have potential to contribute to community-level metabolic activities. Ecologically divergent microbial communities are presumed to differ in metabolic repertoire and function, but detecting such differences is challenging because the required analytical methodology is complex. Here, we present a novel Bayesian model suitable for this task. Our model, BiomeNet, does not assume that microbiome samples of a certain type are the same; rather, a sample is modeled as a unique mixture of complex metabolic systems referred to as “metabosystems”. The metabosystems are composed of mixtures of subnetworks, where subnetworks are mixtures of reactions related by function. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among IBD patients. We inferred that this metabosystem is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an important antioxidant, possibly contributing to gut inflammation associated with IBD. PLOS Computational Biology Methods article.This is a e.g., the Earth Microbiome Project e.g., the Human Microbiome Project Microorganisms comprise up to one-third of the Earths' biomass, and those living on a human can outnumber their cells by a factor of ten High-throughput shotgun sequencing yields enormous numbers of environmental DNA sequences, some being homologous to genes known to encode an enzyme and thus assignable to a metabolic function. Development of dedicated analytical methods for these data lags behind the capacity to generate it. The more popular strategies, although yielding promising results, highlight the analytical challenges. First, functional differences among microbiomes often stem from differing abundances of shared metabolic functions rather than presence-absence polymorphisms e.g., sets of reactions related by function). In order to discover metabosystems and subnetworks, and group microbial communities according to differential usage of the metabosystems and subnetworks, we propose BiomeNet, a novel mixed-membership statistical model for metabolic network data. The model takes the reaction abundance data for each metagenome sample as its input. Reactions and their abundances are derived from the abundance of enzyme-encoding gene sequences found within shotgun metagenomic datasets. Suitable datasets are now readily available from public resources such as MGRAST e.g., a subnetwork might be comprised of parts of different KEGG pathways), (iv) differential usage of subnetworks is modelled through metabosystem composition, and (v) samples with the same typological labels  need not be identical; rather, the full community metabolism of a sample can exist as a mixture of different metabosystems.Here, we introduce a Bayesian modelling approach for inferring differential usage of metabolic networks among microbial communities. We approach the problem by considering metabolic structure and function as arising from overlapping metabolic phenotypes referred to as “metabosystems”. A metabosystem is further characterized by a mixture of overlapping metabolic “subnetworks”  and its variants. BiomeNet takes advantage of dependencies between reactions encoded by metabolic networks without any data transformation and reduction. Moreover, BiomeNet is specifically designed to provide explanatory capabilities. Differentiating metabosystems discovered by BiomeNet can be explained by their differential usage of metabolic subnetworks, which in turn are interpretable as a small set of strongly connected metabolic reactions. Because interpreting principal components discovered by PCA is not trivial We validate our inference algorithm via simulation and apply it to datasets from two studies of functional divergence among gut microbiomes e.g., reactions) to contribute to other structures to different degrees . Aside from avoiding the need to place arbitrary boundaries on the components of a biochemical network, this framework reflects how community-wide metabolic activities of a microbiome arise from mixtures of organisms having different metabolic repertoires e.g., stool samples are comprised of mixtures of the epithelium and luminal niche communities BiomeNet is a hierarchical mixed-membership model, where metabolic reactions are mixed to form subnetworks, subnetworks are mixed to form metabosystems, and environmental samples are treated as potential mixtures of metabosystems. We explicitly model metabolism as a hierarchy because biochemical networks are widely considered to be organized in this way. For example, the KEGG pathways database arranges biochemical reactions into sub-pathways (consecutive reaction steps within curated pathways), which are arranged into “pathway modules” that are intended to represent functional units Within BiomeNet, each enzymatic reaction is decomposed into substrate-product pairs . DependeL subnetworks each contributing to different degrees. We model their composition with a mixture variable φ. For example, if we assume that we have 10 subnetworks (L = 10), we can look at metabosystem k and see it has mixing probabilities for each subnetwork kφ  =  . We can see from this example that metabosystem k is mainly comprised of 20% subnetwork 3, 10% subnetwork 6 and 70% subnetwork 9.Metabosystems are modeled as a mixture of θ. For example, if we have 3 metabosystems (K = 3), and a microbiome sample has a metabosystem mixture of θ = , then θ indicates that this sample consists of 20% metabosystem 1 and 80% metabosystem 3.Finally, each microbiome sample is modeled as a mixture of metabosystems. These metabosystems can be thought of as different facets of community-level metabolic activities. Considering the case of gut microbiome samples from diseased and healthy individuals, it is unlikely that the community metabolism of all diseased individuals will be exactly the same. Individuals with a more severe case of the disease might have a larger contribution from a “dysbiotic metabosystem” to their microbiome. Thus, we do not assume that samples are necessarily comprised of just one metabosystem. We denote the metabosystem mixture for a sample as Our model is completely unsupervised; the membership of reactions to subnetworks, the contribution of subnetworks to metabosystems, and the mixture of metabosystems within a sample are learned from the data. Collapsed Gibbs sampling N microbiome samples in the data, and those data are comprised of a total of nI reactions in the nth microbiome sample, and a total of niJ substrate-product pairs in the ith reaction of the nth sample. Because we expect that a microbiome sample could be a mixture of partially overlapping assemblages of microbes with varying types of ecological interaction, we model each sample as a mixture of K metabosystems, where K is assumed to be known and fixed in advance. The relative contribution of each metabosystem to the microbiome associated with the thn sample is modeled through latent variable nθ, a probability vector of K values summing to one. Thus, we haveSuppose we have a total of niZ denotes the metabosystem assignment for the ith reaction in the nth sample. The θ variables will be inferred from the data. We assume an independent and identical (iid) sparse symmetric Dirichlet prior on nθ.θα is a positive parameter. The mean of K, for i = 1,…, K, and the variance of θα is closer to 0, in which case, the probability that a randomly drawn point from this distribution is a sparse vector is larger. The sparsity introduced by a prior can be viewed as equivalent to the penalty added to the likelihood in the penalized likelihood method L) of metabolic subnetworks. Therefore, metabosystems differ with respect to their mixture probabilities of the different subnetworks. The contribution of each subnetwork to the thk metabosystem, kφ, is modeled by a vector of L mixing probabilities that sum to one. For K metabosystems, there will be K probability vectors of L mixing probabilities. Thus element klφ in K × L matrix φ represents the relative contribution of subnetwork l in metabosystem k. Let niY denote the subnetwork assignment for the ith reaction in the nth sample. Then we model niY as:Next, we assume each metabosystem is comprised of a fixed number  and product group (R). The compounds in the substrate group associated with a subnetwork are used as substrates in reactions that belong to that subnetwork. The product group associated with a subnetwork consists of products that are produced by at least one of the reactions in the subnetwork. Note that a compound can belong to both the substrate and the product group. Such a compound will be involved in the intermediary reactions of the subnetwork. In general, membership of a compound to a substrate or product group is considered to be a “soft”  membership.Reactions within a subnetwork are linked through their shared chemical compounds. We model subnetworks as a subset of compounds that are converted to another subset of compounds. It is reasonable to assume that the substrate and product sets cannot be arbitrary sets of compounds. Therefore, we assume that compounds are grouped together and make up substrate groups and product groups. Each subnetwork has its own substrate group  and subnetwork (Y) assignments for each reaction conditional on the assignments of all other reactions.The complete likelihood of the data given the hyper-parameters of the prior distributions is:-niZ and -niY denote the metabosystem and subnetwork assignment for all reactions in all samples except only reaction i in sample n. The individual terms in the above equation can be analytically derived  within the model. Thus, each microbiome sample is interpreted as a mixture of such structures. In unsupervised applications such as those presented in this paper, trying several different K values to find the value that shows separation of classes is often considered a natural way to choose K. Although this tactic requires some degree of heuristic judgment, typically it is difficult to avoid at least some heuristics in the context of unsupervised learning methods The purpose of BiomeNet is to learn the structure of the data. It is an unsupervised learning method. As with most other unsupervised learning methods, the validity of the inference is mainly judged through the scientific background of the problem and the interpretability of the results L as long as L is not too small. If L is larger than needed, there will be redundant subnetworks in BiomeNet, but they will carry very little weight for any of the metabosystems, and their reactions will have only a trivial impact on the reaction composition of each metabosystem. Alternatively, the informative subnetworks should make consistent contributions to each metabosystem, and their reactions should be highly influential on the reaction composition of each metabosystem. Thus, BiomeNet should be able to infer a consistent reaction profile for each of the K metabosystems, as long as the L value is not too small. This can be visually verified by using a heat map that portrays differences in reaction composition among metabosystems. The details for computing the reaction composition of a metabosystem, and for comparing the composition of different metabosystems are given in L value, the approach can be used to identify a minimum value for L.Ideally, inference under BiomeNet should be largely robust to the choice of K according to biological criteria. This approach avoids the computational burden associated with assessing many values of both K and L. However, we can use the same heat map described above to check for divergence among the K metabosystems. If there is no signal for divergent metabosystems , differences between metabosystems will be similar to those observed for the same metabosystem over different values of L. If at least some of the metabosystems are divergent, differences in reaction composition will be large as compared to those within the same metabosystem. In this way, we can assess the chosen value of K. Further details are given in In our analyses of real data, we chose a value of i.e., θ, αφ, αδα, and γα). The values of θα and φα control the extent by which subnetworks and metabosystems are mixed, while δα and γα control the size of the subnetworks. If very small values are chosen for δα and γα, then a relatively larger value of L should be chosen. Because we want (i) only a few subnetworks to contribute significantly to each metabosystem, and (ii) each subnetwork to consist of relatively few reactions, we chose a value for the concentration parameters close to zero (0.01). Users can control the extent of mixing for their data by resetting the concentration parameter values.The hyper-parameters of our model are the concentration parameters of the symmetric Dirichlet distributions . We compared the estimated mixture weights for metabosystems in each sample with the corresponding weights used for simulation. For each simulation, the inference algorithm was able to recover mixture weights that were very close to the actual metabosystem and subnetwork composition despite fixing value of the concentration parameters at 0.01 . Althougi) verify that observed differences in gut communities of carnivores and herbivores indeed reflects differences in community metabolic function, and (ii) gain insights into the differences in metabolic functions of those communities.Carnivorous, omnivorous and herbivorous mammals are well known for diverse digestive physiologies. Metagenome sequencing of fecal samples from 33 mammal species revealed that 16S communities and metagenomes within the mammalian gut differ according to dietary niche of the host http://sourceforge.net/projects/biomenet/. This dataset yielded 2,824 unique reactions between 2713 compounds. Reaction abundances for samples, as input into BiomeNet, range from 12,626 to 174,103 (see K = 3). The number of metabosystems was initially chosen to match the number of categories for dietary niche . However, because the model does not assign a diet status to a particular metabosystem, they are simply designated as metabosystems 1, 2 and 3, and the uniqueness of their reaction composition was assessed for these data.We obtained metagenomic data for 38 samples of mammals L = 100 subnetworks, we obtained an estimate of the contribution of different metabosystems to each gut community sample. As seen in the simplex plot within 1θ<15%). Interestingly, omnivores did not form a separate cluster; some omnivore communities (black dots) had mixtures more similar to carnivores and others more similar to herbivores (a priori (and possibly incorrect) assignment of one metabosystem as unique to omnivores.Using BiomeNet with rbivores . This hii.e., L = 50, 100, 150 & 200). Even though the labeling of a metabosystem is arbitrary, they can be distinguished if they have a characteristic composition of reactions. For these data, the metabosystems identified by BiomeNet had different reaction compositions that were largely robust to L. This is illustrated by the heat map in L = 50, JSD is consistently lower in the diagonal matrices as compared to L>50. Also when L = 50, some comparisons between metabosystems 2 and 3 have JSD scores similar to those observed for comparison within the same metabosystem. Taken together, the results indicate that these metabosystems have characteristic reaction compositions, with stable mixture weights in each sample when K = 3 and L≥100. Consequently, it was easy to coordinate metabosystems across the different analyses . Recall that the model will not assign a health status to a particular metabosystem.We illustrate the value of our approach to human microbiomics by applying it to a sample of adults who are classified either as healthy or as having IBD. The dataset consists of K = 3. Again, the three metabosystems are not equally divergent; while metabosystems 2 and 3 are divergent from each other, they are even more divergent from metabosystem 1. We also evaluated a model having K = 2 metabosystems, and found that no separation of samples was possible. Because each metabosystem has a characteristic reaction composition, it was easy to coordinate metabosystems across the different analyses when K = 3 . We found that 15 of the 22 principal subnetworks (mixture weight>2/L) in these data make a large contribution to the divergence among metabosystems. Three of those 15 subnetworks  are diagnostic of metabosystem 2 due to their very large relative contribution to that metabosystem  within subnetworks 38, 64 and 73. Subnetworks 38, 64 and 73 were comprised of 29, 19 and 18 principal reactions, respectively. Within each subnetwork, the principal reactions had a cumulative probability density>0.99  are abundant in subnetwork 38, and hence metabosystem 2. Reactions responsible for transport of N-acetylglucosamine and fucose are potentially meaningful because they suggest that metabosystem 2 is more dependent on glycans derived from host-associated substances, like mucin and shed epithelial cells, as a source of energy. Although these transporters do not point directly at the cause of gut inflammation associated with IBD, it does suggest that establishment of community metabosystem 2 could explain the resistance of IBD to moderate dietary intervention because the endogenous glycans provide a persistent source of nutrients for the community. Interestingly, extreme intervention whereby an exclusive liquid diet is administered up to 12 weeks  can sometimes induce remission of IBD in pediatric cases Subnetwork 64 contains reactions associated with ascorbate metabolism. Two reactions that convert ascorbate to dehydro-gulonate-6P have high relative-abundance in IBD patients suggesting the potential for reduced ascorbate levels within the gut due to microbiome metabolic activity. Remarkably, direct measurement reveals reduced ascorbate levels in IBD patients Subnetwork 73 is enriched in genes involved in the modification and transport of sugars and the metabolism of benzoate , our analyses with the current implementation were informative. For example, we found that samples of IBD patients have a high prevalence of a community metabosystem that we hypothesize is resistant to moderate dietary intervention, is closely associated with the human gut epithelium, and reduces the availability of an important antioxidant. Our finding that reactions within the most discriminatory subnetworks, although being highly connected, do not map to contiguous subsets of the main KEGG pathways illustrates the importance of learning the structures of the networks from the data.A wide variety of problems in computational biology have been addressed by using probabilistic graphical models e.g., scaling counts, mapping reads to EC numbers, etc.). Decisions must be made during the processing of any metagenomic dataset, and these could impact downstream analysis of community level metabolic capacity. Clearly, further simulation-based research is needed to investigate the sensitivity of various analytical methods (including BiomeNet) to the upstream details of data collection and processing. Such a comprehensive investigation is beyond the scope of this study.To validate the BiomeNet inference algorithm, we simulated hierarchical network data over many different combinations for the number of compounds, reactions, subnetworks and metabosystems. Reliable estimates of the mixing probabilities under this design, even when there was a large discrepancy between the fixed value of the concentration parameter and the true value for the generating process, confirmed the reliability of the algorithm. We note, however, that there are other steps involved in the processing of real metagenomic samples that are not included in our generative process . Indeed, microorganisms within a microbiome sample are expected to show metabolic interactions that range from negligible to obligate. We followed Boon et al. e.g., via antibiotic treatment) and assessing the extent to which that system returns to the same pre-disturbance composition of subnetworks.We chose to use the terms “subnetwork” and “metabosystem”, rather than “pathway” and “community”, so as to clearly delineate our model-derived structures from those entities having more biology-centred definitions . Our modelling approach is therefore suited to investigating questions about how the level of an individual's health status might be determined by mixtures of different metabolic phenotypes.It is important to note that we are working with a microbiome's latent capacity to process metabolites, as inferred from its metagenome. Thus the structures referred to as “metabosystems” reflect a latent aspect of metabolic phenotype. We modelled each sample as a mixture of metabosystems because microbial communities are thought to be composed of partially overlapping assemblages of microbes with varying types of ecological interaction BiomeNet provides the capability to focus attention on the fundamental structure of a complex metabolic network, which is necessary if researchers want to improve their understating of microbial community function. We note that this will also be the case when seeking a better understanding of the taxonomic composition of community structures. Along these lines, Arumugam and coauthors BiomeNet is suitable to investigating the latent metabolic structure of any microbial community. As long as abundance data can be obtained for sequences with assigned metabolic function, the model can be applied to samples from any environment  and over any scale . BiomeNet can easily accommodate the abundance data generated from high-throughput sequencing of RNA transcripts of uncultivable microorganisms. Thus, it could be employed to investigate the temporal dynamics of community metabolic structure within serially-sampled metatranscriptomic data.Text S1Network generation under the model, and validation of the inference algorithm. An overview of the generative process under BiomeNet and a detailed description of how we used simulation to verify that our sampling algorithm can recover the parameter values used to generate reactions for simulated microbiome samples.(PDF)Click here for additional data file.Text S2Analytical solutions for the individual terms of the posterior distribution of the latent variables. For inference under BiomeNet we sample from the posterior distribution of latent variables given the data. We use collapsed Gibbs sampling by integrating out the latent variables θ, φ, δ, γ and sample from the posterior distributions of the metabosystem (Z) and subnetwork (Y) assignments for each reaction conditional on the assignments of all other reactions. This is a high dimensional distribution, and the analytical solutions for the individual terms are given in these notes.(PDF)Click here for additional data file.Text S3Characterizing the reaction composition of a metabosystem, and measuring compositional differences between metabosystems. A detailed description of the method for characterizing the composition of a metabosystem at the level of its metabolic reactions, the method for measuring compositional differences between metabosystems, and the method for assessing robustness of metabosystems to the L value. The criteria for classifying principal subnetworks and discriminatory subnetworks are also provided.(PDF)Click here for additional data file.Text S4PCoA analysis of mammalian microbiome samples. PCoA analysis of Enzyme Commission assignments and KEGG Orthology assignments for the mammalian dataset reveals a separation between carnivore and herbivore gut microbiomes.(PDF)Click here for additional data file.Text S5Source and processing of metagenomic data. The source of the two gut metagenome datasets and a description how those data were processed to obtain abundance values for substrate-product pairs that were input into the model.(PDF)Click here for additional data file.Text S6Robustness of metabosystem composition to number of subnetworks. Evaluation of alternative numbers of subnetworks (L) in the model reveals that the reaction composition of the metabosystems is relatively stable to the specified value of L.(PDF)Click here for additional data file.Text S7Subnetwork composition of mammalian metabosystems. A presentation of the inferred contribution of 100 subnetworks to three metabosystems in the model, and the identification of the most discriminatory subnetwork for metabosystem 1.(PDF)Click here for additional data file.Text S8Subnetwork composition of the human IBD/healthy metabosystems. A presentation of the inferred contribution of 100 subnetworks to three metabosystems in the model, and the identification of the most discriminatory subnetworks for the metabosystem that was most associated with IBD (metabosystem 2).(PDF)Click here for additional data file.Text S9Core subnetworks. Definition and identification of core subnetworks under the BiomeNet modeling framework.(PDF)Click here for additional data file.Table S1Composition of subnetwork 49 inferred from the mammalian dataset. The table gives the KEGG reaction numbers, substrates and products for the principal reactions in mammalian subnetwork 49. Because the model does not rigidly define subnetworks, each reaction in the dataset will have an estimated mixing probability. As the majority of reactions make only a trivial contribution to this subnetwork (nearly zero), we filtered out any reaction with a contribution less than 2/R, where R is the count of unique reactions summed over all the samples in a dataset. This resulted in a subset of 25 reactions having a posterior density>0.99.(PDF)Click here for additional data file.Table S2Composition of subnetwork 38 inferred from the human dataset. The table gives the KEGG reaction numbers, substrates and products for the principal reactions in human subnetwork 38. Because the model does not rigidly define subnetworks, each reaction in the dataset will have an estimated mixing probability. As the majority of reactions make only a trivial contribution to this subnetwork (nearly zero), we filtered out any reaction with a contribution less than 2/R, where R is the count of unique reactions summed over all the samples in a dataset. This resulted in a subset of 29 reactions having a posterior density>0.99.(PDF)Click here for additional data file.Table S3Composition of subnetwork 64 inferred from the human dataset. The table gives the KEGG reaction numbers, substrates and products for the principal reactions in human subnetwork 64. Because the model does not rigidly define subnetworks, each reaction in the dataset will have an estimated mixing probability. As the majority of reactions make only a trivial contribution to this subnetwork (nearly zero), we filtered out any reaction with a contribution less than 2/R, where R is the count of unique reactions summed over all the samples in a dataset. This resulted in a subset of 19 reactions having a posterior density>0.99.(PDF)Click here for additional data file.Table S4Composition of subnetwork 73 inferred from the human dataset. The table gives the KEGG reaction numbers, substrates and products for the principal reactions in human subnetwork 73. Because the model does not rigidly define subnetworks, each reaction in the dataset will have an estimated mixing probability. As the majority of reactions make only a trivial contribution to this subnetwork (nearly zero), we filtered out any reaction with a contribution less than 2/R, where R is the count of unique reactions summed over all the samples in a dataset. This resulted in a subset of 18 reactions having a posterior density>0.99.(PDF)Click here for additional data file.Data File S1Posterior mixing probabilities of the principal reactions in all subnetworks (L = 100). Posterior probabilities are given for both the mammalian and human datasets. Because many reactions will have trivially small mixing probabilities for many subnetworks (nearly zero), we filtered out any reaction with a contribution less than 2/R, where R is the count of unique reactions summed over all the samples within the given dataset. The data are presented in a spreadsheet document, with the mammalian dataset and the human IBD/healthy dataset provided within separate sheets. Each sheet has 100 rows, one for each subnetwork in the model. Each row provides the KEGG reaction ID and mixing probabilities for a particular subnetwork. The data in each row is sorted according to its mixing probabilities.(XLSX)Click here for additional data file.


Ambiguity in malignant transformation of glioma has made prognostic diagnosis very challenging. Tumor malignant transformation is closely correlated with specific alterations of the metabolic profile. Exploration of the underlying metabolic alterations in glioma cells of different malignant degree is therefore vital to develop metabolic biomarkers for prognosis monitoring.1H nuclear magnetic resonance (NMR)-based metabolic analysis on cell lines  developed from gliomas of different malignant grades (WHO II and WHO IV). Several methods were applied to analyze the 1H-NMR spectral data of polar extracts of cell lines and to identify characteristic metabolites, including principal component analysis (PCA), partial least squares discriminant analysis (PLS-DA), fuzzy c-means clustering (FCM) analysis and orthogonal projection to latent structure with discriminant analysis (OPLS-DA). The expression analyses of glial fibrillary acidic protein (GFAP) and matrix metal proteinases (MMP-9) were used to assess malignant behaviors of cell lines. GeneGo pathway analysis was used to associate characteristic metabolites with malignant behavior protein markers GFAP and MMP-9.We conducted Stable and distinct metabolic profiles of the five cell lines were obtained. The metabolic profiles of the low malignancy grade group  were clearly distinguished from those of the high malignancy grade group . Seventeen characteristic metabolites were identified that could distinguish the metabolic profiles of the two groups, nine of which were mapped to processes related to GFAP and MMP-9. Furthermore, the results from both quantitative comparison and metabolic correlation analysis indicated that the significantly altered metabolites were primarily involved in perturbation of metabolic pathways of tricarboxylic acid (TCA) cycle anaplerotic flux, amino acid metabolism, anti-oxidant mechanism and choline metabolism, which could be correlated with the changes in the glioma cells’ malignant behaviors.Our results reveal the metabolic heterogeneity of glioma cell lines with different degrees of malignancy. The obtained metabolic profiles and characteristic metabolites are closely associated with the malignant features of glioma cells, which may lay the basis for both determining the molecular mechanisms underlying glioma malignant transformation and exploiting non-invasive biomarkers for prognosis monitoring.The online version of this article (doi:10.1186/1476-4598-13-197) contains supplementary material, which is available to authorized users. Gliomas, which are the most aggressive type of brain tumors, show high morbidity, a high recurrence rate, and high mortality. Survival from gliomas depends on the tumor type and grades of malignancy. Accordiet al. performed metabolic profiling of glioma tissues and their normal counterparts. t1 was 6.6 μs. Water suppression was achieved by irradiation of the water resonance during the recycle delay ( RD ) of 4 s and the mixing time (τm) of 120 ms. The spectral width was 10 kHz with an acquisition time per scan of 1.64 s, and 256 transients were collected into 32 K data points for each spectrum. The free induction decay (FID) was zero-filled to 64 K and an exponential line-broadening function of 0.3 Hz was applied to the FID before Fourier transformation. Both phase and baseline corrections were carefully performed. The 1H NMR spectra were referenced to the methyl group of TSP (δ 0.00).All NMR spectra were reduced to 2587 integrated regions with a width of 0.003 ppm (bin) corresponding to the region of δ 9.5-0.8 using the MestRova6.5 software . The region of δ 5.5-4.5 was removed to eliminate artifacts related to the residual water resonance. .Before multivariate statistical analysis, the integral values were mean-centered and pareto-scaled. To checFCM is a clustering method that allows one piece of data to belong to two or more clusters and is extensively used in pattern recognition, 47. Theik is the degree of membership of xi in the cluster k, xi is the i-th measured data, vk is the center data of the k cluster. We used the FCM clustering algorithm through the Fuzzy Logic Toolbox in MATLAB .Where m is any number greater than 1, uTwo criteria were used to identify the characteristic metabolites. One was the VIP score of the OPLS-DA model and the For relative quantification of characteristic metabolites, the relative integrals of metabolites were used for comparison between two groups. The average changes and standard error were calculated.Pearsons’s correlation coefficients of cell samples in two groups were further calculated to display the relationships between the relative integrals of spectral peaks in a certain biological profile, as described previously. A heatmThe network of the metabolites with significance correlations was displayed by MATLAB Bioinformatics toolbox. Significant positive correlations were shown in red, while significant negative correlations were in blue. In addition, GeneGo MetaCore was used to analyze the network that describes the interaction between the characteristic metabolites and GFAP/MMP-9.Additional file 1: Figure S1: The proliferation ability of five glioma cell lines. Differences in the 490 nm absorbance among five cell lines were compared by One-way ANOVA. Values represent the mean ± SD in triplicate. (TIFF 945 KB)Additional file 2: Figure S2: Network of the shortest directional paths leading to characteristic metabolites related to GFAP/ MMP-9 regulation. Small molecules appear as purple hexagons, reactions as grey boxes, enzymes as orange shapes, transcription factors as red stars, ligands and extracellular peptides as green shapes, and transporters as purple "X" shapes. Metabolites with available data points are tagged with blue circles. Arrows denote mechanisms of interaction, in which green signifies activation and red indicates inhibition. Grey interactions represent transport or consumption/production of metabolic intermediates. (TIFF 3 MB)


Chlamydomonas reinhardtii cultured in the presence of acetate perform mixotrophic growth, involving both photosynthesis and organic carbon assimilation. Under such conditions, cells exhibit a reduced capacity for photosynthesis but a higher growth rate, compared to phototrophic cultures. Better understanding of the down regulation of photosynthesis would enable more efficient conversion of carbon into valuable products like biofuels. In this study, Flux Balance Analysis (FBA) and Flux Variability Analysis (FVA) have been used with a genome scale model of C. reinhardtii to examine changes in intracellular flux distribution in order to explain their changing physiology. Additionally, a reaction essentiality analysis was performed to identify which reaction subsets are essential for a given growth condition. Our results suggest that exogenous acetate feeds into a modified tricarboxylic acid (TCA) cycle, which bypasses the CO2 evolution steps, explaining increases in biomass, consistent with experimental data. In addition, reactions of the oxidative pentose phosphate and glycolysis pathways, inactive under phototrophic conditions, show substantial flux under mixotrophic conditions. Importantly, acetate addition leads to an increased flux through cyclic electron flow (CEF), but results in a repression of CO2 fixation via Rubisco, explaining the down regulation of photosynthesis. However, although CEF enhances growth on acetate, it is not essential—impairment of CEF results in alternative metabolic pathways being increased. We have demonstrated how the reactions of photosynthesis interconnect with carbon metabolism on a global scale, and how systems approaches play a viable tool in understanding complex relationships at the scale of the organism.Cells of the green alga  Chlamydomonas reinhardtii has been widely used as a model organism to study photosynthesis  of this organism were presented and used for prediction of metabolic fluxes in different growth conditions  and Flux Variability Analysis (FVA) for the prediction of metabolite flux through a metabolic network reconstruction  were subtracted from maximal fluxes under phototrophic conditions (b). Conversely, minimal fluxes under phototrophic conditions (c) were subtracted from maximal fluxes of mixotrophic conditions (d).FVA is an FBA-based method for characterizing all feasible states of genome-scale metabolic models that satisfy a set of given constraints and objective function  environment, used in conjunction with Gurobi optimizer solver (version 5.6) employing a linear programming based optimization algorithm , flux substitutable (where the range of possible fluxes span zero) and flux blocked (reactions with minimum and maximum flux of zero). This method uses FVA results to determine whether a flux is always required for optimal biomass production, is potentially used for optimal biomass production or is never used for optimal biomass production.To determine which reactions and metabolic pathways are active or dormant in a particular condition, a reaction essentiality analysis was performed from the non-overlapping reactions derived from FVA  were used in this study. Cells were cultured in 250 ml conical flasks with 200 ml medium, which were placed in a shaker at 180 rpm and illuminated on a 16 h light/8 h dark cycle with light provided by warm-white LED lamps (color temperature 3000–3200 K), at 140 μmol m−2 s−1, 22°/16°C day/night. Mixotrophic cultures were grown in a Tris-Acetate-Phosphate (TAP), with added potassium phosphate (pH 7.0) and Hutner trace elements  was measured using an Ocean Optics USB4000 spectrophotometer . Specific growth rates (μ) were derived from cells in an exponential phase of growth, from two time points  with associated OD readings used in the equation below.For inoculation, 250 μl phototrophic cultures in exponential growth phase were axenically transferred to 250 ml conical flasks containing 200 ml of the appropriate medium. Following introduction of algae, cell growth was monitored at intervals for 12 days, until a stationary or death phase was reached. The optical density of cultures at 680 nm . Intact C. reinhardtii cells in culture medium were placed into the chamber, maintained at 20°C and continuously stirred. Saturating light was provided by a Led Engin LZ4 warm white LED  driven by a laboratory built constant current power supply. Rates of photosynthesis were normalized to cell number for each sample. Oxygen evolution was determined every 24 h from Day 4 until cells reached a stationary phase, expressed as oxygen evolution on a cellular basis.Measurements of O2 evolution steps of the TCA cycle are bypassed, resulting in retention of organic carbon by the cell. Model simulations are consistent with published experimental data, which have shown that ICL activity is essential for efficient mixotrophic growth  whilst mixotrophic growth was simulated using the phototrophic model as a base model and allowing the uptake of acetate at an experimentally defined rate Hoober, . All othIn phototrophic simulations, pyruvate, originating from carbon fixation is converted into acetyl-CoA and fed into the TCA cycle. ICL activity was redundant and the model chose to export isocitrate to the cytosol in exchange for malate. Cytosolic isocitrate was ultimately converted into biomass and the newly imported malate was converted into oxaloacetate and exported into the cytosol which fed back into pyruvate metabolism.In addition to increasing fluxes through enzymes involved in the TCA cycle and localized in the mitochondria, acetate also increased fluxes associated with the glycolytic pathway. Oxaloacetate, generated in TCA cycle reactions is converted into glycerate 2-phosphate (2PG) and exported into the cytosol, where a flux partition occurs, resulting in the majority of flux continuing through gluconeogenesis leading to the formation of both starch and sucrose, accumulating within biomass. Both starch and sucrose are the main products of photosynthesis , the primary reaction of photosynthetic carbon fixation. The reactions of gluconeogenesis in the mitochondrion are otherwise inactive. The predominant flux from 3PG was branched toward the Calvin-Benson cycle in the chloroplast. A further branching of flux toward erythrose 4-phosphate (E-4P) and sedoheptulose 7-phosphate (S7P) and their immediate removal from gluconeogenesis toward carbon fixation is observed. The resulting flux toward glucose 1-phosphate (G1P) production was reduced due to branching in the network and when compared to mixotrophic simulations, was reduced by a factor of 2.4, and as such, only starch was accumulated within biomass.Phototrophic metabolism Figure  on the o2 into organic compounds. In mixotrophic simulations  and fructose 6-phosphate (F6P) via the reversible action of the enzymes ribulose 5-phosphate epimerase (RPEh) and transketolase (TKT2h) respectively. It is with these reactions that the OPPP combines with the Calvin-Benson cycle and gluconeogenesis and ultimately demonstrates the interconnectivity of photosynthesis with central carbon metabolism.In addition to altering fluxes in central carbon metabolism, acetate is also predicted to modulate fluxes in photosynthesis and the Calvin-Benson cycle. The Calvin-Benson cycle uses the products of photosynthetic electron transport, ATP and NADPH, to convert COs Figure  the Calvb6f from ferredoxin. As a result, ATP production resulting from CEF increased without production of NADPH, as described previously. The activity of CEF was otherwise non-evident with phototrophic simulations  and 1546 (70%) respectively]. Flux essential reactions for phototrophic growth and mixotrophic growth comprised the lowest subset of reactions with 16 essential reactions in each condition, representing less than 1% of reactions, whilst 626 reactions (28.6%) were blocked for phototrophic simulations verses 629 (28.7%) for mixotrophic growth.2 transport into the cytosol (CO2t), the conversion of ribulose 5-phosphate and Xu5P via ribulose-5-Phosphate 3-Epimerase (RPEh), cytochrome b6/f complex (CBFC), ferredoxin-NADP+ reductase (FNORh) and the two photosystems (PSI and PSII). Here, it seems that the activity of CSm, allowing for the entry of acetyl-CoA into the TCA cycle, and PEP carboxykinase suggest that TCA cycle itself is fundamentally important to provide a heightened biomass for mixotrophic growth, as these reactions were all substituble for phototrophic growth. The finding that CEF was substitutable for both growth regimes is important indicating its non-essential role in both mixotrophic and phototrophic metabolism.Out of the 16 essential reactions identified under mixotrophic growth, 10 were also deemed essential for phototrophic growth. These reactions all consisted of photon exchange and uptake. The remaining six reactions were classified as substitutable  whilst acetate uptake (EX_ac(e)) and transport into the cytoplasm ACt were blocked. There were no blocked reactions observed for mixotrophic growth, however, there were seven substitutable reactions that were classed as essential for a phototrophic simulation. These included COiCR1080 to predict primary metabolism with respect to phototrophic and mixotrophic growth. To further asses the reliability of model predictions, growth rate, and oxygen evolution, were measured to compare predicted growth and photosynthetic oxygen evolution to address the initial question of the reported down regulation of photosynthesis with mixotrophic growth.We used the modified C. reinhardtii cell growth occurred following a logistic curve for both phototrophic and mixotrophic cultures  to evaluate the down regulation of photosynthesis associated with a mixotrophic growth regime, in the presence of acetate. Furthermore, model predictions have been validated using experimental results presented here and can be compared to results in the literature (Merchant et al., It is widely accepted that growth in the presence of acetate induces a down regulation of photosynthesis in the model organism Mixotrophic simulations included the uptake of acetate set at an experimentally determined level and allowed for the free exchange of gasses. It has been previously reported that the incorporation of acetate into acetyl CoA might occur via two possible pathways. The first pathway involves a two-step reaction involving ACK, prior to phosphate-acetyltransferase whilst the second pathway involves a single step conversion catalyzed by ACS (Johnson and Alric, C. reinhardtii has the capacity to convert acetate to acetyl-CoA in the cytosol, into the mitochondria through the TCA cycle, into the glyoxylate cycle and in the chloroplast due to localization of the enzyme ACS in these organelles. Our analysis suggests that acetate taken up into the cytoplasm is converted to acetyl-CoA by the enzyme ACS. However, our essentiality analysis did show this reaction to be substitutable for both conditions. Therefore, we are not able to conclusively say which reaction is responsible for acetate assimilation.Different models contain different structures, constraints and different optimization criteria, hence used to address different questions. Based on the annotated genome and metabolic reconstruction, Regardless of the primary acetate assimilatory reaction, we predict that acetyl-CoA feeds directly into a simplified TCA cycle, using the mitochondrial ICL with reducing power being consumed through oxidative phosphorylation. Operation of mitochondrial ICL was deemed essential for mixotrophic growth, but substitutable for phototrophic growth. Our model simulations are thus consistent with the experimental observation that acetate induces the expression of ICL and that ICL is required for growth on acetate (Plancke et al., 2 fixation within the chloroplast, yet still exhibiting a greater biomass than phototrophically growing cells. The suppression of CO2 fixation by acetate has been predicted under a mixotrophic growth regime at low light (Boyle and Morgan, C. reinhardtii mutants devoid of active Rubisco are still able to grow in the presence of acetate, albeit sub-optimally, compared to wild type (Pinto et al., 2 fixation indicating an overestimation of the inhibitory effect of acetate.Acetyl-CoA was then fed into the mitochondria with the export of succinate toward mitochondrial respiration and increasing flux toward ubiquinol. In addition, acetate increased fluxes along the pathway of gluconeogenesis whilst suppressing CO6fb complex. Previously, De Oliveira Dal'Molin et al. (6fb complex and feredoxin NADPH oxidoreductase has been characterized (Iwai et al., 2. As such, our mixotrophic simulations suggest C. reinhardtii prefers to assimilate acetate rather than CO2 by way of suppressing the CO2 fixation step, thereby alleviating the requirement for NADPH. Acetate assimilation via ACS however still requires ATP (Morales-Sanchez et al., We observe an increased flux through the CEF reactions, consistent with the suggestion that CEF around PSI explains the down-regulation of photosynthesis (Johnson and Alric, n et al.  reportedn et al. . Consistn et al. . The genn et al. . The wayn et al. . CEF alsn et al. . HoweverHere we have presented a GEM which is able to predict and explain the role of CEF in acetate metabolism while demonstrating the non-essentiality of CEF. It is well known that acetate metabolism leads to an increased growth rate and biomass. Model simulations are able to reproduce this and suggest that an enhanced biomass is achieved in mixotrophic cells by increased fluxes into starch and sucrose metabolism resulting from increased gluconeogenesis. In addition, the OPPP was active resulting in the incorporation of 6PGC into R5P. R5P is used in the synthesis of nucleotides and nucleic acids, supporting greater cell profilation and increased biomass (Bar-Peled and O'Neill, As a tool, flux balance models are becoming increasingly popular for explaining biological phenomena. As we have shown here, FBA is a powerful tool for data qualification. Of course, assumptions are made in constraint based modeling approaches and, as such, the questions investigated need to be applicable to the methodology being used. To accurately predict the fate of acetate using constraint based modeling techniques presents a challenge due to the presence of isozymes. To fully constrain the solution space requires integration of targeted omics data.We have modeled acetate metabolism in the light and as such, in a photosynthetic organism, metabolic pathways that are specifically active in the night are ignored. For example, starch degradation was constrained to zero to reflect the suppression of this reaction in the light. As a result, although starch contributed to the biomass, its accumulation was not specifically optimized account for low synthesis of starch. Experimental studies have shown that phototrophic growth favors starch accumulation when compared to mixotrophic cultures (Singh et al., Just as the ratio of ATP and NADPH have been shown to modulate the reactions of photosynthesis, elemental ratios of carbon and nitrogen have also been shown to affect cellular metabolism of photosynthetic microalgae (Talmy et al., Chlamydomonas reinhardtii, with an accurate representation of CEF, which is now able to explain the down regulation of photosynthesis observed under mixotrophic growth conditions in the presence of acetate. The predictive capabilities of the model were used to highlight changes in metabolism that were essential for this trait. We can conclude that acetate incorporation into metabolism is achieved via reactions of the TCA cycle before entering central metabolism requiring CEF. CEF serves to support the production of a proton motive force that allows ATP generation without the net formation of NADPH, serving as a balance to meet metabolic demands imposed on the system. The functioning of CEF is however non-essential. In doing so, we have demonstrated how the reactions of photosynthesis interconnect with carbon metabolism on a global scale, and how systems approaches play a viable tool in understanding complex relationships at the cell-wide scale.In conclusion, we have produced a curated version of a GEM of The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


E. coli and find that up to 80% of its EFMs are thermodynamically infeasible. Moreover, we identify glutamate dehydrogenase as a bottleneck, when E. coli is grown on glucose and explain its inactivity as a consequence of network embedded thermodynamics. We implemented tEFMA as a Java package which is available for download at https://github.com/mpgerstl/tEFMA.Elementary flux modes (EFMs) are non-decomposable steady-state pathways in metabolic networks. They characterize phenotypes, quantify robustness or identify engineering targets. An EFM analysis (EFMA) is currently restricted to medium-scale models, as the number of EFMs explodes with the network's size. However, many topologically feasible EFMs are biologically irrelevant. We present thermodynamic EFMA (tEFMA), which calculates only the small(er) subset of thermodynamically feasible EFMs. We integrate network embedded thermodynamics into EFMA and show that we can use the metabolome to identify and remove thermodynamically infeasible EFMs during an EFMA without losing biologically relevant EFMs. Calculating only the thermodynamically feasible EFMs strongly reduces memory consumption and program runtime, allowing the analysis of larger networks. We apply tEFMA to study the central carbon metabolism of  Based on a steady-state analysis of a stoichiometric matrix  these methods allow for phenotypic predictions from genotype dataConstraint-based reconstruction and analysis methods have been proven to be valuable tools in gaining system wide understanding of cellular metabolism12EFMA decomposes the stoichiometric matrix into non-decomposable, non-zero steady-state pathways, called EFMset al.Regardless of the theoretical challenges, several software tools are available and allow the calculation of the full set of EFMs at least in small or medium scale (metabolic) models11in vivo as they are in opposition to other constraints that have not been accounted for, like known regulatory mechanisms15EFMA utilizes stoichiometric information only. Yet, many of the topologically feasible EFMs are infeasible E. coli under glucose saturated conditions.Here we present a novel computational tool – thermodynamic EFMA (tEFMA) – which integrates the cellular metabolome into the EFMA. This allows us to verify the thermodynamic feasibility of EFMs already during the runtime of the EFMA and curbs the explosion of the number of EFMs without losing any biologically relevant EFMs. Computationally, our new approach successfully tackles the major bottleneck of double description based EFMA by strongly reducing computational costs, both in terms of runtime and resource consumption. Biologically, tEFMA allows the identification of infeasible pathways based on an unbiased analysis derived from first principles. More specifically, tEFMA correctly predicts the inactivity of the glutamate dehydrogenase (GDH) in m  metabolites and r reactions can be represented by an m × r matrix, S. At steady-state all flux distributions, v, obey Sv = 0 and virrev ≥ 0, where virrev is a sub-vector of v containing only irreversible reactions. We assume that the network contains only irreversible reactions, as any reversible reaction can be split into an irreversible forward reaction and an irreversible backward reaction. Of particular interest are so called EFMs, ieiv > 0) is omitted, the remaining reactions can no longer carry a steady-state flux. Geometrically, the EFMs (in a network of irreversible reactions) can be regarded as extreme rays, i.e. edges, in a convex polyhedral coneThe stoichiometry of a metabolic network with S) each row of this matrix is processed and converted to binary form. For each row (i.e. reaction) intermediate EFMs (that are the columns of the matrix) are combined such that their fluxes are nonnegative and therefore convertible to a bit representation and added to the matrix. New intermediates are added to the quickly growing list of intermediate EFMs if they are not a superset of any other intermediate EFMs. The iteration stops if all reactions are processed and the intermediate EFMs are fully converted into binary format. The remaining intermediate EFMs are then, in fact the EFMs. A step by step example can be found in the The binary (null-space) approach represents EFMs as binary bit vectors of the supporting reactions. These bit patterns are generated iteratively. Starting from an initial solution matrix . That is why the limits in Eq. (8) were expressed in terms of logarithms. The LP checks whether all reactions contributing to an EFM, ke, are simultaneously feasible [Eq. (5)] and consistent with a metabolome within the given error bounds riG, while we are only interested in the feasibility of Eqs. (4-8). Therefore, any  solution suffices, which poses a computationally less challenging problem.Eqs. (1) and (2) identify isolated, thermodynamically infeasible reactions based on (measured) metabolite concentrations. However, NET analysis does not only study a reaction in isolation, but rather considers a reaction's feasibility in the context of pathways. NET analysis utilizes the thermodynamic interdependencies between reactions and verifies if a given network structure is consistent with a (measured) metabolome. To this end NET analysis is solved by the linear program (LP) given by22The basic feature of NET analysis is illustrated in i we may find that 18, 41, and 12 intermediate EFMs have positive, zero, and negative flux values in reaction i. This gives rise to 18 × 12 = 216 potentially new intermediate EFMs of which only 22 EFMs are actually added to the list of new intermediates as only these pass the (tree-based) adjacency and superset testing of the EFM enumeration procedure. In tEFMA we check the feasibility of the original 18 + 12 intermediate EFMs and remove infeasible EFMs there. Suppose that 8 out of the 18 positive intermediate EFMs are infeasible and can be removed instantly. Rather than 216 potentially new intermediates we now just get 10 × 12 = 120 potentially new intermediates of which only 17 EFMs are actually added to the list of new intermediate EFMs as these pass the (tree-based) adjacency and superset testing. (The numbers for this example were taken from line i = 10 in In tEFMA every intermediate EFM is checked at the beginning of each iteration against a given metabolome according to Eqs. (4-8) and immediately removed if infeasible. The efficiency of this approach is illustrated in T = 310.15 K (37°C).In the remainder we assume that efmtool, which was originally developed by Terzer and Stellingefmtool. The new classes are responsible for reading the additional information, call CPLEX  and handle infeasible EFMs. To invoke the new functionality we modified two already existing Java classes and the XML file that handles command line arguments  based on experimental metabolite concentrations measured by Bennett et al.We calculated thermodynamically feasible EFMs in medium scale metabolic models of We compared tEFMA against an ordinary EFMA followed by NET analysis. The sets of thermodynamically feasible EFMs were identical in both analyses. For growth on glucose about one third of all EFMs were thermodynamically feasible. The reduction in the number of feasible EFMs is highly condition specific as on glycerol and acetate the numbers of feasible EFMs are roughly cut in half. These comparisons were based on the full metabolic model, M1, without any other adaptations, i.e. also unused uptake reactions were subject to the analysis. If all unused uptake reactions were removed from the models, then the changes in the number of feasible EFMs was even more pronounced.On glucose minimal medium only 19% of the EFMs were thermodynamically feasible, while on acetate minimal media 76% were feasible (using model M2). However, in the case of glucose 19% corresponded to more than 30,000 feasible EFMs, while on acetate roughly 900 EFMs remained feasible. Thus, growth on glucose still opened dramatically more metabolic possibilities (counted by the number of feasible EFMs) than growth on any other carbon source.We verified the stability of the feasible EFMs by randomly perturbing the metabolite concentrations (see methods section for details). For all tested perturbations  the median number of feasible EFMs remained constant see the . MoreovefG′-values (see methods section for details). Up to a perturbation magnitude of 1 kJ/mol our results stayed essentially constant  oxidizes malate to generate oxaloacetate as part of the tricarboxylic acid cycle. tEFMA correctly identified the reverse reaction to be infeasible. Similarly acetaldehyde dehydrogenase (AdhE), which catalyzes the reduction of acetyl coenzyme A to acetaldehyde, was identified to be infeasible under the three tested growth conditions in accordance with well established knowledge. Both conclusions could have been made without the help of tEFMA, as evaluating Eqs. (2) and (3) for Mdh and AdhE unambiguously identified the reactions' directions without considering the network structure of metabolism.E. coli grown on glucose. The latter could not have been concluded without a NET analysis or tEFMA. For example, within the error bounds of the measured metabolite concentrations the reactions phosphoglycerate kinase (Pgk), glyceraldehyde 3-phosphate dehydrogenase (Gapd), and fructose bisphosphate aldolase (Fba) were found to be reversible if analyzed individually. Only together tEFMA identified them to be infeasible in direction of gluconeogenesis  pathway produces glutamate in two steps: (i) glutamate is used to produce glutamine by the energy dependent glutamine synthase and (ii) the amide group is then transferred reductively from glutamine to α-ketoglutarate to form glutamate. Both pathways were identified in an ordinary EFMA and produce 1 mole of glutamate net. For growth on glucose, however, tEFMA identified inconsistencies between GDH and the lower part of the glycolysis as well as between reactions GDH and aconitate hydratase (ACONTb). We found that on glucose no thermodynamically feasible EFM was supported by an active GDH feasible EFMs is again infeasibleCurrently DDM is the most common approach for calculating EFMs9To curb the explosion of the number of (intermediate) EFMs, we solved many LPs to determine their feasibility. In our application LPs are uncritical in terms of memory consumption. Overall we saved memory by removing infeasible EFMs at the price of an increased computational load to evaluate the LPs. Fewer (intermediate) EFMs meant a shorter list of (intermediate) EFMs, too. This reduced the time to perform the adjacency and superset tests on the EFMs. In the tested cases, the overall runtime decreased at least by 50%. Note that the scaling and efficiency of the DDM critically depends on the order in which constraints are processed31E. coli on our computer infrastructure. More (omics-)data, like regulatory constraintsIt is known that out of all EFMs in large networks few are physiologically significanta posteriori. tEFMA will aid such studies in providing better computational performance and allowing larger systems to be analyzed.Although tEFMA utilizes an optimization principle to fit the metabolic profile, it still retains the ability to unbiasedly characterize all metabolic capabilities of an organism. However, tEFMA cannot predict individual metabolic fluxes. In fact, even the combination of two thermodynamically feasible EFMs might result in an infeasible flux distribution2937404142fG, for each metabolite. Our analysis showed that an error in ΔfG of up to 1 kJ/mol did not cause alterations. Such accuracy is achievable with current (reactant contribution) methods for the estimation of the Gibbs energyThe success of tEFMA is dependent on the availability of a measured metabolome. Measurement errors in the concentrations were taken into account, and tEFMA was found to be robust against further perturbations. More critical for tEFMA is the requirement for accurate data on the Gibbs free energy of formation, Δet al.tEFMA is inherently condition specific and in principle has to be repeated upon any change in the environment. In practice, however, that might not be necessary as Ishii et al.P. tricornutumet al.tEFMA's condition specificity is in strong contrast to the approach taken by Hunt tEFMA retains the ability to allow for a fully unbiased analysis of metabolism. In fact, the predicted inactivity of GDH under growth on glucose was completely derived from first principles. This allows to draw very general statements of biological relevance without relying on optimality criteria or particular flux distributions. The inactivity of GDH for instance, allows glutamate synthesis only via the ATP consuming GOGAT pathway. The increased energy demand for glutamate synthesis might cause problems during recombinant protein production, which induces additional energy requirements in the host. Thus by activating GDH rather than GOGAT the metabolic burden is reduced.ad hoc assumptions are required to estimate the missing compartment specific concentration dataCurrently an assumption-free tEFMA can only be performed on prokaryotes. tEFMA on eukaryotes would require compartment specific concentration data. A theory to describe the thermodynamics of inter-compartmental transport is availableIn summary, we developed tEFMA, a tool that presents an important step forward to the analysis of genome-scale metabolic networks. tEFMA integrates NET analysis into EFMA and succeeds in calculating only EFMs, that are thermodynamically consistent with a given metabolome. By doing so, it dramatically reduces the hardware requirements for such an analysis to be carried out and paves the way to enumerate EFMs in large-scale metabolic networks. This is possible as the calculated set of EFMs is reduced by the large number of thermodynamically infeasible EFMs. To show the accuracy of the tool we presented the correct identification of several infeasible pathways without making wrong predictions. Furthermore, we pointed out that tEFMA correctly distinguishes between the GDH and GOGAT pathways to produce glutamate. Additionally, we verified that the patterns, and therefore pathways, which were found to be infeasible in the smaller model remained infeasible in the larger model.M.P.G., C.J. and J.Z. conceived and designed the study; M.P.G. and C.J. developed the software; M.P.G. and J.Z. developed the models; M.P.G. run the experiments; M.P.G. and D.E.R. contributed analysis tools and performed the analysis; M.P.G., D.M., C.J. and J.Z. wrote the manuscript.Supplementary file 1Supplementary file 2Supplementary file 3


A central unsolved problem in early evolution concerns self-organization towards higher complexity in chemical reaction networks. In theory, autocatalytic sets have useful properties to help model such transitions. Autocatalytic sets are chemical reaction systems in which molecules belonging to the set catalyze the synthesis of other members of the set. Given an external supply of starting molecules – the food set – and the conditions that (i) all reactions are catalyzed by at least one molecule, and (ii) each molecule can be constructed from the food set by a sequence of reactions, the system becomes a reflexively autocatalytic food-generated network (RAF set). Autocatalytic networks and RAFs have been studied extensively as mathematical models for understanding the properties and parameters that influence self-organizational tendencies. However, despite their appeal, the relevance of RAFs for real biochemical networks that exist in nature has, so far, remained virtually unexplored.Escherichia coli, for the existence of RAFs. We find that the largest RAF encompasses almost the entire E. coli cytosolic reaction network. We systematically study its structure by considering the impact of removing catalysts or reactions. We show that, without biological knowledge, finding the minimum food set that maintains a given RAF is NP-complete. We apply a randomized algorithm to find (approximately) smallest subsets of the food set that suffice to sustain the original RAF.Here we investigate the best-studied metabolic network, that of The existence of RAF sets within a microbial metabolic network indicates that RAFs capture properties germane to biological organization at the level of single cells. Moreover, the interdependency between the different metabolic modules, especially concerning cofactor biosynthesis, points to the important role of spontaneous (non-enzymatic) reactions in the context of early evolution.The online version of this article (doi:10.1186/s13322-015-0009-7) contains supplementary material, which is available to authorized users. E. coli.Autocatalytic sets were initially proposed as chemical reaction networks with intrinsic properties that could promote a natural rudimentary selection process en route towards self organization in chemical evolution -4. UntilE. coli metabolic network data ” in the original data set, plus the ones produced in the periplasm, the introduced general catalysts, and a few essential species such as ATP, to make a total of 438 food molecules. The resulting reaction network, consists of 1199 distinct molecules types (including the 438 food molecules), 1826 reactions  and 42 catalysts. We then applied the RAF framework to analyze this CRS for the existence and structure of autocatalytic sets.E. coli growth on glucose-6-phosphate and glucose as in [E. coli Kegg pathways [A second food set was created based on the laboratory conditions given for se as in . The reapathways . HierarcE. coli metabolic network results in a maximal RAF set (maxRAF) consisting of 1787 reactions. This corresponds to 98% of the full 1826-reaction metabolic network, that is, only 39 reactions of the full network are not part of the maxRAF. When ATP or an equivalent compound such as ADP is available in this food set, the resulting RAF set is also a so-called “constructible” autocatalytic set (CAF set). This is in agreement with previous results from [Applying the RAF algorithm to the lts from  where ATAn outline of the number of reactions per functional category in the maxRAF is presented in Table E. coli metabolic network consists of 438 molecule types, 324 of these being chemical species that are exchanged with the environment in [A crucial determinant for the existence (and size) of RAF sets is the composition of the food set. As described above, the initial food set for the nment in . A largenment in  where itnment in -46.However, this initial food set can be reduced without diminishing the size of the maximal RAF set. Out of the 438 initial food molecules, there are 117 “essential” ones: removing any one of these individually reduces the size of the maximal RAF set. In the majority of cases (103) the RAF set is reduced by less than 30 reactions, but there are 7 molecules that reduce the size of the RAF set by more than 1000 reactions when removed from the food set, in particular the generic catalysts.Removing the remaining 321 molecules from the food set, i.e., using only the 117 essential food molecules, also results in a reduced maxRAF. So, at least some subset of these 321 molecules needs to remain in the food set to maintain the maxRAF. This brings up the question of whether it is possible to (efficiently) find a minimum food set that maintains a given RAF set in a reaction network. Unfortunately, this problem turns out to be NP-complete, as the following theorem states.Consider the following combinatorial optimization problems.min-F RAF:F⊆X, with k.INSTANCE: A CRS F′ of F of size at most k for which QUESTION: Is there a subset min-F generation:F−generated, and a positive integer k.INSTANCE: A set of reactions F′ of F of size at most k for which F′−generated?QUESTION: Is there a subset F−generated means that each reactant in F or can be created from F by using a series of reactions only from Recall that The min-F RAF and min-F generation problems are NP-complete.See the This seems a rather technical result, but it implies that there is no hope of constructing an efficient  algorithm for finding a minimum food set to maintain the same maxRAF set. This, therefore, presents a limit to our ability to study a given reaction network analytically.However, we can still take a heuristic approach and construct a randomized search algorithm to sample food subsets, and then take the smallest set from the resulting samples as an approximate solution to the min-F problem. This randomized algorithm is similar to that for sampling irreducible RAF sets as described in section “min-F search algorithmF.Randomly reorder the list of molecule types the original food set fi∈F do: fi from F.Remove Apply the RAF algorithm.fi to F, otherwise leave it out.If the resulting  RAF set is smaller than before, return For each next element F.Return the (reduced) food set E. coli data set always returns the same smallest size for the food set of 123 molecules. This includes the 117 essential molecules, plus some combination of six molecule types from the remaining 321 compounds. This combination of six molecule types is not always the same, though, but they do come from a very small subset. Table Repeating this algorithm any number of times on the E. coli network it seems very likely that the minimum food set is of size 123, but that it is not unique.Table With such a minimum food set, however, the maxRAF set is not “constructible” anymore , although there is still a CAF subset of 434 reactions within the maximal RAF. For the remainder of our analysis, we use the essential 117 molecules plus the first set of six additional molecules from Table This large number of “essential” molecules in the food set is to some extent an artifact arisen from how the initial metabolic network was constructed  and fromE. coli. As recently summarized by Mackie et al. [E. coli can grow under different conditions, for example, under aerobic and anaerobic conditions, or using different carbon sources. The extended food set allows for all of these alternative pathways to be functioning within the RAF network. This raises the question of why to use E. coli as a model organism for probing questions regarding self-organization of primordial metabolism. The reason is simple: even though other metabolic networks exist [E. coli’s is the best studied and annotated biological network available, even if not perfect  act as catalysts, either by themselves or as part of a catalyst compound. Thus, in the E. coli RAF network, at least 65% of the reactions are catalyzed by a cofactor and this number would be larger were complete annotations for the genes available  is only a catalyst in the conversion of uracil to UMP (and is a substrate in only 13 reactions), but the removal of this conversion reaction reduces the RAF size by 1377 reactions, even though UMP can be produced by seven other distinct reactions. This shows the central role of PRPP in biological networks. In The extensive biological action of the different cofactors can be observed by the uneven distribution of the catalysts according to their functional annotations, see Figure E. coli metabolic network. An obvious question arises: “Is there any modularity in this RAF set?”The maxRAF contains 98% of the reactions in the i is i reaction steps away from the food set. Since the maxRAF (with the minimum food set) is not a CAF, obviously there will be some reactions that are not in any of these levels. These are the “non-CAF” reactions.First, we looked at hierarchical levels of reactions. Starting with the full maxRAF and only the food molecules, we considered all reactions that can proceed catalyzed, i.e., all reactions in the maxRAF that have all their reactants and at least one of their catalysts in the molecule set. This represents the “level 0” reactions. Next we added all the products of these level 0 reactions to the molecule set, and considered all additional reactions that then proceed catalyzed. This represents level 1 . We repeated this procedure for subsequent levels, until the number of reactions that can proceed catalyzed does not further increase. In short, a reaction in level E. coli maxRAF results in a number of reactions in each level as shown in Table Applying this analysis to the size of such a smallest subset is NP-hard). Therefore, determining the distance (number of reaction steps) from the food set of these non-CAF reactions appears to be intractable.Finding a minimum subset of reactions that, when allowed to proceed uncatalyzed at least once, realizes the full maxRAF turns out to be an NP-hard problem   always results in an irrRAF of size one. This is not surprising, as our hierarchical levels analysis above resulted in 63 reactions in level 0. Since all of these reactions have their reactants and at least one catalyst in the food set, they are by definition RAF sets by themselves . We refer to these as “trivial” (irr)RAFs. Removing these trivial irrRAFs from the network, however, breaks the original maxRAF, as the resulting RAF set now contains only 17 reactions (with irrRAFs of sizes two and three). So, the “trivial” RAFs are also “essential” for the full maxRAF.Recall that an irreducible RAF set (irrRAF) is an RAF set from which no reactions can be removed without losing the RAF property. Applying the irrRAF sampling algorithm  removal of a reaction. Figure E. coli network we use here [E. coli metabolism [The reactions whose removal reduces the size of the RAF the most involve nitrogen assimilation, glutamine synthase (GS) and mureine recycling. The latter seems surprising but is easily explained, because in the use here , a mureitabolism , and witE. coli RAF. Of the 76 reactions that reduce the size by more that 100 reactions, 43 (57%) fall in the functional category synthesis of cofactor and prosthetic groups. This is intuitively understandable because cofactors are catalysts. It furthermore underscores the importance of cofactors as mediators of metabolism [Also of interest is the central role that cofactor biosynthesis assumes in the tabolism ,54,55. FFinally, there are clear intermediate levels in the (reducing) RAF sets. As Figure The irrRAF search algorithm gives insight into the importance of individual reactions on the size of the RAF set. We can perform a similar procedure for the molecules. Figure E. coli metabolism. But if this is the periphery, it would leave only 128 compounds in the core. This might seem like an unrealistically small core, but we note that there are only 303 essential genes in E. coli and the metabolic network model of E. coli needs just 250 genes to be able to produce biomass [Obviously the molecules that are involved in many reactions  from the food set, since its removal also does not affect the size of the RAF. In this case, the source of carbon becomes ATP itself, by its conversion into adenosine in the nucleotide salvage pathway. This captures an aspect of E. coli’s versatility since E. coli can grow aerobically or anaerobically, both in silico and in vivo, using adenosine as the sole carbon and nitrogen source [However, not all of these 39 food molecules are essential to maintain a similar RAF size Table  and thisn source .E. coli KEGG metabolic pathways. Based on the relationship between the different E. coli metabolic pathways with the 53 hierarchical levels retrieved, it is possible to represent the CAF network in a tree-based structure containing several grouped pathways  formation of N-carboxymethanofuran [Among the caveats to the present analyses, the underlying databases are not complete. As one example, biotin does not occur as a cofactor in the present annotations from the UNIPROT database for rboxyase . Anotheranofuran . In modeanofuran  and sponanofuran . For thiE. coli, the full extent to which gene products can substitute for each other is not known, although in one classical study, 620 genes in E. coli were found to be essential in rich medium (263 of which had no known function), while 3126 were dispensable [E. coli genes were essential (37 of which had no known function), and 3985 were dispensable [E. coli metabolism and that there is still much to be learned about its map.Another caveat is promiscuity (or messiness) in enzyme function, that is, the inherent ability of enzymes to catalyze several different selectable reactions , wherebypensable . A more pensable . This inpensable  built inlargest irrRAF within the E. coli metabolism network. However, at present it is not clear whether this can be computed efficiently.Finally, although we can easily find RAFs, including CAFs and irreducible RAFs, there are also limits to what can be calculated. For example, we have shown here that finding the minimal food set needed to maintain a given RAF is a computationally intractable (NP-complete) problem in general. So too is finding a smallest irrRAF , but her2 and CO 2 to yield organic products. Of interest, Kauffman’s speculations entailed the synthesis of large peptides from small ones, and early work showed that the synthesis of both amino acids and peptides under hydrothermal vent conditions are exergonic processes [The origin and initial interest in RAFs stem from early speculation about chemical evolution  and the rocesses , wherebyrocesses ,69.E. coli is a heterotroph that can live anaerobically but can also, like human mitochondria, use O 2 as the terminal electron acceptor in its ATP-generating electron transport chain. In that sense the E. coli metabolic network is hardly an ideal model for early chemical evolution. In addition, during evolution abiotic catalysts and metals in primordial RAF sets have been replaced by sophisticated chemical catalysts, as studies of metal and cofactor gains and losses across protein families have shown [ve shown -72. Compve shown . Moreoveve shown , such thve shown -77 whereve shown .E. coli to recycle pentoses to hexoses [et al expanded contemporary central carbon metabolism by assuming a relaxed specificity of enzymes [E. coli connects input sugars and the key precursors metabolites essential for biomass and energy production by the minimal number of enzymes, suggesting that contemporary metabolism is a small subset of the original possibilities.Finally, early enzymes probably had a more relaxed substrate specificity than in modern metabolism. This reasoning is the basis of “The Game of the Pentose Phosphate Cycle” study where Meleindez-Hevia and Isidoro showed that generic aldolases and ketolases could generate a large set of sugar phosphate interconversions and the subsequent growing specificity of the enzymes lead to a minimal solution, that in fact is equivalent to the naturally occurring pathway in  hexoses . Similar enzymes . With thE. coli represents the result of billions of years of catalytic refinement through natural variation and natural selection. However some of the properties germane to early evolution are common to all life forms and should still be at least partially conserved and, it is generally of interest to know whether the best-studied metabolic system is an RAF. With a few restrictions, for example the introduction of generic catalysts where no cofactors are involved, it indeed is. This is an encouraging result for future studies on the metabolic networks of ostensibly more primitive organisms such as acetogens and methanogens [E. coli, but also more similar to chemistry at hydrothermal vents, and whose metabolism furthermore involves a more prominent role of catalysis by metals [The metabolic network of hanogens ,81 whosey metals ,82.E. coli RAFs might point to an interesting aspect of early chemical evolution. We see here that the size, hence in some respects the complexity, of RAFs within the E. coli metabolic network are dependent upon cofactors: a small number of catalysts that promote a large number of reactions each. Regardless of where life arose, in the very earliest phases of chemical evolution, there must have been both thermodynamically controlled reactions (the most stable compounds accumulate) and kinetically controlled reactions (the most rapidly synthesized products accumulate). By lowering the activation energy of a reaction, cofactors influence the latter class of reactions more than the former as seen in the PLP example before mentioned [E. coli metabolic map as harboring some relics from early evolution, or not. In our opinion, some of these original imprints may still be present in the metabolism of modern organisms, as seen by their recurrent use of the same set of metals and organic cofactors as catalysts of biologic reactions, a set much smaller than the number of protein families that have evolved to catalyze them. The directives of the continuity principle in evolution demand that complex biochemistries had to be preceded by simpler chemistries. Thus, the initial RAF set would certainly be much simpler than the one analyzed in this paper but migth have already manifest the principle of cofactor and metal dependencies as recurrently is observed across studies showing their central role in modern metabolism [The critical role of cofactors in the entioned . Hence ttabolism ,59,83.E. coli reaction network can produce useful insights into primordial RAFs by identifying the essential role of metals and molecules such as ATP, CoA or thiamin in metabolism. This suggests the existence of some sort of abiotic autocatalysis at the onset of primordial metabolic networks. We have also shown here that maximal RAFs can be efficiently detected in real biological data, but the identification of large irreducible RAFs and the minimal food sets required to support a maximal RAF remain challenging problems.We have shown that the F′−generated and/or an RAF, for any given set F′.First note that both problems are in the complexity class NP, since we can determine in polynomial time (in the size of the input) whether a set of reactions is I of ‘min-F generation’ there is a corresponding instance I′ of ‘min-F RAF’ obtained by (i) making every molecule in X catalyze every reaction in , and (ii) taking X to be the molecules in the support of I′ has an affirmative answer if and only if I does.Next, notice that it suffices to show that the simpler problem ‘min-F generation’ is NP-complete, since for any instance We will show that ‘min-F generation’ is NP-complete by exhibiting a  reduction from the following set-theoretic decision problem.Exact cover by 3-sets (X3C)Y with |Y|=3q, q an integer; collection S of 3-element subset of X.INSTANCE: Finite set S contain an exact cover for Y, i.e., a subcollection S′ of S such that every element of Y occurs in exactly one member of S′?QUESTION: Does Y occurs in at least one element (3-element subset) of S. As an example of X3C, consider the set Y={a,b,c,d,e,f} and The decision problem X3C was one of the early ones to be shown NP-complete by Karp . We may S′={{a,b,c},{d,e,f}} is the (unique) subset of S that provides an exact 3-cover for Y.In this case Y,S) of X3C, we will construct an associated set X involved in these reactions is the (disjoint) union Y∪S∪W, where W:={ws:s∈S}. Thus |X|=|Y|+|S|+|W|=3q+2|S|. Moreover, we will take the food set F to consist of all of X.Given an arbitrary instance  has an exact 3-cover, if and only if F′−generated for some subset F′ of F of size at most q=|Y|.S′ is an exact 3-cover for Y. Then |S′|=q and every element of Y is generated by a reaction that has its (sole) reactant in S′. It follows that for every s∈S  the associated reaction y+y′→ws has reactants that can be generated from S′. This ensures, in turn, that the other associated reaction ws+y″→s can proceed. Consequently, all of S can be constructed, and so each of the reactions s→a+b+c for all s={a,b,c}∈S can also now proceed. In summary, the reactants of all reactions in S′. Thus F′−generated for any subset F′=S′ of F(=X) of size q that provides an exact 3-cover for Y.First, suppose that F′−generated for some subset F′ of F(=X) of size at most q=|Y| (we will show that this implies that S contains an exact 3-cover). For each molecule m in F′ for which either: m=y∈Y, orm=ws∈W.Conversely, suppose that y by s for any s∈S that contains y ; in case (ii) we replace m by s (i.e. the same s appearing in ws). Then s generates y in case (i), and s generates the reactants required to generate ws in case (ii). In this way we can replace F′ by a subset S′ of S, with we proceed as follows. In case (i) select replace S′−generated. Thus, it is possible to generate each element of Y by some series of reactions from S′.and for which Y are those that have a single reactant in S, and any s∈S that is the product of any sequence of reactions from s are either present or produced earlier in that sequence of reactions. It follows by an inductive argument that each molecule in Y must be able to be generated by just a single reaction from S′, and so S′ is a 3-cover for Y. This requires that 3|S′|≥|Y|, and so |S′|≥q,which, combined with Inequality  S′ is an exact 3-cover for Y, as required.Now, the only reactions that generate molecules in mentclass2pt{minim