Saccharomyces cerevisiae growing in the presence of two carbon sources. Even though diauxic shifts emerge naturally from the model when two resources are qualitatively very different, the model predicts that the existence of such shifts is not a prerequisite for species coexistence in competitive communities.Microbes are capable of physiologically adapting to diverse environmental conditions by differentially varying the rates at which they uptake different nutrients. In particular, microbes can switch hierarchically between different energy sources, consuming first those that ensure the highest growth rate. Experimentally, this can result in biphasic growth curves called “diauxic shifts” that typically arise when microbes are grown in media containing several nutrients. Despite these observations are well known in microbiology and molecular biology, the mathematical models generally used to describe the population dynamics of microbial communities do not account for dynamic metabolic adaptation, thus implicitly assuming that microbes cannot switch dynamically from one resource to another. Here, we introduce dynamic metabolic adaptation in the framework of consumer-resource models, which are commonly used to describe competitive microbial communities, allowing each species to temporally change its preferred energy source to maximize its own relative fitness. We show that dynamic metabolic adaptation enables the community to self-organize, allowing several species to coexist even in the presence of few resources, and to respond optimally to a time-dependent environment, thus showing that dynamic metabolic adaptation could be an important mechanism for maintaining high levels of diversity even in environments with few energy sources. We show that introducing dynamic metabolic strategies in consumer-resource models is necessary for reproducing experimental growth curves of the baker’s yeast  Saccharomyces cerevisiae on two different resources and we show that dynamic metabolic strategies allow the community to self-organize and to ensure the coexistence of multiple species competing for few resources.Since a celebrated experiment by Monod in 1949, we know that microbes can adapt their metabolic strategies in response to their environment, thus uptaking different nutrients at different rates depending on their relative quality and availability. It is currently unclear whether this physiological plasticity of microbes contributes to maintaining the high degree of diversity found in natural microbial communities, even in the presence of very few resources. By introducing dynamic and optimal metabolic strategies in consumer-resource models, we show that we can correctly reproduce the experimental growth of  Biodiversity is one of the most fascinating aspects of nature: from the microscopic to the continental scale, complex communities composed of tens to thousands of species compete for resources and yet coexist. In particular, the survival of a species depends on the availability of resources in the environment, which is not static and can be altered by the presence of other species in the community. Furthermore, biodiversity is crucial for the functioning and maintenance of whole ecosystems, directly impacting their productivity, stability and many other properties . It is tEscherichia coli and Bacillus subtilis grown in a culture medium containing two different sugars exhibit a biphasic growth curve, which he called “diauxie”. Instead of metabolizing these two nutrients simultaneously, bacteria consumed them sequentially using the most favorable one first  and once it had been depleted, following a lag phase, they resumed growth using the other sugar. Since then, diauxic growth has been the subject of thorough empirical study   m speciem species and p resources, if the total maximum resource uptake rates δσ , does not depend on the species’ identities. In mathematical terms, if m > p species can coexist. This requirement is compatible with the experimental observations that led to the formulation of the metabolic theory of ecology [δσ) depend only on the characteristic mass of a species. It is indeed possible to show analytically that our model can strictly violate the CEP if the CTR σ = dδσ, where d > 0 regulates the speed of adaptation.Considering now our model in the general case of cies see . We focu ecology  , if δσ = δ∀σ  and if si, belongs to the convex hull of the metabolic strategies Eσ) will lead to the extinction of at least m − p species, i.e. the system will obey the CEP; in this sense the system allows coexistence only when fine-tuned, a situation that is unlikely to be true for all natural communities. However, if we now use  is possible only if j, then there will be extinctions and in the end the CEP will hold  -dimensional simplex where our system can be represented. In other words, we find that if the degradation rate μj of resource j becomes too large, then again all the j-th components of the metabolic strategies will become null . On the other hand, if we introduce the resource degradation rates in MacArthur’s consumer-resource model with fixed metabolic strategies, extinctions will occur and the CEP will hold  see , and if i-th components of the metabolic strategies vanish . Increasing the value of d leads to metabolic strategies that adapt more rapidly, and as a consequence species’ growth rates will be optimized for longer periods of time. Thus, in a community in which the CTR is the same for all species, stationary population densities will be higher for larger values of d. When d tends to zero, instead, we recover the case of fixed metabolic strategies and thus the CEP will determine the fate of the community. As shown in d. On the other hand, if the system is subject to variable environmental conditions like the ones discussed previously  becomes less and less variable across different species. We suggest that this requirement is compatible with the experimental measurements of the scaling of vital and metabolic rates with body size that led to the metabolic theory of ecology , accordiy traits –57  + 2% (w/v) glucose. 1 mL of the overnight culture was spun down and resuspended in CSM + 0.5% (w/v) galactose to a concentration of 1.6 ⋅ 105 cell/mL. Eight wells of a 96-well plate were inoculated with 150 μL of the resuspended culture and incubated with constant shaking at 30°C in a plate reader. The 96-well plate was sealed with a sealing membrane that allowed gas exchange. The temperature on the top of the 96-well plate was kept at 31°C to avoid condensation on the membrane. Optical density (OD) measurements were taken every 10 min, for a total duration of about 70 h. To build the calibration curve used to convert OD to cell density, 1.4 mL of the same overnight culture were spun down and resuspended in 1 mL of CSM + 0.5% (w/v) galactose. The density of this suspension was measured using a Coulter counter and serial dilutions of this suspension were inoculated in a 96-well plate covered with the same sealing membrane used for the growth curve measurement. The OD of the wells containing the serial dilution of the suspension was measured after equilibration to 30°C using the same plate reader used to measure the growth curves, and these measurements were used to build the calibration curve converting OD to cell density.The HK459 of  and is iS. cerevisiae is grown on galactose as the primary carbon source, the sugar is partially respired and partially fermented. Yeast cells excrete ethanol as a byproduct of fermentation, which can then be used as a carbon resource. For this reason, in order to describe such system we use our adaptive consumer-resource model with m = 1, p = 2 and we slightly modify the equations for the temporal dynamics of ethanol concentration to take into account the fact that this resource is not initially present in the system but is produced by the yeast. In particular, the equations we used in order to describe the system are  is the relative likelihood of the two models, and as such measures the probability that the model with fixed metabolic strategies minimizes the information loss (i.e. it is a better fit to the data than the one with adaptive metabolic strategies). In our case, by comparing the fits shown in AIC = −938, so the probability that the results could be better explained using the model with fixed metabolic strategies is infinitesimal, even if the curve can nevertheless reproduce a diauxic behavior. The situation is of course even more extreme if we compare the fits shown in AIC = −1327. We show in Figure C in Notice that since the model has several parameters  there can be several different choices that lead to apparently equivalent fits. We therefore used a Markov Chain Monte Carlo algorithm  to fit t to show  that expS1 Text(PDF)Click here for additional data file.S1 Data(XLS)Click here for additional data file.


The role of our gut microbiota in health and disease is largely attributed to the collective metabolic activities of the inhabitant microbes. A system-level framework of the microbial community structure, mediated through metabolite transport, would provide important insights into the complex microbe-microbe and host-microbe chemical interactions. This framework, if adaptable to both mouse and human systems, would be useful for mechanistic interpretations of the vast amounts of experimental data from gut microbiomes in murine animal models, whether humanized or not. Here, we constructed a literature-curated, interspecies network of the mammalian gut microbiota for mouse and human hosts, called NJC19. This network is an extensive data resource, encompassing 838 microbial species  and 6 host cell types, interacting through 8,224 small-molecule transport and macromolecule degradation events. Moreover, we compiled 912 negative associations between organisms and metabolic compounds that are not transportable or degradable by those organisms. Our network may facilitate experimental and computational endeavors for the mechanistic investigations of host-associated microbial communities. Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.12336164 Recent advances in metagenomics have revealed that alterations in the human gut microbiota are implicated in a number of disorders, such as obesity, inflammatory bowel disease, colorectal cancer, and diabetes7. At the center of the gut microbiota functions are the various interactions between microbes and their interplay with the host environment8. Microbes degrade diet-derived and host-derived chemical substances, and release the degradation products to other members of the community. The microbial transport of nutrients and metabolic byproducts gives rise to competition for resources and cooperative relationships via metabolic cross-feeding8. The metabolites secreted by the microbes are absorbed by host tissues, and translate into beneficial or detrimental mediators of host physiology9. As a result, such microbe-microbe and microbe-host interactions form a complex ecological network in the gut environment10.The mammalian intestinal tract is colonized by various microorganisms, called the gut microbiota or microbiome12. This method, by its nature, does not delineate biochemical reactions to the species from which they originate, making it difficult to elucidate interspecies interactions. On the other hand, there exist previous works on the modeling of diverse interspecies interactions explicitly mediated by metabolites that are transported (imported or exported) by individual microbial species14. Yet, these works are based on error-prone, automated identification protocols for transportable metabolites, which are possibly inaccurate to some degrees. There are ongoing computational efforts towards biologically realistic microbial interactions, by using manually curated, constraint-based metabolic models or relatively simple kinetic models16. Nevertheless, most of these models are far from the scale of diversity seen in the gut community, which typically comprises hundreds of different microbial species. Notably, this scale of microbial diversity has been recently captured by constraint-based metabolic models with semi-automatic model reconstructions17, but they still exhibit limited biological accuracies20.In the microbiome research, one common practice for reconstructing metabolite-mediated microbial networks is to combine the entire biochemical reactions inferred from annotated metagenomes10. This network is primarily based on biological knowledge and experimental evidence documented in the literature. The network NJS16 encompasses >4,000 small-molecule transport and macromolecule degradation events of >500 bacterial and archaeal species and 3 human cell types. Although NJS16 is useful to explore the microbial community inside the human gut, mechanistic studies in the microbiome research field have been mainly conducted on animal models, rather than on human subjects, due to the technical and regulatory limitations on human experimentation22. Regarding animal models, physiological, anatomical, and genetic similarities between humans and mice, as well as massively accumulated knowledge of mouse genetics, have facilitated the use of murine models, to elucidate causality and mechanisms of host-microbiota interactions23. In this regard, a phylogenetic extension of NJS16 to murine gut microbes would be useful for the system-level mechanistic exploration of gut microbiota functions using murine animal models.Recently, we have constructed an extensive, literature-curated interspecies metabolic interaction network of the human gut microbiota, NJS16, which represents another system-level framework for gut microbiota analysis10. Specifically, NJC19 greatly expands the diversity of microbial species and host cells to those relevant to the mouse gut environments, and even covers a certain range of eukaryotic microbes that were completely missing in the predecessor NJS16. Therefore, NJC19 serves as a global network template, adaptable to the gut microbiota of either a mouse, human, or humanized mouse. Moreover, not only does NJC19 incorporate metabolite transport and macromolecule degradation events of the microbiota, but it also provides literature-annotated, negative information of which metabolic compounds are not able to be transported or degraded by the organisms. Such negative information would be useful to curate computational microbial models, such as constraint-based metabolic models, which can include false-positive transport reactions from automatic genome annotations.Here, we present a literature-curated, interspecies metabolic interaction network of the microbiota associated with the mouse and human gut, NJC19. To our knowledge, NJC19 represents the largest ever, literature-based network data resource for the mammalian gut microbiota, as a compilation of information from 769 research and review articles and textbooks  was given to species absent in our previous network, NJS1610. In the case of the metagenome sequence data, the number of the detected species was rather excessive for our further processing; therefore, among those species, we only considered the species inhabiting ≥90% of the metagenome samples (with the relative abundance ≥0.001%) in each study. We found that the genera of these selected species account for the vast majority [89.6 ± 4.3% (avg. ± s.d.)] of the total microbial abundances in the metagenome samples. In addition, we manually considered some relevant species, such as Citrobacter rodentium32  and the degradation of macromolecules , reported in literature. For the small-molecule metabolites, we mostly considered primary metabolites, i.e., nutrients and metabolic byproducts associated with microbial growth or reproduction. In addition, literature sources that report the mRNA or protein expression for metabolite-specific enzymes or transporters were considered. When encountering the information of which chemical compounds are not able to be transported or degraded by a given organism, we recorded this negative information as well, as part of our collected data. Despite technically not being a part of the gut microbiota, some host cells directly affect or are affected by microbial metabolism, and thus were considered to be a functional extension of the microbial community. In a similar fashion to our previous network NJS16 for the human case, the specific mouse tissue cells that we considered were the intestinal absorptive cell, the mucin-secreting goblet cell, and the bile acid-secreting hepatocyte. Although the hepatocyte is not part of intestinal tissue, its secreted bile acids are utilized by microbes in the gut. In the case of the mouse intestinal absorptive cell, the information from a manually-curated, genome-scale metabolic model (iSS1393) was adopted34, and removed the incorrectly-placed components and added new links found from literature, according to more specific and accurate information. The revised NJS16 was finally connected to the above mouse gut microbiota interaction network through the common chemical compounds shared by the both networks, to form the mouse and human gut microbiota interaction network, NJC19  file of NJC19 is provided for interactive network visualization35.In parallel, we carefully re-examined the existing components of NJS16Our network NJC19 offers the reference map of the mammalian gut microbiota and chemical compound relationships (from 769 literature sources), which can be adapted for each context of mouse, human, and humanized mouse microbiomes. In NJC19, one set of nodes corresponds to organisms , while the other set corresponds to chemical compounds . An organism and a chemical compound are connected if the organism imports, exports, or degrades the chemical compound. NJC19 comprises 838 microbial species  in the mouse and human gut, 6 mouse and human cell types metabolically interacting with those microbes, and 283 chemical compounds —all interconnected by 8,224 small-molecule transport or macromolecule degradation events. In addition, NJC19 provides information on small molecules and macromolecules that are reportedly not transportable or degradable by certain organisms—described through 912 negative metabolic associations. These negative associations can be particularly useful for the curation of automatically-generated metabolic models, which may include false-positive transport reactions derived from inaccurate genome annotations.k metabolites follows an exponential distribution P(k) ∝ erk−  by k species follows a power-law distribution P(k) ∝ kγ− 39. Therefore, for these two studies, microbial producers of a given metabolite are defined as the microbial genera, with each having the species whose majority (>50%) can produce that metabolite in NJC19. We also defined microbial consumers in a similar way, although they were excluded from Fig. To further assess the validity of our network, we examined the correlations between microbe-metabolite links in the network and measured metabolite levels in the mouse gut and portal vein plasma. Specifically, we examined whether the abundance increase/decrease of microbes associated with a particular metabolite in our network is consistent with the shift of the metabolite level across different experimental conditions. Regarding this analysis, three published mouse studies were found to provide the information of both microbial and metabolite levels in their collected samples: one study is for antibiotics (cefoperazone) treatment and recovery37, and thus the metabolite concentration changes here are not likely to be a mere consequence of the microbial load changes. To test the statistical significance of these correlations, we introduce quantities fij, gij, and fij’ for each pair of mouse groups i and j: fij (gij) denotes a fold change from group i to group j in the measured producer (metabolite) abundance averaged over the replicates in the group i or j. fij’ denotes a group-i-to-j fold change in the average abundance of randomly-assigned producers, while the number of those randomly-assigned producers from all the data sources in Fig. P value as the probability of satisfying fij’ ≥ fij (fij’ ≤ fij) for all -pairs that have fij and gij with both ≥ 1 (≤1). Accordingly, our P value calculation reveals that the producers in NJC19 and the detected metabolic compounds are significantly correlated in Fig. P = 0.02 for Fig. P < 10–4 for Fig. P = 0.06 for Fig. Figure Supplementary Table


MEtabolic models Reconciled with Gene Expression (MERGE), a computational pipeline that we used to predict tissue‐relevant metabolic function at the network, pathway, reaction, and metabolite levels based on single‐cell RNA‐sequencing (scRNA‐seq) data from the nematode Caenorhabditis elegans. Our analysis recapitulated known tissue functions in C. elegans, captured metabolic properties that are shared with similar tissues in human, and provided predictions for novel metabolic functions. MERGE is versatile and applicable to other systems. We envision this work as a starting point for the development of metabolic network models for individual cells as scRNA‐seq continues to provide higher‐resolution gene expression data.Metabolism is a highly compartmentalized process that provides building blocks for biomass generation during development, homeostasis, and wound healing, and energy to support cellular and organismal processes. In metazoans, different cells and tissues specialize in different aspects of metabolism. However, studying the compartmentalization of metabolism in different cell types in a whole animal and for a particular stage of life is difficult. Here, we present  MERGE is computational pipeline that can convert tissue‐level RNA‐seq data from Caenorhabditis elegans into predicted tissue flux potentials that indicate metabolic function.Monitoring tissue‐ and cell‐type specific metabolic activities by metabolomics remains challenging.  Caenorhabditis elegans is a bacterivore that can be fed individual bacterial strains. Caenorhabditis elegans tissues and metabolism share many functions with mammals. Therefore, it provides a relatively simple model for understanding animal metabolism at a systems level. We have previously reconstructed a C. elegans genome‐scale metabolic network model  , a combined approach Fig A that stC. elegans metabolism  the intestine, which receives, metabolizes, and delivers nutrients to the other tissue; (ii) the intestinal lumen from which bacterial nutrients are imported by the intestine; (iii) the other tissue; and (iv) the extracellular space through which nutrients are exchanged between the intestine and the other tissue  and simultaneously maximized to get Zfitmax  during the first step. Then, while Zfitmax is held constant and the low flux sum is tightly constrained, the total flux in the entire network is minimized based on a parsimonious FBA approach (pFBA)   is defined for each tissue (T) as a function of three sets of variables: (i) the reaction network of the tissue defined as reactions in OFD and ALT , wherein all metabolic genes are expressed at the maximum level found in any tissue. Thus, FPA of the target reaction yields a dimensionless value between 0 and 1 for each tissue, which is named relative flux potential (rFPk) . We describe the concept of FPA by a toy network Fig A. FPA us ALT Fig C, (ii) e ALT Fig  of everyPk) Fig A.FPk, we maximized the flux of the target reaction such that a weighted sum of all fluxes is limited by an arbitrary number called flux allowance (a)  called distance order, which controls how fast the influence of remote reactions decays with distance. In the toy example  Fig A. The wemple Fig A, assumirFP values converged to relative expression levels of ldh‐1 , as the weights, and hence the influence, of other reactions decayed to zero. At lower distance orders, the contribution of other reactions in the pathway became evident, and the difference between LDH flux potential of muscle and neurons was reduced. Importantly, FPA used the presumed pathway , degradation (N = 50), or both (N = 62) based on high‐confidence predictions  and glutamine  is consistent with this molecule being secreted to blood during exercise in humans , extreme values (0 and 10) had a larger impact resulting in the loss of some of the key predictions Fig . In thisC. elegans metabolic network model , intestine (I), other tissue (X), and extracellular space (E)  and extracellular reactions for the intestine were placed in L. Transportable and exchangeable metabolites and extracellular reactions for the X tissue were placed in E. Transport reactions were distributed to exchange metabolites between I and L and between E and X. Exchange reactions were used in L to bring in nutrients from the environment, and in E to secrete by‐products to the environment, with the exception of oxygen, water, orthophosphate, and protons, which could be both taken up and secreted through E.Reactions of iCEL1314 were used to build a dual‐tissue metabolic network model of four compartments: lumen ( (E) Fig A. Internet al, Tissue‐level expression profiles were obtained from the reference study (Cao μ) and standard deviations (σ) that defined these curves were used to set thresholds for high expression (> μHES), low expression (< μLES + σLES), and rare expression (< μLES). Then, for each tissue, genes were categorized accordingly  difference in each interval is separately evaluated. If FC is > 4 in the first interval or 1.5 in others, the gene is labeled as highly expressed in tissues after the interval evaluated. Likewise, if the expression level increases by 4 in the last interval or 1.5 in others, the gene is labeled as lowly expressed in tissues before the interval. If a tissue expression is inconsistently labeled as high and low during the evaluation of different intervals, then it was maintained as moderate. To minimize the effect of noise at low expression levels, the jump in TPM value in an interval was considered significant only if the greater value was higher than a threshold (τrel = μHES − σHES). Also, moderate expression levels were recategorized as high only if they were above this threshold, and as low only if they were below it. The general form of this algorithm is explained in detail in Moderately expressed genes were reevaluated with a heuristic algorithm that categorized some of these genes as highly or lowly expressed depending on their relative expression levels in different tissues. This algorithm evaluates one gene at a time. First, TPM values of the queried gene are listed for all seven tissues in an ascending order. Thus, expression level increases from one tissue to the next in six intervals. The fold change , 243 side nutrients, and three storage molecules . When dea priori  in some parts of the network or a very large bacterial intake flux (≫ 1 unit). This is because some metabolites have very small stoichiometric coefficients in reactions that appear during bacterial digestion or biomass assembly. To avoid this scaling problem, the maximum flux capacity of each reaction was first determined in each available direction (forward or reverse) using FVA  for each reaction that depends on rarely expressed genes, such that yi is 1 if the reaction has no flux and 0 otherwise (ROFF.Define a binary integer variable (therwise . Flux thyif for the forward and yir for the reverse direction), such that yi is 1 if the reaction carries flux greater than ε in the pertaining direction and 0 otherwise  for each highly expressed gene that is associated with at least one reaction in RON. These genes are expected to be associated with flux‐carrying reactions and make the set GON. Constrain zi to be less than or equal to the sum of y values for all RON reactions associated with the gene  for subsequent steps. The δlow value used in this study was 1E‐5.Perform FBA to minimize total flux of reactions that depend on lowly or rarely expressed genes . The totZtotal and its minimum value as Ztotal,min. Constrain Ztotal to be less than or equal to Ztotal,min plus a small tolerance value  for subsequent steps. The Δtotal value used in this study was 0.05Ztotal,min. The flux distribution obtained in this step defines PFD . These are latent reactions.y values (see above) of latent reactions determined  as a percentage of bacterial intake by mass (see above for the method of constraining). An arbitrary upper limit of 1% was used for all stored metabolites combined.Constrain the uptake of side nutrients as a percentage of bacterial intake by mass. The overall uptake of these nutrients was limited by 2% of bacterial intake and the uptake of individual nutrients by 0.5% (see below for the choice of parameters).X and E compartments. Use only rarely and lowly expressed genes in the intestine to constrain reactions in the I and L compartments. Highly expressed genes in the intestine are ignored in this step.Integrate gene expression of the six non‐intestinal tissues one by one with the model. Use all categorized genes in the target tissue to constrain reactions in X compartment and constrain the model with these fluxes for the next step. An efficient method is taking a weighted sum of the fluxes through the metabolites of the E compartment and adding exchange reactions that exchange these metabolites, which are then constrained with the calculated metabolite fluxes  of reactions that carry material to and from the e fluxes . The weis et al,  were uses et al, .I and L compartments, while the flux to and from the X compartment is taken into account by the constraints from the previous step.Finally, integrate all categorized intestine genes with Since all tissues are taken into account in the last step, the integration from that step shows the overall flux load and nutritional requirements. To warrant a bacterially dominated diet, different side nutrient uptake rates were tested for the second step. Because the intake of bacteria itself is not constrained, strict limitation of side nutrients as a percentage of bacterial intake results in the excessive intake of bacteria to allow sufficient uptake of side nutrients for the integration, as a result of which bacterial biomass is wasted and the ratio of side nutrients within the used resources is increased. Based on trials with different ratios , the oveet al, Whether a reaction was part of the metabolic network of a tissue was determined based on OFD (see above) and FVA  the minimum flux the reaction can take, the negative of which shows the flux capacity in the reverse direction .Use the flux of the reaction from integration  and the flux capacity of the reaction calculated by FVA to determine whether the reaction is in the tissue network:oIf the reaction has non‐zero flux in the tissue OFD, then it is part of the tissue metabolic network. These reactions were labeled as OFD .oIf the reaction carries no flux in OFD, but has non‐zero flux capacity based on FVA, then it carries flux in alternate solutions of integration for the tissue of interest and is therefore part of the tissue network. These reactions were labeled ALT.oIf the reaction has zero flux capacity, then it does not carry flux in the solution space (SLNS) of the tissue of interest, and hence not part of the tissue network. These reactions were labeled NONE.I and L compartments for the intestine, and those in the X and E compartments for the other tissues. As an exception, if a reaction in the I or L compartment was labeled ALT for intestine integration but was not in SLNS for any other tissue integration, then it was considered as not part of the intestine network.All FVA and OFD analyses were carried out with the dual‐tissue model. However, tissue networks were eventually defined in a single‐tissue format  using thFlux potential analysis in a tissue is performed with the following steps:Divide reversible reactions into two separate reactions, one representing the forward direction and the other representing the reverse. The reverse reaction has the reactants and products swapped. Therefore, all reactions in the modified model have only a forward direction.Choose a target reaction. If the analysis is targeting a metabolite, choose a demand or export reaction that drains the metabolite to analyze its production potential, or a sink or import reaction that introduces the metabolite to analyze its consumption potential. If these reactions do not exist, insert a demand or sink reaction to the model accordingly.c) for each reaction for the tissue of interest (see below). This calculation is done only once for all FPA performed for a particular tissue. For the dual‐tissue model, expression coefficients in I and L compartments are always those based on intestine gene expression, while the coefficients of X and E reactions are variable.Calculate gene expression coefficients (d) of each reaction in the network from the target reaction (see below).Calculate the metabolic distance (If the target reaction is part of a reversible reaction in the unmodified model (see above), block the reaction that represents the other direction in the original model. This step prevents loops.If the target reaction is a sink, demand, or transport (to or from extracellular space) reaction, block all other reactions of these types that act on the same metabolite. This step prevents short cuts during metabolite‐level analyses.Block all reactions that are not part of the tissue network (see above for the determination of tissue networks).Perform FBA such that:oThe objective function is the maximization of flux in the target reaction .oAll reaction fluxes are constrained between 0 and 1000 .oa)  . The weia) . The allFP) of the target reaction in the tissue of interest.The maximum flux obtained from the FBA step gives the flux potential  of the target reaction in the tissue of interest.The ratio of I and X compartments were not targeted when FPA was performed on non‐intestinal tissues and intestine, respectively. As a specific rule, during FPA for the intestine, all reactions in the X compartment were blocked.In the dual‐tissue model context, reactions in Tissue expression profiles  were used to determine gene expression coefficients of each reaction for each tissue. If a reaction was associated with only one gene, the profile was first normalized by the maximum value, and then the reciprocal of the normalized value for a tissue defined the coefficient of the reaction in that tissue . If multE compartment), which were assigned a zero coefficient for all tissue evaluations. Also, transport reactions between I and E compartments were assigned a zero coefficient when the target reaction is in the X compartment. This rule prevents the penalization of a non‐intestinal tissue for having to transport a metabolite through a longer route than the intestine.Reactions that are not associated with any genes were typically assigned an expression coefficient of 1. Exceptions included bacterial intake and degradation reactions and all exchange reactions .Convert this metabolic network to a reaction tree such that each node represents a particular reaction and is connected to two types of other nodes called “to” nodes and “from” nodes. The “to” nodes represent reactions that consume the products of this reaction and the “from” nodes represent ones that produce its reactants. To prevent creating short cuts in the network, ignore hub metabolites such as atp, nadh, and h2o when linking reaction nodes. In this study, 21 frequent metabolites were ignored.i, first eliminate the reverse of this reaction in the network  and traverse the tree from this reaction to all others that are reachable. When a reaction is reached for the first time, fix the path to that reaction before traversing the tree further to others. Because of this path fixing, the path from reaction i to any reaction j will cover the least number of steps possible, thereby showing the distance from reaction i to reaction j.Given a query reaction i to reaction j. A loop occurs when a reversible reaction of the original metabolic network is traversed twice, i.e., when both the forward and the reverse reactions originating from a reversible reaction are part of the path found. Such paths are not valid and cannot be used for calculating the shortest distance. For all such cases, eliminate the first reaction in the path that creates a loop and find the shortest path from reaction i to reaction j again.Check for loops in the path from reaction i to reaction j. The length of this path defines the distance from reaction i to reaction j.Since the previous step can still produce an invalid path with loops, repeat that step until a valid path is found from reaction i. Use the maximum distance observed in the network for reactions that are not reachable starting from reaction i.Apply the previous three steps to find the distance to all reactions reachable from reaction i to any reaction j in the metabolic network.Repeat the previous four steps using every reaction in the network as the query. The result is a square distance matrix that gives distance from any reaction i to j is not necessarily equal to the distance from j to i. Set the final distance between i and j as the minimum of these two values. This step converts the distance matrix to a symmetric one. During FPA, the row of the distance matrix that represents the target reaction can be used to define the distance between this reaction and all network reactions (columns).Due to the structural properties of metabolic networks, the distance from The loop corrections in the fourth and fifth steps do not warrant shortest paths to be found. However, such corrections were necessary for < 1% of all distances calculated and more than a hundred such cases were manually verified to have yielded the shortest distances. Thus, the compromise made in this algorithm to make the search for the shortest path computationally feasible had a negligible effect on the accuracy of the calculated distances.The exclusion of hub metabolites such as NAD and ATP in the second step means that some redox and energy reactions may appear very distant to a target reaction, and therefore, the weight of their flux may be very low during FPA. This does not mean redox and energy balance can be neglected, as redox, mass, and energy balances are always established by FBA during FPA. However, the influence of the relative expression of redox and energy genes may be diminished by the large distances, depending on the target reaction and the distance order used.https://github.com/WalhoutLab/MERGE), which includes scripts that reproduces the results here, examples of integration of iCEL1314 with whole‐animal datasets, and a preliminary integration of a human model  (Yilmaz & Walhout, et al, Metabolic models: iCEL1314 is available at the WormFlux website (Predictions: The computer code, metabolic models, and datasets produced in this study are available in the following databases: LSY and AJMW conceived the work and wrote the paper. LSY designed and implemented MERGE with help from XL. XL reproduced the results in MATLAB environment, created the GitHub repository, and performed applications with human model. SN helped with metabolic network model updates. BF, XL, and FS reconstructed the ascaroside biosynthesis pathway and helped with metabolic network model updates. All authors carefully reviewed and edited the paper.The authors declare that they have no conflict of interest.AppendixClick here for additional data file.Expanded View Figures PDFClick here for additional data file.Table EV1Click here for additional data file.Table EV2Click here for additional data file.Table EV3Click here for additional data file.Table EV4Click here for additional data file.Table EV5Click here for additional data file.Table EV6Click here for additional data file.Table EV7Click here for additional data file.Table EV8Click here for additional data file.Review Process FileClick here for additional data file.


Fragilariopsis cylindrus, which enabled us to study its metabolic robustness using sensitivity analysis. We find that the predicted growth rate was robust to changes in all model parameters  except the carbon uptake rate. Constraints on total cellular carbon buffer the effect of changes in the input parameters on reaction fluxes and growth rate. We also show that single reaction deletion of 20% to 32% of active (nonzero flux) reactions and single gene deletion of 44% to 55% of genes associated with active reactions affected the growth rate, as well as the production fluxes of total protein, lipid, carbohydrate, DNA, RNA, and pigments by less than 1%, which was due to the activation of compensatory reactions  with more highly connected metabolites involved in the reactions that were robust to deletion. Interestingly, including highly divergent alleles unique for F. cylindrus increased its metabolic robustness to cellular perturbations even more. Overall, our results underscore the high robustness of metabolism in F. cylindrus, a feature that likely helps to maintain cell homeostasis under polar conditions.Diatoms are major primary producers in polar environments where they can actively grow under extremely variable conditions. Integrative modeling using a genome-scale model (GSM) is a powerful approach to decipher the complex interactions between components of diatom metabolism and can provide insights into metabolic mechanisms underlying their evolutionary success in polar ecosystems. We developed the first GSM for a polar diatom,  Diatoms often dominate in the water column and sea ice of polar habitats, which exhibit large seasonal changes in temperature and light ,2. They Phaeodactylum tricornutum [P. tricornutum [Fragilariopsis cylindrus [Although our knowledge on the peculiar physiology and metabolism of polar diatoms has made significant progress ,4, we cacornutum . The usecornutum ,15,16,17cornutum ,19,20,21cornutum . It has cornutum . The FBAylindrus ,24.F. cylindrus is that it contains 6071 highly divergent alleles (sequence divergence of up to 6%) out of a total of 21,066 predicted genes [A special feature of the 61.1 megabase’s draft genome of ed genes . Interesed genes ,25. Recoed genes ,26 is roF. cylindrus including its special feature of highly divergent alleles, and we analyzed the robustness of algal growth to both perturbations of cellular biochemical composition and metabolic network structure.In this study, we developed a genome-scale metabolic model of Phaeodactylum tricornutum (iLB1025), which was developed by Levering et al. [Fragilariopsis cylindrus (CCMP1102). BlastP analyses revealed that 93.6% of proteins in the P. tricornutum model (see F. cylindrus genome) have significant homologous proteins in the F. cylindrus genome using an E cut-off <0.1 and overall identity >20%. In 39%  from the P. tricornutum model based on the general high similarity between proteins of P. tricornutum and F. cylindrus and included reactions for which no significant homologous genes were detected without any gene sequence association to provide a first robust reconstruction of a metabolic model for F. cylindrus. Additionally, subcellular locations of homologous proteins in F. cylindrus were predicted using web-based software  and shown to be identical for 96.6% of proteins in P. tricornutum  and on our BlastP analyses. We also added the protein IDs of 53 allelic variants corresponding to protein IDs that were already included in the model , and 88 subsystems (see file model_setup.m). The model was constrained with 69 parameters based on experimental data for F. cylindrus performed in our lab and data available from previous studies  flux distribution. Here, we used an objective function that first maximizes biomass production, since ming FBA ,15,17. Ihia coli ,30,31, trevisiae , and thelongatus  in optimlongatus , our ass+) and performing FBA. Since no FBA solutions were obtained or all fluxes were 0, it was therefore verified that ATP and NADP could not be produced from nothing. Leak tests also show that no metabolite is produced when all exchange reactions are closed.Network evaluation of proper behavior and quality assurance was evaluated following standard methods  ,36. The F. cylindrus increase metabolic robustness to cellular perturbations. Note that the MOMA algorithm looks for an optimal flux distribution, as done by FBA, while also minimizing metabolic changes for acclimation in the MMS relative to the control (IM). It therefore better reflects the tendency of biological systems to buffer cellular perturbations on a short-term period, while FBA predicts the final steady-state distribution of fluxes, including potential long-term acclimation responses.Sensitivity analyses of the FBA output were performed for parameters, reactions, and genes. For the parameter sensitivity analysis, we used local and global sensitivity analyses. Local sensitivity analysis evaluates the sensitivity of the growth rate to single parameter changes, while global sensitivity analysis gives information on the sensitivity of each parameter and their relative interactions. The parameter sensitivity analysis evaluates the robustness of the model. Regarding the sensitivity analysis on reactions or genes, we performed single reaction or gene deletion in order to produce a model with a modified structure (MMS) and compared it to the full initial model (IM or control). This sensitivity analysis on reaction or gene evaluates model structural robustness. In this case, we computed growth rates for the MMS and the IM using FBA and quadratic minimization of the metabolic adjustment (MOMA). The evaluation of gene structural robustness was performed with and without inclusion of divergent allelic variants to further test the hypothesis that the highly divergent alleles in https://github.com/michellavoie4/Resilience-Fcylindrus). The scripts for the local and global sensitivity analysis to changes in the 69 parameters of the model are detailed in the files localsens_script.m and globalSA_script.m using the functions localsensFBA.m and FBAlight.m. The global sensitivity analysis was done using the Morris method, which is recommended for models with a high number of parameters. When running the Morris method, we used the Sensitivity Analysis For Everyone (SAFE) toolbox in MATLAB, taking into account the latin hypercube resampling strategy and 6500 model evaluations [Model development, sensitivity analyses, and flux distribution calculations were performed using MATLAB 2018 . All custom codes are available on GitHub (luations .singleRxnDeletion or singleGeneDeletion using FBA or MOMA (see the file ReactionDeletionSensitivity.m) with the prior addition of constraints on photon uptake  to avoid modeling unrealistically high light harvesting in response to deletions. We set the computed growth rate to 0 when reaction or gene deletions lead to infeasible problems.Sensitivity of growth to reaction or gene deletion was assessed with the Constraint-Based Reconstruction and Analysis (COBRA) toolbox functions http://www.gurobi.com) with the Constraint-Based Reconstruction and Analysis (COBRA) toolbox v3.0 [−6 for the reaction of the objective function and 10−9 for all other reactions in the model.FBA and MOMA were performed using the Gurobi Optimizer Version 7.5.2  solver  was exported to Python 3  for furtNetworkx . The genWe considered the three connectivity indices total degree, in-degree, and out-degree. When considering metabolite nodes only, “total degree” describes the total number of reactions connected to a metabolite, “in-degree” the number of reactions producing a metabolite, and “out-degree” describes the number of reactions using a metabolite as a substrate. We also calculated the betweenness and closeness centrality indices. Betweenness centrality describes the number of shortest paths crossing a given node and is thus a proxy of influence a node has over the flow of matter in the network. Closeness centrality is the reciprocal of the sum of the length of all shortest paths between the node and all other nodes in the network and is thus a measure of closeness for a given node to all other nodes in the network.Fragilariopsis cylindrus using available physiological and genomic data. The model allows to determine the robustness of the growth rate and metabolism to cellular perturbations, such as changes in concentration of biochemical components or inactivation of a given reaction or gene.We developed the first genome-scale model of the polar diatom 2 (produced mostly from pyruvate dehydrogenase and HCO3−) is fixed as organic carbon  by a chloroplastic phosphoenolpyruvate carboxylase (JGI protein IDs: 259279), an enzyme of the C4 photosynthesis pathway which is incomplete in the model, and leads to amino acid synthesis (glutamine). The remaining part of the absorbed CO2 (90%) is fixed by Rubisco (JGI protein IDs: 184116 and (147482 or 196615 or 195439)).An FBA using the exchange constraints and parameters listed in F. cylindrus. Regarding the ATP:NADPH balance, we considered two scenarios: (1) no redox exchange between chloroplast and mitochondria or (2) a coupling of mitochondrial ATP generation to electron transfer at photosystem I  flux equals to 0 , 0.27 mmol ATP gDW−1 h−1 were produced in the mitochondria rather than in the chloroplast. The model simulates efficient communication between both organelles and suggests that a small proportion of mitochondrial ATP gross production has to be synthesized to control the cellular ATP:NADPH ratio in F. cylindrus under optimal/suboptimal light conditions. Therefore, under both scenarios, mitochondrial ATP production through respiration contributes a small fraction of <13% towards the total cellular ATP production when growth is optimal.FBA modeling also enabled us to decipher cell bioenergetics in g et al.  based ong et al. ). DuringF. cylindrus using FBA was between 0.37 and 0.46 d−1, considering a carbon uptake rate between 0.70 and 0.85 mmol C mg DW−1 h−1. This carbon uptake rate is based on our own laboratory measurements of short-term 14C uptake rates in optimally growing F. cylindrus cells (1.04 mg C mg Chl a−1 h−1 ± (SD) 0.12)  0.12) . This mo m−2 s−1 , the simLocal sensitivity analysis showed that modeled growth rates were robust  to an arbitrary selected (but quantitatively significant) 40% increase or decrease in 68 out of the 69 parameters independently. Essentially, only carbon uptake rate controls the growth rate. More specifically, the growth rate increased by 40% or decreased by 29% in response to a 40% increase or decrease in carbon uptake rate, respectively . Most seF. cylindrus growth to changes in model parameters. Our results highlight the need to accurately measure and constraint the carbon uptake rate, which is by far the most sensitive parameter when modeling microalgal growth rate with FBA. Simultaneously, we show that reliable modeling of the growth rate can be achieved for F. cylindrus even under uncertainties about parameters that are currently not well constrained. It indicates that the reconstructed model can support suitable conclusions regarding the growth of F. cylindrus.To assess the strength of potential interactions among parameters, a local sensitivity analysis with 100,000 combinations of random parameters, which varied by 40%, was initially performed. The maximum relative increase or decrease in growth rate for multiple random local sensitivity analyses was 47.1% and 48.5%, respectively, suggesting that no strong synergistic interactions occur among parameters. Next, we calculated the relative error on growth rate due to changes by a factor of 1.4 of all combinations of the nine most sensitive parameters determined during our initial local sensitivity analysis  and observed that the growth rate increased or decreased by less than 48.9% and 48.3%, suggesting that the interactions among parameters is quantitatively small, underscoring the robustness of F. cylindrus growth rate to changes in concentrations of main cellular components  can be explained by two reasons. First, the sum of all biosynthetic rates of main cellular components must equal the fixed carbon uptake rate, and hence, a given relative change on one parameter will be compensated for by other components. Secondly, parameters of the model are cellular concentrations that are converted to stoichiometric coefficients, which are normalized with respect to the total mass per reaction in order to keep the reaction mass balance; this normalization also buffers the changes in the input parameters on reaction fluxes and growth rate. It is noteworthy that both explanations should generally also hold true for GSM developed for other species, suggesting that robustness of the growth rate and metabolism likely also occur in other (diatom) species. Using a coupled physiological-genome-scale model, Broddrick et al. [P. tricornutum grown in a sinusoidal light regime to changes in the biomass composition, light intensity, and parameters related to cell physiology. They generated 1000 random combinations of parameters, for which a given percent of perturbations were applied (±0% to 50%) , findinP. tricornutum modeled growth rate can be robust to changes in model parameters and compared the results to those found for the model parametrizes for F. cylindrus. A local sensitivity analysis using parameters for P. tricornutum yields similar trends to that for F. cylindrus , and this predicted excess in cell nitrogen could act as a buffer providing the required amount of nitrogen for optimal growth. To our knowledge, the presence and quantitative importance of a putative storage of cellular nitrogen in the vacuoles of F. cylindrus or P. tricornutum remains to be determined. Further experimental and modeling work is necessary in order to test the interesting hypothesis stating that storage of inorganic nitrogen in polar algae can favor growth rate robustness.In ylindrus , althougF. cylindrus metabolic network to perturbations without changing the intrinsic model structure, we analyzed the robustness of the modeled growth rate and metabolism to structural modifications within the network   and 396 reactions (68%) of active reactions abolished growth according to FBA and MOMA, respectively (see In addition to testing the robustness of the etwork) . We fouvely see . This is+ + NADP + 2 FDXRD < = > NADPH + 2 FDXOX, where FDXRD is reduced ferredoxin and FDXOX is oxidized ferredoxin) or thioredoxin reductase (NADPH + NAD < = > NADP + NADH), were also modulated to re-equilibrate the cell redox state. Among the energy dissipation pathways, photorespiration was only activated for two reaction deletions  in order to compensate the loss in glycine biosynthesis, but the Mehler reaction, as well as plastid terminal oxidase-PTOX, always remained inactive, according to FBA. In comparison, photorespiration was activated during deletion of 37% robust reactions, according to MOMA analysis. In all cases of robust reaction deletions (and predicted by FBA and MOMA methodology), the biosynthetic fluxes of proteins, lipids, carbohydrates, DNA, RNA, and pigments in cellular components varied by <0.1%. However, this metabolic flexibility entails a significant energy cost. According to FBA, photon harvesting and gross chloroplastic ATP and NADPH synthesis through the photosynthetic linear electron flow were consistently increased when deleting any of the robust reactions, while the cyclic electron flow at PSI and mitochondrial ATP production were activated when deleting 40% and 57% of the robust reactions, respectively. In comparison, according to MOMA analysis, photon harvesting and gross chloroplastic ATP and NADPH synthesis through the linear electron flow was constant but mitochondrial ATP production was activated when deleting any of the robust reactions, and the cyclic electron flow at PSI was activated during the deletion of 60% of the reactions.Interestingly, when using either the FBA or MOMA methodology, after reaction deletions of robust reactions, the proportion of reactions being activated in the MMS in comparison to the control (IM) was always higher than the proportion of reactions being inactivated, suggesting that the robustness to reaction deletions is achieved through activation of compensatory reactions. This compensatory response was due to the presence of enzymes catalyzing the same reaction but using different energy sources  or to enzymes catalyzing the same reaction in different cellular compartments, such as the cytosolic (JGI protein IDs 170472 or 209612), the mitochondrial (JGI Protein ID 193396), or the chloroplastic (JGI Protein ID 238714) aspartate aminotransferase, as well as the cytosolic (JGI Protein ID 236986) or mitochondrial (JGI Protein ID 246065) threonine aldolase with differential activation of energy sources or metabolite transporters. Fluxes through other reactions modulating the cell redox state (NADPH), such as ferredoxin-NADP reductase , as well as N, P, and C uptake reactions; light harvesting; and biomass reactions leading to the synthesis of main cellular components . According to FBA, the compensatory responses in energy production were smaller when deleting sensitive reactions than when deleting robust reactions. Specifically, photon harvesting and gross chloroplastic ATP and NADPH synthesis through the linear electron flow was increased for 80% of sensitive reaction deletions, and mitochondrial ATP production was activated for 42% of sensitive reaction deletions. The cyclic electron flow around PSI, however, was activated for 46% of sensitive reaction deletions. According to the MOMA analysis, the cyclic electron flow at PSI was activated for 60% of single reaction deletions, and mitochondrial ATP production was always activated when deleting single sensitive reactions, as found when deleting robust reactions, but to a lesser extent. All the previously discussed contrasting cellular responses to single reaction deletions of robust or sensitive reactions are summarized in The differences in structural robustness between reactions of the model can partly be explained by changes in degree number  and centrality of metabolites involved in both reaction groups . Mean anSimilar results were found for the betweenness centrality indices; the mean and median betweenness centrality increased by 77% and 50% for the robust set of metabolites compared to the sensitive set of metabolites, respectively . The higF. cylindrus was related to a flexibility in the choices of metabolites for a compensatory response by a given reaction. Moreover, our results have potential applications for the computational analysis of metabolic networks. We propose that the proportion of metabolites with low degree numbers can be used as indicators of network stability after reaction deletions. However, further modeling and experimental studies on other microorganisms are required to validate this potential network theory metric of robustness systematically.In brief, our analysis of metabolite centrality and degree number revealed that the network structural robustness increased as the proportion of metabolites involved in a low number of reactions decreased. Structural robustness was also linked to an increase in the proportion of high-degree metabolites involved in a high number of reactions . Our network theory analysis suggests that metabolic robustness in F. cylindrus into our model further increased the predicted growth rate robustness of F. cylindrus to a single gene deletion analysis, with 55% or 44% of robust active genes for the FBA or MOMA method, respectively (F. cylindrus genes (70% to 76%) out of all included genes in the model are predicted to be dispensable’ i.e., that only 24% to 30% of genes are predicted to be essential. While studies on the structural robustness of the genetic network in microalgae are scarce, modeling and knock-out experiments in yeast, bacteria, and multicellular eukaryotes have also shown that only between 5% to 37% of all genes are essential at any given experimental conditions when considering one gene at a time [F. cylindrus metabolic network will require further studies combining metabolic modeling and experimental gene/reaction deletion under different growth conditions.Structural robustness at the genetic level was higher than at the reaction level; percentages of robust genes (affecting the growth rate by less than 1%) out of all active genes reached 42% and 29% for the FBA or MOMA method, respectively, without including highly divergent allelic variants A compareectively B, lendint a time . In yeast a time . ResolviFragilariopsis cylindrus and developed a MATLAB/Python workflow to analyze the sensitivity and robustness of the model. Our methodology is transferable to GSMs of other species, with some modifications in the code, and will help to improve the analysis of cellular metabolism in future studies using systems biology approaches. Specifically, our results highlight the high robustness of the F. cylindrus growth rate and metabolism to an array of cellular perturbations. Strikingly, our in silico predictions confirm that the highly divergent alleles that are unique to F. cylindrus increase metabolic robustness to cellular perturbations and likely contribute to the ecological success of F. cylindrus in polar environments. Since our model does not account for regulatory mechanisms, such as feedback interactions, allosteric enzyme activation, or transcription regulation, which enhance network stability to changes in the cell biochemical composition or reaction deletions, we speculate that the predicted model robustness may well be even more important for F. cylindrus than predicted by our genome-scale model. Our genome-scale model provides the basis to further study F. cylindrus metabolism constrained with physiological, metabolomic, and/or transcriptomic data. It unlocks new possibilities to decipher the intertwined relationships between environmental factors and microalgal metabolism, which will be likely of interest in theoretical and applied biology, as well as in microalgal-based biotechnology approaches.We have derived the first genome-scale model for the polar diatom


High-throughput omics technologies have enabled the comprehensive reconstructions of genome-scale metabolic networks for many organisms. However, only a subset of reactions is active in each cell which differs from tissue to tissue or from patient to patient. Reconstructing a subnetwork of the generic metabolic network from a provided set of context-specific active reactions is a demanding computational task.swiftcc and swiftcore as effective methods for flux consistency checking and the context-specific reconstruction of genome-scale metabolic networks which consistently outperform the previous approaches.We propose swiftcore is freely available for non-commercial use in the GitHub repository at https://mtefagh.github.io/swiftcore/.We have derived an approximate greedy algorithm which efficiently scales to increasingly large metabolic networks.  Constraint-based reconstruction and analysis (COBRA) is the current state-of-the-art in the genome-scale metabolic network modelling [in silico analysis for drug discovery or many other applications [odelling . COBRA mications –4.Gene inactivity moderated by metabolism and expression (GIMME) [Integrative metabolic analysis tool (iMAT) [Integrative network inference for tissues (INIT) [human proteome atlas (HPA) to reconstruct tissue-specific metabolic networks. Metaproteomic and taxonomic data have been exploited for a context-specific reconstruction procedure applied to a naphthalene-degrading bacterial community [Context-specificity assessed by deterministic reaction evaluation (mCADRE) [Cost optimization reaction dependency assessment (CORDA) [flux balance analysis (FBA), rendering it more computationally efficient.Context-specific metabolic networks are extensively studied because of their higher explanatory and predictive power –8. To da (GIMME)  uses qual (iMAT) , 11 intes (INIT) –14 uses ommunity . RegrEx ommunity , 17 is b(mCADRE)  is also (mCADRE) . Cost op (CORDA)  relies sOne approach to this problem is to curate a list of active reactions and develop a framework to find the sparsest subnetwork containing the specified reactions. Although this subnetwork is assumed to be as sparse as possible, we should avoid flux inconsistencies such as when one of the desired reactions is included in the subnetwork, yet it is blocked and cannot carry non-zero flux at the steady-state condition. In this regard, context-specific reconstructions seek to generate minimal consistent subnetworks including a given set of core reactions.FASTCORE [It is known that identifying a consistent subnetwork with the minimum possible size such that it contains some core reactions is an NP-hard problem . To addrFASTCORE  exhibitsm specific metabolites in an organism, and n reactions involving at least one of these metabolites. Under average physiological conditions, the irreversible reactions Let v of length n a flux distribution if the absolute values of its entries are the rates of the corresponding reactions in vi≥0 for all We call a vector m and distinguish reactants from products by negative signs. Afterward, we construct the stoichiometric matrix by stacking these vectors for all the reactions in m×n matrix S. The mass balance constraint asserts that the concentration of each metabolite is constant throughout the time-scale of interest which is equivalent to say that Sv=0 in our notation.We represent the relative quantities of metabolites in each reaction by an associated vector of length Sv=0 such that vi≥0 for all vi=0 for all the steady-state flux distributions, and unblocked otherwise. We call a metabolic network with no blocked reactions a flux consistent metabolic network [We refer to any solution of  network .In this paper, we present an algorithm that given a flux consistent metabolic network and the subset FASTCC [FASTCORE, is currently the fastest algorithm dedicated to this task.A closely related problem to the context-specific reconstruction is to check the flux consistency of a given metabolic network by detecting the blocked reactions. FASTCC  which isv such thatAs a simple observation, all the irreversible reactions in vi>0 for all v exists, an arbitrary (possibly reversible) u such thatwhere c>0 is large enough, then uj+cvj≠0 and u+cv would be a steady-state flux distribution in which Rj is active.since if Quantitative flux coupling analysis (QFCA) [SWIFTCC in this paper. However, this is presented as only a preprocessing step in the original paper instead of a separate algorithm. For the sake of completeness, we have also compared SWIFTCC as implemented in the QFCA against FASTCC. Additionally, we have benchmarked FASTCC++ and SWIFTCC++ which are the original algorithms plus the preprocessing step explained in the SWIFTCC to develop an analogous method for the context-specific reconstruction problem with the same order of speed-up which SWIFTCC offers.s (QFCA)  uses thiv in analogy to This homogeneous problem is equivalent to the following v if necessary, so that the nonzero entries of by scaling uk which satisfies the conditions of  of Let tisfying . Note thuk, we consider the solution ofx is a random vector generated from the zero-mean normal distribution with variance σ2. This problem tries to find a u which is sparse in l1 norm, and which is dense in l∞ norm constraint [σ2 manages the trade-off between these two objectives and is set by a simple rule which doubles σ whenever SWIFTCORE is robust across a wide range of σ.In order to generate the next nstraint . The choFinally, this problem is equivalent to the following LPx is sampled from the standard normal distribution. More generally, ω to customize the loss corresponding to each reaction. In the current work, we have only experimented with σ. However, the accompanying package supports any positive weight vector ω.where k until no reaction remains in v, they imply that Subsequently, we keep iterating over ities to  and 5)  k until SWIFTCORE is ultra-fast in comparison to nonlinear methods such as the model-building algorithm (MBA) [FASTCORE algorithm which is again based on linear programming but is still several times slower, mainly due to flipping the signs of the columns of the stoichiometric matrix that correspond to the reversible reactions. We refer the interested reader to the associated paper [SWIFTCORE in the way explained below.Altogether, this algorithm is based on linear programming, and hence, hm (MBA)  which ared paper  for moremixed-integer linear program (MILP) corresponding to the direction of a reversible reaction or two separate iterations over the forward and reverse directions like in the FASTCORE, a common way of dealing with reversible reactions is to iterate over instances of the metabolic network with a predetermined direction for that reversible reactions. Instead of determining a direction for the reversible reactions, signs of the different entries of x merely encourage one of the two possible directions in a “soft” manner instead of a “hard” constraint. The objective function of . HoweveSWIFTCC and SWIFTCORE in an open-source package freely available for academic use on GitHub. It is written in MATLAB® with zero dependencies, though it supports Gurobi™ or CPLEX™ optimizer for improved performance. Additionally, if any other LP solver has been set up for the COBRA toolbox v3.0 [We have implemented both box v3.0 , it can SWIFTCC or FASTCC none of which can readily be parallelized in an obvious way and this direction is left for future research.The partitioning preprocessing step described in the GitHub repository.Last but not least, the benchmark codes to reproduce all the figures in this article are also publicly available in the same SWIFTCORE, we have benchmarked both SWIFTCORE and FASTCORE on the flux consistent part of the Recon3D model [n=10600. All simulations were performed on a desktop PC with AMD Ryzen™7 1800X eight-core processor and 16 GB of memory, and the CPLEX™ optimizer was employed as the LP solver. Furthermore, in the published benchmark code we double check if the reconstructed subnetwork is flux consistent and contains the core reactions and SWIFTCORE always passes these sanity checks.To assess the performance of 3D model  with ranSWIFTCORE with reduction version we have included the SVD and full coupling reduction techniques described before in contrast to the other vanilla version which excludes them. In spite of the fact that the vanilla version solves more LP problems, it is actually more efficient nonetheless : Platform independentProgramming language: MATLAB®Other requirements: The COBRA and Bioinformatics toolboxes for MATLAB; use of Gurobi™ or CPLEX™ is optional for improved performance (free academic licenses are available for both)License:SWIFTCORE is distributed under the GNU GPL v3.0.Any restrictions to use by non-academics: licence neededTo the end of this Appendix, without loss of generality we assume that all the reactions are irreversible, i.e., Mi,Mj) for which there exists a reaction Mi and Mj, respectively.We define the skeleton digraph of a metabolic network as We define the mapping Sk denote the kth column of S. Suppose that 1TS=0. Then for any ∂ is the incidence matrix of G and F is the nonnegative l×n matrix whose entries areAl=∈f(Rk) and flk=0 if Al∉f(Rk).Let v∈Rn, denoted by supp(v), is defined to be the set of its nonzero indices. With a slight abuse of notation, this is also used to show the set of reactions in 1TS=0. We claim that G for any steady-state flux distribution v. The sketch of the proof is to first note that∂(Fv)=Sv=0 and hence supp(Fv) is strongly connected and so is The support of a vector G into its strongly connected components, and any reaction which is not inside a strongly connected component would be blocked. Then the flux consistency checking algorithm is called on each one of them to get the rest of blocked reactions. It only remains to show that the assumption 1TS=0 holds for a broad class of metabolic networks with a slight modification to internalize their boundary reactions but without changing their steady-state flux distributions.This observation gives rise to a preprocessing step for any flux consistency checking algorithm by partitioning The boundary reactions On the other hand, internal reactions SI denote the submatrix of S restricted to the columns indexed by w∈Rm denote the positive vector of the molecular masses of w>0 which fulfils the mass conservation law is assumed to satisfy wTSI=0 by our earlier convention. A metabolic network is called stoichiometrically consistent if there exists at least one molecular mass vector w such thatLet S and and stoichiometrically inconsistent otherwise . We notew>0 is an arbitrary molecular mass vector and W is the diagonal matrix whose diagonal entries are w. We associate the additional row with a fictitious extracellular metabolite Mm+1, and because of wTSI=0, the stoichiometry of the internal reactions do not involve this newly added metabolite. Since the last row of S′ is a linear combination of the other rows, we have S′v=0⇔Sv=0. Therefore, we can replace S by S′ and the set of the steady-state flux distributions does not change. Furthermore, if Si is either nonnegative or nonpositive, then the ith entry of −wTS has the other sign and hence with respect to S′ all reactions are internal, i.e., Mm+1 in this new setting. Eventually,Consider the following stoichiometric matrixG and f we only need to know the signs of the elements of S′, thus this can be done without computing w explicitly. Even when we do not know whether the metabolic network is stoichiometrically consistent or not, we can still construct G, and if it is not strongly connected, we conclude that the metabolic network has either stoichiometric or flux inconsistencies.As a final remark, we recall that in order to construct