Phytophthora infestans is a plant pathogen that causes an important plant disease known as late blight in potato plants (Solanum tuberosum) and several other solanaceous hosts. This disease is the main factor affecting potato crop production worldwide. In spite of the importance of the disease, the molecular mechanisms underlying the compatibility between the pathogen and its hosts are still unknown.S. tuberosum leaf, PstM1. This metabolic network simulates the effect of this disease in the leaf metabolism. PstM1 accounts for 2751 genes, 1113 metabolic functions, 1773 gene-protein-reaction associations and 1938 metabolites involved in 2072 reactions. The optimization of the model for biomass synthesis maximization in three infection time points suggested a suppression of the photosynthetic capacity related to the decrease of metabolic flux in light reactions and carbon fixation reactions. In addition, a variation pattern in the flux of carboxylation to oxygenation reactions catalyzed by RuBisCO was also identified, likely to be associated to a defense response in the compatible interaction between P. infestans and S. tuberosum.To explain the metabolic response of late blight, specifically photosynthesis inhibition in infected plants, we reconstructed a genome-scale metabolic network of the S. tuberosum and the first genome-scale metabolic model of the compatible interaction of a plant with P. infestans.In this work, we introduced simultaneously the first metabolic network of The online version of this article (10.1186/s12864-018-5192-x) contains supplementary material, which is available to authorized users. This type of plant-pathogen interaction is thus known as incompatible. On the other hand, sometimes plant pathogens develop strategies to evade plant defense responses, become virulent and establish the disease. In those cases, the plant-pathogen interaction is known as compatible and the infected plant is considered non-resistant or susceptible [Phytophthora infestans, one of the most destructive pathogens of Solanum tuberosum. This susceptibility is triggered by effector proteins of the pathogen [Plants use various strategies to resist pathogen attack and to avoid the development of diseases, such as, massive transcriptional reprogramming, production of reactive oxygen species (ROS), reinforcements of the cell wall and synthesis of antimicrobial secondary metabolites and pathogenesis-related proteins involved in resistance –3. In thceptible , 5. To sceptible , 6, whilpathogen , some ofpathogen .P. infestans is a hemi-biotrophic plant pathogen causing the disease known as late blight of potato, which was the same plant disease responsible for the Irish famine in the mid-nineteenth century [S. tuberosum is the fourth leading food crop  for human consumption [P. infestans has remained as the most destructive pathogen in plantations of this crop, leading to annual losses that would have been enough to feed several hundred million people [ century . S. tubesumption , and it sumption , 11. Aftn people . The econ people .Successful biological systems analysis requires that we understand the functional interactions between the key components of biological organisms and how these interactions change in disease states. Computational modeling has been widely used in order to understand the complexity that arises from the understanding of such interactions, by means of the application of mathematics, physics and computer science. Computational models allow us to understand how new properties emerge from the interconnection between system components and thus to study their behavior in response to stimuli and changes in the environment . Even thThese approaches have generated large amounts of data, allowing us to understand, to a certain extent, some of the main mechanisms involved in potato late blight. Nevertheless, due to the heterogeneity of this information, a full view of the disease is still fragmented. For this reason, and to get a better understanding of the molecular mechanisms underlying the compatible interaction inside the host cell, it is highly suitable and necessary to gather and integrate this information into a single computational model of the disease. This model should capture the time-dependent nature of this biological system, integrate various ranges of spatial and temporal scales, and allow us to explore the possible molecular mechanisms underlying the compatible interaction.To this end, in recent years, the scientific community has made multiple efforts to integrate functional genomic characterization and biochemical knowledge into models known as genomic-scale metabolic reconstructions (GEMR). These models are based on a detailed knowledge of the system’s individual components , to allow the reconstruction of the system through a bottom-up approach. The aim is to understand the properties that arise from the interactions between the metabolic system’s components in response to environmental stimuli, and their behavior through time –22.Arabidopsis thaliana [Hordeum vulgare [Zea mays [Sorghum bicolor [Saccharum officinarum [Brassica napus [Oryza sativa [Solanum lycopersicum [During the past years, this approach has been widely implemented in plants, with the development of GEMRs for several species, including thaliana –26, Hord vulgare , Zea mayZea mays –30, Sorg bicolor , Saccharicinarum ; Brassicca napus , 32, Orya sativa , and Solpersicum . In genepersicum .Once the mathematical model is generated in step 3, the phenotypic predictions of the organism’s metabolic activity can be established through modelling methods based on restrictions, which include an in silico simulation of the model under inferred metabolic objectives and a set of restrictions that represent genetic or environmental conditions , 37. A wGiven that genomic information used to generate the metabolic reconstructions does not consider the real expression of each gene or the subcellular localization of gene products, flux restrictions based on different “omics” data  must be integrated into the GEMRs, in order to recreate specific metabolic phenotypes , 39, 40.S. tuberosum and generate a genome-scale metabolic model of the compatible interaction between S. tuberosum and P. infestans, through the incorporation of expression data of the pathosystem into the model. Previous work on the compatible interaction had already identified a decrease in photosynthetic activity of infected plants, however, the underpinnings behind it remain unknown [In this study, we report the first genome-scale reconstruction of  unknown . Hence, The reconstruction of the genome-scale metabolic model followed six major steps: (1) automatic reconstruction of draft network via homology searches for the identification of metabolic activities and biochemical reactions; (2) manual and semiautomatic refinement of the reconstruction (3) establishment of gene-protein-reaction (GPR) association; (4) generation of a genome-scale metabolic model in steady state; (5) incorporation of gene expression data of the compatible interaction into the metabolic model; (6) flux balance analysis using a pre-defined objective function. In addition, model predictions were contrasted against experimental observations.The draft network included 1288 reactions and 1482 metabolites, 217 of which were dead-ends that decreased the metabolic network’s connectivity. A manual search of the dead-ends metabolites allowed us to identify 448 biochemical reactions, with biological and/or genomic evidence for potato, which refined 40 metabolic pathways totally or partially, including glycolysis/gluconeogenesis, pyruvate metabolism, glyoxylate and dicarboxylate metabolism (photorespiration module), oxidative phosphorylation, carbon fixation in photosynthetic organisms, amongst others  and light (photon). FBA solutions showed that the model was able to simulate leaf biomass synthesis, which was represented by the conversions of biomass precursors: protein (amino acids), sugars, nucleotides, cell wall  and fatty acids (hexadecanoic acid).Hereby, we present a metabolic model of Solanum lycopersicum) [Arabidopsis thaliana [Oryza sativa) [A. thaliana [A. thaliana [A. thaliana model [The model properties of PstM1 were compared with the versions of the genome-scale metabolic model of tomato (ersicum) , a closethaliana , 25, 42  sativa) . The Pstthaliana , A. thalthaliana  respectiA. thaliana model [P. infestans that were evaluated in this work, a total of 995 (48%) reactions in the potato model simulations could carry flux from nutrients to the specified biomass components, and in the simulations of the tomato model, between 16.8 and 17.3% of the reactions carried flux to represent three specific metabolic scenarios. It is probable that the reason for a higher number of reactions used in the potato model simulations is that the objective function was the maximization of leaf biomass synthesis, with the purpose of evaluating the possible metabolic scenarios in three moments  of the compatible interaction between potato and P. infestans. While in the tomato model, the objective function was the total flux minimization for three metabolic scenarios: heterotrophy, phototrophy and photorespiration.Our potato model contained fewer blocked reactions than the other C3 plant models compared here. However, the percentage of the reactions used for biomass synthesis in all these models was similar. The percentage for the potato model was 60.5%, compared to 56.5% for the tomato model, 67.3% for the na model , and 57.To determine the metabolic profile for each infection time point, we performed a FBA with flux boundaries established from the gene expression data see . Our stuS. tuberosum PstM1 includes the definition of the following balanced photosynthetic light reactions taken from literature sources [Photophosphorylation, the synthesis of ATP in photosynthesis, occurs in chloroplasts . Noncycl sources , 50, 51:2 fixation; therefore, the metabolic flux in the cyclic photophosphorylation was not required [Our results showed that the metabolic flux for noncyclic photophosphorylation slightly diminished throughout the infection time points Fig.  and thatrequired . The cycrequired  and its required . Our resrequired , 55. TheP. infestans and S. tuberosum has been reported in other studies. For example, in a previous study, the decline in the efficiency of photosystem II [− 1 DW h− 1, suggesting interconversion of metabolites in all reactions in this pathway. At 1 and 3 dpi, the variation of the metabolic fluxes in response to the compatible interaction was from 0 to 28 mmol g − 1 DW h− 1and from 0 to 25.7 mmol g − 1 DW h− 1, respectively. At 3 dpi, six reactions completely lost their flux capacity, showing a higher decrease of the global metabolic capacity in this time compared with the two previous times of infection.The decrease in photosynthetic ability during compatible interaction between ystem II  and downystem II . During ystem II . We eval2O) by formation of glyceraldehyde 3-phosphate (GAP) using NADPH an ATP produced in the light reactions; and 3) the regeneration of RuBP [The Calvin cycle involves three main phases: 1) carboxylation of ribulose-1,5-bisphosphate (RuBP) to form 3-phosphoglycerate (PGA), mediated by Ribulose-1,5-bisphosphate carboxylase/oxigenase enzyme (RuBisCO); 2) reduction of PGA to the level of a sugar  that regulates basic acclimation, developmental and defense processes in plants [2O2, at the site of attempted invasion [2O2 in potato tuber tissue following inoculation with P. infestans was previously reported [2O2 [The highest flux of carboxylation of RuBP was obtained in the model optimization of 0 dpi Fig. . At thisoduction , 61. In n plants , includin plants . One of invasion . The quireported . Our rested [2O2 .2O2 production here was zero. During incompatible plant-pathogen interaction, an initial and very rapid accumulation of H2O2 is followed by a second and prolonged burst of H2O2 production [2O2 production occurred  in leaves , 76; likIn the Calvin cycle, the RuBP is both consumed and synthesized . The synS. tuberosum and the first genome-scale metabolic model of the compatible interaction of a plant with P. infestans. The metabolic flux of the light reactions and carbon fixation cycle, including photorespiration and starch synthesis, suggests a suppression of the photosynthetic capacity as consequence of the compatible interaction between P. infestans and S. tuberosum. Our results suggest that the suppression of the photosynthetic capacity could be associated with a quick defense mechanism, which is not sufficient to trigger an effective defense response in the plant. The results shown here are in silico metabolic predictions, which closely match previous studies of plant physiology.In this work, we simultaneously introduced the first metabolic network of The PstM1 generated in this study can be used to simulate different metabolic scenarios of the potato plant, integrating gene expression data through constraints into fluxes of the reactions. For its part, the genome-scale metabolic model of the compatible interaction of potato plant allows the prediction of other metabolic mechanism involved during patosystem activity and is an useful tool for proposing novel directed hypotheses, guiding research to conduct metabolic engineering in the plant, and identifying emerging properties of the compatible interaction, which otherwise could not be observed through the study of individual molecules and processes. Moreover, PstM1 reconstruction alone can also be informed by new biological data in order to highlight different processes relative to potato metabolism.An initial automatic draft reconstruction was first created by means of RAVEN  softwareThe reconstruction refinement stage was divided into six phases: (1) manual gap refinement of the metabolic network and manual refinement of the reversibility and directionality of the reactions; (2) automatic-specific-organism filling; (3) semiautomatic-specific-organism gap find and gap fill; (4) establishment of the directionality and reversibility of the reactions through Gibbs free energy of reaction value (ΔrG′°) ; 5) inc inc5).FiS. tuberosum in the KEGG Pathways database, we verified that their catalyzing enzymatic activity was reported in the Plant Metabolic Network (PMN) database specific for potato (PotatoCyc) [During manual refinement, the network’s connectivity was verified in a pathway by pathway basis, as well as in a metabolite by metabolite basis . For thitatoCyc) . In addiS. tuberosum, we used the KEGGREST R package, which allowed us to obtain all of the metabolic pathways reported for this organism in the KEGG pathways database [In order to verify that the metabolic pathways reported in this reconstruction were present in the metabolism of database . By compS. tuberosum in KEGG was done using the g2f R package [S. tuberosum in PotatoCyc.During the process of automatic-specific-organism filling, a database construction of all the biochemical reactions reported for  package . Later,  package . Since trG′° values obtained from EQuilibrator [rG′° by calculating the Gibbs free energy of formation of a compound (ΔfG′°), through the group contribution method for thermodynamic analysis [fG′° in Equilibrator are pH 7.0 and ionic strength 0.1, and in MetaCyc these are pH 7.3 and ionic strength 0.25. Since the parameters are located in a pH range of 7.0–7.3 and ionic strength of 0.1–0.25, the reversibility R script [rG′° values from both databases. When both reversibilities were below − 1, the GEMR reversibilities were established as forward irreversible. Due to lack of biological evidence and discrepancies between the ΔrG′° values of the databases, the remaining reactions were determined as reversible.The reversibility and directionality of the reactions that were not manually corrected were determined through Δlibrator  and Metalibrator  databaseanalysis . The parR script  was implDuring the fifth phase of the reconstruction refinement process, we included 13 exchange reactions which transport metabolites that cannot by synthesized by the cell, from the limits of the system to the cytoplasm, that are precursors to other metabolites . FinallySijvj = 0. Where Sij is the entries of the stoichiometric matrix  [From the genome-scale metabolic reconstruction of potato, a SBML version was generated using the Python package COBRApy . Consecu≤ vjmax) , 27.OFbioamass , one (1 dpi) and three (3 dpi) days post inoculation), with three biological replicates. The tag annotation was performed by BLASTN [Gene expression data of the compatible interactions was obtained from the study of Gyetvai et al. . We usedy BLASTN . The souy BLASTN . The uniy BLASTN . As the y BLASTN .From the previously built gene expression database, we generated an expression set for each infection time point by means of the R package Biobase . The genOFbioamassFBA represents a constraint-based modeling approach that allows the prediction of metabolic steady-state fluxes, by applying mass balance constraints into a stoichiometric model . The reasubject toTo constrain the space of all the possible steady-state flux distributions in the optimization, we imposed thermodynamic constraints to reaction reversibility as well as upper and lower bounds constraints on reactions fluxes from known expression values for the particular enzyme that catalyzes the reaction.Additional file 1:Refined pathways in the metabolic network reconstruction. (PDF 88 kb)Additional file 2:S. tuberosum in SBML format. (XML 2677 kb)Genome scale metabolic model of Additional file 3:Metabolic fluxes of the carbon fixation pathway and other reactions of interest. (PDF 34 kb)Additional file 4:S. tuberosum in xls format. (XLSX 161 kb)Genome scale metabolic network reconstruction of


Escherichia coli, we shed light on how metabolic regulation are organized by showing which reactions within metabolic networks are more prone to transcriptional or allosteric regulation. Applied to a human genome-scale metabolic system, our method detects disease-associated reactions. Thus, our study deepens the understanding of the organizing principle of cellular metabolic regulation and may contribute to metabolic engineering, synthetic biology, and disease treatment.Cellular systems shift metabolic states by adjusting gene expression and enzyme activities to adapt to physiological and environmental changes. Biochemical and genetic studies are identifying how metabolic regulation affects the selection of metabolic phenotypes. However, how metabolism influences its regulatory architecture still remains unexplored. We present a new method of extreme pathway analysis  to deduce regulatory structures from pure pathway information. Applying our method to metabolic networks of human red blood cells and  Organisms are constantly faced with variable internal physiological states and environmental conditions. The ability to rapidly shift between phenotypes to deal with these challenges is essential for the competitive fitness and survival of an organism –3. It isThe mechanisms controlling metabolic processes, including regulatory circuits and logics, have been intensively studied , especiaPreviously, some studies , 21–24 dEscherichia coli and Saccharomyces cerevisiae on two alternative substrates . Then, a reaction ej if and only if ith element of ej, 1 ≤ i ≤ n and 1 ≤ j ≤ l. We define ej as an employer extreme pathway of Shannon entropy and conditional entropy are used to measure the role on average of a reaction in eliminating the uncertainty of a metabolic system. Suppose a metabolic network of equivalent reaction couple on Shannon entropy.Based on the above probability distributions, the Shannon entropy n theory , where XG was built for each metabolic system or subsystem in which individual reactions are nodes and the weight of the arc connecting two nodes, local regulatory distance, A weighted graph global regulatory distance, G. Intuitively, the global regulatory distance measures the indirect impact of flux change between two reactions.The The regulatory distance of two EqSets equivalent reaction set on Shannon entropy (EqSet). Second, an EqSet of k (k ≥ 1) internal reactions First, each exchange reaction forms an individual i, j = 1, ⋯, k, ∀i = 1, ⋯, k, ρe is the effective radius within an EqSet that represents the maximum regulatory distance of any reaction to its nearest counterpart in the same EqSet.∀k EqSets, i < k) that are predicted to be regulatory, the regulatory importance of an EqSets is determined by the nearby EqSets within the distance of ρs because of the constraint that the regulatory influence of an EqSet i < j ≤ k) exists locally, where ρs is the effective radius between EqSets that designates the maximum regulatory distance that an EqSet influences. We built two group of EqSets with the nearby EqSets of τ nearby EqSets standing at last of the queue τ is the size of a window sliding on Given a metabolic system with i < j ≤ k), of μ. To sum up, The regulatory importance, s is the length of σ is represented asl is the number of lost internal EqSets and d is the number of the missing internal EqSets that contain biologically meaningful reactions. It is proven in Statement H in The output EqSet sequence σ0, the corresponding p-value is defined as the probability that a randomly arranged sequence of internal EqSets has an evaluation score no higher than σ0. Although the p-value can be estimated by stochastic simulation, we provide a dynamic algorithm in Algorithm B in For an output sequence of the sorting algorithm whose evaluation score is μ, ρe, ρs and τ) used in the EqSet sorting algorithm. Assume that the ranges of μ, ρe, ρs and τ are limited and discrete, the algorithm starts from a random point p-value. When all four parameters have been adjusted, the search algorithm moves on to the next iteration by updating from the first one again. If a local optimal setting of the parameters is found, the algorithm will start another try to search for the local optimal parameters from another randomly picked starting point. The algorithm will stop and return the best parameter values among all the tries when it reaches the maximum number of search steps. The search algorithm described above is illustrated in Fig D in A heuristic search algorithm was built in order to quickly find the nearly optimal values for the four parameters % as a test set, where x ∈ {10, 20, 30, 40, 50, 60, 70, 80, 90}. Given a sequence of internal EqSets, we extracted the subsequence that consists of the EqSets in the training set, on which the p-value for the training set is computed. We found the optimal setting of the parameters and the corresponding p-value for the training set. We repeated this process 100 times, which provided the mean of the p-values on the training sets. After that, we selected the subset of ρe with the lowest average p-values and counted the average rate of the disease-related EqSets being in the top 10% of the test set sequences. This rate shows the capability of the sorting algorithm for predicting disease-related EqSets.Since the EqSets of a certain metabolic network vary with the parameter p-value, which is the probability that the rank summation of the regulatory EqSets on a random sequence is lower than that on the sequence given by our algorithm. , in which each reaction pair satisfies the assumption that the conditional entropy of one reaction, given the other, equals zero. An EqSet is treated as a potential entity for metabolic regulation. The EqSet that contains at least one regulated reaction is defined as a regulatory EqSet. A greedy algorithm is used to organize the EqSets in a sequence according to their regulatory importance. The algorithm starts from an empty sequence. Under the assumption that the EqSets in the current sequence are regulatory, the algorithm iteratively picks up the EqSet from the rest that is most important for regulation and adds it to the end of the sequence. The EqSets ranked higher in the sequence are expected to have greater likelihood of containing strictly regulated reactions. The resulting EqSet sequence is evaluated by a thm. See .ρe). And the regulatory influence of an EqSet is restricted to other EqSets within the regulatory distance given by a parameter, inter-EqSet effective radius (denoted as ρs). Second, a sliding window of size τ is employed on the sequence to define the available regulatory EqSets. The Eqset that leaves the window is considered to be out of control, which simulates a disturbance in the regulatory system. Thus, the EqSet that best compensates for the disturbance will be considered to be of high flexibility in this case. Briefly, the values of ρe, ρs and τ have an inverse relation with the degree of flexibility, and consequently reflect a trade-off between efficiency and flexibility.The regulatory importance of an EqSet is defined by regulatory efficiency and flexibility. The regulatory efficiency of an EqSet is measured by the conditional entropies that depend on the reactions’ participation ratios on the extreme pathways. It characterizes the EqSet’s average effect on determining the “on/off” state of each extreme pathway, as well as the degree to which its regulatory function cannot be replaced by other EqSets. The flexibility of an EqSet is modeled in two aspects: First, the regulatory distances between reactions and between EqSets are defined according to the topology of the metabolic network. And the regulatory influence of a reaction is restricted to a local scope in order to speed up the shift of a cell’s metabolic states. Therefore, an EqSet is restriced further to include only reactions within certain regulatory distance given by a parameter, intra-EqSet effective radius (denoted as μ).The regulatory importance of an EqSet calculated above is then adjusted according to the size of the EqSet for the reasons listed below: Assuming that each metabolic reaction has an equal probability of obtaining a regulatory function because of gene mutations, it is more likely that a mutation that brings a regulatory function to a reaction occurred earlier in a bigger EqSet than in a smaller one. If the reaction happened to be of regulatory importance, the mutation is more likely to increase in frequency within the population by means of natural selection. Thus, an EqSet that contains more members will gain some advantages in acquiring regulated reactions compared to smaller counterparts with reactions that have similar degrees of regulatory importance. Therefore, we give a bonus for each extra reactions in an EqSet. The amount of the bonus is controlled by a parameter, bonus ratio (denoted as E. coli (iJR904) [http://systemsbiology.ucsd.edu. As network properties and regulation demands differ between metabolic systems, the parameters ρe, ρs, τ and μ have to be optimized case by case.We use the metabolic reconstructions of the human red blood cell (hRBC) , E. coli(iJR904)  and glob(iJR904)  as exampThe human erythrocyte is a complete cell with a simple metabolic system. It has been well studied, which makes it an attractive case for our research. The hRBC metabolic model used here consists of 39 metabolites and 51 reactions, of which 19 are exchange reactions  whereas elementary modes are not.As a comparison, we applied our method to elementary modes . The resp and t, that affect the number and complexity of the artificial pathways  on most sequences  Lower p-values are achieved at certain parameter values for each target subnetwork. Differences in network properties and regulatory demands may be one reason, and the other may be due to the different biases which are introduced when dividing the genome-scale metabolic networks into target subsystems and surrounding subsystems  methods that predict lethal reactions, such as gene deletion analysis , the patIt is worth to note that the consideration of only subsystems of genome-scale metabolic networks is a trade-off between computational costs and accuracy. Although dividing the global metabolic network to a target subsystem and a surrounding subsystem does not change the space of steady states of the global system, constraining the analysis to the target subsystem does impact the extreme pathways detected , 98. ForAnother challenge for the future work is to integrate omics data, such as transcriptomic and proteomic data, to refine our evaluation of the regulatory cost of each reaction, which will help improve the prediction quality of our approach. Valuable improvements will include determining the most possible regulated reactions in an EqSet, and increasing the agreement between the predicted EqSet sequence and the real sequence that occurs in nature. Furthermore, a quantitative estimation of the probability or confidence level that a reaction is regulatory or disease-associated is also in demand.S1 Text(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 TableP-value and the paramters for the sequence are listed at the end of the table.(XLSX)Click here for additional data file.S4 TableP-value and the paramters for the sequence are listed at the end of the table.(XLSX)Click here for additional data file.S5 TableP-value and the paramters for the sequence are listed at the end of the table.(XLSX)Click here for additional data file.S6 TableP-value and the paramters for the sequence are listed at the end of the table.(XLSX)Click here for additional data file.S7 TableP-value and the paramters for the sequence are listed at the end of the table.(XLSX)Click here for additional data file.


Genome-scale metabolic models are instrumental in uncovering operating principles of cellular metabolism, for model-guided re-engineering, and unraveling cross-feeding in microbial communities. Yet, the application of genome-scale models, especially to microbial communities, is lagging behind the availability of sequenced genomes. This is largely due to the time-consuming steps of manual curation required to obtain good quality models. Here, we present an automated tool, CarveMe, for reconstruction of species and community level metabolic models. We introduce the concept of a universal model, which is manually curated and simulation ready. Starting with this universal model and annotated genome sequences, CarveMe uses a top-down approach to build single-species and community models in a fast and scalable manner. We show that CarveMe models perform closely to manually curated models in reproducing experimental phenotypes . Additionally, we build a collection of 74 models for human gut bacteria and test their ability to reproduce growth on a set of experimentally defined media. Finally, we create a database of 5587 bacterial models and demonstrate its potential for fast generation of microbial community models. Overall, CarveMe provides an open-source and user-friendly tool towards broadening the use of metabolic modeling in studying microbial species and communities. Linking the metabolic phenotype of an organism to environmental and genetic perturbations is central to several basic and applied research questions. To this end, genome-scale metabolic models provide a mechanistic basis allowing to predict the effects of, e.g. gene knockouts, or nutritional changes ,2. IndeeAn emerging application of genome-scale models is the study of cross-feeding and nutrient competition in microbial communities . HoweverSeveral metabolic reconstruction tools are currently available, each offering different degrees of trade-off between automation and human intervention  see Sup; (iii) aIn this work, we present CarveMe, a new reconstruction tool that shifts this paradigm by implementing a top-down reconstruction approach Figure . We begiCarveMe provides a Python script to build an universal draft model of metabolism by downloading all reactions and metabolites in the BiGG database  into a sEscherichia coli biomass composition  were estimated using the formula:R is the universal gas constant, and the temperature T was set to 298.15 K (25 C). The reaction quotient (Q) denotes the product-to-substrate ratio, which was limited by the physiological bounds imposed on metabolite concentrations. A recent study showed that absolute metabolite concentrations are conserved among different kingdoms of life , and complete medium . The model was tested for biomass and ATP production. Unlimited ATP generation was detected by flux variability analysis  and the The universal biomass composition does not contain membrane and cell wall components specific for Gram-negative and Gram-positive bacteria, which can lead to false negative gene essentiality predictions for lipid biosynthesis pathways that generate these membrane/cell wall precursors. We generated specialized templates for Gram-positive and Gram-negative bacteria by adding these components to the respective biomass composition. The Gram-positive template includes glycerol teichoic acids, lipoteichoic acids and a peptidoglycan unit. The Gram-negative template includes phosphatidylethanolamines, murein and a lipopolysaccharide unit. We also provide a template for cyanobacteria that contains a thylakoid compartment for photosynthesis, and a template for archaea that contains ether lipids in the cell membrane composition and lacks peptidoglycans.In all cases, the final biomass composition is normalized to represent 1 gram of cell dry weight. During reconstruction, the user can select the universal bacterial template or one of the specialized templates. Furthermore, a utility to automatically generate customized templates with user-provided biomass compositions is included.The amino acid sequences for all genes in the BiGG database were downloaded from NCBI and stored as a single FASTA file. This file is used to align the input genome files given by the user (using DIAMOND ) and finAlternatively, the user can provide an alignment file externally generated with eggnog-mapper , which pThe alignment scores obtained in the previous step are mapped to reaction scores using gene-protein-reaction (GPR) associations , and spontaneous reactions are given a neutral score.s is the reaction scores vector (determined in the previous step), v is the flux vector, yf and yr are binary vectors indicating the presence of flux in the forward or backward reaction, S is the stoichiometric matrix, ϵ is the minimum flux carried by an active reaction (default: 0.001 mmol/gDW/h), M is a maximum flux bound (default: 100 mmol/gDW/h), and –1).Carving is the process of converting a universal model into an organism-specific model by removing reactions and metabolites unlikely to be present in the given organism. This is performed by solving a mixed integer linear program (MILP) that maximizes the presence of high-score reactions and minimizes the presence of low-score reactions while enforcing network connectivity (i.e. gapless pathways):After solving the MILP problem, all inactive reactions are removed from the model, including all consequently orphaned genes and metabolites. The final model is then exported as an SBML file. The user can select between the latest (FBC2) or the legacy (COBRA) version.CarveMe allows the generation of ensemble models. This is performed by randomizing the weighting factors of reactions without genetic evidence, and solving the MILP problem multiple times to generate alternative models. The size of the ensemble (number of models) is selected by the user, and the final ensemble is exported as a single SBML file.T) is used to determine a positive outcome . Simulation results with multiple thresholds  are reported in this work.For the purpose of phenotype array simulation and gene essentiality prediction, a voting threshold . According to the level of confidence, these can be provided as ‘hard’ or ‘soft’ constraints.Soft constraints are specified as a mapping from reactions to one of three possible values that modify the MILP objective, giving a different weight to the binary variables associated with the respective reactions: 1) forward direction preferred; –1) backward direction preferred; 0) reaction should not occur.Hard constraints are simply a list of flux bounds , lb and ub are the lower and upper flux bound vectors, and The user can  provide a list of media where the organism is expected to grow. If the model does not reproduce growth on these media after reconstruction, CarveMe will perform additional gap-filling to enable the expected phenotypes. The implementation is similar to bottom-up gap-filling methods, except that the reactions scores previously calculated are used as weighting factors. This increases the probability that a pathway with some level of genetic evidence is selected over an alternative pathway with lower evidence. The problem is formulated as follows:CarveMe provides a script to merge a selected set of single-species models into a microbial community model. The result is an SBML model where each species is assigned to its own compartment and the extracellular environment is shared between all species. Several options are provided, such as the creation of a common community biomass reaction, creation of isolated extracellular compartments connected by an external metabolite pool, and the initialization of the community environment with a selected growth medium. The model can be readily used for flux balance analysis (just like a single-species model) to explore the solution space of the community phenotype, and also for the application of community-specific simulation methods ,11.Shewanella oneidensis the default carbon source was dl-lactate. A phenotype was considered viable if the growth rate was at least 0.01 h–1. The experimental data used for validation was obtained from . For each type of array , the default source of the given element  was iteratively replaced with the respective compounds in the array. For ned from ,37–40.E. coli, M9 (with succinate) for Pseudomonas aeruginosa, LB medium for Bacillus subtilis and S. oneidensis, and complete medium for Mycoplasma genitalium. The experimental data used for validation was obtained from  for ned from ,37,40–42The performance metrics used to evaluate the phenotype array simulations and gene essentiality predictions were defined as follows:The reconstructions were performed using the genome sequences and growth media provided in . The uptframed python package (version 0.4) for metabolic modeling, which provides an interface to common solvers , and import/export of SBML files through the libSBML API  , a databE. coli (strain K-12 MG1655) and B. subtilis (strain 168). These are the most well-studied Gram-negative and Gram-positive bacteria, respectively, with highly-curated metabolic models. We also selected four organisms that are not part of the BiGG database, namely M. genitalium (strain G-37), P. aeruginosa (strain PA01), R. solenacearum (strain GMI1000) and S. oneidensis (strain MR-1).The quality of the models generated with CarveMe was evaluated regarding their ability to reproduce experimental data and compared to previously published manually curated models. Two reference model organisms were selected as case-studies, https://kbase.us/) (The genomes of these strains were downloaded from NCBI RefSeq (release 84)  and usedase.us/) . Figure M. genitalium (no Biolog data available) and R. solanacearum . The predictive ability of the models was evaluated in terms of multiple metrics: accuracy, precision, sensitivity, specificity, and F1-score .All the models were used to simulate substrate utilization (Biolog phenotype arrays) and gene essentiality, and the results were systematically compared against published experimental data. Two exceptions were R. solanacearum) required one single gap-filling reaction (asparagine synthetase) to reproduce growth on minimal medium. All the models generated with modelSEED required the specification of the minimal media during reconstruction. Without this a priori information, the models were unable to reproduce growth on the given media.Notably, four out of five models generated with CarveMe were able to reproduce growth on minimal media from genome data alone, without specifying any growth requirements during reconstruction or performing any additional gap-filling after reconstruction. The other model (S. oneidensis), but perform worse on other metrics. For E. coli, the CarveMe model performs very closely to the iML1515 model, outcompeting the modelSEED model. In the case of B. subtilis, both CarveMe and modelSEED perform considerably worse than the iYO844 model. This difference in performance can be explained by the lack of annotated transporters for B. subtilis, which have been manually added in the curated model.Regarding substrate utilization, it can be observed that the performance of CarveMe models is in-between the performance of manually curated models and those generated with modelSEED Figure . In someB. subtilis the automated reconstructions now perform more closely to the manually curated model, with the modelSEED reconstruction outperforming CarveMe. For the other organisms, one can also observe a smaller performance gap between the manually curated models and the automatic reconstructions, with CarveMe generally outperforming modelSEED.To test the influence of transporter annotation, we repeated the simulations for all models, this time allowing free diffusion of any metabolites without associated transporters . It can M. genitalium (modelSEED outperforms CarveMe for most metrics) and S. oneidensis .Regarding the ability to predict gene essentiality, the same general pattern can be observed, with CarveMe models displaying a performance in-between the manually curated models and modelSEED Figure . Two excE. coli and B. subtilis using three distinct biomass compositions: our universal (core) biomass compositon, our Gram-negative and Gram-positive compositions, and the organism-specific compositions taken directly from the manually curated models (One common pattern for most CarveMe models (and modelSEED to some extent) is a slightly decreased sensitivity with regard to gene essentiality  when compared to the manually curated models. One possible reason is the utilization of generic biomass templates that exclude non-universal cofactors  and othed models . ConfirmA general limitation in building genome-scale metabolic models, given the available data, is the existence of several equally plausible models. This has been explored by Biggs and Papin , showingN = 100) for all organisms and repeated the phenotype array simulations and gene essentiality predictions using different voting thresholds  to determine a positive prediction (see Methods). To confirm that the ensemble generation is unbiased, we calculated the Jaccard distance between every pair of models in each ensemble , whereas the E. coli ensemble shows the lowest variability (average distance of 0.04). This distance is a reflection of the degree of uncertainty in the network structure.We generated model ensembles , which is also the organism with smaller number of genes. The most extensively gap-filled subsystem across all organisms, ‘Cofactor and Prosthetic Group Biosynthesis’, is also the same for both collections. Overall, this shows that the quality of the CarveMe models  is comparable to the manually-curated AGORA collection, which further highlights the advantages of our top-down curation approach.Finally, we compared the number of gap-filled reactions between CarveMe and AGORA models (40 models in common) and observed that they are well correlated   that areMycoplasma genus with as few as 238 reactions (Mycoplasma ovis str Michigan), whereas the larger metabolic networks belong to the Klebsiella and Escherichia genera, with up to 2472 reactions (Klebsiella oxytoca str CAV1374). We note that these numbers are indicative, as they can be biased or restricted by the quality of the gene annotation and the scope of the reaction database.Here, we analyse the distribution of the number of (annotated) metabolic genes, reactions and metabolites across all organisms Figure . It is pInterestingly, as the size of the metabolic networks grows, there there is an asymptotic trend of the number of metabolites with respect to the number of genes and reactions Figure  and C. TWe further looked at how frequently individual reactions and metabolites occur across species Figure . The freNext, we illustrate the use of our model collection to build microbial community models and explore inter-species interactions. We created random assemblies of microbial communities of different sizes  and calculated their metabolic interaction potential . In briThe results obtained with this collection Figure  closely a priori (e.g. microbes that cannot be cultivated under well-defined media). In case a generated model is not able to reproduce growth on a given medium, CarveMe can additionally perform gap-filling to enable the expected phenotype. The implemented gap-filling approach differs from methods that simply minimize the number of added reactions , which account for differences in membrane/cell wall composition. In future releases, we aim to provide a larger collection of universal models in order to improve coverage of all domains of microbial life (such as yeasts and other eukaryotes).The universal model and, consequently, all generated models are pre-curated for common structural and biochemical inconsistencies and can be readily used for simulation. Nonetheless, these models should still be considered as drafts subject to further refinement, as they might require organism-specific curation to reproduce certain phenotypes. The pipeline allows users to provide their own templates at any desired taxonomic level and provides methods to facilitate the creation and curation of such templates . For instance, a user might decide to manually curate a universal model for a particular species and use it to reconstruct multiple strains of that species.carving procedure can work with genetic evidence alone (i.e. without requiring the specification of a medium composition), any collected experimental data  can be provided in a simple tabular format as additional input for reconstruction. Also, it implements a modular architecture that facilitates modification/integration of new components. For instance, sequence alignments are performed with diamond . Anothegithub.com/cdanielmachado/carveme with an open source license. All the models, data and scripts used in this work are available at github.com/cdanielmachado/carveme_paper. The database with the 5587 model collection is available at github.com/cdanielmachado/embl_gems.CarveMe is available at Supplementary DataClick here for additional data file.


Metabolism has been a major field of study in the last years, mainly due to its importance in understanding cell physiology and certain disease phenotypes due to its deregulation. Genome-scale metabolic models (GSMMs) have been established as important tools to help achieve a better understanding of human metabolism. Towards this aim, advances in systems biology and bioinformatics have allowed the reconstruction of several human GSMMs, although some limitations and challenges remain, such as the lack of external identifiers for both metabolites and reactions. A pipeline was developed to integrate multiple GSMMs, starting by retrieving information from the main human GSMMs and evaluating the presence of external database identifiers and annotations for both metabolites and reactions. Information from metabolites was included into a graph database with omics data repositories, allowing clustering of metabolites through their similarity regarding database cross-referencing. Metabolite annotation of several older GSMMs was enriched, allowing the identification and integration of common entities. Using this information, as well as other metrics, we successfully integrated reactions from these models. These methods can be leveraged towards the creation of a unified consensus model of human metabolism. MetabolSince the available amount of omics data is increasing in a rapid way, computational tools have been an important asset to process all the gathered information. Genome-scale Metabolic Models (GSMMs) are an example of such tools, providing mathematical representations of molecular entities at a system level that can help grasp the connection between genome and metabolism , 4]..4].The process to obtain a model representing a set of biochemical transformations that may occur in the cell, begins with a Genome-scale reconstruction (GENRE), which can also be represented as a metabolic network. Then, there is the need to curate the functional genome annotation through literature review and manual curation using available experimental data. The four main four steps for the model reconstruction are, thus, the draft reconstruction, model curation, creation and validation.Throughout the last 10 years, several models of the human cell metabolism have been developed . The firWith human genome sequencing as a starting point, both Recon1  and the A few years later, a new version of the Recon model was presented by Thiele et al. , in paraThe most recent human metabolic model is Recon3D . This moDifferent human models and other sources may be merged into a consensus metabolic model, integrating relevant biological entities (metabolites and reactions) shared between two or more models based on their information and external databases. However, those entities are typically identified without a shared standard, which is a possible limitation for the integration process.A contains a metabolite M1 that has an external database identifier also found on a metabolite C1 of model B, both M1 and C1 can be considered identical, a property that can be leveraged to integrate the two models. Building over the incremental identification of shared metabolites, we can also infer shared reactions (and pathways) present in the models.Metabolites present in human models can typically include information such as their name, InChI key, chemical formula, identifiers for external databases, such as HMDB , KEGG 1, PubChemIn this work, we will apply a cross-reference integration process to find the shared metabolites across different models, and consequently increase the available information for the metabolites present in each model. Also, using the previously described property, we will perform an integration of reactions of the same models by using the processed metabolites to connect their reactions.2The pipeline devised for this work includes three main steps, namely data retrieval and preprocessing, metabolite integration and subsequent integration of reactions.2.1For this work, we used most of the available human metabolic models. 2.2A metabolite integration tool was created using Java and a Neo4J graph database, which includes metabolite information from databases  and from human metabolic models B. Nodes The graph database was initially loaded with metabolite data from metabolic models containing references to external database identifiers. These were then used to query PubChem Compound, KEGG Compound and LipidMaps databases based on their RESTful application programming interfaces (APIs) using previously implemented loaders, while information from CHEBI, HMDB and DrugBank databases were loaded using OBO and XML parsers.Identification of shared metabolites on different models was performed by a cross-reference integration process, which creates a second level of metabolite nodes on the graph database representing clusters of metabolite instances from the different databases. Each node has connections to metabolites from different models being referenced by a database identifier.2.3A process for reaction integration was devised, based on previously determined metabolite clusters. Firstly, we selected seven models for this process  since Recon3D integrates reactions from all of the other six models. In the next step, we exclude reactions that do not contain metabolites, since we would not be able to integrate them with the clusters. Also, reactions that involve more than one compartment are excluded to avoid integration of metabolic processes shifting metabolites across compartments and transport reactions involving a single metabolite in two compartments, since this information is not taken into account in the integration process, and also due to the fact that these reactions often do not represent enzymatic reactions (such as diffusion).C is a set of metabolites from different models that represent the same real metabolite, we assume each metabolite m ∈ C is now represented by its cluster C. Thus, each reaction will be represented by a set of pairs containing a metabolite cluster and a stoichiometric coefficient. This representation allows us to integrate reactions by finding those with identical clusters and stoichiometry for all involved metabolites in both the reactants and products of each reaction.The metabolite clusters identified using the methods described in the previous section are then used to replace the original metabolites found in the metabolic models. Since a cluster ρ(r) yielding the set of cluster-stoichiometry pairs for a given reaction r and a θ(m) function returning the set of reactions in which the metabolite cluster m is involved. The process used for reaction integration is presented on Our integration algorithm requires some important functions to be defined, namely Algorithm 1Y = {}R = full set of reaction identifierswhileR ≠ {} doP = θ(m), ∀m ∈ ρ(R1)         Y = Y ∪ x   R = R − C   endThe reaction clusters generated through this process are guaranteed to contain reactions with equal stoichiometry, assuming the metabolite clusters are correct. We further enhanced this clustering process by adding reactions to clusters if the external identifiers can be matched. This assumption can be considered valid on some cases where the model reconstruction includes reactions from previous models, as is the case of Recon 1 through 3 and HMR versions 1 and 2. This process is done iteratively through each pair of models deemed suitable for these comparisons.https://www.bio.di.uminho.pt/humanmodelintegration/The results from this work are available online on the following link: 3To assess the viability of the pipeline, first we show how the databases assist the integration/creation of the metabolite clusters . In FiguLooking at When evaluating the effects of the integration of the reactions, we first decided to compare how the three Recon models have evolved. For that, we analysed the amount of intersected reaction clusters between these models .We concluded that the majority of the Recon1 metabolites were integrated with the other two versions (with the exception of 25 clusters). For the Recon2, we reach a similar result. However, around 1300 clusters are only shared with Recon3D; those are most likely reactions from the models that were originally integrated with the Recon2 model coming from the HepatoNet and EHMN models. Regarding the Recon3D, about 2700 clusters were not integrated with the other models. Lastly, one unexpected result of our integration method is the fact that around 280 clusters are only shared by Recon1 and Recon2. When analyzing some of these clusters in Recon1 and 2, despite the stoichiometry being correct, we verified that the identifiers of the metabolites associated with some of these reactions do not match with the third version of the model. Therefore, it is likely that these metabolites could not be integrated using our tool.Since the last two versions of the Recon models were augmented with the other metabolic models, we performed an evaluation of our own integration of those models to assess how the models can be interconnected. We first decided to compare all the three versions of Recon with both HMR1 and HMR2.0 .There are some relevant points to highlight from the Aside from the HMR models, EHMN and HepatoNet have also been integrated with the Recon models since its second iteration. We also verified this fact in our integration results . In thisThere is a sharp increase in the amount of unique clusters. Although Recon3D has a small decrease on this number, both HMR2 and Recon2 have increased theirs, probably due to the absence of HMR1 and Recon1, respectively. Looking at the clusters all five models share, the number is lower than in the previous analysis , since HAs a final part of our study, we evaluated the proportion of reactions that each model contains from the other ones .Since Recon3D is the most current and updated human metabolic model and encompasses all the other models being analyzed, it is the one who has a higher proportion in all the other models, with the exception of the HMR1. This model is the least integrated, even with its second version. This is mainly due to the dissimilarities of the nomenclature of both reactions and metabolites (even different from HMR2), which makes it harder to integrate.When looking at the Recon family of models, Recon2 is almost entirely integrated with Recon1 and Recon3D has more than 80 % of the reactions on Recon2; however, Recon2 should have a higher proportion when compared to Recon3D as well as Recon3D when compared to Recon1. This can be explained, for example, as the removal or modification of certain metabolites or reactions throughout the iterations of the models that are not logged or due to errors on the integration process. In the former case, if a metabolite or reaction is altered in a next revision, the integration process may not recognize these changes and will lead to the creation of two clusters rather than a single one.Although our results show that it is possible to integrate a large portion of most current human GSMMs, there are some limitations that need to be addressed as part of future work.The fact that we impose that integrated reactions must contain exactly the same stoichiometry-metabolite pairs further impairs the algorithm’s ability to capture these minor differences between revisions and models as integrated entities. On the other hand, some metabolite clusters may wrongly contain several unrelated metabolites that, when used to integrate reactions, may lead to large reaction clusters that group reactions that are not identical. This may occur when different metabolites share the same information, grouping them as a cluster (as is the case for some cofactors). One solution would be restricting the amount of databases included in the integration, at the cost of losing potentially correct clusters due to the loss of information. Manual curation could also solve these problems although the purpose of this work is to implement an automated method.4In the present work, we attempt to enrich human metabolic models with external database identifiers to improve one of their main limitations, namely, their integration with other biological information repositories. With the presented pipeline, we provide a semi-automated tool to enrich the metabolite information that each model contains. Using these results, we decided to integrate the reactions for all the models present in the most recent reconstruction of the human metabolism (Recon3D). Although this process shows some interesting results, issues that come from Gene to Protein Rules and reactions that include more than one compartment have to be addressed in future work.Concluding, this work demonstrates that our presented pipeline can help to bridge the different human metabolic models. Despite requiring some manual curation, this work is a good starting point to bridge these models to achieve one of the most desired objectives in this field of study, the reconstruction of a unified human metabolic model.


Folate metabolism in mammalian cells is essential for multiple vital processes, including purine and pyrimidine synthesis, histidine catabolism, methionine recycling, and utilization of formic acid. It remains unknown, however, whether these processes affect each other via folate metabolism or can function independently based on cellular needs. We addressed this question using a quantitative mathematical model of folate metabolism in rat liver cytoplasm. Variation in the rates of metabolic processes associated with folate metabolism  in the model revealed that folate metabolism is organized in a striking manner that enables activation or inhibition of each individual process independently of the metabolic fluxes in others. In mechanistic terms, this independence is based on the high activities of a group of enzymes involved in folate metabolism, which efficiently maintain close-to-equilibrium ratios between substrates and products of enzymatic reactions. In mammalian cells, folate metabolism is involved in purine and pyrimidine synthesis, utilization of formic acid, histidine catabolism, and recycling of methionine from homocysteinede novo, and therefore must obtain them from food and intestinal bacterial flora. To become metabolically active, folates must be covalently bound to glutamate. The main form of folate circulating in the blood is the monoglutamate of 5-methyltetrahydrofolate, which is actively transported into cells by specific transporters. In the cytoplasm, folates are converted to polyglutamate forms that contain five or six glutamate residues per folate molecule, preventing their transport from the cell and significantly increasing their affinity for folate-related enzymes13. Under physiological conditions, folates undergo slow, non-enzymatic oxidation and degradation, which probably governs the rate of folate efflux from cells. The sum of intracellular folate concentrations forms the intracellular folate pool available for multiple intracellular metabolic processes. The rate of each metabolic process associated with folate metabolism is determined by cellular needs for the corresponding metabolites. It remains unknown, however, whether the associated biochemical processes can function independently or are coupled to each other via folate metabolism. In this study, we addressed this question using a quantitative mathematical model of folate metabolism.Mammalians cannot synthetize folates 17. Several previously developed mathematical models of folate metabolism were aimed at understanding the mechanism of methotrexate action in cancer cells and optimization of antitumor therapy24 or describing folate metabolism in microorganisms with the goal of developing new antifolate drugs25. The most extensive modeling of folate metabolism and its connection with other metabolic systems in animal cells was performed in a series of studies published by Nijhout, Reed, and coauthors31. A more recent approach to analysis of folate metabolism utilized a hybrid stochastic model to more accurately describe the metabolic system at very low folate concentrations32.Mathematical modeling is a powerful tool for analysis of complex metabolic systemsThe models mentioned above can simulate various aspects of folate metabolism. However, in order to study the interdependence of different metabolic processes associated with folate metabolism, we needed to (i) develop a new model that incorporates fluxes of all associated metabolic processes as input parameters, and (ii) utilize a consistent set of species and tissue-specific parameters that would enable rigorous quantitative analysis. Accordingly, for this study, we developed a quantitative mathematical model of cytosolic folate metabolism in rat liver that includes all reactions of folate and methionine metabolism in hepatocytes as well as the first reaction of the transsulfuration pathway, which is catalyzed by cystathionine β-synthase. Most of the model parameters, including all enzyme activities, were based on published data for rat liver or hepatocytes. The rates of purine and dTMP synthesis, histidine degradation, and influxes of formate and methionine Fig.  were use37, the model predicted that this increase is significantly smaller in the liver than in tissues lacking the transsulfuration pathway, such as heart muscle.Using this model, we studied the dependence of steady-state metabolite concentrations and reaction rates on the size of the folate pool and the effects of activation of each metabolic process associated with folate metabolism on the other processes and folate metabolism in general. Analysis of the model revealed that a group of highly active enzymes involved in folate metabolism, SHMT, MTHFC, and MTHFD, maintain the corresponding reversible reactions near equilibrium, providing the opportunity to activate or inhibit each individual metabolic process while exerting a minimal impact on the other processes in the system. Additionally, the model made several unexpected predictions regarding folate metabolism. First, liver cytoplasmic folate metabolism can maintain physiological formate levels even in the absence of an external source of formate. Second, folate metabolism ensures that vital metabolic processes continue at their physiological rates even when the size of the folate pool drops significantly below physiological levels. Third, although deficiency in folates causes an increase in homocysteine levels (a risk factor for cardiovascular diseases)The model consists of two parts, which describe metabolism of folates and methionine. The part of the model describing the kinetics of the concentrations of folates and associated metabolites is a system of ordinary differential equations constructed according to the scheme shown in Fig. VX is the rate of the reaction catalyzed by the enzyme X or the flux of substance X. Other designations and abbreviations are listed in the Table 15. Concentrations of ATP, ADP, NADP, NADPH, and a number of other metabolites are assumed to be constant  in the MS reaction, histidine catabolism, and formate utilization/production. The rates of these processes, which produce or consume one-carbon equivalents, are represented in the model by five input parameters described below.The main metabolic processes associated with cytoplasmic folate metabolism in mammalian cells are De novo purine synthesis occurs via a linear chain of reactions, of which two, catalyzed by GT and AT, depend on [10-THF] and were included in the model. The rate of production of GAR, the substrate for GT reaction, is the model parameter that determines the rate of purine synthesis (VGAR). For simplicity, we assume that AICAR, the substrate for the AT reaction, is produced directly by the GT reaction (system of model equations (de novo purine synthesis.epend on 0-THF andVTSmax), which is a model parameter.dTMP is synthesized from dUMP via the TS reaction. We assumed that the concentration of dUMP is constant and the rate of dTMP synthesis in the model is determined by TS activity (15. The influx of methionine (VMet) is a model parameter.The rate of the MS reaction in liver depends on [Met], which in turn depends on Met influx from food or other sourcesVFIGlu) is a model parameter.FIGlu, one of the final products of histidine degradation, is the substrate for the bifunctional enzyme GFIT/FITCD in folate metabolism. The influx of FIGlu  is utilized in the liver. Therefore, we used the rate of total formate production in the rat body, normalized against liver mass, as the model parameter describing formate influx into liver folate metabolism (VFormate). For purposes of normalization, we assumed that the liver constitutes 5% of rat body mass41.Formate can be produced in a number of intracellular processes, including catabolism of tryptophan, cytochrome P450-catalyzed demethylation, peroxisomal α-oxidation of phytanic acid, and degradation of glycine, serine, sarcosine, or dimethylglycine in mitochondriaWe varied the model input parameter values and folate pool value during the model analysis. The physiological values of these parameters are presented in Table 42. Steady-state analysis of the model was done using the AUTO software43. The characteristic time of each individual metabolite was computed as described under Results and discussion in the section named “Characteristic times in folate metabolism.”Kinetics of the model was studied using the CVODE method for solving stiff systems of ordinary differential equation46. Many authors have reported sums, e.g., [10-THF] + [5-THF] and [THF] + [CH2-THF], as more reliable values than the measured individual concentrations of these folates46. Also, information regarding components of the intracellular folate pool such as CH-THF and DHF is very scanty, and show only that these species do not exceed 10–16% of the intracellular folate pool51.A major problem in simulation of folate metabolism is the wide scatter in the experimental data for folate concentrations, which is in turn associated with a wide scatter in the size of the folate pool. Folate pool sizes in liver of rats fed a standard diet, reported from the middle of the 1990s to the present, vary from 5 to 26 µmol per kg tissue  had a normal physiological value while those of the others, and the activity of TS, were equal to zero. Methionine influx cannot be equal to zero in the model because this would result in cessation of all metabolic processes due to accumulation of all folates in the form of CH3-THF. Thus, we also kept methionine influx at a normal level. Under these conditions, the steady state disappears at different folate pool sizes specific for each non-zero metabolic process associated with folate metabolism Fig. . Methion2.The existence of the steady states in the model when only one of pathways producing or consuming one-carbon groups is active reveals that folate metabolism does not require a balance between external producers and consumers of one-carbon groups associated with this metabolic system. Indeed, each of the metabolic processes associated with folate metabolism can function alone, absolutely independently of the others. Analysis of the model reveals that in this case, all necessary one-carbon groups are produced or consumed in the SHMT reaction using serine and glycine as a source or sink. This is illustrated in Fig. Three characteristic times that determine the rate of response of folate metabolism to metabolic perturbations can be distinguished in this metabolic system. Changes in folate pool size associated with consumption and excretion of 5-methyltetrahydrofolate by cells, and non-catalytic degradation of folates proceeds with a characteristic time of several days  Figs , 4. In tFigure Activation of histidine catabolism (increase in FIGlu influx) up to about 80-fold affects the concentrations of input metabolites involved in other metabolic processes, as well as the TS reaction rate and folate concentrations, even less than activation of formate influx Fig. .Similarly, a significant increase in GAR influx (activation of purine synthesis) or in methionine influx does not affect other metabolic processes associated with folate metabolism Figs , 4a,b. IVTSmax). An increase in TS activity causes a corresponding increase in the TS reaction rate until it becomes equal to the maximal rate of the DHFR reaction  remain unaffected (not shown). In the case of an increase in methionine influx, concentrations of intermediates of methionine metabolism change according to predictions of a published model of methionine metabolismThe upper limits for activation of formate, FIGlu, or GAR influx decrease with the size of the folate pool Fig. . The uppThus, our data show that metabolic processes associated with folate metabolism have large activation capacities, and that any one of them can be activated or inhibited more or less independently from the others. Moreover, the rate of any of these processes can be increased to its upper limit without significantly affecting the maximal rate of any other process. Figure The mechanism of independent functioning of different metabolic processes in folate metabolism is based on a group of highly active enzymes  that catalyze fast reversible reactions. These enzymes maintain the distribution of folate metabolites close to equilibrium during various perturbations in folate metabolism, thus providing stable conditions for all metabolic processes associated with this metabolic system. In general a decrease in activity of these enzymes causes a decrease in the upper limits of activation of metabolic processes associated with folate metabolism Fig. .38. Our estimations show that in rat liver under physiological conditions, utilization of formate is the most intensive metabolic process associated with cytoplasmic folate metabolism  entering folate metabolism in rat liver are converted to serine, whereas a small fraction (∼23%) is eliminated as CO2 via the FTHFD reaction , acts as the main source of one-carbon groups for folate metabolism in the cytoplasmm Tables . The totm Tables . Toxicokion Fig. . The amoion Fig. . Activatnts Fig. 55.Figure53. Our results demonstrate that at least in rat liver, cytoplasmic folate metabolism can maintain significant formate levels in the absence of folate influx from mitochondria or other tissues. In the model, accumulation of formate after an increase in serine levels is fast and reversible  connected via folates and functioning almost independent of each other. Interestingly, the degree of independence between the systems can be different at the same metabolic network topology. Indeed, Fig. Our results reveal that rat liver folate metabolism represents a typical case of modular organization of cellular metabolism2 via FTHFD. Accordingly, it is reasonable to assume that the majority of formate produced in cells is not determined by the need to fuel folate metabolism, but is instead associated with other cellular needs such as regulation of glycine levels via the glycine cleavage system in mitochondria. This assumption is supported by the results of our model, which demonstrate that cytoplasmic folate metabolism in the liver can maintain significant formate levels even in the absence of formate influx from external sources such as mitochondria or other tissues , etc. In previous work, we obtained strong evidence that adenylate and glutathione pools are determined by the rate of ATP and reduced glutathione turnover in the cell, respectivelySupplementary information Rat liver folate metabolism can provide an independent functioning of associated metabolic pathways


Metabolism is highly regulated, allowing for robust and complex behavior. This behavior can often be achieved by controlling a small number of important metabolic reactions, or metabolic valves. Here, we present a method to identify the location of such valves: the metabolic valve enumerator (MoVE). MoVE uses a metabolic model to identify genetic intervention strategies which decouple two desired phenotypes. We apply this method to identify valves which can decouple growth and production to systematically improve the rate and yield of biochemical production processes. We apply this algorithm to the production of diverse compounds and obtained solutions for over 70% of our targets, identifying a small number of highly represented valves to achieve near maximal growth and production. MoVE offers a systematic approach to identify metabolic valves using metabolic models, providing insight into the architecture of metabolic networks and accelerating the widespread implementation of dynamic flux redirection in diverse systems. Interventions in metabolic networks can improve microbes for chemical production. Here, the authors develop a tool to identify metabolic valves that can decouple growth and production to systematically improve the rate and yield of biochemical production processes. These regulatory systems are the basis for ubiquitous cellular phenomena including complex cell cycles, robustness to changing environments, and eukaryotic development through stem cell differentiation and tissue morphogenesis. The architecture of these systems can vary tremendously, from regulating short pathways, to having global metabolic effects4. Engineered applications of these systems have been developed to understand complex cellular processes5, implement genetic logic7, and improve microbes to produce valuable chemicals13, using control points identified by biochemical assay, or intuited from models of metabolic structure. The choice of such control points is further complicated for non-natural objectives, such as chemical production, where few biological examples exist.Biological regulatory networks allow for metabolic transitions which are apparent in a range of biological processes14. In particular, these models have been used extensively for designing microbial cell factories15. This is commonly accomplished using mixed-integer linear programming (MILP) techniques to identify network modifications, which can then be implemented by modulating gene function. In particular, a large number of algorithms have been developed to identify such interventions to improve microbes for growth-coupled chemical production18. These strategies rely on the simultaneous production of both biomass and product; however, the burden imposed by high-flux production pathways can severely limit this strategy when producing chemicals at high yields, which is particularly evident when considering the trade-offs between yield and productivity19. Furthermore, growth-coupling can require specific network features, which may not exist in all organisms22. Instead, growth and production could be separated, allowing production processes to be operated in two stages, where biomass is accumulated before high-rate production is initiated. A phenotypic shift can be realized using a number of stimuli including inducers24, internal metabolites26, and cell density28. Although many strain design algorithms exist, these algorithms identify static interventions to achieve a single steady-state growth-coupled phenotype. None of these algorithms is suitable for identifying dynamic interventions, where multiple phenotypes must be considered. In this paper, we present a novel and systematic approach to identify metabolic valves and apply it for the production of 87 metabolites that can be produced by the genome-scale model of Escherichia coli.Metabolic network structure has been studied using metabolic models for diverse purposes including consolidating high-throughput -omics data, identifying drug targets, and predicting metabolic phenotypes7  a set of static knockouts and 2) a set of dynamically controlled valves, to enable the transition between high flux for each of these targets Fig. . Static 7 Fig.  to enabl7 Fig. . For som 30 Fig. ; however 30 Fig. . Since t a set ofE. coli31. We present a strategy for the production of α-ketoglutarate (AKG), an important intermediate in the tricarboxylic acid (TCA) cycle with uses as a dietary supplement, to illustrate the role of valves and knockouts for redirecting flux, and their impact on the phenotypic space . Both strategies achieve over 90% of theoretical maximum biomass yield in the growth state. Alternatively, an intermediary stage could be included for high expression of the production pathway at the end of the growth stage , to reduce the need for heterologous protein expression in the production stage.We searched for intervention strategies for all 87 organic products that can be derived from glucose in our model (Supplementary Table gapA), pyruvate dehydrogenase  and phosphoglucomutase ; citrate synthase  from the TCA cycle; and oxygen exchange (EX_o2(e), passive) used in oxidative phosphorylation. These valves were relatively evenly distributed amongst the degree of reaction connectivity, indicating their high representation is not solely owed to their branched nature  is the only single valve identified in the TCA cycle, and connected to AKG, a precursor to amino acids . These reactions are also important for controlling ATP generation through pyruvate kinase  and NADH generation through PDH, allowing alternate routes for entry into the TCA cycle. These results highlight the importance of the pyruvate node for controlling metabolic flux.Contrarily, we have identified valves which could be applied to a majority of tested products. For example, CS was identified as an effective valve to decouple 55 products. It lies at an important branchpoint which has been successfully dynamically controlled to improve the production of isopropanol from acetyl-CoAAKGDH, which produces succinyl-CoA from AKG, was uniquely identified as a valve for partial decoupling. It is proximal to a highly regulated branch point for the production of amino acids from AKG, which also has implications in nitrogen metabolism and cofactor balance. We identified AKGDH as a suitable valve for AKG production, as well as glutamate, arginine, and proline which are derived from AKG. Another important valve in amino acid metabolism is phosphoglycerate dehydrogenase (PGCD), the committing step into serine, cysteine, and glycine metabolism from 3-phosphoglycerate (3PG). It is regulated through feedback inhibition by serine, to maintain appropriate concentrations of these amino acids. PGCD and PGM share a common metabolite (3PG) and were both identified as top valves. By controlling this node, flux can either be directed through PGM toward pyruvate and downstream products, or through PGCD to produce amino acids such as serine and cysteine.We also identified higher-order strategies which required actuating multiple valves simultaneously. By applying two or three valves, we identified strategies for 64 and 68 products, respectively, compared to 56 products using single valves. This indicates that multiple valves can be required to decouple growth and production for some targets. We also identified clusters of valves which include reactions from a wide range of different subsystems for both fully  and a minimum product yield of 70% of theoretical maximum in the production state. Strategies also targeted over 90% of theoretical maximum growth rate in the growth state. We identified solutions for 61 of the 84 targets using single valves  flux bounds for certain reactions, i, to define upper bounds on uptake rates , or fix parameters such as ATP maintenance:Stoichiometric metabolic models are defined by the reactions present in a given organism, based on genome sequences and experimental validation. Central to this metabolic model is the stoichiometric matrix We assume here that all fluxes in the network are explicitly or implicitly bounded by these constraints Eqs. –3.The MoVE algorithm aims to find a minimal set of knockouts and a set of dynamically regulated valves to allow switching between two distinct metabolic phenotypes. Here, we have applied this algorithm to achieve efficient switching between two relevant phenotypes for two-stage bioproduction processes: growth and production. This is accomplished by formulating a mixed-integer linear program, which can then be solved using a range of commercial or open-source solvers. Diverse optimization problems, including those relying on stoichiometric models, have been solved in this fashion.r denotes the production state (state 2) flux vector and a second flux vector, f, is introduced to represent the growth state (state 1), subject to similar flux bounds: γi ≤ fi ≤ δi, and steady-state constraints: N · f = 0.To consider multiple phenotypes in a dynamic context, we require the specification of flux vectors for both of these states and variables describing both static (knockout) and dynamic  interventions. Furthermore, this method must remain scalable to genome-scale models, given these additional variables and constraints. In MoVE, T (t × n) and t (t × 1) to formulate linear inequality constraints for undesired flux vectors in the production state  and d (d × 1) impose constraints for the desired flux vectors in the production state :Similarly, the parameters D consists of two rows derived from Eqs. rP and ‘rS, the second contains non-zero values only for the rB (−1) and again for the substrate uptake rate rSd is of size 2, and contains ‘0’ elements.In this case, G (g × n) and g (g × 1) to represent desired phenotypes in the growth state  and substrate uptake rates .Furthermore, constraints are added to describe desired flux vectors in the production (Eq. ) and groMoVE applies the constraints defining the undesired Eq.  and desi45, a minimal set of knockouts to eliminate undesired functionality. For computation of MCS, the primal problem described above ove Eqs. –4 is traity Eqs.  and 9 aru, w, vpIrr, vpRev, vnRev and the production state variables are further separated into reversible and irreversible components. Following, the stoichiometric matrix N, the identity matrix I, and the undesired flux matrix T are split into two submatrices containing the reversible  and irreversible  reactions (columns).To enable efficient calculation of MCS, new dual variables are introduced, zpi = 0 ⇔ vpi = 0, zpi = 1 ⇔ vpi ≠ 0 for all reactions, and additionally zni = 0 ⇔ vni = 0, zni = 1 ⇔ vni ≠ 0 for reversible reactions. If the value of an indicator variable is 1, then its associated reaction is in the cut set and can carry no flux as demanded by the constraints for ri.This makes it possible to use Boolean indicator variables Although identified MCSs will successfully eliminate undesired functionality Eq. , these Myi thus indicate whether a reaction can carry flux (yi = 1) or not (yi = 0) in the growth state. Up to max_valves reactions of a MCS  are allowed to carry flux in the growth state. Hence, the valve reactions are those for which yi = 1 and zi = 1. The reactions for which yi = 0 and zi = 1 are static knockouts and are disabled in both production and growth state, whereas all other reactions are available in both states.The Boolean variables Finally, these variables and constraints are combined to allow the direct identification of optimal combinations of valves and knockouts . It is important to note that since any feasible solution will achieve desired functionality (in both states) and eliminate undesired functionality, solving the algorithm to optimality is not absolutely essential.49 and CellNetAnalyzer v2017.4 (CNA)50. Mixed-integer linear programs were solved using ILOG CPLEX , via the provided Java virtual machine interface in CNA.Simulations were performed in MATLAB 2010b using the COBRA toolboxE. coli simulations were performed on the SciNet general purpose cluster51. The cluster is composed of 3864 nodes using Infiniband interconnect. Each node contains 2x Intel Xeon E5540 processors for a total of 8 cores or 16 threads per node, with 16 GB of RAM. Simulations were performed in parallel for each metabolite and set of parameters. Each simulation was performed on 4 nodes, using 16 threads per node, for 8 h. The MILP was solved in two steps, ramp-up and distributed tree search. In the ramp-up phase, the same problem is solved on each node using different startup parameters for two hours. Following the ramp-up phase, the optimal startup parameters are used to start a distributed search tree for the remaining 6 h. The optimal feasible solution from this process is returned.Genome-scale S. cerevisiae solutions were solved for two hours using 4x Intel Xeon CPU E7-4830 processors, for a total of 32 cores.Genome-scale E. coli core model31 was derived from iAF126052 and is available from the BiGG database53 (http://bigg.ucsd.edu/models/e_coli_core). Maximum glucose uptake rate was set at 10 mmol gdw−1 h−1 and minimum ATP maintenance at 8.39 mmol gdw−1 h−1.The E. coli genome-scale model iJO136633 was used for all genome-scale simulations and available from the BiGG database (http://bigg.ucsd.edu/models/iJO1366). Maximum glucose uptake rate was set at 10 mmolg dw−1 h−1 and minimum ATP maintenance at 3.15 mmol gdw−1 h−1. Target reactions were chosen from the total set of export reactions by eliminating non-organic molecules and those which were not producible from glucose based on a flux variability analysis. A set of exchange reactions, excluding the target reaction, common fermentation products, and non-organic molecules, was removed from the model to improve computational feasibility; this list is provided in The E. coli core model were solved to optimality using an upper bound of three valves in negligible computational time. Strategies for the genome-scale model were solved using the distributed MILP search method with an equality constraint on the number of valves. Searches explicitly specified one, two, or three valves. To identify the optimal valve for each metabolite, all reactions were allowed to be used as valves for fully coupled strategies, and only non-essential valves for partially coupled strategies. To identify valves which could be applied to many products, we ran independent optimizations with each valve explicitly specified .Strategies for the S. cerevisiae genome-scale model were identified using iMM90454 which is available from the BiGG database (http://bigg.ucsd.edu/models/iMM904). Maximum glucose uptake rate was set at 10 mmol gdw−1 h−1 and minimum ATP maintenance at 1 mmol gdw−1 h−1. A set of exchange reactions, excluding the target reaction and reactions required for wild-type growth, was removed from the model to improve computational feasibility; this list is provided in Strategies for the 55. Connectivity for each reaction was determined as the sum of the connectivities of all metabolites involved in that reaction. The connectivity of each metabolite is determined as the number of reactions in which it partakes.Reaction connectivity was determined in Python 3.5 using the COBRApy packageIntervention strategies were determined using one, two, or three metabolic valves. Higher-order valves which improved the objective  were used to generate an adjacency matrix for clustering, using the co-occurence frequency as a similarity metric. The resulting sparsely connected matrix was clustered using an iterative spectral clustering approach. Several iterations of spectral clustering were performed using the scikit-learn package (v0.19.0). Following, a new similarity matrix was generated based on the mutual information available between clustering solutions to identify the most represented solution, this clustering result is returned. The numbers of clusters was chosen to ensure clusters contained at least two members.https://github.com/lmse/move and as Supplementary Software The MoVE algorithm is available at Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Software 1Supplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4