Genome-scale metabolic models (GEMs) allow predicting metabolic phenotypes from limited data on uptake and secretion fluxes by defining the space of all the feasible solutions and excluding physio-chemically and biologically unfeasible behaviors. The integration of additional biological information in genome-scale models, e.g., transcriptomic or proteomic profiles, has the potential to improve phenotype prediction accuracy. This is particularly important for metabolic engineering applications where more accurate model predictions can translate to more reliable model-based strain design.Bacillus subtilis, which uses publicly available proteomic data and enzyme kinetic parameters for central carbon (CC) metabolic reactions to constrain the flux solution space. This model allows more accurate prediction of the flux distribution and growth rate of wild-type and single-gene/operon deletion strains compared to a standard genome-scale metabolic model. The flux prediction error decreased by 43% and 36% for wild-type and mutants respectively. The model additionally increased the number of correctly predicted essential genes in CC pathways by 2.5-fold and significantly decreased flux variability in more than 80% of the reactions with variable flux. Finally, the model was used to find new gene deletion targets to optimize the flux toward the biosynthesis of poly-γ-glutamic acid (γ-PGA) polymer in engineered B. subtilis. We implemented the single-reaction deletion targets identified by the model experimentally and showed that the new strains have a twofold higher γ-PGA concentration and production rate compared to the ancestral strain.Here we present a GEM with Enzymatic Constraints using Kinetic and Omics data (GECKO) model of B. subtilis metabolic engineering. We expect that the new model can be used to guide future metabolic engineering efforts in the important industrial production host B. subtilis.This work confirms that integration of enzyme constraints is a powerful tool to improve existing genome-scale models, and demonstrates the successful use of enzyme-constrained models in  Bacillus subtilis is the model organism for Gram-positive bacteria and one of the best-characterized bacteria. Its genome has been sequenced and the microbiological, molecular and genetic methodologies for its cultivation and manipulation are well established , as shown in Eq. The enzymatic data reported in Table Since we considered reactions catalyzed by unique enzymes, the number of enzyme-constrained reactions (17) is equal to the number of enzymes.Rj includes a pseudo-metabolite representing enzyme usage, which is limited by protein abundance.In summary, each constrained metabolic reaction kcat values and the known protein abundances  in the cell was assumed to be 0.55 g/gDW, corresponding to the value measured for E. coli , growth rate and acetate production rate [We also tested the prediction performance of the ec_iYO844 model under perturbed genetic conditions. We simulated the metabolic behaviors of five single-gene/operon deletion strains: ∆mdh and ∆sdhABC strains, in which the MDH and SUCD1 reaction is blocked, respectively, with predicted acetate flux value close to zero. However, upon integration of enzymatic data in the model, the predicted acetate secretion rates became more consistent with the experimental values, although the model was still unable to predict the highest rates measured (∆zwf and ∆sdhABC strains). An overall improvement was also observed in the flux value prediction of the G6PDH reaction , in three cases , with experimental flux ranging from 0.6 to 6.5 mmol/gDW/h), two of which corresponding to a flux value wrongly predicted as zero by iYO844. Conversely, in the ∆sdhABC strain, ec_iYO844 captured the G6PDH flux value less accurately than iYO844 indicating that the absolute protein levels in this strain may differ from those in the wild-type strain, which were used in the simulation.While the mutant strains prediction error showed a considerable decrease using ec_iYO844 compared with iYO844, not all the individual flux predictions were similarly improved Fig. . This waDW/h imposed by enzymatic information  was constrained (kc_iYO844 model). The results showed that this method has lower prediction error  than iYO844 , but, also in this context, the predictions obtained by ec_iYO844 are the most accurate . The three models  were also solved via pFBA instead of MoMA, but conclusions do not change and the resulting prediction errors with pFBA are always higher than the respective ones with MoMA (data not shown).Taken together, the results showed that new model is also superior in terms of mutant strain flux predictions, although with a percent improvement in prediction accuracy lower than what was observed for the wild-type strain. The strong assumption that proteomic profile is the same in wild-type (for which proteomic data was available) and single-gene/operon mutants may be partly responsible of the less accurate predictions obtained for mutant strains. For the enzyme-constrained model, we also used an alternative approach, similar to the MOMENT method , in whicpgk and ∆tkt). On the other hand, the model developed was able to predict the essentiality of three additional central carbon metabolism genes , for a total of 5 out of 11 correctly predicted knockout phenotypes. No difference was observed in the accuracy of the prediction for the remaining essential genes belonging to other pathways: 67 of them were correctly predicted as essential by both models.The new model was also evaluated by gene essentiality analysis Table , a step The impact of the specific types of enzymatic data used to develop the enzyme-constrained model on model performance was analyzed in two tests.First, among the 17 enzyme-constrained reactions, we identified triose-phosphate isomerase (TPI), glyceraldehyde-3-phosphate dehydrogenase (GAPD_NAD), CS and PGCDr as the minimum set required to achieve the final prediction performance of the model developed, namely a prediction error equal to 0.27 for the wild-type strain and to 0.43 for the mutants, and 76% of accuracy for central carbon gene essentiality. This result, however, is expected to depend on the study on which the model is applied, with prediction accuracy increasing with the number of enzyme-constrained reactions. This outcome is also suggested by our gene essentiality analysis, in which a significant improvement was observed for central carbon pathway but not in other pathways that were not subjected to enzymatic constraints.d-glyceroyl-phosphate via the GAPD_NAD reaction) as a central node between glycolysis and pentose phosphate pathway, and the key role of citrate synthesis  as central node between glycolysis and the entering of TCA cycle. To better elucidate the role of these two reactions, we performed three simulations in which the GAPD_NAD and CS reactions were individually or jointly constrained as the sole constraint(s) of the ec_iYO844 model. The model reached its lowest error only by constraining both reactions. The individual constraint of GAPD_NAD or CS was not able to fix the PPP flux distribution, while the improvement in the TCA cycle fluxes was observed by individually including the CS constraint.By considering the prediction error for wild-type and mutant strains as the only performance measure, the GAPD_NAD and CS constraints were sufficient to reach the maximum predictive power. The importance of these constraints could be due to the key role of glyceraldehyde 3-phosphate , and of pgm and eno (PGCDr constraint).Conversely, considering the accuracy of gene essentiality analysis, the TPI and PGCDr constraints were needed to correctly predict ely Fig. . To bettkcat values by using randomized kcat for all the 17 reaction constraints. The results  is significantly higher than the value obtained by the enzyme-constrained model , and even higher than the one of the model without constraints (0.47). The knowledge of specific kcat values is therefore essential to obtain accurate predictions. We also tested the effect of kcat randomization for 15 of the 17 reactions, leaving the GAPD_NAD and CS constraints  to their correct values. The results  values demonstrated a relevant FV reduction for ec_iYO844 compared to iYO844, with a 120-fold decrease of median FV Fig. a p-valub, in ordpgs operon, which includes the enzyme-coding genes responsible for the biosynthesis of this polymer, is not expressed in B. subtilis 168 laboratory strains. However, we previously demonstrated that pgs operon transcription could be activated in a B. subtilis 168 derivative by two mutations: swrA+ and degU32(Hy), thereby engineering γ-PGA production [Poly-γ-glutamic acid is a biodegradable, water-soluble, non-toxic, and edible biopolymer that has a large number of biotechnological applications, ranging from biomedicine to bioremediation. For its unique proprieties, different studies for improving the microbial production of γ-PGA were carried out , 53. Theoduction . In this2 + nadh + succoa) and the succinyl-CoA synthetase (SUCOAS) reaction (atp + coa + succ ↔ adp + pi + succoa) as the single-reaction deletion targets yielding the highest γ-PGA flux  h + nadph + succ, respectively) are consecutive reactions forming a bypass for the production of succinate (succ) from akg  and the succinate-semialdehyde dehydrogenase (SSALy) bypass reactions. While the SUCOAS and AKGD reactions are downstream of the akg production in the TCA cycle, OXGDC and SSALy  combination see Fig. . Using eIn summary, the two models showed the same results in terms of recommended single-reaction deletion list (AKGD or SUCOAS), but the predicted fluxes showed quantitatively different values due to the constraints of the GECKO model. Such constraints also determine the difference between the two models in the suggested double-reaction deletion list, with iYO844 recommending the deletion of a reaction (OXGDC or SSALy) for which ec_iYO844 predicted a negligible flux.B. subtilis the odhA–odhB–pdhD and sucC–sucD genes encode the two target reactions, respectively. Since the entire 2-oxoacid dehydrogenase multienzyme complex, encoded by odhA, odhB and pdhD genes, is necessary for the AKGD catalysis and the pdhD gene is also responsible for the pyruvate dehydrogenase (PDH) reaction, only odhAB and sucCD, both in operon architecture, were finally selected for in vivo deletion, giving rise to strains PB5691 and PB5716, respectively  was only slightly lower than PB5383 (0.54 h−1) and the growth profiles during fermentation were very similar among the three strains  significantly lower than the knockout strains . The production rate per biomass unit of PB5691 (0.18 g/gDW/h) was also significantly higher than the one of PB5716 (0.11 g/gDW/h) even if the two mutants reached a comparable maximum concentration of γ-PGA. In summary, the implementation of the identified knockouts yielded a twofold higher maximum concentration and per-cell production rate of γ-PGA, with the deletion of odhAB being the most promising one in terms of production rate per biomass unit, as predicted by the enzyme-constrained model.The optimal single-reaction genetic configurations identified by in silico design were experimentally tested, comparing the γ-PGA biosynthesis performance of the PB5383 producer strain , used asl-glutamate (EM+ medium), a direct precursor of γ-PGA, as in the original E medium composition, significantly improved biopolymer production compared to the EM− medium for all strains . The per-cell production rate showed a significant difference between the reference strain (0.4 g/gDW/h) and the mutants, and between the two mutants , with the odhAB deletion strain showing again higher production (0.7 g/gDW/h) than the sucCD mutant (0.43 g/gDW/h). The differences observed between fermentations in EM− and EM+ were expected, since l-glutamate is a direct precursor of γ-PGA; its presence results in increased γ-PGA flux, as previously measured [The addition of 40 g/L of ins Fig. d, while ins Fig. a. The remeasured . For thiB. subtilis. We showed that the resulting model, ec_iYO844, provides more accurate prediction of metabolic phenotypes compared to the original non-enzyme constrained model. Both secretion and intracellular flux predictions are considerably better with ec_iYO844 than iYO844 for wild-type and, to a lesser extent, mutant strains. Notably, the large errors in wild-type flux predictions observed in the original model, i.e. for the pentose phosphate pathway (in which no flux was predicted), acetate secretion and TCA cycle , are all fixed in ec_iYO844. Moreover, the new model does not require to fix glucose uptake rate to an experimentally determined value, as was the case with the original model, since the glucose uptake flux is determined by enzyme capacity constraints. This advantage has been previously highlighted for other models adding constraints to existing genome-scale model [kcat of enzymes are essential to achieve the improved prediction performance, since a randomized set of kcat values could not provide a similar accuracy. However, not all the enzyme constraints for reactions were essential to reach the predictive accuracy of the ec_iYO844 model: constraints for only four  of the 17 reactions were sufficient under the conditions that we used in this study. It is important to highlight that this result is expected to be specific for the data used to evaluate predictions.Following the principles of the recently proposed GECKO method, we integrated enzymatic and proteomic data for 17 central carbon-related pathways in an existing genome-scale metabolic model of le model . A datasB. subtilis. The poor availability of high quality enzyme kinetic data has been identified as a major impediment for developing improved computational models of cellular metabolism in general [While the originally proposed GECKO method adopted a genome-scale constraining of reactions in yeast, in this study only 17 reactions involved in central carbon metabolism were enzyme-constrained based on manually curated enzyme kinetic and proteomic data. This small-scale constraining was sufficient to demonstrate the potential of this approach with the experimental data used, but larger-scale constraining would be expected to provide benefits for the prediction of reactions and metabolic engineering targets outside of central carbon metabolism. The limitations of small-scale constraining were apparent in the gene essentiality predictions for genes outside of central carbon metabolism, which were not affected by enzyme constraints for central carbon metabolic reactions. The primary challenge for developing constraints for reactions outside of central carbon metabolism is the limited availability of enzyme kinetic data for even relatively well-characterized organisms like  general .In contrast to essentiality predictions, enzyme constraints showed significant effect in reducing flux variability in reactions outside of central carbon metabolism. Out of the reactions with non-zero variability in the original iYO844 model, 81% of the reactions showed reduced flux variability. This demonstrates that enzymatic constraints can have an impact on different pathways apart from the one in which constrained are added. The result obtained for ec_iYO844 is consistent with the improvements observed in yeast with genome-scale enzyme constraining. The reduction in flux variability suggests that the ec_iYO844 model could be better for strain design than the original iYO844 model even for products that do not directly come from central carbon metabolism.The evaluation of the models in a metabolic engineering study enabled the identification of two promising gene deletion targets in TCA cycle that led to the improvement in the production of γ-PGA, a biopolymer with a large number of applications. The model without and with the integration of enzymatic data predicted the same single-reaction deletion targets (AKGD and SUCOAS). However, differences were observed in the quantitative prediction of γ-PGA flux of mutant strains and in the list of recommended double-reaction targets. Among these, a remarkable difference was that the original model led to the selection of AKGD with OXGDC/SSALy as best deletion combination, while the enzyme-constrained model predicted that OXGDC/SSALy do not carry significant flux due to an undetectable protein level for one of the corresponding enzymes. Therefore, the strain design based on the original model was unnecessarily complex since the same result could be reached with a single-reaction knockout (AKGD).B. licheniformis, but, to our knowledge, no forward engineering studies have been done to confirm the effect of these knockouts. For this reason, the AKGD and SUCOAS reactions  were selected as deletion candidates in this study to test their effect on γ-PGA biosynthesis.Considering the single-reaction deletion targets, the inverse correlation of γ-PGA production with the level of the enzymes catalyzing SUCOAS and AKGD was previously observed by Yu et al.  in B. liodhAB and ΔsucCD) were constructed in vivo by implementing gene deletions in a previously engineered strain (PB5383), capable of γ-PGA production. Fermentation experiments showed that both mutants could reach a significantly higher (twofold) maximum γ-PGA concentration than PB5383 over a three-day growth in E medium without glutamate. The ΔodhAB strain also significantly outperforms the others in terms of per-cell γ-PGA production rate, with a two-fold improvement over PB5383. These results demonstrated that TCA cycle flux was successfully diverted towards glutamate, and subsequently toward γ-PGA production, by implementing the knockouts recommended by the model. As expected, the addition of l-glutamate in the medium increased γ-PGA production in all strains, since l- and d-glutamate are precursors of γ-PGA, but the ΔodhAB strain still showed improved production compared with the other strains.The two knockout strains (ΔB. subtilis genome-scale metabolic model with significantly improved ability to predict metabolic flux distributions and phenotypes. The improved model relies only on a limited set of enzymatic constraints derived from measured protein expression profiles and kinetic parameters reported in the scientific literature. The application of this model to predicting metabolic phenotypes and metabolic engineering designs demonstrated the utility of the model and the value of relatively limited enzymatic constraints. This work paves the way for improving genome-scale metabolic models of other industrially attractive organisms by incorporating enzyme kinetic and proteomic data available in databases and the scientific literature.In summary, we have developed a


Directly-regulated reactions include those whose flux is regulated by transcriptomic alterations (~890) or via proteomic or phospho-proteomics alterations (~140) in the enzymes catalyzing them. We term the reactions that currently lack evidence for direct regulation as (putative) indirectly regulated (~930). Many metabolic pathways are predicted to be regulated at different levels, and those may change at different media conditions. Remarkably, we find that the flux of predicted indirectly regulated reactions is strongly coupled to the flux of the predicted directly regulated ones, uncovering a tiered hierarchical organization of breast cancer cell metabolism. Furthermore, the predicted indirectly regulated reactions are predominantly reversible. Taken together, this architecture may facilitate rapid and efficient metabolic reprogramming in response to the varying environmental conditions incurred by the tumor cells. The approach presented lays a conceptual and computational basis for mapping metabolic regulation in additional cancers.Altered metabolism is a hallmark of cancer, but little is still known about its regulation. In this study, we measure transcriptomic, proteomic, phospho-proteomic and fluxomics data in a breast cancer cell-line (MCF7) across three different growth conditions. Integrating these multiomics data within a genome scale human metabolic model in combination with machine learning, we systematically chart the different layers of metabolic regulation in breast cancer cells, predicting which enzymes and pathways are regulated at which level. We distinguish between two types of reactions, directly and indirectly regulated.  Here we aim to chart the transcriptional, post-transcriptional and post-translational regulation of MCF7 breast cancer cell metabolism on a genome scale. This is performed via measurements of multi-omics data employing MCF7 breast cancer cells under three different in vitro growth conditions, and its analysis via an integration of this data within a genome scale metabolic model (GSMM) of human metabolism. Our approach is inspired by previous large-scale omics studies of the multi-level regulation of bacterial metabolism9 and yeast10, which have advanced our understanding of the organization and regulation of metabolism in these organisms.Cancer cells adapt their metabolism to facilitate biomass formation to support their rapid proliferation. Transcriptional regulation alone does not account for many of the metabolic alterations observed in cancer16. GSMMs have also been used to predict post-transcriptional regulation of metabolic enzymes in healthy tissues17 but going beyond that to systematically analyze metabolic regulation in cancer is addressed here for the first time to the best of our knowledge.Genome scale metabolic modeling is an increasingly widely used computational framework for studying metabolism. Given the GSMM of a species alongside contextual information such as growth media and omics data, it has been shown that one can fairly reliably predict numerous metabolic phenotypes, including cells’ growth rates, metabolite uptake and secretion rates and internal fluxes, gene essentiality, and more. Over the last few years, GSMMs have successfully served as a basis for many computational studies of cancer, e.g.We collected omics measurements in MCF7, a breast cancer cell line, grown under three different conditions: (1) Minimum Essential Medium (MEM) with glucose and without glutamine (MEM-Gln), (2) MEM with glucose and glutamine (MEM) and (3) MEM with glucose, glutamine and supplemented with Oligomycin – an inhibitor of ATP synthase that inhibits cell respiration (MEM+Oli). The media were chosen because they reflect multiple stress conditions for the cell: one media (glutamine deprivation) is chosen because MCF7 cells rely on glutamine as the main source of energy, and the other media (supplement of Oligomycin) is chosen because it emulates tumor hypoxic conditions.13C assisted metabolomics experiments using our in-house developed software that simulates dynamics of metabolites 13C labeling, Isodyn22. Fitting the data allows determining the metabolic flux profiles of MCF7 breast cancer cells under three different growth conditions (see methods). Figure The measurements were repeated twice under each condition at two time points - after 8 and 24 hours, resulting in overall 6 × 2 multi-omics datasets. Each such dataset includes the gene-expression of 1372 metabolic genes, proteomics for 486 metabolic enzymes , phosphorylation values for 71 phosphorylation sites on metabolic enzymes, and flux measurements of 44 metabolic reactions (see methods). To obtain flux measurements, we fitted all the data obtained through spectrophotometric measurements and 24 and in human26, point to the significant differences between the mRNA and protein levels of many metabolic enzymes and call for a systematic study of their potential functional regulatory implications.To obtain a genome wide view of pathway-level differences in the transcriptional data across the different growth conditions, we first compared (using a t-test) the metabolic gene expression values between the different growth conditions to identify metabolic pathways that were significantly up or down regulated in any of these conditions compared to the others. We found that upon oligomycin treatment, carnitine shuttle pathway is downregulated compared to the other growth conditions, as well as the urea cycle/amino group metabolism pathway. On the other hand, fatty acid activation and C5-Branched dibasic acid metabolism (among other pathways) were found to be elevated upon such treatment - a full table listing the significant growth condition-specific changes is provided in SI Table 27 to infer the likely metabolic fluxes given these data in a genome wide manner. After an initial validation of these predictions, we proceeded to compare the flux predictions of the resulting reactions to the corresponding enzymes’ omics data to identify their regulation. This is performed in a stepwise manner as follows  transcriptionally regulated reactions (TR) are those reactions whose enzymes’ gene expression levels match the predicted fluxes. (2) translationally regulated reactions (TL) are those reactions whose predicted flux levels do not match their gene expression levels, but they match the protein levels of their enzymes.GSMM based identification of post-translationally directly regulated reactions:Post-translationally regulated reactions’ (PTL) assignments are given to the reactions where both the enzymes’ gene expression and proteomics levels do not match the predicted flux levels but the predicted flux levels across the different growth condition can be significantly associated with changes in the phosphorylation levels of the enzymes.Building machine learning predictors of additional directly regulated reactions: For the majority of the metabolic reactions, however, we did not find omics evidence testifying that they are directly regulated at any of these three levels. One major reason for that may be the limited scope of the proteomics and phospho-proteomics measurements. We, therefore, built machine learning based predictors of TR and TL regulation based on the reactions that have already been labeled as such via the model-based analysis in step (1). Then, we applied these predictors in a genome wide manner to further identify sets of reactions that are predicted to be TR or TL regulated (detailed below). We then performed various genome wide analyses to further test and validate the veracity of these predictions.Identifying stochiometrically coupled, indirectly regulated reactions: Finally, even after this prediction step, a large set of reactions still remains unassigned and are labeled as indirectly regulated. A major likely source of such indirect regulation is metabolic regulation28, which manifests itself in the stoichiometric coupling of the fluxes of different reactions across the metabolic network, and which we study further using the human metabolic model.Our main goal in this study is to use the measured multi-omics data to systematically chart the different layers of metabolic regulation in breast cancer cells that orchestrate the actual metabolic flux across the network’s reactions occurring in each growth condition. Ideally, measuring the actual fluxes in each condition directly via tracing experiments would be adequate, but obviously, this can currently be done only for a small number of fluxes that are mainly involving central cell metabolism. Hence, alternatively, we integrated the various omics data measured in each growth condition within a genome scale model of human metabolismBelow we provide a detailed description of each of these four steps and the results they uncover.17, a computational method that systematically predicts metabolic fluxes in a GSMM by incorporating omics data (transcriptomics and/or proteomics) that represent the activity level of the metabolic enzymes. iMAT considers the gene expression or protein levels as cues for the likelihood that the enzymes in question carry a metabolic flux in their associated reactions. It then leverages the GSMM to accumulate these cues into a global flux distribution that is stochiometrically consistent and maintains mass balance across the entire metabolic network (see methods).We first aimed to predict the fluxes of the reactions in each condition, to determine which reactions are directly regulated and at what level they are regulated. To this end, we used iMAT 13C Metabolic Flux Analysis (13C MFA). To this end, we combined both mRNA and protein expression measurements and used iMAT, a tool that extends upon the standard flux balance analysis (FBA) to predict the flux distribution that is the most likely given both types of data. Briefly, following a procedure already established and validated by17, the activity level of an enzyme was set according to the proteomics data when these data were available and according to the gene-expression otherwise, leaving the activity level unconstrained when large disparities existed between the gene expression and the proteomics data (see methods). Reassuringly, the accuracy of predicting the experimentally measured fluxes was significant across all growth conditions . To this end we discretized the gene expression measurements and the predicted fluxes into three levels of activity: low (TR-low), moderate (TR-moderate) and high (TR-high)). We then compared predicted flux level of each reaction to the discretized gene-expression level of the pertaining enzymes (see methods). Reactions whose predicted flux levels matched gene expression levels of their enzymes across the different measurements were considered to be TR. For the three conditions , 562, 550 and 556 reactions (approximately 28% of the model reactions) were identified as TR, respectively. Supporting these predictions, we found that the group of predicted TR reactions is enriched with transcription factor binding sites , ChEA33  and ENCODE35 ) (see methods).Given these network wide flux predictions, we next set to identify the reactions that are translationally (TL)-regulated. Among those, about 15 reactions are predicted to be TL-upregulated (the discretized flux/proteomics activity state is higher than the discretized transcriptomics state), and about 35 are predicted to be TL-downregulated (the discretized flux/proteomics activity state is lower than the discretized transcriptomics state) , we searched for reactions whose (discretized) predicted flux activity levels were different from the transcriptomic levels of their enzymes. Such transcriptomic/flux ‘discordant’ reactions whose activity levels were high (low) according to the gene expression of their enzymes but low (high) according to the flux predictions are considered to be post-transcriptionally down-(up-)regulated. The correlation between the proteomics data and the predicted fluxes for this subset of TL predicted reactions was high and significant , as would be expected -regulated. Overall, 34, 39, 42 such reactions have at least one measured phosphorylation site in MEM, MEM-Gln and MEM+Oli, respectively. We next inferred the impact of each of the measured phosphorylation sites on enzyme activity. The phosphorylation data included 56 metabolic enzymes phosphorylated at 71 different phosphorylation sites catalyzing 164 metabolic reactions. For each of the reactions, we computed the Spearman rank correlation between the predicted flux (computed via integrating the pertaining transcriptomics and proteomics data) and the corresponding site phosphorylation levels across all growth conditions and time points measured  regulated, we used the fluxes predicted in the previous step as a reference point. That is, reactions whose predicted flux activity markedly differed both from their transcriptomics and proteomics expression levels (that are hence not predicted to be TR or TL regulated) may be in vivo36 activity, and (2) phosphorylation on S293 causes pyruvate dehydrogenase (PDHA1) enzyme inactivation37. Our predictions match both; for the CAD enzyme, we detected a high positive correlation (0.718) and for PDHA1 we obtained a strong negative correlation of −0.6. To test and validate these predictions in our cells further, we performed western blot experiments for both proteins (CAD and PDH together with their phosphorylated forms). We observed a marked phosphorylation of PDH in the predicted conditions for MEM-Gln and MEM+Oli compared to MEM growth condition, indicating its reduced activity under these conditions  phosphorylation of S1859 in carbamoyl-phosphate synthetase 2 (CAD) enhances its ons Fig. . This is phosphorIn the previous steps, we have identified about 500 reactions that are directly regulated at one of the three regulatory levels described above . In these reactions, the predicted flux changes were significantly associated with molecular alterations in the pertaining enzymes. However, this leaves a large number of about 1450 reactions that were not assigned to any of these direct regulatory levels, which can be attributed to the limited scope of our measurements. In order to predict additional reactions that are likely to be directly regulated at TR or TL level, we built five Support Vector Machine (SVM) classifiers for five different direct regulation levels: TR-high, TR-low, TR-moderate, TL-up and TL-down. The goal of each classifier is to predict whether a reaction is regulated at one of these levels or not. The classifier was trained and evaluated using the reactions that have already been labeled as TR or TL regulated in the previous analysis at step (1), using a standard train and test 5-fold cross validation. The classifier input features included the gene expression, proteomics, predicted fluxes and metabolic network characteristics  of the given reactions, and the TR/TL labels already assigned in the previous steps (see methods). The accuracy of the classifier was measured by comparing the predicted labels against the known labels. The resulting classifiers achieved a high cross validation prediction accuracy  reactions where their flux may be primarily metabolically-regulated by changes in their substrate and product levels due to changes in the flux activities of other reactions in the metabolic network. That is, their flux may be stoichiometric coupling (SC-regulated) to the flux of other reactions in the metabolic network40.After the predictions we performed at step 1–3, around 1000 reactions yet remained not to be predicted as directly regulated, some of which are likely to be further identified as regulated with more extensive data. However, many of these remaining unassigned reactions may still be truly 41. Accordingly, a perturbation in enzyme abundance or activity can be propagated through reactions stoichiometry coupled to the reaction catalyzed by such enzyme. To study such dependencies on a genome-scale, we used flux sampling to quantify the pairwise stoichiometric couplings between all the metabolic reactions in the human network, identifying for each reaction how tightly its flux is coupled to the flux of each of the other reactions, in each of the different conditions (see Methods).In the framework of MCA , it has been established that network structure is an important determinant of metabolic control42 theory: In the framework of MCA, enzyme activities catalyzing reversible reactions, which often are in rapid equilibrium, usually have low flux control coefficients and hence are poor targets of direct regulation. Indeed, the combination of the ‘directional flexibility’ of candidate SC-regulated reactions with their enhanced coupling to other directly-regulated reactions is likely to facilitate the formation of stoichiometrically feasible flux distributions across the metabolic network, providing a way for efficiently regulating the metabolic state with minimal cellular costs in terms of transcriptomics, proteomics and phospho-proteomics regulation.Remarkably, we found that the ~1000 ‘unassigned’ indirect reactions have significantly higher stoichiometric couplings to the TL and PTL directly regulated reactions than among themselves across the different growth conditions . These findings point out that the regulation of cellular metabolism may be governed in a hierarchical manner where the flux of many indirectly regulated reactions is determined via stoichiometric coupling to the flux of others, directly regulated reactions. Finally, we found that the group of ~1000 indirectly regulated reactions is highly enriched with bi-directional reactions . This observation can be explained by metabolic control analysis (MCA)This study integrates transcriptomics, proteomics, phospho-proteomics and fluxomics data with metabolic modeling to provide the first chart of metabolic regulation in MCF7 breast cancer cells on genome scale. We classified the metabolic enzymes as those that are predicted to be directly regulated at three distinct levels  and those that are predicted to be indirectly regulated, given the current coverage of omics data. As expected, we found that citric acid cycle is generally upregulated both on the transcription and translational level. Interestingly, while on the transcriptional level fatty acid oxidation was found to be generally down-regulated, it is up-regulated on the translational level. In addition, oxidative phosphorylation – another hallmark of cancer, was found to be up-regulated only on the translational level (not including MEM+Oli medium). These findings further highlight the pivotal role of translational regulation in cancer and the importance of obtaining higher coverage of proteomic data, whenever possible.Remarkably, we found that the flux of the indirectly regulated reactions is coupled to the flux of directly regulated ones. We also found that the indirectly regulated reactions are enriched with bi-directional reactions. These findings might open an opportunity for further research to determine an extent by which their activity levels are set by other reactions. Taken all together, these findings suggest that the regulation of breast cancer cell metabolism is controlled in a hierarchical manner where the direct regulation of about half of the reactions suffices to orchestrate the flux regulation through the whole metabolic network via flux coupling.44. Consequently, the machine learning predictors built for predicting transcriptional regulation and post-transcriptional regulation, but not post-translational regulation. Fourthly, as we employ coarse discretization to overcome some of the noise in the data, we only identify regulatory alterations in reactions that are differentially active across the conditions of study. This limitation is partly mitigated, however, by analyzing three very distinct metabolic states. Future work should aim to address these limitations by incorporating data sets covering more conditions, measuring a wider range of omics data with higher coverage, and ideally, move to perform such measurements in patients’ tumor data. With the advent of omics technologies such data may become readily available soon and may be benefit from the conceptual and computational framework laid out in the current study.Like almost any other computational, genome scale investigation, our approach has quite a few limitations. First, the data itself, is still limited and noisy, and the coverage of different layers of omics data is uneven, due to obvious technical limitations. Second, guided by the data we collected, we focused here on studying post-translational modifications mediated by phosphorylation. However, obviously, post-translational modifications occur via a variety of additional mechanisms, including, e.g., acetylation, glycosylation and allosteric regulation13C labeling are understandably even more limited in their scope, covering only central carbon metabolism. Aiming to make the best use of the available data and to obtain a genome-wide view of breast cancer cell metabolism, we used a modeling approach to integrate the data and infer the most likely genome-scale flux distributions. Additional work aiming to deal with the limited coverage problem was carried out via creating SVM predictors that used the known network properties together with measurements with high coverage and helped us extend the scope of the study to the utmost. With rapid advancement of high-throughput technology and accumulation of more comprehensive omics data across additional cellular conditions, the conceptual and computational framework exhibited here lays the methodological foundations for gradually obtaining a more comprehensive view of metabolic regulation in both breast cancer and other cancer types.Although we analyzed multiple layers of omics data, their coverage has been limited: while we had gene expression data for all 1372 metabolic genes, the coverage of our cutting-edge proteomics measurements provided data for only 486 metabolic enzymes and 71 of their phosphorylation sites. Flux measurements using 2 and saturated humidity. Growth medium was replaced every 2–3 days.Breast cancer cell line, MCF7 was purchased from ATCC and cultured in MEM without phenol red  containing 10% Fetal Bovine Serum (Sigma), 10 mM d-glucose (Sigma-Aldrich), 1 mM sodium pyruvate , 2 mM glutamine (Gibco), 0.1% antibiotic , 0.01 mg/ml insulin (Sigma), and 1% non-essential amino acids . The cells were maintained at 37 °C with 5% CO45. Besides that, they also have elevated mitochondrial activity, and considering that hypoxia is a common condition in the tumor microenvironment, the study of metabolism in the presence of strong stress condition such as hypoxia is also particularly interesting. Therefore; to study the regulation of breast cancer cells, we applied these two perturbations; glutamine deprivation and mitochondrial inhibition by oligomycin.Many breast cancer cells, including MCF7, display glutamine addiction habits; that is, they rely on glutamine as the main source of energy rather than glucose13C2]-glucose (Sigma) or 4 mM [U-13C5]-glutamine (Sigma) with or without oligomycin (1 µM). For the MEM-Gln systems the replaced growth medium did not contain glutamine but only 10 mM -glucose (Sigma). The cells were counted at 0 h, 8 h and 24 h after tracer introduction, and cell pellet and media were immediately frozen to use in later analysis. For the proteomic experiments heavy labeled MCF7 cells were used as an internal standard. To obtain complete labeling, cells were cultured in DMEM deprived of lysine and arginine, and supplemented with the heavy versions of these amino acids, 13C615N2-lysine (Lys8) and 13C615N4-arginine (Arg10). After ten cell doublings, complete labeling was achieved and validated by mass spectrometric analysis.For the experiments, MCF7 cells were seeded and 48 h later, the medium was exchanged with an adaptation medium, MEM without phenol red (Gibco) containing 10% dialyzed Fetal Bovine Serum (Sigma) and the above-mentioned supplements. For the metabolomics experiments, after 24 h of incubation with adaptation medium, for the MEM systems, the medium was exchanged with the same medium containing 10 mM , was used to simulate the transfer of the tracers from -glucose or [U-13C5]-glutamine medium into intracellular metabolites. Isodyn is a program written in C++ and designed to simulate the dynamics of metabolite labeling by stable isotopic tracers22. This program automatically constructs and solves a large system of ordinary differential equations which describe the evolution of isotopologue concentrations of metabolites produced in glycolysis, TCA cycle and PPP. Initially, all the metabolites except for introduced labeled substrates with known isotopologue composition in the medium are considered to be non-labeled and initial total concentrations of intracellular metabolites are calculated as a function of model parameters assuming a steady state at the initial moment. There is a function designed specifically for each type of reaction  and these functions simulate transformation of carbon skeleton (specific transition of labeled carbon) and consumption and production rates of each isotopologue in the considered system. These transformations redistribute 13C isotopes in all metabolites, so that, individual rates which determine the values of the derivatives for the isotopologues are calculated for each isotopologue. To solve this system, a method of numerical integration is chosen arbitrarily . Isodyn simulates a real-time course of label propagation starting from the initial values of experimental conditions of incubation. As it compares the experimental and computed data for corresponding time points, reaching an isotopic steady state is not necessary.Our in-house developed software, Isodyn [Cell extracts were obtained from fresh plates 24 h after incubation with the corresponding growth medium. Then, cells were incubated for 30 min on ice with lysis buffer, scraped, sonicated and centrifuged at 15,000 g for 20 minutes at 4 °C. Supernatants were recovered and the protein content was quantified by the BCA kit (Pierce Biotechnology). Western blot analysis was carried out size-separating an equal amount of protein by electrophoresis on SDS polyacrylamide gels, and then the proteins were electroblotted onto polyvinylidene fluoride transfer membranes (PVDF) . The membranes were blocked with 5% of non-fat dry milk in PBS with 0.1% Tween, and then incubated with specific primary antibodies overnight at 4 °C. Next, membranes were treated with the appropriate secondary antibody for 1 hour at room temperature. All blots were visualized on Fujifilm X-ray  with chemiluminescence detection using Immobilon ECL Western Blotting Detection Kit Reagent . The antibodies used were CAD (Santacruz Biotechnology), CAD-P , PDH (Merck Millipore) PDH-P  and β-actin . Also, anti-mouse (Dako) and, Anti-rabbit (Amersham Biosciences) secondary antibodies were used.mRNA was extracted from cells using GeneAll Hybrid miRNA kit according to manufacturer instructions. mRNA was then processed on Atlas machine using Affymetrix Human Gene 2.1 ST Array Strip and WT expression kit. CEL files were analyzed using Affymetrix Expression Console software. The data were converted to log2 RMA values.52. From each sample, 10 ug were taken for proteomic analysis, and the rest was used for phospho-peptide enrichment with IMAC. Single runs were performed for each proteomic and phospho-proteomic sample.MCF7 cells were lysed in buffer containing 4% SDS, 100 mM DTT in Tris-HCl pH 7.5. Equal protein amounts were combined with the SILAC standard and 5–10 mg proteins were digested using the FASP protocolhttp://www.proteomexchange.org/)MS analysis was performed on the EASY-nLC1000 nano-HPLC coupled to the Q-Exactive MS (Thermo Scientific). Peptides were separated on PepMap C18 columns using 200 min gradients. Raw MS files were analyzed with MaxQuant. Database search was performed with the Andromeda search engine using the Uniprot database. A decoy database was used to determine a 1% FDR cutoff on the peptide and protein levels. For phospho-proteomic analysis, the database search included p(STY) sites as variable modifications. Data are available via ProteomeXchange with identifier PXD006449 . The exchange of metabolites with the environment is represented as a set of exchange (transport) reactions, enabling a pre-defined set of metabolites to be either taken up or secreted from the growth media. The steady-state assumption represented in equation (1) constrains the production rate of each metabolite to be equal to its consumption rate. Enzymatic directionality and flux capacity constraints define lower and upper bounds on the fluxes and are embedded in equation (2).A metabolic network consisting of In the following, flux vectors satisfying these conditions will be referred to as feasible steady-state flux distributions.54. A correction for multiple hypotheses was done using false discovery rate method of 0.05.Based on iMAT results, which was used to predict the regulation of the reactions in the metabolic model, a hypergeometric p-value was computed for each pathway in the model for being enriched with reactions that are regulated in each level. Data for reactions and their pathways were taken from BIGG database56. By using the CBM approach, we assign permissible flux ranges to all the reactions in the network, in a way that satisfies the stoichiometric and thermodynamic constraints embedded in the model and maximizes the number of reactions whose activity is consistent with their expression state. iMAT’s solution may not be unique as a space of alternative optimal solutions (in terms of its objective function) may exist. Therefore, we sampled 2,000 different flux distributions that are all consistent with the reactions’ state of activity or inactivity defined in one of iMAT’s optimal solutions. To address the potential degeneracy of the CBM solutions, we used the artificial-center-hit-and-run (ACHR) sampling approach57 which is an efficient sampling approach for a linearly constrained space58 . The mean flux distribution obtained over the 2,000 samples then serves as an approximation of the source metabolic state.We first employed a discrete representation of significantly high or low enzyme-expression levels across tissues. Gene expression and proteomics levels were discretized to highly (1), lowly (-1), or moderately (0) expressed, for each sample. This discretization was conducted as follows: the 1/3 of the proteomics with the highest values to be considered as highly expressed, and vice versa for lowly expressed. When proteomics data was not available, transcriptomics data was used . One could argue that the different levels of coverage between transcriptomics and proteomics could suggest using different thresholds for determining ‘active’ and ‘inactive’ genes in the respective analysis; To keep a systematic approach, here we opted to treat both data measurements in the same, uniform, way  and according to the proteomics low (high), and left their corresponding enzymes/reactions unconstrained. In iMAT analysis, the discretized gene expression levels were incorporated into the metabolic model to predict a set of high and low activity reactions. Network integration was done by mapping the genes to the reactions according to the metabolic model (see methods), and by solving a constraint-based modeling (CBM) optimization problem to find a steady-state metabolic flux distribution. CBM models the cell as a network of metabolic reactions controlled by hundreds of genes and enables the prediction of feasible metabolic behavior under different genetic and environmental conditions, that are expressed as constraints in the networkTo map the gene expression to expression on the reaction level, we used the boolean gene-protein-reaction (GPR) associations available in the H. sapiens recon1 metabolic model, downloaded from the BIGG database (52). These rules indicate which genes need to be expressed using the two Boolean operators “and” and “or”. An example of such a rule is the following:R1 = (g1 or g2) and g3 (indicating that either gene 1 or gene 2 (or both) need to be expressed in combination with gene 3 to allow reaction 1 activity.OR rules were converted to the maximum transcription level of either of the genes, i.e. (g1 or g2) was converted to maxAND rules were converted to the minimum transcription level of either of the genes, i.e. (g1 and g2) was converted to min.Bi-directional reactions are those that can potentially carry flux in both directions (this information is provided in the human GSMM model).We compared the discretized gene expression measurements to the activity levels of the predicted fluxes; we took 1/3 of the reactions with the highest flux values to be considered as highly active, and vice versa for lowly active reactions. The rest of the reactions considered to be moderately active. If the activity level of a reaction matches the discretized value according to the gene expression, in at least 3 out of the 4 cell line replicates, the reaction is considered to be TR. For the rest of the reactions, if the activity level of a reaction matches the discretized value according to the proteomics, the reaction is considered to be TL.Among the reactions that haven’t been classified as TR or TL in the way that mentioned above, we found the sub group of reactions that were associated with at least one phosphorylation site. Reactions whose predicted flux activity markedly differed from their transcriptomics or proteomics expression levels, and that were associated with at least one phosphorylation site in 3 of the 4 cell line replications, were predicted to be potentially post-translationally (PTL) regulated.30, we found how many of the genes have (at least one) TFs that bind to their promoter region, from exploring Jaspar31, Transfar32, ChEA33 and ENCODE35 databases. Same for all model genes. These values were used in the hypergeometric calculation.First, we found the reactions that were predicted to be TR in all condition. Then, using the reaction-gene matrix, we found the list of genes that catalyze this group of reactions. Using ENRICHR toolWe built and trained five SVMs classifiers . We applied an SVM classifier with a quadratic kernel for each classifier, with the following features:(1–4) gene expression measurements under 4 data points(5–8) predicted fluxes under 4 data points(9) A binary integer indicating if the reaction is reversible.(10) An integer value associated with a unique metabolic pathway.(11) The total number of metabolites participating in the reaction.(12) The total number of substrates participating in the reaction.(13) The total number of products participating in the reaction.For the labels, we used the classification of the reactions from the previous steps . All SVM classifiers were trained on part of this data, and later tested on all data .Cross-validation was performed by setting aside one fifth of the regulated-predicted reactions in the training set. The classifier was trained on the remaining four. The classifier’s accuracy was measured by comparing the predicted labels against the known labels.For each growth condition, we found 2000 different flux distributions using flux balance analysis. Then, for each pair of reactions, we calculated the Spearman correlation between their flux values. For the coupling calculations, we used the absolute values of these correlations (as coupling between reactions can be either positive or negative).59. More specifically, first, all the p-values were sorted in increasing order, P1, P2,.., Pn. Next, we filtered p-values Throughout our paper P-values were filtered by False Discovery Rate (FDR) to correct for multiple testingSupplementary informationSupplementary Dataset 1


We validate the General Evolution Criterion, stating that the change in the chemical affinities proceeds in a way as to lower the value of the entropy production.Replicators are fundamental to the origin of life and evolvability. Biology exhibits homochirality: only one of two enantiomers is used in proteins and nucleic acids. Thermodynamic studies of chemical replicators able to lead to homochirality shed valuable light on the origin of homochirality and life in conformity with the underlying mechanisms and constraints. In line with this framework, enantioselective hypercyclic replicators may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, which can be an obstacle for the emergence of evolutionary selection properties. We analyze the entropy production of a two-replicator system subject to homochiral cross-catalysis which can undergo SMSB in an open-flow reactor. The entropy exchange with the environment is provided by the input and output matter flows, and is essential for balancing the entropy production at the non-equilibrium stationary states. The partial entropy contributions, associated with the individual elementary flux modes, as defined by stoichiometric network analysis (SNA), describe how the system’s internal currents evolve, maintaining the balance between entropy production and exchange, while  The importance of studying chemical systems subject to various architectures, and capable of spontaneous mirror symmetry breaking (SMSB), owes to the problem of the origin of biological homochirality, an outstanding problem in origin of life research ,2, as weSpontaneous mirror symmetry breaking, or absolute asymmetric synthesis (AAS), refer to the transformation of achiral or racemizing initial products to final chiral reaction products in detectable enantiomeric excesses, and in the absence of any chiral polarization or external chiral forces and influences. SMSB and AAS involve transformations yielding nonracemic  outcomes as non-equilibrium steady states (NESS) ,4,5,6. TReaction networks able to lead to SMSB require, as a necessary but not sufficient condition, nonlinear kinetic dependences of enantioselective autocatalysis. Although a rare reaction in laboratory chemistry ,12, it isimultaneous emergence of biological homochirality during the formation of replicator networks with catalytic activity . Furthermore, such an hypothesis also implies that the current chiral machinery present in extant living beings, capable of transferring chirality and which is highly resistant to racemization, is a complex SMSB network which evolved from the primordial ones.Enantioselective hypercycles enable quadratic (first order) autocatalysis to achieve the enantioselective behavior of cubic (second-order) autocatalysis, and therefore may lead to spontaneous mirror symmetry breaking  for specific reaction rate constants in systems with thermodynamic architectures that maintain them out of equilibrium with their surroundings . The sigbalance of the former and the latter at a NESS, for non-equilibrium systems in terms of the extreme flux modes, as defined by stoichiometric network analysis (SNA) [The question of biological homochirality requires an understanding of the non-equilibrium thermodynamic conditions that may lead to stable deviations from the racemic composition. The purpose of this work is to place a strong emphasis on the entropic changes and exchanges associated with SMSB. In so doing we will understand how such chemical dynamical systems can be conceived and in strict obeyance of the thermodynamic laws. This approach is developed in detail employing a model of two cross-catalyzed chiral replicators. This may be regarded as a primitive infrabiological system  built ouis (SNA) .The so-called hypercycle model  solves tA represents the achiral resources needed to form the chiral replicators which engage in homochiral mutual cross-catalysis, Equations (1) and (2). We place these micro-reversible reactions within an open flow system, The species The resultant fourteen transformations are numbered sequentially as indicated, a convenience for setting up the stoichiometric network analysis (SNA)  that folintersected with the positive orthant of a 14-dimensional Euclidean space), and corresponds to the set of all the stationary state reaction rates [The chemical pathway structure of the reaction plus flow scheme Equations (1)–(6) is provided from knowledge of the right null space of on rates . Knowlede COPASI ) yields j-th transformation  the inflow of achiral resource A, (ii) its conversion into enantiomers of the replicators, and followed by (iii) the outflow of these enantiomers from the reactor. After SMSB, these racemic flux equalities are broken, indicating that relatively more flux flows through one of the corresponding flux mode pathway than through its oppositely handed flux mode pathway. This can be appreciated clearly, in for example, the SMSB bifurcations revealed by the partial entropy productions for each EFM, see Figures 4 and 5. After SMSB, we have A SNA stability analysis of the racemic configuration can be carried out following the procedure established in , and leaA is allowed to enter and exit the reactor, but none of the replicators, then SNA proves that the racemic state is absolutely stable, and for all values of closed “unproductive” pathways, while the fifth is the unreactive flow-through of the resource A. In this case, the non-equilibrium racemic states (which define the thermodynamic branch) are the only stable outcomes: the equalities By marked contrast, if only the achiral species The reaction rate constants in Equations  and (2) There is a relatively long induction period for which both replicators remain close to their initially extremely low concentration values, followed by a relatively rapid consumption of the shared achiral species A lnv7v8+v−v10lnv9vj and in the following way:SNA reveals the specific reaction pathways that are responsible for producing entropy . Thus frunidirectional extreme flux modes only and necessarily in the presence of the open unidirectional modes—and cannot produce entropy of and by themselves. Note furthermore that the input/output unreactive flow of resource A plays no role whatsoever in the production of entropy, since Equation  belolculated  using Taith reaction (if it appears in that pathway) by the number of nonzero entries appearing in the ith row of the matrix As these are defined for each elemementary flux mode (EFM), they generally involve combinations of partial entropy productions associated to either a forward or reverse internal transformation and entropy exchange contributions coming from one or more of the input/output fluxes. Therefore, they can have have, in principle, any sign: either positive or negative. The relative weights for each partial entropy contribution are a consequence of the network stoichiometry. These weights simply count the number of times a given transformation occurs in the set of all the EFM pathways of the network. They must be included to avoid the multiple counting of any specific partial contribution. The partial entropy associated to each EFM pathway is obtained by dividing the partial entropy of the Equation . Then, squality)  involvinity) [σe :(24)σe=Rresolves the entropy balance between production and exchange in terms of the individual entropic contributions coming from each elementary pathway within the reaction network. At a NESS the entropy production is balanced by the entropy exchanged with the environment: The reference concentrations ality in  resolvesM EFMs, the sum is extended over M. We evaluate this sum to cover the time range subsequent to the large production peak in Mirror symmetry breaking lifts the degeneracy in the values of the partial entropy productions associated with the EFM pair The entropy production Equation  can be wflows Jk ,27. For on rates :(25)σ=∑kNow, the General Evolution Criterion (GEC) ,27 stateJ: both the internal reversible reactions and on the irreversible pseudoreactions, or matter fluxes, that maintain the system out of equilibrium. This explicit dependence is made manifest, see Equation (A18). We thus evaluate this expression for our model and confirm its validity and the compliance of the GEC over the full time range of our simulation.Note: the derivative of the entropy production with respect to the time-variation of the flows  account ,26,27, s account . We are We first consider the total derivative of the entropy production This complete time dependent behavior is resolved into two important contributions : (i) oneWe conclude from this analysis that the increase of the entropy production along the non-equilibrium racemic thermodynamic branch see  can leadWe have analyzed entropic pathway features underlying spontaneous mirror symmetry breaking for two chiral cross-catalyzed replicators. We have underscored the role of the open elementary flux modes (EFM), as defined by stoichiometric network analysis, for driving transitions from the unstable racemic thermodynamic branch to the branch of organized scalemic states, e.g., from racemic to homochiral, which takes place in the non-linear regime of non-equilibrium thermodynamics.In our chiral replicator network, the EFMs can be organized into three distinguishable classes. Namely (i) internal closed pathways  showThe GEC states that the generalized forces  evolve in such a way as to lower the entropy production. In open flow systems, the affinities depend on both the internal reversible reactions and on the irreversible matter fluxes. We derive this dependence Equation (A18) and calculate the GEC based on this analytic result, it agrees identically with the calculation of the GEC from the numerical simulation of the rate equations. This confirms the dependence of GEC on the matter fluxes and shows how the lowering of the entropy production predicted by GEC is achieved and consistent with the interdependence of the chemical reactions and the matter fluxes into and out from the reactor.unidirectional matter fluxes responsible for the production of entropy and the role of external controlling factors, such as the input/outflow flows and their representation as pseudo-reactions. SNA leads to the expression for the rate of change of the total entropy (density) of the system partial entropy productions over all the extreme flux modes (EFM), both the internal closed pathways and the open unidirectional ones. This yields insight into the coupling between chemical reactions and the input/output matter fluxes. At a NESS, the sum over all EFMs vanishes identically, and implies the balance between entropy production and entropy exchange. The entropy production is minimized at the final chiral NESS.The EFM approach to entropy production, entropy transport and total entropy balance described here applies to any mass-action chemical reaction network in an open system and under a variety of system architectures. The usefulness of this SNA approach is the identification of the specific The hypercycle model involving solely the mutual cross catalyses was chosen for the purposes of illustrating in detail the methods and techniques. Naturally, more chemical realism can be built into the model by adding in the direct uncatalyzed synthesis of the replicators  . This ta


Mycobacterium tuberculosis (M. tuberculosis) to microbicidal intracellular environment of host macrophages is fundamental to its pathogenicity. However, an in-depth understanding of metabolic adjustments through key reaction pathways and networks is limited. To understand how such changes occur, we measured the cellular metabolome of M. tuberculosis subjected to four microbicidal stresses using liquid chromatography-mass spectrometric multiple reactions monitoring (LC-MRM/MS). Overall, 87 metabolites were identified. The metabolites best describing the separation between stresses were identified through multivariate analysis. The coupling of the metabolite measurements with existing genome-scale metabolic model, and using constraint-based simulation led to several new concepts and unreported observations in M. tuberculosis; such as (i) the high levels of released ammonia as an adaptive response to acidic stress was due to increased flux through L-asparaginase rather than urease activity; (ii) nutrient starvation-induced anaplerotic pathway for generation of TCA intermediates from phosphoenolpyruvate using phosphoenolpyruvate kinase; (iii) quenching of protons through GABA shunt pathway or sugar alcohols as possible mechanisms of early adaptation to acidic and oxidative stresses; and (iv) usage of alternate cofactors by the same enzyme as a possible mechanism of rewiring metabolic pathways to overcome stresses. Besides providing new leads and important nodes that can be used for designing intervention strategies, the study advocates the strength of applying flux balance analyses coupled with metabolomics to get a global picture of complex metabolic adjustments.Metabolic adaptation of  Mycobacterium tuberculosis (M. tuberculosis), tuberculosis (TB) causing bacteria in human, is a very successful pathogen, that still claims millions of lives worldwide every year  in concomitance with deprivation of nutrients and essential micronutrients  and reactive nitrogen intermediated (RNI). The complex consists of four enzymes, alkyl hydroperoxide reductase subunit C (AhpC), a thioredoxin-related oxidoreductase (AhpD), dihydrolipoamide acyltransferase (DlaT) and lipoamide dehydrogenase (Lpd). DlaT and Lpd also act as E2 and E3 elements of pyruvate dehydrogenase (PDH) that produces acetyl coenzyme A (CoA)  , a centrproaches . Since tpathways . Integraustments . In recerculosis . Howeverin silico techniques may be put to use to decipher cellular metabolism from data on a subset of metabolites. Genome-scale metabolic models (GEMs), which enable the integration of various omics data, can be used along with flux balance analysis (FBA) techniques to simulate perturbations in cellular metabolism  metabolomic was used to measure metabolites from M. tuberculosis H37Rv cells (henceforth referred to as M.tb) cultured under different stresses. To get a comprehensive picture, the metabolomics data obtained across all stresses were analyzed using statistical approaches and FBA simulations. To this end, a previously published GEM of M.tb  was manually curated so that it could best mimic the observed metabolic states of M.tb grown under stresses. Further, given the lack of an appropriate framework, new approaches were designed for integrating metabolite data in FBA simulations.This study aimed to understand the early metabolic adaptation to the microbicidal stresses namely, acidic, oxidative, iron deprivation and nutrient starvation that in silico simulations, indicated a complex rewiring in M.tb metabolic network during stresses, with nutrient deprivation causing maximum perturbations, suggesting an intriguing association of all cellular metabolites to the nutrient availability. Some of the observed metabolic changes like the release of excess ammonia during acid stress could be comprehended as adaptations of M.tb to the alleviation of stresses. However, unlike the general concept, the present study showed that increased flux through L-asparaginase rather than urease might be responsible for the generation of excess ammonia as an early stress response. Additionally, metabolomics data analyses point to quenching of protons through GABA shunt pathway or sugar alcohols as possible mechanisms of early adaptation to acidic and oxidative stresses in M.tb. Besides these new observations, our FBA analyses suggested a probable anaplerotic path for the generation of TCA intermediates from phosphoenolpyruvate using phosphoenolpyruvate kinase under nutrient stress and for the first time indicated the use of alternative cofactors to rewire metabolic pathways to overcome stresses.The metabolic measurements coupled with the M.tb cultures were grown in 7H9 media  at 37°C with shaking at 180 rpm till the absorbance at OD600 nm reached to 0.6–0.7. Cultures were then harvested, washed, and resuspended in 10 ml of respective stress media for 36 h. The study was performed by using well-established in vitro models mimicking stress conditions such as acidic stress (pH 5.5), oxidative stress, iron deprivation (no iron supplemented) in Sauton’s minimal medium  and used for positive ionization mode (HILIC Chromatography). For negative ionization mode, the dried metabolite extract from M.tb was dissolved in 50 μl ultrapure water (T3 RPLC Chromatography). For both modes, 10 μl of the sample was injected into the mass spectrometer using Shimadzu Prominence HPLC autosampler.The dried metabolite extract from Targeted metabolomic analysis was performed using multiple reaction monitoring (MRM) based approaches, as previously described . Hundred1  (c/ODc) X ODs], where P is peak area. The normalization parameters are given in The data matrix file obtained from LC-MRM/MS was used as input to perform statistical analysis by using online tool MetaboAnalyst1 . The oriss (ODs)  Normalizt-test, PCA, and PLS-DA were performed to identify metabolites that were differential between control and stresses. For univariate a fold change cut-off >1.5 or <0.5, p-value ≤ 0.05 and FDR ≤ 0.05 were considered significant ; the methods applied for each condition are mentioned in nificant . Multivanificant .M.tb that were differentially affected during stresses. Default pathway analysis algorithm ‘Global Test’ and ‘Relative Betweenness Centrality’ were used for analysis. The metabolic pathways with Pathway impact values ≥0.1, p-value (p < 0.05) and false discovery rate (FDR) (FDR < 0.05) was considered to be affected significantly /([ATP] + [ADP] + [AMP])  .M.tb cells were washed with ice-cold 1xPBS and then resuspended in 300 μl of 1xPBS with the protease inhibitor. Cells were then lysed by bead beating, after adding 0.1 mm zirconia beads to each sample. The cell lysate was centrifuged at 10,000 rpm at 4°C for 20 min. The supernatant was filtered by a 0.22-micron filter. The protein concentration of the resultant supernatant was measured. An equal amount of protein from each sample was taken, and the volume was made up to 10 μl. To each 10 μl of the sample, 90 μl of reaction mix (urease buffer and urea) was added. The samples were homogenized and incubated at 37°C for 30 min. Then, as per manufacturer protocol, 80 μl of reagent-1 followed by 40 μl of reagent-2 were added. Samples were incubated for 30 min at room temperature). Absorbance was measured at 670 nm in a multi-well plate reader (Biotek). All the experiments were performed at least three times.The urease activity was measured as per manufacturer protocol by the colorimetric method at 670 nm using urease activity assay kit . Post-exposure to respective stress conditions, The ammonia released was estimated by the colorimetric method at 430 nm by using Nessler’s reagent as described  with modThe pH was measured as described in earlier literature . The samRNA extraction was performed by using the Trizol method as describe . After gM.tb encompassed the full set of 87 metabolites that were measured in our study (M.tb metabolism (viz. iEK1011)  and Cytosine Deaminase (CSND) were added. While there was genomic evidence for the former (enzyme encoded by Rv1205 and Rv2491), the latter was added during the gap filling step based on its presence in other mycobacterial species .It was observed that none of the existing genome-scale metabolic models of ur study . To addriEK1011)  was augmM.tb were obtained from the NCBI database and subjected to analysis using PRIAM2  is a widely used constraint-based approach for analyzing GEMs. It predicts metabolic fluxes by optimizing a given objective function . The comormation . HoweverM.tb. While one of the methods relied on minimizing the total internal flux through the metabolic model, the other approach was based on optimizing flux through the objective function while constraining flux through a newly defined sink function . In the case of simulating the iron deficient condition, the uptake of ferric ammonium citrate was not allowed. Similarly, uptake of small amounts of H2O2 [upto 1 mM/h/g dry weight] was enforced on the M.tb model for simulating the oxidative stress condition. The input conditions while simulating nutrient starvation were the same as the control condition.Subsequently, we explored the possibility of using modified versions of known FBA approaches to study metabolic changes in tion see . The inpMycobacterium cultures by University of Hyderabad Institutional Biosafety Committee under the Department of Biotechnology, Govt. of India. The protocols of handling Mycobacterium tuberculosis for study in the laboratory were approved by the Institutional Biosafety Committee No. UH/SLS/IBSC/Review/SB-R-11 and SB-R-14.All experiments were performed in the facilities (F-60) approved for p-value < 0.05; false discovery rate < 0.05  and goodness of predictability (Q2) values is given in The quality of the PLS-DA models as described in terms of goodness of fit  approaches  was noted to be an essential reaction for the survival of M.tb during oxidative stress  during nutrient starvation were noted. Both these reactions are intermediary processes leading to inosine (Ins) production. Pertinently, Ins modifications in DNA and RNA has previously been shown to be a highly regulated strategy among pathogens during stress conditions . Further, only nine of them could be associated with the perturbed reactions in our in silico study  mediated conversion of Asn to Asp during nutrient starvation was also found to be low. Instead, the accumulation of AKG during nutrient starvation could probably be attributed to altered flux through the reaction catalyzed by aspartate transaminase (ASPTA), wherein turnover of AKG to oxaloacetic acid (OAA) was predicted to be lower than normal. The lower turnover of OAA was however compensated by anaplerosis by PEPCK. As mentioned earlier, during nutrient starvation, the conversion of PEP to OAA was observed to be active by simulations   levels were observed in all stresses, especially during nutrient starvation. One possible source of AKG is glutamate, catalyzed by enzyme glutamate dehydrogenase (GDH) . This anulations . The samer study . On the er study .Interestingly, flux leading to AKG was also observed in certain other reactions during acidic stress. However, the mechanism of AKG accumulation and utilization was predicted to be different during acidic stress as compared to nutrient starvation. The measured concentration of Asp and Glu were low, which was probably suggestive of higher utilization of these amino acids. Concomitantly, flux through reactions leading to the generation of AKG and ammonia from Asn was higher .M.tb during acidic stress and negligible during nutrient starvation or oxidative stress. To test, if the released ammonia is also associated with alleviation of acidic stress, the pH levels of the cell cultures, pre- and post-stress were measured  reaction, which may be responsible for the generation of excess ammonia during acidic stress  . PPP is oduction . This poM.tb during hypoxia (M.tb. Therefore, it is likely, that although cofactors play a part in metabolic rewiring, there are other factors, such as post-translational modifications (Some of our earlier studies which inspected the cross-talks between metabolic network, gene regulatory network, and host-pathogen interaction network of  hypoxia  had sugg hypoxia . Urease  hypoxia , varied  hypoxia . It was  hypoxia . Most ev hypoxia . Howeverications , which mThe study was limited to identification of 108 metabolites available as standards due to which several metabolites including lipids were not identified. Despite a limited number of metabolites that could be measured by LC-MS/MRM from the entire pool of metabolites owing to these technical limitations, mathematical tools like FBA was used to overcome such constraints. It may, however, be noted that FBA comes with certain limitations . FirstlyM.tb during early stress adaptation from a small subset of measured metabolite concentrations. Using in silico approaches, we were able to predict the probable alterations in the paths of the flow of metabolic fluxes, thereby leading to adaptation to stresses. Understanding that in silico method has limitations due to the incompleteness of the genome-scale metabolic models and non-availability of thermodynamic parameters for all the enzymatic reactions in case of M.tb, efforts were made to improve the existing M.tb metabolic model with regards to the metabolites which were measured through LC-MRM/MS. In spite of our best efforts, we were unable to capture all the measured metabolites in the M.tb model. In particular, metabolites from the sugar alcohol metabolic pathway could not be captured. Thus, there exists an opportunity to improve the in silico model of M.tb metabolism. While this study was a single time-point study, a time-course experiment would provide better perception on how the mycobacterial system responds to these stresses over time for early adaptation. Such studies and leads from these observations are under investigations. Conclusively, with this study, together with earlier reports (M.tb.In this paper, we have discussed approaches to comprehend the genome-scale metabolic changes in  reports , 2014, wAll datasets generated for this study are included in the manuscript/in silico analyses. AR, AS, AC, TB, AD, SSM, SB, and SCM analyzed the data and wrote the manuscript. SR, SSM, SB, and SCM supervised the project.AR, TM, KB, and LM performed the experiments. AC and AS performed the SSM, AD, TB, and AS were employed by Tata Consultancy Services Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.