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


Metabolic alterations can serve as targets for diagnosis and cancer therapy. Due to the highly complex regulation of cellular metabolism, definite identification of metabolic pathway alterations remains challenging and requires sophisticated experimentation.We applied a comprehensive kinetic model of the central carbon metabolism (CCM) to characterise metabolic reprogramming in murine liver cancer.We show that relative differences of protein abundances of metabolic enzymes obtained by mass spectrometry can be used to assess their maximal velocity values. Model simulations predicted tumour-specific alterations of various components of the CCM, a selected number of which were subsequently verified by in vitro and in vivo experiments. Furthermore, we demonstrate the ability of the kinetic model to identify metabolic pathways whose inhibition results in selective tumour cell killing.Our systems biology approach establishes that combining cellular experimentation with computer simulations of physiology-based metabolic models enables a comprehensive understanding of deregulated energetics in cancer. We propose that modelling proteomics data from human HCC with our approach will enable an individualised metabolic profiling of tumours and predictions of the efficacy of drug therapies targeting specific metabolic pathways. However, despite all these advances, the overall death rate for cancer has declined at a much slower pace in the past 40 years compared to other major causes of mortality such as cardiovascular and infectious diseases.2 This is, to a large extent, explained by suboptimal long-term anti-proliferative efficacy of newly developed molecular-targeted drugs.3 Cancer cells display a marked capability to compensate for the inactivation of signalling pathways—and other growth-promoting mechanisms—that are considered essential for neoplastic progression.5 This translates into the emergence of therapy resistance, a major obstacle of clinical oncology.6 To achieve effective and long-lasting therapy responses it is therefore of pivotal importance to identify processes that are at the same time essential and unique, thereby avoiding resistance via usage of alternative pathways. Metabolism represents such a process as it is essential for cellular survival and growth, e.g. by providing energy, reductive power and building blocks for anabolic reactions. In light of the uniqueness of metabolic pathways, their functional inactivation can usually not be compensated, resulting in robust cellular damage and/or death.7Numerous initiatives around the world in conjunction with the unprecedented development of high-throughput analytical methodology have spiralled up the molecular knowledge about cancer in dizzying heights.8 However, it also became evident that a reliable analysis of metabolism, especially under in vivo situations, is challenging to perform.9 This is due to various factors, such as the rapid turnover of substrates and products, the intricate complexity of the metabolic network, the central importance of external stimuli such as hormones, growth factors and the cellular microenvironment.10 One main reason for the insufficient understanding of metabolic changes in tumours is the strong focus on changes in the expression level of metabolic enzymes and transporters. The importance of downstream kinetic regulation, for instance by allosteric effects or reversible phosphorylation, has been underestimated or completely disregarded in the last two decades.11 Choosing glucose metabolism of the liver as an example, we have recently demonstrated the necessity to combine existing knowledge on gene expression changes with the complex kinetic regulation of enzymes in order to understand the metabolic response of the liver to varying external challenges.12 Here, we present an innovative concerted approach to study cancer metabolism by combining a novel physiology-based kinetic model of the central metabolism,13 with high-quality quantitative proteomics data and molecular biological experimentation to elucidate metabolic differences between liver cancer  and the normal liver in a murine model. Using relative changes in the expression level of metabolic enzymes in HCC and normal liver cells to scale maximal enzyme activities, we simulate the metabolic response of HCC and the normal liver to variations in the metabolite and hormone profile of the blood plasma. This enables the definition of conditions at which the metabolism of the tumour becomes severely impaired while the metabolism of normal liver cells remains largely unaffected. We strongly believe that the herewith presented approach bears translational potential and will outline a basic roadmap to achieve this.The notion that tumours display specific metabolic alterations that can be exploited for diagnosis and therapy of cancer has received widespread attention in recent years.14 Briefly, male ASV-B mice express the early region of the SV40 large T (SV40lT) oncogene under control of the mouse antithrombin III promoter. ASV-B mice show time-dependent liver tumour development with first evidence of dysplasia at 8 weeks, adenomas at 12 weeks and hepatocellular carcinoma (HCC) at 16 weeks of age. All mice were maintained under specific pathogen-free conditions under a 12 h light/dark cycle with free access to food and drinking water and cage enrichment at the animal facilities in Berlin (Charité) and Aachen . Animal procedures were performed in accordance to approved protocols  and followed recommendations for proper care and use of laboratory animals. For tissue preparation, 16-weeks-old ASV-B or tumour-free male control mice  were sacrificed by cervical dislocation and liver tissue samples were snap-frozen in liquid nitrogen. Further analyses of tissue samples were performed within 2–4 weeks.The murine HCC model  was established and initially characterised by Dubois and co-workers.13 The model was used to simulate the impact of nutrient supply (including oxygen), hormonal stimuli and protein abundance of metabolic enzymes on the functional output of the liver. The model comprises the central hepatic metabolic pathways of: glycolysis, gluconeogenesis, glycogen synthesis, glycogenolysis, fructose metabolism, galactose metabolism, the creatine-phosphate/ATP shuttle system, the pentose phosphate cycle composed of the oxidative and non-oxidative branch, the citric acid cycle, the malate aspartate redox shuttle, the glycerol-3-phosphate redox shuttle, the mitochondrial respiratory chain, the beta-oxidation of fatty acids, fatty acid synthesis, ketone body synthesis, cholesterol synthesis, triglyceride synthesis and degradation, the synthesis and hydrolysis of triglycerides, the synthesis and export of the very-low density lipoprotein (Vldl), the urea cycle, the metabolism of the amino acids serine, alanine, glutamate, glutamine, aspartate and ethanol metabolism. Furthermore, the model contains the key electrophysiological processes of the inner mitochondrial membrane including the mitochondrial membrane potential, mitochondrial ion homeostasis and the generation and utilisation of the proton motive force. All modelled reactions and transport processes are depicted in our previous publication . The metabolic model is coupled to a phenomenological model of hormonal signalling by glucagon and insulin affecting the short-term regulation of metabolic enzymes by reversible phosphorylation (see below). Uptake, metabolisation and generation of glucose, fructose, galactose, pyruvate, lactate, glycerol, ammonia, serine, alanine, glutamate, glutamine, fatty acids, ethanol, acetate, urea, acetoacetate, β-hydroxybutyrate, oxygen and VLDL particles are being described by the model.We have recently developed a comprehensive kinetic model of the central metabolism of hepatocytes.15 Glycolysis and gluconeogenesis as well as fatty acid synthesis and β-oxidation are inversely regulated by glucagon and insulin signalling via phosphorylation and de-phosphorylation of key regulatory enzymes. In the model, the plasma concentration of insulin and glucagon is directly translated into the phosphorylation state of interconvertible enzymes by a phenomenological sigmoid function (γ-function) also used in the work published by Bulik et al.12 Moreover, we used phenomenological transfer functions to compute the plasma concentrations of insulin and glucagon and of non-esterified fatty acids (NEFA) directly from the plasma level of glucose. This setting rests on the assumption that the release of insulin and glucagon from pancreatic islet cells is mainly controlled by the plasma glucose level and that high concentrations of glucagon and epinephrine stimulate the hormone-sensitive lipase (HSL) in adipose tissues, thus creating an inverse relationship between the plasma level of glucose and NEFA.The metabolism of the liver is strongly controlled by hormones, in particular insulin and glucagon.16 and the eluates dried and reconstituted to 20 µl of 0.5% acetic acid in water. Five microliters were injected in duplicate on a UPLC system (Eksigent Technologies) coupled to a LTQ Velos Orbitrap (Thermo Fisher Scientific), using a 240 min gradient ranging from 5 to 45% of solvent B . For the chromatographic separation 30 cm long capillary (75 µm inner diameter) was packed with 1.9 µm C18 beads . On one end of the capillary nanospray tip was generated using a laser puller, allowing fretless packing. The nanospray source was operated with a spray voltage of 2.1 kV and an ion transfer tube temperature of 260 °C. Data were acquired in data dependent mode, with one survey MS scan in the Orbitrap mass analyzer  followed by up to 20 MS/MS scans in the ion trap on the most intense ions. Once selected for fragmentation, ions were excluded from further selection for 30 s, in order to increase new sequencing events.Murine liver samples were immediately frozen in liquid nitrogen and re-suspended in urea buffer  containing 100 µl of zirconium beads for protein extraction. Samples were homogenised on a Precellys 24 device (Bertin Technologies) for two cycles, 10 s at 6000 rpm. After centrifugation to remove beads and tissue debris, protein concentration was measured by Bradford colorimetric assay and 100 µg were taken for protein digestion. Leftover samples were frozen at −80 °C. The disulfide bridges of proteins were reduced in DTT 2 mM for 30 min at 25 °C and successively free cysteines alkylated in iodoacetamide 11 mM for 20 min at room temperature in the dark. LysC digestion was then performed by adding 5 µg of LysC  to the samples and incubating it for 18 h under gentle shaking at 30 °C. After LysC digestion, the samples were diluted three times with 50 mM ammonium bicarbonate solution, 7 µl of immobilised trypsin (Applied Biosystems) was added and samples were incubated 4 h under rotation at 30 °C. Eighteen micrograms of the resulting peptide mixtures were desalted on STAGE Tips17 and maintained in Dulbecco’s modified Eagle’s medium  containing 10% foetal bovine serum and 1% penicillin-streptomycin (Thermo Fisher Scientific) in collagen-coated flasks. All experiments were conducted within four days after primary cell isolation. HCC cells were isolated from 16-weeks-old ASV-B mice and cultivated in the medium described above. After an initial adaptation period of one to two months they started to proliferate and grow stably under cell culture conditions.Primary hepatocytes from C57Bl/6 J were isolated as described earlier18 with slight modifications. Mouse livers were perfused with ice-cold University of Wisconsin organ preservation solution (UW), submerged in UW and kept on ice. Cylindrical cores with a diameter of 5 mm were prepared using a manual biopsy punch  and placed in a Krumdieck tissue slicer  containing ice-cold oxygenated Krebs-Henseleit buffer . William’s E Medium  supplemented with 2.75 mg/ml D-glucose and 50 µg/ml gentamycin (Sigma–Aldrich) was used as the standard culture medium. To assess urea synthesis under stimulated conditions, DMEM (high glucose) with additional urea cycle substrates (2 µM ornithine and 10 µM NH4Cl (both Sigma–Aldrich)) was used. To determine the effect of complex I inhibition, PCLS were cultured in DMEM standard medium with or without 0.5 mM metformin . Slices were incubated in a 6-well culture plate containing three slices per well and 3.5 ml medium. After 1 h of pre-incubation, slices were transferred to fresh medium and incubated for 24 h. Viability of the cultured tissue was confirmed by quantification of ATP with the Bioluminescence Assay Kit CLSII (Merck) and results were normalised to total protein content. Culture medium was collected and stored at −80 °C for later analysis of urea production. The concentration was determined by the University Hospital RWTH Aachen Central Laboratories applying standard diagnostic procedures.Precision cut liver slices (200 µm thickness) were prepared from both normal and tumour-bearing murine livers based on a published protocol20 with the mouse UniProt database  and a common contaminants database (247 protein entries). Carbamidomethylation of cysteines was chosen as fixed modification, oxidation of methionine and acetylation of N-terminus were chosen as variable modifications. Two missed cleavage sites were allowed, and peptide tolerance was set to 7 ppm. The search engine peptide assignments were filtered at 1% FDR at both the peptide and protein level. The ‘match between runs’ feature was not enabled, ‘second peptide’ feature was enabled, while other parameters were left as default. For protein quantification LFQ intensities calculated by MaxQuant were used.21 The minimum LFQ ratio count was set to 2 and a MS/MS spectrum was always required for LFQ comparison of the precursor ion intensities; only unique and unmodified peptides were used for LFQ quantification, in order to keep the LFQ calculation isoform specific. Before comprehensive data analysis, data quality was evaluated using the in-house developed quality control software PTXQC.22Proteomics raw data were analysed using the MaxQuant proteomics pipeline v1.4.1.2 and the built in Andromeda search engine23 This package assesses the significance of fold changes using parallel linear models sharing variance parameters. This method was originally developed for microarray data but turns out to be particularly suited for shotgun proteomics as it alleviates the scarcity of the measurement matrix by sharing the variance between proteins. Out of 2124 detected proteins, 1579 were used and tested for significance of their fold changes (detected in at least two samples in each condition). Nine hundred and thirty four proteins were found to have significant fold changes (FDR 5%). Metabolically relevant pathways for mouse were obtained from the GSKB R package,24 which propose a pre-processed metabolic pathway collection. The Piano R package was used to estimate the significance of the directional regulation of the pathways.25 The methods used to generate a consensual p-value in PIANO were: mean, median, sum, maxmean, stouffer, fisher, reporter, tailStrength, wilcoxon and PAGE. The FDR and t-values yielded by the LIMMA package were used as gene level statistics. The scripts and data can be accessed here: https://github.com/adugourd/Berndt_Egners_Mastrobuoni.In total, 28 proteomic samples were analysed, coming for 14 mouse livers, with seven healthy and seven tumourous livers. Hence, the dataset comprised seven biological replicates for each condition, with two technical replicates per mouse liver. All bioinformatic analyses were performed in R. For each protein, technical replicates were averaged. Box and density plots were generated to assess the homogeneity of the sample distributions. Clustering was performed over complete cases of proteomics samples using the complete method and Euclidean distance (see pheatmap and hclust R packages) as well as principal component analysis. Differential analysis was performed using the LIMMA R package.t-test using the GraphPad Prism 5.0 software (GraphPad Software) if not denoted otherwise. Differences were considered statistically significant at p < 0.05.All data are presented as mean ± standard error of the mean (SEM). Statistical analysis was performed by unpaired, two-tailed Students 13 We used the protein abundance data obtained from the murine samples to scale the activity  values) of the metabolic enzymes to generate tumour-specific kinetic models. These tumour-specific kinetic models were constructed by scaling the maximal activity of each enzyme and transporter in the network according totumour and Econtrol denote the LFQ intensity of the enzyme in the tumour and the control tissue. 13 EquationFor the generation of the tumour-specific kinetic model we used the quantitative proteomics data together with Hepatokin1, a fully kinetic model of the central carbon metabolism of the liver.20 The proteomics experimental design consisted of 2 conditions (HCC and control (ctr)), seven biological replicates per condition and two technical replicates per biological replicate. In total, 2124 proteins were detected across the 28 samples. Each pair of technical replicates was averaged resulting in 14 biological samples  and Gapdh  are significantly upregulated in HCC tissues  of the respective enzymes to generate a kinetic model of the central metabolism of murine HCC. To assess the functional consequences of alterations in metabolic enzyme expression, we applied the model to a typical 24 h physiological plasma concentration profile of exchangeable metabolites and the hormones insulin and glucagon. We used the plasma profile as model input and computed the diurnal variations in the concentrations of all model metabolites and fluxes for normal liver and murine HCC , explaining its antidiabetic properties.29 Using the reported inhibition concentrations of metformin of 0.5 mM for complex I28 and 0.055 mM for G3pdh,29 we simulated the effect of metformin on HCC and healthy liver. We put the external conditions to their mean value over one day and varied the metformin concentration from 0 to 1 mM. Figure We hypothesised that the reduced capacity of oxidative phosphorylation in HCC can be exploited for cancer therapy by serving as a metabolic target to selectively impair HCC metabolism while leaving healthy liver intact. This was further strengthened by modelling the oxygen consumption as a function of mitochondrial complex I activity, demonstrating consistently lower values of tumour compared to control liver Fig. . The ant30 However, exploitation of metabolic vulnerabilities to identify effective and specific anti-cancer agents remains challenging. The advancement of analytical technologies like shotgun proteomics opened the way for global snapshots of the molecular makeup of healthy tissues and tumours.32 The increased sensitivity of these technologies together with improved data reproducibility enable for the first time to map the biochemical network in its totality.9 However, due to (i) enormous plasticity and dynamics, (ii) multi-level regulatory mechanisms and (iii) a highly complex network of reactions, cellular metabolic processes are difficult to study. Mathematical models are useful tools to unravel this complexity, and various tools have been established to develop and analyse genome-scale metabolic models cells.33 Using omics data to scale cell-wide network models of metabolism has led to the identification of novel drug targets and biomarkers.34 Naturally, mathematical models are always simplifications of multi-level biological phenomena; however, hitherto published metabolic models of liver metabolism specifically lack important regulatory aspects, e.g. hormonal influences and allosteric parameters. In addition, they are very often not based on data that have been established experimentally but on information solely extracted from published literature.The fundamental metabolic reprogramming processes that tumour cells undergo to support growth and survival have received widespread attention in recent years and are now considered as an emerging hallmark of cancer.13 The influence of fluctuating nutrient (like glucose and glutamine) and oxygen concentrations within a physiological range are also taken into account. As demonstrated by us earlier, these parameters are at least equally important for modelling the metabolic performance as the changes in enzyme abundance . Applying the model to the central metabolism of HCC, we took advantage of the fact that HCCs originate from hepatocytes,35 i.e. metabolic enzymes in normal and malignant cells only differ in their expression level. This enabled us to re-parameterise the hepatocyte model by scaling the enzyme activities between HCC and normal hepatocytes according to the observed changes of protein abundances that we assessed by quantitative mass spectrometry. It has to be taken into account that relative abundances of cell types other than HCC cells also contribute to the determined protein expression profiles to a certain extent. Immunohistochemistry staining, however, demonstrated negligible infiltration of immune cells in HCC tumour nodules. We therefore assume that the contribution of other cell types to the final proteomics datasets is rather small. This assumption is substantiated by the fact that experimental results obtained from isolated HCC cells were well in line with calculated model predictions. The present study proves that our approach is able to transform mass spectrometry protein data into biologically and clinically meaningful metabolic predictions about the HCC tissue turnover activity of various metabolites. Comparison of simulated normal and HCC liver metabolic performance reveals fundamental differences. We validated several of the calculated model output parameters successfully using different experimental approaches. Glycolytic and respiratory activity were determined by measuring the extracellular acidification and oxygen consumption rates, confirming that HCC cells show increased glycolytic and reduced mitochondrial activity. These findings are well in line with earlier reports using transcriptomics, metabolomics or enzyme activity measurements on different murine HCC models.38 Increased glycolytic activity is consistently found in independent analyses of human HCC tissue with different omics approaches and non-invasive imaging (NMR spectroscopy), pointing towards the Warburg effect as a metabolic hallmark of human liver cancer.41Here, we used a comprehensive kinetic model of the central carbon and lipid metabolism of hepatocytes that incorporates not only the metabolic reaction network but also enzyme regulation by allosteric effectors and by reversible phosphorylation due to changing insulin and glucagon signalling as in Berndt et al.42 Butler et al. showed that the human hepatocellular carcinoma cell lines Huh-7, HepG2 and LH86 do not express the urea cycle enzyme carbamoyl phosphate synthetase 1.43 A comprehensive microarray analysis of 521 patient-derived HCC samples revealed suppression of urea cycle-associated enzymes.44 On the other hand, arginase I and carbamoyl phosphate synthetase (Cps) were found overexpressed in human HCC and their detection via immunohistochemistry was suggested to improve the histopathological diagnosis of HCC.45 Our approach now reveals—for the first time—reduced urea cycle activity in a murine HCC model, nicely confirming that systematic integration of protein expression data is a prerequisite to comprehend metabolic pathway activity.46 The analysis of HCC-specific changes of lipid metabolism has received a lot of attention recently (over 20 studies using human samples and different omics approaches were published in the last 10 years47). The reported results are very heterogeneous, precluding the identification of an HCC-specific lipid metabolism pattern. If anything, activation of fatty acid catabolism (most importantly β-oxidation) could be considered a hallmark of HCC-specific lipid metabolism as it was reported by the majority of publications.47 Of note, the activity of anabolic lipid metabolism pathways in HCC has received significantly less attention. Our approach of combining quantitative proteomics with mathematical modelling predicted reduced activity of several anabolic lipid pathways in HCC, e.g. synthesis of triacylglycerides, cholesterol and fatty acids as well as VLDL secretion. We were able to functionally validate the calculated reduction of triacylglyceride synthesis, underscoring the eligibility of the comprehensive kinetic model to forecast alterations of lipid metabolism in HCC. In summary, the results of all validation experiments show striking consistency with the calculated model simulations indicating that our kinetic model is indeed a powerful tool to reproduce HCC metabolism in a reliable manner.The kinetic model predicted HCC-specific alterations of urea and triacylglyceride synthesis as well as glycogen storage, all of which represent key functions of normal liver. The functionality of the urea cycle in HCC tissue has been under debate for quite some time. It had been established rather early on that HepG2 cells, one of the most widely used human HCC cell lines, harbour a defective urea cycle and it was later shown that this is due to ornithine transcarbamylase and arginase I deficiency.48 Metformin was subsequently shown to exert anti-tumour effects against established human HCC cell lines and in HCC xenografts in nude mice.49 Our results confirm the cell line data reported by Miyoshi et al. and furthermore show that primary hepatocytes are not affected by metformin at the doses found to inhibit HCC cells. These results demonstrate the versatility of our kinetic model as, in addition to depicting metabolic activities, it is able to predict metabolic vulnerabilities. We propose that the herewith outlined experimental approach will also be able to identify innovative targets for the therapy of human HCC. One could even envision an application in a clinical setting where mathematical modelling of biopsy-derived quantitative mass spectrometry-based proteomics data could assist the design of a personalised therapy tactic. Future work with patient samples will need to thoroughly test this hypothesis before a potential exploitation for HCC therapy.The feasibility of the translational application of our kinetic model to estimate and evaluate the performance of therapeutic agents with prediction of possible adverse effects is demonstrated by calculating the outcome of metformin treatment on HCC viability. The antidiabetic drug metformin received a lot of attention in recent years after it was reported to reduce cancer risk and mortality in diabetic patients.supplemental material, figures and figure legends in one fileexecutable SBML file of Hepatokin1


Streptomyces coelicolor M1152 is a widely used host for heterologous expression of BGCs, a systemic understanding of how its genetic modifications affect the metabolism is lacking and limiting further development. We performed a comparative analysis of M1152 and its ancestor M145, connecting information from proteomics, transcriptomics, and cultivation data into a comprehensive picture of the metabolic differences between these strains. Instrumental to this comparison was the application of an improved consensus genome-scale metabolic model (GEM) of S. coelicolor. Although many metabolic patterns are retained in M1152, we find that this strain suffers from oxidative stress, possibly caused by increased oxidative metabolism. Furthermore, precursor availability is likely not limiting polyketide production, implying that other strategies could be beneficial for further development of S. coelicolor for heterologous production of novel compounds.Many biosynthetic gene clusters (BGCs) require heterologous expression to realize their genetic potential, including silent and metagenomic BGCs. Although the engineered   •Time-series transcriptomics and proteomics of S. coelicolor M145 and M1152•Application of GEM to interpret changes in the proteome on the systems level•Limited effect of improved precursor supply on enhanced production in M1152•Reduced rate of germicidin in M1152 suggests a need for other expression hosts Systems Biology; Omics; Metabolic Engineering Streptomyces coelicolor has been the de facto model actinomycete for the production of antibiotics. Being known for over 100 years, the interest in this organism predates the golden age of antibiotic research. With its complex life cycle, featuring mycelial growth and differentiation, spore formation, programmed cell death, and the ability to produce multiple colored secondary metabolites, it has assisted greatly in our understanding of how streptomycetes sense their surrounding   . Heterols (BGCs) . These Bormatics .S. coelicolor as a heterologous production host relies on a metabolism that has evolved to provide the necessary precursors to produce a broad range of complex molecules. Many of these molecules are produced when the strain is experiencing nutrient-limiting conditions that lead to growth cessation and complex re-modelling of its metabolism (S. coelicolor M145 (S. coelicolor A3(2)  . This haor A3(2) .S. coelicolor M145 as a host for heterologous BGC expression, strain M1146 was created by the sequential deletion of its four major BGCs   . This shibiotics . Up to nibiotics  and is tS. coelicolor M1152 has been confined to transcriptome profiling of batch fermentations  open access and contribution, (2) version control, (3) continuous development and integrated quality control with memote  newh memote , baker'sh memote , and Chih memote . The recS. coelicolor, while tracking development using Git for version control  and abundances. The GECKO toolbox modifies the structure of an existing GEM to integrate turnover rates and proteome data. Consequentially, this constrains the range of estimated fluxes to a biologically feasible range as determined by the amount and efficiency of each enzyme. Note that this approach regards the maximum catalytic activities but does not consider other kinetic parameters such as affinity constants. The overall flux variability of the resulting enzyme-constrained model (EcSco-GEM) is drastically reduced compared with the classic genome-scale model (1) flux variability. As reactions with high variability result in low certainty in the estimated fluxes, the observed reduction in flux variability is therefore a qualitative measure of the increased accuracy achieved by constraining the range of possible fluxes to those satisfying the limitation in protein allocation.To include explicit constraints regarding enzymes catalyzing metabolic reactions, the GECKO formalism  was applle model G, particIn our endeavor to describe the metabolic differences between M145 and M1152 we generated in total 17 time- and strain-specific enzyme-constrained models by combining EcSco-GEM with estimated growth, secretion, and uptake rates, as well as proteome data from cultivations that are detailed and analyzed later in the article.S. coelicolor Sco-GEM models can simulate behaviors of  earlier . Culture earlier A and 2B. earlier . Both D-depleted . The RNAdepleted  and weredepleted  , an increase in oxidative phosphorylation, and a decrease in fatty acid biosynthesis D and S4.Amycolatopsis sp. , delaying phosphate depletion by M1152 to 47 h after inoculation  biosynthesis in elicolor , one canelicolor . MalonylAlthough the proteome data are an integral part of the EcSco-GEM models, RNA-seq data were used to both verify the trends and to gain further insights into the regulatory changes that are not captured by the metabolic models. As the proteomic data, the RNA-seq data showed large global differences between M1152 and M145, revealing 499 differentially expressed genes with a significance threshold of p < 0.01.Unsupervised clustering of the significantly changed genes reveal differences in regulatory systems related to redox regulation, signaling, and secondary metabolism. The significantly changed genes were clustered into seven groups with K-means clustering, with clusters 1–3 containing genes that are upregulated in M1152 compared with M145, and clusters 4–7 vice versa . A Gene The enriched processes upregulated in M1152 point to increased oxidative stress : antioxiscbA (SCO6266) and its downstream gene scbC (SCO6267), which stands out by being almost 6-fold upregulated in M1152. This high expression level is likely due to the deletion of scbR2 (SCO6286), the last gene selected to be part of the cpk BGC  to this enzyme introduction of a (secondary) copy of germicidin synthase gene y of gcs . Thus, trpoB mutation, and increased oxidative metabolism and oxidative stress. As Act itself works as an electron acceptor one may hypothesize that its presence could relieve some of this stress. Another approach is to reintroduce scbR2 to avoid influencing the related regulators of development and secondary metabolism.Although earlier work has suggested a competition for common precursors between fatty acids and secondary metabolites biosynthesis , our resS. coelicolor seems to have a complex and not fully elucidated regulatory system, several studies have shown that manipulation of regulatory genes can affect the production of secondary metabolites .Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Eduard J Kerkhoven . Here, the latest version of the Sco-GEM is available in both YAML and SBML level 3 Version 1. In addition, users can contribute to further model development by posting issues or suggest changes. The proteomics data are available from ProteomeXchange: PXD013178 via the PRIDE partner repository (GSE132487 (M145) and GSE132488 (M1152). Normalized counts are also found in The models and scripts generated during this study are available at GitHub (pository . NormaliAll methods can be found in the accompanying