We found that in ccRCC, but not in prostate adenocarcinoma, flux balance analysis could predict essential metabolic genes beyond random expectation. Five of the identified metabolic genes, AGPAT6, GALT, GCLC, GSS, and RRM2B, were predicted to be dispensable in normal cell metabolism. Hence, targeting these genes may selectively prevent ccRCC growth. Based on our analysis, we discuss the benefits and limitations of flux balance analysis for gene essentiality predictions in cancer metabolism, and its use for exposing metabolic liabilities in ccRCC, whose emergent metabolic network enforces outstanding anabolic requirements for cellular proliferation.Flux balance analysis is the only modelling approach that is capable of producing genome-wide predictions of gene essentiality that may aid to unveil metabolic liabilities in cancer. Nevertheless, a systemic validation of gene essentiality predictions by flux balance analysis is currently missing. Here, we critically evaluated the accuracy of flux balance analysis in two cancer types, clear cell renal cell carcinoma (ccRCC) and prostate adenocarcinoma, by comparison with large-scale experiments of gene essentiality  The regulation of metabolism has been recognised to be of central importance in cancer12456789101213141516Under these premises, metabolic modelling using flux balance analysis (FBA)19212223252728293031323335363738AGPAT6, GALT, GCLC, GSS, and RRM2B, which, although essential for cancer cells, are potentially nonessential in normal cells.In this study, we critically and systematically assessed the benefits and limitations of FBA for performing genome-scale predictions of gene essentiality in cancer metabolism. In particular, we were interested in the use of FBA to expose metabolic liabilities in clear cell renal cell carcinoma (ccRCC), the most common form of kidney cancerFlux balance analysis (FBA) is possibly the only modelling approach that has the potential to predict gene essentiality in cancer metabolism at the genome scale43in silico single-gene knockout, and the gene is essential if the in silico single-gene knockout ablates biomass production. A gene knockout ablates biomass production if there is no flux distribution that allows the biomass equation to carry a flux, or if the knockout results in a substantial flux reduction. However, a gene knockout consents biomass production if there is no change in the flux through the biomass equation. Single-gene knockout resulting in no change in biomass production is mostly explained due to one of the following reasons: 1) gene redundancy, i.e., more than one gene encodes for the reaction(s) associated with the knockout; 2) pathway redundancy, i.e., there is an alternative pathway with the same overall stoichiometry that can compensate for the knockout; or 3) the reaction(s) encoded by the knocked-out gene are not active (dead end) at the studied condition. Depending on this outcome, a gene is declared essential or nonessential in silico for a certain cancer. If constraint B) is implemented, an in silico single-gene knockout may ablate or consent biomass production, depending on which profile of exchange fluxes is used as a constraint. In this case, the corresponding gene is declared essential in silico for the cancer type only if biomass production is ablated using exchange flux profiles from at least 70% of its corresponding cancer cell lines.Here, we considered two typical sets of constraints: A) the topology of the cancer specific-metabolic network; and B) a profile of experimentally measured fluxes for a number of exchange metabolites  in a panel of cancer-specific cell lines . Using either of these two constraints we predicted gene essentiality using FBA by introducing a constraint that disables flux in the univocally encoded reaction(s). This constraint is commonly referred to as in vitro: in this case, a panel of cancer-specific cell lines derived from prostate adenocarcinoma (PC) or clear cell renal cell carcinoma (ccRCC), both cultured in defined serum-containing medium. The cells were transfected with a library of siRNA oligonucleotides that target approximately 230 metabolic genes. In the PC screen, induction of caspase activity was quantified after 96 h following transfection, whereas in the ccRCC screen, reduction in cell number was monitored. If at least 70% of the cancer cell lines passed a given threshold for caspase activity or cell number reduction, then the gene was declared essential in vitro for this cancer type . The accuracy of the predictions was calculated using the Matthews correlation coefficient (MCC) and the related Fisher’s exact test statistics.In principle, the proposed approach should capture all metabolic liabilities related to biomass formation induced by the network topology and to the activation of metabolic pathways induced by the exchange flux profile of a certain cancer. At the same time, it is noteworthy that the FBA problem formulated herein will not uncover other metabolic liabilities known to be associated with cancer survival, for example, maintenance of anti-oxidant poolsin vitro gene essentiality in the metabolism of ccRCC, as this is the most common form of kidney cancer4647in vitro depends on the threshold chosen for the mean cell number reduction. We selected a 30% reduction for benchmarking purposes because the quantity of essential genes appears to reach a plateau at this value; note that no siRNA caused a cell number reduction greater than 50% , namely AGPAT6 and GALT  as constraints50and ODC1 . It is lin vitro but were not captured by FBA are essential because the gene products carry out metabolic tasks that are not ascribable to the biomass production simulated here. Alternatively, it also possible that redundant pathways available in the metabolic network are not active due to the presence of regulation in vitro or in vivo that is not considered in the FBA simulations, as suggested by studies of gene deletion in yeastTaken together, these results suggest that in ccRCC metabolism, FBA is able to predict gene essentiality, although to a limited degree. Gene essentiality as exposed by FBA is in turn attributable to a rewiring of the metabolic network and exchange fluxes that contribute to biomass production. Conversely, it is conceivable that the 14 genes that were found to be essential in vitro if the corresponding siRNA caused apoptosis with a caspase activity z-score ≥ 2.5  in at least 2 of the 3 cell lines, as adopted in the original study. Using these criteria, 14 metabolic genes were found to be essential in the PC cell lines  cell lines ll lines . The topssential . We alsoential 50.p = 0.233, p = 0.635, in silico , as opposed to ccRCC (7 cell lines). However, it is also possible that the altered exchange fluxes in PC cells fuel pathways other than those required for biomass production and are therefore not captured by the FBA model used here. One of these pathways could indeed involve the synthesis of cholesterol for the production of steroid hormones, which play a major role in the development of PCContrary to the results obtained for ccRCC, the accuracy of FBA predictions in PC was considerably lower when using metabolic network topology as the sole constraint in silico even though they are not utilised in any metabolic reactions by cells in vitro . To explore the extent to which the medium composition affects the accuracy of FBA predictions, we repeated all simulations using Ham’s medium, a nutrient poor medium adopted in previous studies to predict in silico gene essentiality of cancer cells33in silico increases for both ccRCC  induced by incorrect assumptions regarding the unavailability of certain metabolites to the cells. The results of the accuracy achieved by FBA in these scenarios are reported in In FBA, the definition of metabolites available for uptake is a decisive constraint for the prediction of gene essentialityth ccRCC  and PC , we performed a sensitivity analysis on these thresholds for all tested scenarios . In the case of ccRCC, we observed a positive relationship between the accuracy of FBA predictions and the strictness of the definition of the threshold for cell death, at least up to the point where the number of essential genes in vitro is less than 10, which occurs for mean cell number reduction >40% (in silico predictions is significant in ccRCC (but not in PC) for a reasonable range of thresholds upon which a gene is declared essential in vitro.Given that the definition of gene essentiality ion >40% . This trion >40% . In partin silico predictions of gene essentiality. In particular, we tested the extent to which exchange fluxes from ccRCC cell lines can be used to infer gene essentiality attributable to the ccRCC phenotype. To this end, we selected some genes that were differentially classified as essential depending on the cell line flux profile, but still classified as essential in ccRCC according to a consensus outcome, i.e., essential in >70% of cell lines. We chose to test the predictions for GCLC, GSS, SLC7A9 , and PNP . In addition, we tested UMPS and RRM2B, which were deemed essential in silico for all ccRCC cell lines upon implementation of every exchange flux profile. Next, the corresponding genes were silenced in five of the seven cell lines whose exchange fluxes were used to constrain the FBA predictions . In accordance with the threshold for cell death adopted above, a gene was declared essential in vitro for ccRCC if more than 70% of cell lines tested  exhibited at least 30% mean cell number reduction compared to control .Because FBA proved powerful in exposing the metabolic liabilities of ccRCC, we decided to validate some of the RRM2B, GCLC, UMPS, and GSS were confirmed in vitro. However, PNP and SLC7A9 knockouts showed mixed effects across cell lines in vitro. Hence, the essentiality of these genes in ccRCC could not be inferred from this experiment. Overall, this result suggests that ccRCC cell line exchange fluxes can entail some common metabolic requirements associated with the ccRCC phenotype, which can be exploited to predict gene essentiality in ccRCC metabolism. However, the exchange flux measurements appear to be insufficient per se to achieve reliable predictions for a specific cell line. Indeed, we observe that only 17 of the 30 individual predictions were replicated in vitro if the cell-line-specific exchange fluxes were used for the prediction of essentiality for the corresponding cell line.At the level of gene essentiality in ccRCC, the consensus predictions for in silico and validated in vitro. This list includes ten metabolic genes: AGPAT6, CAD, DHCR24, FDFT1, GALT, GCLC, GSS, ODC1, RRM2B, and UMPS. First, we predicted whether these gene knockouts would be toxic for the execution of essential metabolic functions, i.e., whether the in silico gene knockouts compromise the metabolism of normal cell types. As previously describedin silico upon application of the corresponding in silico gene knockout. In all normal cell types, the simulation revealed that knockout of CAD or UMPS ablates the de novo biosynthesis of pyrimidines, while FDFT1 and DHCR24 knockouts impede the production of cholesterol in normal human cell types  using RNAi. These four genes were not part of the siRNA screening library but were predicted by FBA to be essential both in silico and in vitro. In accordance with the in silico predictions of toxicity, we observed cell death when UMPS was knocked out in HK-2 cells, while GCLC, GSS, and RRM2B knockouts caused a minor cell number reduction, above the adopted threshold for cell death . Examination of the flux space in ccRCC revealed that this reaction fuels the production of UDP-glucose, which is needed for the biosynthesis of glycogen. Knockout of in ccRCC . The essGCLC, GSS, and RRM2B, were classified as essential only when constraints on exchange fluxes were implemented. Their essentiality is likely to be due to a loss of redundancy in the ccRCC network when metabolite fluxes are constrained by measured uptake and secretion rates. To explore how the fluxes were distributed before the implementation of the exchange fluxes, we relieved each of these constraints one at the time until biomass production was restored, thereby allowing us to associate gene essentiality with a particular exchange flux. We found that RRM2B is associated with the flux of 3-ureidopropionate, a product of the uracil degradation pathway, which is secreted by all ccRCC cell lines (range: 0.016 to 0.102 fmol cell−1 h−1) . Thus, it is necessary for cells to activate a flux to degrade UDP to sustain the given 3-ureidopropionate secretion rate, and one of these steps is catalysed by RRM2B. According to the Human Protein Atlas, the two other genes associated with this step (namely RRM1 and RRM2) are not expressed in ccRCC, and thus they cannot compensate for this flux if RRM2B is knocked out, making RRM2B essential.The three additional genes, l−1 h−1) , left. TGCLC and GSS, the essentiality is associated with the secretion of glutamate, which occurs at remarkably high rates (approximately 4 to 50 fmol cell−1 h−1) in ccRCC cell lines. The analysis of the ccRCC flux space unveiled that elevated rates of extracellular glutamate accumulation derive from the catabolism of extracellular glutathione (GSH) carried out by different gamma-glutamyl transferases. Indeed, the reconstructed ccRCC metabolic network does not include alternative pathways that support the secretion of glutamate, such as the xC– system. Despite the evidence that the xC– system, an antiporter responsible for cystine uptake via a 1:1 exchange with glutamate, is expressed in the kidneySLC7A11, is reported at the protein level by the Human Protein Atlas; it was therefore not included in the reconstructed network. In the absence of alternative pathways, the only flux distribution returned by FBA that fits glutamate secretion requires the cleavage of extracellular GSH. This is in turn dependent on the secretion of de novo synthesised intracellular GSH, which is catalysed by GSS and GCLC  may be a factor that affects the reliability of this prediction, as recognised in earlier works on FBA predicted gene essentiality58In the case of and GCLC , right. in vitro. We evaluated the efficacy of this method for two cancer types, clear cell renal cell carcinoma (ccRCC) and prostate adenocarcinoma (PC), for a variety of parameters: types of FBA constraints used, complexity of the in silico medium , and the numerical threshold for cell death applied to the in vitro experiments. A summary of the accuracy for all tested scenarios is given in In the last decade, increasing evidence supports the notion that cancer cells reprogram their metabolism and are therefore susceptible to disruption of the metabolic networkin silico serum-containing medium, which allows the flexible uptake of 150 different metabolites (Matthews Correlation Coefficient = 0.235). The accuracy improved with stricter definitions of the threshold for cell death in vitro, whereas it worsened when a more restricted medium metabolite composition, as found in Ham’s medium, was applied in silico. This medium composition is not representative of the actual culture conditions used for the in vitro experiments, but had previously been used in similar studies39Our findings suggest that FBA is sufficiently accurate to expose metabolic liabilities in ccRCC. The highest accuracy was achieved by FBA using a ccRCC-specific metabolic network that was further constrained by exchange fluxes determined experimentally across a panel of seven ccRCC cell lines and using an in silico knockout cannot satisfy certain cancer type-specific metabolic requirements, here represented by the profiles of exchange fluxes in several cancer type-specific cell lines (one such requirement could be lactate secretion in a specified range of rates). The number of profiles available for a cancer type may affect the specificity of certain metabolic requirements , therefore biasing the quality of the in silico predictions when these are enforced as constraints in FBA. Third, we disregarded enzyme complexes because current human genome-scale metabolic models do not report such annotation systematically63in silico single-gene knockout and classified as redundant. Furthermore, genome-scale metabolic models such as those used for this study represent the best models to our knowledge in terms of metabolic reactions occurring in a cell, but model incompleteness is known to affect in silico predictions of essential metabolic genesin silico prediction is also affected by the accuracy of the in vitro experiments. Indeed, metabolic screens using siRNA libraries may produce false negatives due to insufficient silencing and are liable to significant off-target effects that can both positively and negatively affect the viability of transfected cells.In general, poor predictions may be ascribed to different assumptions beyond FBA. First, we considered gene essentialities in metabolism based on the ability to carry flux towards biomass formation. Although this is an undisputable requirement for cancer cell proliferation, there is evidence that survival of cancer cells also depends on other metabolic functions, most notably NADPH production and anti-oxidant synthesis45AGPAT6, GALT, GCLC, GSS, and RRM2B, which are essential to ccRCC but are potentially dispensable in normal cell types. In addition, FBA can also be used to explore the mechanisms that render a gene essential in silico.As part of this evaluation, FBA unveiled the inherent fragility of ccRCC metabolic processes that contribute to biomass growth or support certain metabolic requirements. A number of recent studies have evidenced the centrality of metabolism in ccRCC414665GALT expression. In accordance with the findings of our simulations, there is evidence that UGP2 and GALT homologs provide redundancy for this pathway in yeastGALT-deficient mice can sustain glycogen synthesis through the pathway branch catalysed by the murine homolog of UGP2GALT in ccRCC. The pivotal role of GALT in glycogen biosynthesis may in addition underscore the typical phenotype of ccRCC cells, which are characterised by high levels of glycogen accumulation. Finally, FBA using flux rates as additional constraints allowed us to identify gene essentialities associated with specific exchange fluxes in ccRCC cell lines. The essentiality of GCLC and GSS was linked to the secretion of glutamate, whereas the essentiality of RRM2B, an enzyme in deoxyribonucleotide metabolism, was linked to the secretion of 3-ureidopropionate. GCLC and GSS play a fundamental role in the intracellular detoxification of ROS by catalysing two successive steps in the biosynthesis of glutathioneGCLC and GSS in the in vitro experiments stems from their functions in the control of intracellular ROS levels.One of the mechanisms by which this essentiality arises is loss of gene redundancy. AGPAT6 is the only expressed enzyme isoform that can commit glycerol-3-phosphate into glycerolipid biosynthesis. Thus, glycerolipid synthesis is clearly a sensitive pathway in ccRCC, perhaps exacerbated by the lack of expression of enzymes within alternative routes due to a loss of heterozygosity in the corresponding gene loci, as recently suggestedde novo synthesis of GSH is also associated with glutamate secretion in the absence of other systems that can fulfil this function in ccRCC. Although this may be an artefact due to model incompleteness, we show that GCLC-GSS can sustain a flux distribution in which extracellular GSH is catabolised into cysteinylglycine and glutamate, therefore explaining the observed glutamate secretion in ccRCC cell lines. In a similar fashion, the consistent secretion of 3-ureidopropionate observed in ccRCC cell lines combined with an unmatched uptake rate of its direct precursors implies that RRM2B is active in supporting uridine-derived 3-ureidopropionate. RRM2B exerts its function in deoxyribonucleoside biosynthesis and in DNA damage repair, and in this role it appears to hinder cancer progression727374RRM2B function in ccRCC may be different given the lack of expression of RRM1 and RRM2 for supporting nucleotide biosynthesis. Indeed, this pathway was found to be compromised uniquely in ccRCC compared to four other cancer typesHere, we find that In conclusion, in this study we show the strength and limitations of FBA for the prediction of gene essentiality at a genome scale in cancer metabolism. In addition, we report five metabolic genes selectively essential in a particular cancer type, i.e., ccRCC. Importantly, FBA can be used to identify potential mechanisms by which these gene essentialities arise and thereby provide testable hypotheses. We argue that accounting for metabolic liabilities other than biomass generation and the integration of additional layers of high-throughput data may lead to an even more complete description of the essentiality landscape in cancer metabolism.GCLC, GSS, PNP, RRM2B, SLC7A9, and UMPS, 786-O, A498, CAKI-1, TK10, and UO31 cells were transfected in two independent experiments, triplicates each in a 96-well format with 37.5 nM siRNA SMARTpools (Dharmacon siGENOME) targeting the genes of interest using Dharmafect2 as transfection reagent. For the validation experiment for GCLC, GSS, RRM2B, and UMPS, HK-2 cells were transfected in two independent experiments, triplicates each in a 96-well format with 37.5 nM siRNA SMARTpools (Dharmacon siGENOME) targeting the genes of interest using Dharmafect2 as transfection reagent. In all cases, after 96 h (with a media top up after 24 h), cells were fixed in 80% ethanol over night and subsequently stained with DAPI (Sigma). Cell number was determined using an ACUMEN eX3 laser-scanning fluorescent micro plate cytometer. For the purpose of data normalization, the non-targeting RISC-free transfection was used as negative control, while ubiquitin B (UBB) and polo-like kinase 1 (PLK1) served as positive killing control.786-O, 769-P, A498, CAKI-1, RCC4, TK10, UMRC2, and UO31 clear cell renal cell carcinoma (ccRCC) cell lines were maintained (and transfected) in DMEM supplemented with 4.5 g/l D-Glucose, 0.11 g/l Sodium Pyruvate (Gibco), 4 mM Glutamine , 100 Units/ml Penicillin / 100 ug/ml Streptomycin (Gibco) and 10% Fetal Bovine Serum (Gibco). For the RNAi screen, RCC4, UMRC2, A498, 786-O and 769-P cells were transfected in triplicates in a 96-well format with 37.5 nM siRNA SMARTpools (Dharmacon siGENOME) targeting the genes of interest using Dharmafect2 as transfection reagent. For the validation experiment for UBB) and 12 negative controls (RISC-free) were transfected. In a given cell line c for a given replicate r, the cell number reduction caused by siRNA s was linearly interpolated as in equation (1):In the case of ccRCC, cell death was quantified in terms of reduction of cell number upon siRNA transfection in cells scaled to the effect of the negative and positive controls. For each replicate, 9 positive killing controls . This data is collected in z-score was retrieved from the studyin vitro in PC if the caspase activity z-score upon transfection of the corresponding siRNA for at least 2 of the 3 tested cell lines is above 2.5, as adopted in the original study.Then for each cell line, the mean cell number reduction is computed as the average across replicates. We declare a gene essential in silico single gene-knockout test as the universe and it was performed in R. The 95% highest density interval (HDI) for cell number variation relative to RISC-free control was calculated by Bayesian estimation under the following assumptions: data are sampled from a t-distribution of unknown and to be estimated normality (i.e. degrees of freedom); high uncertainty on the prior distributions; the marginal distribution is well approximated by a Markov chain Monte Carlo sampling with no thinning and chain length equal to 100’000. The estimation was performed using the BEST R-packageThe Fisher’s Exact Test was carried out using the total number of tested siRNA in the library that could be compared to the OGDH to its correct associated gene, ODC1, no other modifications to the models were operated. The lists of metabolites available for uptake or secretion in the serum-containing medium (FBS) or in Ham’s medium are given in g in the model:The ccRCC genome-scale metabolic model  was downloaded at www.metabolicatlas.org. The PC genome-scale metabolic model (iProstateCancer1675) was reconstructed using the same pipeline as for iRenalCancer1410vobj is the flux through the biomass equation, S is the stoichiometric matrix of the model  entry is the stoichiometric coefficient of the metabolite corresponding to row i in the reaction corresponding to column j), vis the vector containing the values of the fluxes through each reaction in the model, and α (resp. β) are the lower (resp. upper) bound for the exchange flux corresponding to each metabolite measured inj as DW cell−1 to accommodate the fact that exchange fluxes were measured in fmol cell−1 h−1 instead of mmol gDW−1 h−1 as normally assumed in genome-scale metabolic modelingwhere http://www.metabolicatlas.com/.The problem was formulated using native functions in the RAVEN Toolboxin silico. Besides this, a gene is deemed essential in silico when there is no solution to (2), i.e. there cannot be found a flux distribution such that the biomass equation carries flux. This is indeed valuable in light of the consideration above: among all the available metabolic states permitted by the availability of serum metabolites, no scenario allows for a flux towards all biomass precursors simultaneously.Importantly, for the purpose of the study, the optimization part is not relevant. Indeed, we are interested on whether a feasible region exists upon the constraint imposed by the gene knockout (7), i.e. whether the fact that the encoded reactions cannot carry flux implies no flux in the biomass equation. However, if also exchange fluxes were implemented to perform FBA (6), we took in account a significant reduction (min. 50%) of the optimum  to classify a gene as essential et al. studyvobj > 0. In the end, all exchange fluxes in (6) that required a supplementary flux  were instead bounded to ±1000. This procedure had been repeated for each cell line specific to a certain cancer type, and for all successive simulations, only the exchange fluxes that were feasible in all cell lines for a given cancer were retained. In ccRCC, 61 and 38 exchange fluxes were coordinately bounded for all seven ccRCC cell lines in FBS and Ham’s medium respectively . In PC, 60 and 57 exchange fluxes were coordinately bounded for all two PC cell lines in FBS and Ham’s medium respectively .It should be noticed that, when implementing cell line specific exchange fluxes, a set of numerical constraints had to be neglected and converted to ±1000. This operation is obligated by the fact that some measured fluxes are not consistent with the network topology. Thus, either the measured compounds are not used by the cellular reaction network or further experimental validation is required. It may also be that the model is not complete and it should be updated in an iterative fashion, a process normally encountered in genome-scale modelsin silico and validated as such in vitro. If no solution were found, the gene knockout is deemed toxic for a certain normal cell type. If more than 50% of the 83 normal cell types show no toxicity in any metabolic task upon knockout of a gene essential in a cancer, than the gene is regarded non toxic to normal cells. Furthermore, if knockout of a gene essential in a cancer shows no toxicity in any metabolic task in the supposed cell type of origin, than the gene is regarded selectively essential to a cancer.The test for toxicity in normal cell types was performed as previously describedin silico, different simulations were carried out according to the constraint that first resulted in an unfeasible solution:AGPAT6, and it was found by constraining the flux of the encoded reaction to zero in the generic human metabolic network from which the ccRCC metabolic network topology is derived. This constraint results in an unfeasible solution using the generic network, suggesting that at least one of the isoenzymes must be expressed to sustain biomass formation. In the second scenario, there are two alternative routes to support a flux towards the biomass equation, each encoded by a single gene, but just one is expressed in the cancer-specific metabolic network (loss of pathway redundancy). This was the case of GALT. To verify this, the reaction encoded by GALT was constrained to zero in the generic human metabolic network, and then a second round of single gene-knockouts was performed using the GALT-KO generic human metabolic network. In the end, the double GALT-UGP2 knockout results in an unfeasible solution in the generic human metabolic network, indicative that UGP2 encodes for a potential alternative pathway to GALT that is not expressed in ccRCC.In the case of genes essential using as a sole constraint to perform FBA the topology of a cancer metabolic network, there are two possible explanations. In the first scenario, a reaction essential to carry flux towards the biomass equation is encoded by a single gene in the cancer-specific metabolic network because all other isoenzymes are not expressed in the cancer (loss of gene redundancy). This was the case of GSS and GCLC, this metabolite is glutamate, while for RRM2B 3-ureidopropionate. Further interpretation of the individual mechanisms was achieved by following the fluxes around each key metabolite in the simulation, either when no knockout was applied or when the knockout was applied neglecting the constraint in the key metabolite exchange flux.In the case of genes essential when using also the exchange fluxes to perform FBA, but non essential when the sole topology was used as a constraint, an unfeasible solution is trivially attributable to the implementation of one (or more) of these additional constraints. Therefore, for each essential gene, all constraints in (6) are released (set the lower and upper bound to –1000 and +1000 respectively) one at the time, until the metabolite whose constraint on the exchange flux caused unfeasibility is spotted. For To elucidate the mechanism through which a gene is selectively essential The fraction of ccRCC samples where a protein involved in any of the mechanisms above is stained with at least a weak signal was retrieved from the Human Protein Atlas v. 11How to cite this article: Gatto, F. et al. Flux balance analysis predicts essential genes in clear cell renal cell carcinoma metabolism. Sci. Rep.5, 10738; doi: 10.1038/srep10738 (2015).


Escherichia coli, achieving highly significant overlap with published cases (hypergeometric p = 4.4e-13). We then validate three novel predicted target-replacer gene pairs in new multicopy suppression experiments. We next go beyond PROPER and develop a network-based approach, GEM-PROPER, that integrates PROPER with genome-scale metabolic modeling to predict promiscuous replacements via alternative metabolic pathways. GEM-PROPER predicts a new indirect replacer (thiG) for an essential enzyme (pdxB) in production of pyridoxal 5’-phosphate (the active form of Vitamin B6), which we validate experimentally via multicopy suppression. We perform a structural analysis of thiG to determine its potential promiscuous active site, which we validate experimentally by inactivating the pertaining residues and showing a loss of replacer activity. Thus, this study is a successful example where a computational investigation leads to a network-based identification of an indirect promiscuous replacement of a key metabolic enzyme, which would have been extremely difficult to identify directly.Recent insights suggest that non-specific and/or promiscuous enzymes are common and active across life. Understanding the role of such enzymes is an important open question in biology. Here we develop a genome-wide method, PROPER, that uses a permissive PSI-BLAST approach to predict promiscuous activities of metabolic genes. Enzyme promiscuity is typically studied experimentally using multicopy suppression, in which over-expression of a promiscuous ‘replacer’ gene rescues lethality caused by inactivation of a ‘target’ gene. We use PROPER to predict multicopy suppression in  E. coli. Notably, we predict and validate several new cases where a ‘replacer’ gene can compensate for the loss of an essential ‘target’ gene through a promiscuous activity. Next, we couple our method with a genome-scale metabolic model, in order to search for ‘replacer’ genes that compensate for essential ‘target’ genes by metabolically bypassing them. We use this network-augmented approach to uncover a novel promiscuous pathway for the production of pyridoxal 5’-phosphate (the active form of Vitamin B6) in E. coli. This study represents an important step in understanding promiscuous functions in bacteria, and is a prime example of a systems-level analysis leading to new biological insight.Many enzymes can perform secondary functions at low affinities or rates, but such ‘promiscuous’ functions have never been predicted on a genome-wide scale. Here, we present the first genome-wide method to predict promiscuous functions of metabolic genes, which we apply to  Enzymes have traditionally been associated with discrete activities . Clear-cexisting promiscuous activities on a genome-wide, network scale. A notable recent effort did probe the global relevance of promiscuous enzyme activities, but the study used ‘as is’ data collected from enzyme databases, which, while having the advantage of being fully experimentally verified, include many non-biologically-relevant instances and exclude many biologically relevant ones , or transport processes . Fatty acid degradation and synthesis processes are known to involve enzymes with many potential specificities depending on only small alterations , 26pdxB thiG supporting Vitamin B6 biosynthesis is based on similarities between a portion of thiG and a portion of pdxS from Staphylococcus haemolyticus, as found in our gene similarity trees. pdxS in Staphylococcus haemolyticus was annotated as such based on high similarity (81% identity over 98% of the genes) with the well-studied pdxS gene in B. subtilis . Notably, our list of indirect replacers for pdxB also included hisH, with the predicted function of pdxT. Thus, hisH is a strong candidate for functionally complimenting the potential pdxS function of thiG. However, pdxS is also present in the genomes of certain organisms in the absence of pdxT, and it has been hypothesized that it might operate in these organism as an ammonium-dependent synthase of P5P, thus bypassing the need for the glutamine amidotransferase subunit pdxT , and revealed a potential overlap of ThiG residues with the PdxS active site: Lys-95, Asn-204, and Glu-97 from the E. coli ThiG homology-model lie within 1.4, 2.2, and 4.9 angstroms respectively from the catalytic residues Lys-81, Asp-24, and Asp-102 in PdxS . The third residue of the proposed active site, Asn-204, was not altered since, as noted, this residue comprises part of the primary ThiG dyad active site. We thus created a mutated form of thiG (thiGmut) with the proposed secondary active site disturbed, but the site for the primary activity of thiG unaffected.To validate the putative secondary triad active site of ThiG , we tested whether inactivation of the predicted active site would eliminate the ability of ThiG to replace PdxB thiGmut overexpression on the growth of ΔpdxB cells in minimal media, we transformed ΔpdxB cells with plasmids encoding IPTG-inducible copies of thiGmut (ΔpdxB/thiGmut), thiG (ΔpdxB/thiG), pdxB (ΔpdxB/pdxB rescue plasmid positive control), as well as the empty vector (ΔpdxB/empty negative control). To determine the optimal M9 glucose media conditions for growth comparison, we performed a checkerboard dilution assay in deep-well microplates in which we individually assessed the growth of each strain across a matrix of varied IPTG and ammonium nitrate (NH4Cl) concentrations to identify synergistic combinations of inducer and nitrogen source, respectively. The nitrogen source (NH4Cl) was varied because we observed that vitamin B6 is used heavily as a cofactor in enzymes that participate in amino acid metabolism  for all strains grown at the experimentally observed optimum NH4Cl concentration (~3%), across all IPTG concentrations, revealed highly significant differences between growth of the ΔpdxB/pdxB and ΔpdxB/thiG group versus the ΔpdxB/thiGmut and ΔpdxB/empty group after 96 hours (p< = 4.7e-3), but no significant differences within these groups. Importantly, these findings were consistent with subsequent batch culture growth experiments performed using the optimized concentrations of 10 μM IPTG and ~3% NH4Cl in M9 glucose , was found by coupling our promiscuity predictor with a GEM. Finally, we predict and then experimentally validate the promiscuous active site of thiG for this replacing activity, revealing a striking new promiscuous route for the production of an essential nutrient, p5p, in E. coli.Identifying promiscuous gene functions is a fundamental task in biology. Promiscuous functions have been causally associated with the evolution of new gene functions , 31, andWhile sequence similarity-based methods  are used ubiquitously to determine primary gene functions, their ability to call promiscuous functions is unclear. Our method gives a first estimate, as we were able to experimentally validate around 20% of direct target-replacer pairs we could test in the lab (This is 100x higher than expected if guessing target-replacer pairs randomly). It is likely that the number of target-replacer pairs we validated is an underestimate of true promiscuity, as some true replacers might not show during multicopy suppression due to incorrect expression levels , insufficient effects of target knockout, or other confounding factors. Notably, many of our predictions might be correct even though they cannot be directly validated through multicopy suppression . Our comparison to the work of  emphasizE. coli are available , we choE. coli. Without such a systems approach, it would have been extremely difficult to identify thiG as a candidate replacer for pdxB. Thus, this study serves as a successful example where systems biology can provide a roadmap for biological investigation, identifying the most promising targets to then follow up on with more costly and time-consuming experiments.In all, this work constitutes the first ever genome-wide prediction of metabolic gene multicopy suppression, and the first integration of such predictions with a GEM to achieve network-reliant indirect predictions. We begin with an unsupervised, large-scale method to predict enzyme promiscuity, and finally dial in on and then experimentally verifying a key prediction of biological significance in E. coli; (2) using these trees to build a matrix of promiscuous gene functions; and (3) applying this matrix to determine potential promiscuous gene replacers for target genes of interest. In GEM-PROPER, step (3) is replaced by a GEM-based approach, in which we search for promiscuous functions (from step 2) that can rescue in silico growth of a GEM model after knockout of the target gene. Here, we describe these steps in detail:PROPER proceeds in three steps, as outlined in To identify as many promiscuous gene functions as possible, we performed an unsupervised iterative PSI-BLAST based search for distant sequence relationships between genes in E. coli and all other genes in the SEED database. Our method involved five steps: (1) align the current query sequences; (2) cluster the aligned sequences to reduce sampling bias in sequencing; (3) trim aligned representatives to eliminate non-conserved ends; (4) use trimmed alignments in a PSI-BLAST search against the non-redundant protein database in SEED; and finally, (5) keep PSI-BLAST hits that match certain criteria, as outlined below. These hits would be kept for the next round of PSI-BLAST, and the process would continue for three rounds with increasingly more relaxed thresholds for keeping PSI-BLAST hits.The intuition behind this approach was to use iterative trimming to build a compact protein profile that is effective at recruiting distant homologs. These profiles differ from individual protein domains such as some CDDs in that they capture the conserved arrangement of multiple domains in related protein sequences. The parameters used in this protocol were manually tuned to facilitate inspection of related protein functions in the same tree for expert annotators at SEED. The detailed protocol and parameters are provided in the supplementary materials . For theuncovered region of the query sequence < = 100the query sequence is at least 60% coveredsequence percent identity > = 0.15sequence percent positive match > = 0.30 [This is the percentage of aligned bases with positive scores from the substitution scoring matrix indicating conserved changes ].E. coli variants of the protein. We use MAFFT [As PSI-blast itself can do iterative search, the main difference in our approach was trimming and clustering. By trimming we eliminated non-conserved ends, so the profile is more compact and more effective at recruiting distant homologs during each search. The clustering step keeps only the representative sequences in the profile, thus alleviating some of the sampling bias, i.e., so that the profile is not dominated by se MAFFT  for aligse MAFFT  for treeE. coli that links to other genes with any sequence similarity, which were then candidates for assigning potential (predicted) promiscuous functions to the root gene.This whole procedure provided a tree for each gene in Genes in RAST are annotated with functions, which then (in the case of metabolic genes) link to metabolic reactions. After a few attempts to set distance thresholds in the trees for assigning functions, we found that including all function in the tree as a potential promiscuous function gave optimal results. Therefore, all functions existing in the tree of a root E. coli gene are considered potential promiscuous functions, as are their metabolic reactions. In cases where a gene is promiscuously associated with only one subunit of an enzyme complex, we predicted that entire function is associated with the root gene. We entered these gene-function promiscuous pairings into a matrix for further analysis.To search for direct target-replacer pairs, we identified cases in our matrix in which any of a ‘replacer’ gene’s promiscuously assigned functions is the same as the primary annotated function of a ‘target’ gene of interest.To search for indirect target-replacer pairs, we identified cases in our matrix in which any of a ‘replacer’ gene’s promiscuously assigned functions can metabolically bypass the primary annotated function of a ‘target’ gene of interest. This analysis could only be done for target genes that are conditionally essential in silico, i.e., whose knockout causes in silico death on M9 medium but not on rich medium.Escherichia coli K12 taxon ID 83333.1 as downloaded from SEED [in silico, and the subset of Patrick targets that were also conditionally essential in silico were kept for further analysis. All essentiality tests were done using Flux Balance Analysis testing for a nominal production of biomass [in silico growth was rescued. Cases in which the indirect replacer gene  rescued in silico growth were considered predictions of indirect replacement.The GEM used was a genome-scale metabolic model for rom SEED . Target  biomass . MetabolMulticopy suppression is an established assay that has been described elsewhere  and transformed with ASKA plasmids over-expressing the corresponding predicted replacer gene.llection , which cllection , which cWhen we were developing our assay, we found that knockout colonies usually grew after some amount of time on M9 medium regardless of whether the replacer gene had been added to the plasmid, despite the fact that each of the target strains we tested was previously reported to be non-viable on M9 medium. The previous study by Patrick  had not KanR). Thus we verified correct location of the knockout in each target strain by amplifying and sequencing the area directly flanking the kanamycin insertion, using a kanamycin universal primer and a strain-specific reverse primer located downstream of the knocked out gene. Since the orientation of the kanamycin insertion depends on the orientation of the original knocked out gene, the KanR primer 5’-ATATTGCTGAAGAGCTTGG was used when the original gene had been forward coded and the KanR primer 5’-AATGAACTCCAGGACGAG was used if the original gene had been reverse coded. Correct sequence of the replacer gene was verified by amplifying and sequencing the ASKA plasmid insert .In the KEIO collection each knocked out gene is replaced by the kanamycin resistance gene  containing IPTG. All TR pairs were plated on both M9 with 50μM and 125μM IPTG; TR pairs of particular interest  were plated on 250μM as well. In each TR plating experiment, the empty and frvX negative controls were plated alongside the TR pairs. Plates were wrapped in nylon to avoid dehydration, incubated at 37 and monitored during the next three weeks. Nearly all negative control plates showed some growth phenotype, ranging from very strong  to very weak  pair were grown overnight in LB+CAP, washed and serially diluted in saline (0.9% NaCl). Aliquots (100 ul) of 10ΔglyA, ΔptsI and ΔpabB) was also monitored in liquid culture. Cultures in LB+CAP were washed once in saline and re-suspended at a dilution of 1:100 into M9-glucose-kanamycin-chloramphenicol minimal media supplemented with IPTG (50 μM). Growth measurements were performed in a 96-well plate incubated for 19–24 h at 37°C in a temperature-controlled plate reader with continuous shaking , and OD595 was monitored every 15 min. Each TR pair was loaded into 2 duplicate wells. Growth of the negative controls (empty and frvX plasmids) for each target strain was likewise monitored during every run.Growth of TR pairs that showed exceptionally high growth on the negative control plates  and 25 μg/mL chloramphenicol (ASKA plasmids) selection. Cells were washed in 1x PBS and diluted 1:100 into M9-glucose-kanamycin-chloramphenicol for plate seeding; M9 was prepared without a nitrogen source. A checkerboard matrix was generated in 2mL deep-well, 96-well assay plates by serial dilution of NH4Cl (22.5% w/v maximum concentration) across plate columns and IPTG (500 μM maximum concentration) across plate rows. Wells were uniformly inoculated with cells, and each well contained a final volume of 1.2 mL. Plates were sealed with gas-permeable membranes and grown in a light-protected, microplate incubator shaker at 37°C and 700 RPM; 700 RPM was determined to be equivalent to 300 RPM in a standard incubator shaker. Samples for OD600 measurements were taken at designated timepoints using a SpectraMax M5 microplate multimode plate reader (Molecular Devices), and the gas permeable membrane resealed after each timepoint. 100 μL samples were taken for OD600 measurements to minimize the total volume loss.Overnight cultures of each strain were grown in LB with 30 μg/mL kanamycin (4Cl (w/v) and 10 μM IPTG, in 250 Erlenmeyer flasks. Cultures were grown at 37°C and 300 RPM in an incubator shaker, with samples for OD600 measurements taken at designated timepoints.For batch culture experiments, cells were prepared from overnight cultures as described above. Cells were diluted 1:100 in 30 mL of M9-glucose-kanamycin-chloramphenicol, containing ~3% NHB. bacillus) in complex with pdxT, was downloaded from the pdb database, and the residues of the pdxS active site were identified from the publication  [pdxS units from the multimeric structure were overlaid and were found to be coincident  . Multiplsy.org/; ) based o ID 2htm ). The stng pyMol .hisA/∆hisH and cysM/∆ilvA. Conversely, growth of purE/∆purK, one of the target-replacer pairs predicted by both Patrick and us, was almost entirely inhibited when IPTG concentration was increased to 125uM. These results illustrate that over-expression can also have deleterious effects [frvX caused a decrease of the background seen in the empty plasmid control (see Low (50μM) IPTG concentration was sufficient to induce all of the replacers. Interestingly, increasing the IPTG concentration affected growth sometimes positively and sometimes negatively, depending on the specific strain. Increasing IPTG concentration up to 250μM caused increases in colony size and number, and decreases in incubation times, for  effects . The opttrol see .S1 Text(DOCX)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.S2 FigAll target-replacer pairs predicted by our method were assessed for how often a metabolic target paired with a metabolic replacer, with a non-metabolic replacer, a non-metabolic target with a metabolic replacer, etc. We found that (A) Replacer genes with metabolic primary functions take more metabolic targets than do replacer genes with non-metabolic primary functions; (B) Replacer genes with non-metabolic primary functions take more non-metabolic targets than do replacer genes with metabolic primary functions; and (C) The number of targets replaced by replacer genes with non-metabolic vs. metabolic primary functions is the same.(TIF)Click here for additional data file.S3 FigHistograms are shown of: (A) number of genes represented in each tree; (B) number of unique organisms represented in each tree; (C) number of distinct functions represented in each tree; and (D) number of E. coli metabolic functions present in each tree.(TIF)Click here for additional data file.S4 Fig(TIF)Click here for additional data file.S5 Fig(TIF)Click here for additional data file.S6 Fig(TIF)Click here for additional data file.S7 Fig(A) E. coli thiG is aligned with pdxS, the gene whose function it putatively performs promiscuously. Key residues in both genes are marked, as per the key at the bottom. Two alignments are shown as they came up in BLASTP sequence alignment. (B) The active residues of thiG for its primary function are shown, along with putative active residues for the pdxS function.(TIF)Click here for additional data file.S8 FigMultiple alignments are shown.(TIF)Click here for additional data file.S9 FigThe residues in thiG that we predict can perform the pdxS function show a high degree of conservation, as shown in the plot. This was generated from the output of ConSurf, set with default settings except for a maximum cutoff of 70% homology in the sequences to be aligned (higher cutoffs led to less resolution in distinguishing how conserved the key residues are versus their neighbors).(TIF)Click here for additional data file.S10 Fig(DOCX)Click here for additional data file.S11 FigResults analogous to those shown in Fig 5 of the main text are shown, but at the 48 hour timepoint (instead of 96 hours as shown in the main text). (A) Ranksum test across all IPTG concentrations in the microwell plate experiment . (B) Results of a separate batch culture experiment, with 5–8 replicates per group, which show the same trend of the microwell plates from subfigure A. P-values are from t-tests across replicates of each strain grown in identical condition . #OD600 values in (A) were measured using 100uL of culture, where 300uL of culture would be the equivalent of a normal 1mL cuvette.(DOCX)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.


To overcome these limitations, fermentation engineering should merge with systems metabolic engineering. Modern fermentation engineers need to adopt new metabolic flux analysis tools that integrate kinetics, hydrodynamics, and 13C-proteomics, to reveal the dynamic physiologies of the microbial host under large bioreactor conditions. Based on metabolic analyses, fermentation engineers may employ rational pathway modifications, synthetic biology circuits, and bioreactor control algorithms to optimize large-scale biofuel production.Metabolic engineering has developed microbial cell factories that can convert renewable carbon sources into biofuels. Current molecular biology tools can efficiently alter enzyme levels to redirect carbon fluxes toward biofuel production, but low product yield and titer in large bioreactors prevent the fulfillment of cheap biofuels. There are three major roadblocks preventing economical biofuel production. First, carbon fluxes from the substrate dissipate into a complex metabolic network. Besides the desired product, microbial hosts direct carbon flux to synthesize biomass, overflow metabolites, and heterologous enzymes. Second, microbial hosts need to oxidize a large portion of the substrate to generate both ATP and NAD(P)H to power biofuel synthesis. High cell maintenance, triggered by the metabolic burdens from genetic modifications, can significantly affect the ATP supply. Thereby, fermentation of advanced biofuels (such as biodiesel and hydrocarbons) often requires aerobic respiration to resolve the ATP shortage. Third, mass transfer limitations in large bioreactors create heterogeneous growth conditions and micro-environmental fluctuations (such as suboptimal O The desired biosynthetic pathway for advanced biofuels often requires multiple enzymatic steps. Current molecular biology techniques can effectively alter enzyme levels to increase the flux toward biofuel synthesis. Common strategies include choice of plasmids and its copy numbers, promoter engineering, codon optimization, synthetic scaffolds, directed evolution/modification of key enzymes, improvement of ribosome binding sites, and knockout/knockdown of competitive pathways   , the poor mixing/aeration can cause temperature and pH fluctuations, O2 limitations, substrate/product inhibitions, and accumulations of wastes (such as acetate)  are used for fermentation, gas-liquid mass transfer resistances pose another serious challenge as the gaseous substrates must diffuse across the gas-liquid interface . This has been reported to cause increased production of waste products, such as formate, lactate, and succinate  is used to directly measure enzymatic reaction rates. Compared to other omics studies, 13C-MFA can provide insights into cell's physiology during large-scale fermentations. 13C-MFA uses metabolic reaction stoichiometry and carbon-labeling experiments to precisely estimate metabolite turnover rates   during E. coli fermentation. Recently, proteomic analysis of 13C-peptide labeling has also been developed to assist metabolic flux analysis of heterogeneous microbial systems . Sauer group proposed a “reporter protein”-based 13C-MFA may integrate with microbial kinetics to reveal the changes of cell metabolism throughout its cultivation process. For example, Sauer group have utilized such a dynamic 13C-MFA approach in a fed-batch fermentation to monitor the dynamic changes in intracellular fluxes during the different growth stages. Their results revealed that a riboflavin-producing bacterium's physiology shifted from an overflow metabolism to an exclusively maintenance metabolism at the late fermentation stage  are more promising biofuels than biodiesel/hydrocarbons, as alcohol synthesis pathways are less dependent on the ATP supply and alcohol fermentation can be conducted under anaerobic conditions. Production of biodiesel and hydrocarbon require large amounts of ATP, and their processes are usually restricted to aerobic conditions and their productivities are highly sensitive to the P/O ratio  is naturally tolerant to alcohols and acetate, and it is a robust workhorse for industrial alcohol fermentations. However, the energy metabolism of yeast has a lower net ATP production as additional ATP is consumed during the transport of equivalents of NADH from the cytoplasm into the mitochondria . E. coli has already been engineered to produce higher alcohols, biodiesels and other hydrocarbons that demand large amounts of energy molecules. Another promising chassis is microalgae . Although most studies emphasize their photoautotrophic features, photomixotrophic fermentation has two great advantages for industrial use. (1) Photo-fermentations of organic substrates (sugars) can reach high carbon yields of both biofuel and biomass due to mixotrophic CO2 fixation and light energy harvesting to generate ATP and NADPH .Second, the loss of carbon yield due to ATP/NAD(P)H limitations is often severe in engineered microbial hosts. Therefore, modern fermentation engineering should focus on reducing the metabolic burden and enhancing the prosperity of the energy metabolism. There are several effective strategies to improve NAD(P)H and ATP availability. (1) Adding nutrient sources (such as yeast extract) into cell culture; (2) overexpressing NADH dehydrogenase to enhance the respiration efficiency , and construct sensor-regulator systems to improve cell productivity in industrial bioreactors. Fermentation engineers should have a comprehensive understanding of both the macroscopic  and microscopic (intracellular fluxes) parameters, and thus fill the gaps between laboratory studies and industrial applications. “Scale-down” experiments  with metabolic flux analysis can be routinely used to diagnose the engineered metabolism, verify synthetic biology circuits, and design optimal fermentation strategies Figure . Most imThe 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.


Constraint-based reconstruction and analysis (COBRA) is used for modeling genome-scale metabolic networks (MNs). In a COBRA model, extreme pathways (ExPas) are the edges of its conical solution space, which is formed by all viable steady-state flux distributions. ExPa analysis has been successfully applied to MNs to reveal their phenotypic capabilities and properties. Recently, the COBRA framework has been extended to transcriptional regulatory networks (TRNs) and transcriptional and translational networks (TTNs), so efforts are needed to determine whether ExPa analysis is also effective on these two types of networks.In this paper, the ExPas resulting from the COBRA models of E.coli's MN, TRN and TTN were horizontally compared from 5 aspects: (1) Total number and the ratio of their amount to reaction amount; (2) Length distribution; (3) Reaction participation; (4) Correlated reaction sets (CoSets); (5) interconnectivity degree. Significant discrepancies in above properties were observed during the comparison, which reveals the biological natures of different biological processes. Besides, by demonstrating the application of ExPa analysis on E.coli, we provide a practical guidance of an improved approach to compute ExPas on COBRA models of TRNs.ExPas of E.coli's MN, TRN and TTN have different properties, which are strongly connected with various biological natures of biochemical networks, such as topological structure, specificity and redundancy. Our study shows that ExPas are biologically meaningful on the newborn models and suggests the effectiveness of ExPa analysis on them. Many large-scale biological networks, including metabolic networks (MNs) , signaliEscherichia coli [Sacchoromryces cerevisiae [Helicobacter pylori [Haemophilus influenzae [Methylobacterium extroguens [All the possible phenotypes, i.e. the flux distributions of feasible steady states, of a constraint-based biochemical model form a high-dimensional cone. Network-based pathways such as Extreme Pathways (ExPas)  are defihia coli -19, Saccrevisiae ,21, Helir pylori ,23, Haemfluenzae ,24 and Mtroguens . Besidestroguens  and the E.coli transcriptional regulatory network (TRN) [E.coli transcriptional and translational network (TTN) [E.coli TRN, MN and TTN. In the comparison, differences between biological processes were observed from multiple perspectives, including network structure, reaction participation, specificity and redundancy. The results indicate that ExPa analysis can be extended to biochemical systems of TRN and TTN, which helps researchers to further understand the corresponding biological systems. Besides an improved method was introduced to simplify the calculation and interpretation of ExPas on TRN models [Recently, there emerged two COBRA models of biochemical systems with different types: rk (TRN)  and E.cork (TTN) . What shN models , which cE.coli MN and TTN is computationally intractable. Fortunately ExPa calculation will be much more manageable if a MN or a TTN is divided into smaller sub-networks. Therefore, we chose the sub-networks with relatively complete and independent functions as the representatives of their belonging biologic systems. For the E.coli MN, two sub-networks were chosen: (1) Amino acid, Carbohydrate and Lipid metabolism (sACL) and (2) Membrane and Murein metabolism (sMM). For E.coli TTN, the two sub-networks were: (1) transcription (sTC) and (2) translation (sTL).Firstly, we calculated extreme pathways of the three biological networks mentioned above. Since the number of ExPas grows exponentially with a networks' complexity , the enuThen ExPa analysis was performed on each network/subnetwork and the properties from different aspects were obtained, including the total number of ExPas, the number-based ratio of ExPa to reaction, ExPa length distribution, reaction participation distribution, correlated reaction sets (CoSets), and the inter-connectivity of ExPas. Finally, a horizontal comparison on the properties was made among the five networks/subnetworks.E.coli TRN model which were stumbled through ExPa analysis are also reported in this section. This findings illustrate that ExPa analysis is capable of directing model refinement.Moreover, some incompleteness and incorrectness in the E.coli TRN model was published by Gianchandani et al. in 2009 [Materials and Methods). The final TRN model contains 1009 components, 1106 internal regulatory reactions, and 1009 exchange reactions each corresponding to a component. All the extracellular metabolites were considered as inputs and all protein products were considered as outputs. There were 1599 ExPas, of which 9 were biologically infeasible because they employed conflicting input fluxes, and thus they were excluded from the ExPa set used in analysis.The  in 2009 . It cont 2009 [R*. The TRNE.coli TRN, 16 reactions do not participate in any ExPa; namely they are never used to form a transcriptional state of the network. These unused reactions were categorized into two types as listed in Table In NOT_BirA (absence of protein BirA). However, no regulatory rule corresponds to the presence or absence of BirA, and therefore, the initial steps are unknown. As a result, the internal reactions using NOT_BirA  and the corresponding exchange reactions  will never be initiated. Furthermore, proteins BirA and the gene products of b0774, b0775, b0776 and b0778 do not participate in any other reaction except those in Table E.coli TRN model and necessitate further refinement.Reactions in Table b1814 can be divided by simple logical transformation into 6 rules, of which 3 contradict with each other  are listed in Table The length of an ExPa equals to the number of reactions that participate in it . Figure E.coli TRN represent transcriptional regulatory rules rather than real biochemical reactions as in MN and TTN, and thus the ExPa length in TRN depicts the number of regulatory rules used for expressing certain genes. A regulatory rule describes how environmental stimuli affect transcriptional factors, which in turn affect downstream target genes. Therefore, the ExPa in TRN is reasonably shorter as the biological network has a relatively flat hierarchical structure [The length distributions of ExPas corresponding to those biological processes are very diverse. The longest ExPas consists 51, 82 32 and 109 reactions in sACL, sMM, sTC and STL, respectively, which is much longer than that in TRN (21). Reactions in tructure . The resThe reaction participation rate (RPR) is defined as the percentage of ExPas in which a given reaction participates . Figure Here the top 10 internal reactions with the highest RPRs of each process are sorted in a descending order Table . SeveralCRP_noGLC_1 and Crp_1 relate to the regulation rules of the transcription factor (TCF) C-reactive protein (CRP). Other high rank reactions Fis_1, Lrp_1, Fnr_1, and NOT_ArcA_1 relate to the regulation rules of the TCFs Fis, Lrp, Fnr and ArcA, respectively. In E.coli, the above TCFs belong to the seven global regulators that control most of the regulated genes [NOT_Cra_1 is relevant to the regulation rules of the TCF Cra, a pleiotropic regulatory protein that controls carbon and energy fluxes in enteric bacteria [NOT_PdhR_1 concerns the regulation rules of PdhR, a TCF that controls the respiratory electron transport system in E.coli. Its regulation target, the pyruvate dehydrogenase (PDH) multienzyme complex, plays a key role in the metabolic interconnection between glycolysis and the citric acid cycle [In TRN, the two most active reactions ed genes . The reabacteria ,30. The id cycle .ASPTA. It transfers oxoglutarate and aspartate to corresponding ketoacid, which are indispensable in glyoxylate cycle, an anabolic metabolic pathway occurring in E. coli [ASAD which is the second step in the biosynthesis of amino acids in prokaryotes, fungi, and some higher plants. ASAD forms an early branch point in the metabolic pathway producing lysine, methionine, leucine and isoleucine from aspartate as well as diaminopimelate which plays an essential role in bacterial cell wall formation [asd (encoding ASAD) is lethal to the organism as demonstrated by experiments with Legionella pneumophila, Salmonella typhimurium, and Streptococcus mutans, which indicates that ASAD may also be an essential reaction in the metabolism of E.coli [ASPK, which is the commitment step in the pathway to the synthesis of lysine, methionine, threonine and isoleucine.In sACL, the most active reaction is  E. coli . The secormation . Deletiof E.coli . AnotherACCOAC is most active. It is a rate-determining step in the fatty acid synthetic pathway and may play a pivotal role in regulating fatty acid oxidation [MCOATA transfers Malonyl CoA to acyl-carrier proteins (ACPs). The product Malonyl ACP provides malonyl groups for biosynthesis of fatty acid and polyketide. On the other hand, Malonyl CoA, the substrate of MCOATA, is a highly-regulated molecule in fatty acid synthesis as it inhibits the rate-limiting step in beta-oxidation of fatty acids [MCOATA affects the consistency of Malonyl CoA and guarantees the biosynthesis of fatty acid.In sMM, the reaction xidation . The secty acids . Flux chIn sTC, all the top reactions relate to the formation of the transcription elongation complex, an extremely complicated and highly regulated molecular machine that can sense signals coming from numerous regulatory protein factors, as well as those encoded in the DNA sequence. They are the basis of transcription elongation, because transcription can run smoothly and continuously only depending on their precise work.IF2_RECHARG, Rib_30_ini_FORM and Rib_70_DISS are used by all ExPas. IF2_RECHARG recharges the initiation factor 2 (IF2) with GTP and Rib_30_ini_FORM produces 30S translation initiation complex which consists of 30S subunit, IF1, IF2-GTP and IF3. In bacteria, the correct mRNA starting site and the reading frame are selected when, with the help of IF1, IF2 and IF3, the initiation codon is decoded in the peptidyl site of the 30S ribosomal subunit by the anticodon fMet-tRNAfMet. Furthermore, Rib_30_ini_FORM is also proved to be the intermediate step in the formation of 70S initiation complex (70SIC) which regulates translation initiation, the rate-limiting step in protein synthesis [Rib_70_DISS dissociates 70S ribosomes to 30S ribosomal subunit/IF1/IF3 complex (rib_30_IF1_IF3) and 50S ribosomal subunit (rib_50_inact). This is an essential step before a ribosome can participate in a new round of translation since the initiation complex for protein synthesis involves a 30S subunit. The dissociation of 70S ribosomes contributes to the efficiency and sustainability of protein synthesis [In sTL, the reactions ynthesis . The othynthesis .Reportedly, RPRs help to find important reactions in MN . Our resA correlated reaction set (CoSet) comprises reactions that always participate in the same ExPa set in a given network ; namely A CoSet can be transformed to a graph by treating each reaction as a node and adding an edge between two reactions that involve a common substance. In a certain CoSet, some member reactions are topologically connected while others are not. The correlationship of the second type of reactions often indicates a transcriptional coregulation by the corresponding genes  while thCoSets were calculated for each biological network/sub-network about which several features, including the adjacent ratio, were stretched and shown in Table 2O, ATP and NADP commonly seen in various biochemical reactions. In order to further elucidate the difference in crosstalk between ExPa pairs, all the exchange reactions in the four sub-networks were sorted in a descending order depending on RPR and the top 20% ExPa pairs were neglected in the subsequent crosstalk analysis.Crosstalk analysis was first raised to illustrate the relationship between multiple inputs or outputs of a signaling pathway . The whoE.coli TTN and TRN are more deterministic than those in MN. Reportedly, a large number of genes are regulated by only a few independent regulatory rules in E.coli TRN [E.coli TTN have only one coding gene in the genome [As shown in Figure coli TRN , and thee genome . These fE.coli TRN can be attributed to the fact that the transcription of some genes can be stimulated by different transcriptional factors. For example, two redundant ExPas shown in Figure b2243 in the same environment, but they employ the regulatory rules of 'CRP_noRIB AND Fnr AND NOT(GlpR)' and 'CRP_noRIB AND ArcA AND NOT(GlpR)', respectively. From Figure E.coli MN is more flexible than TTN and TRN.Except sTC, the other networks/sub-networks all have ExPa pairs with identical inputs and identical outputs. These ExPas are redundant pathways which fulfill completely identical function through systemically independent routes. ExPa redundancy was demonstrated in genome-scale MNs ,24, as wE.coli TRN and TTN. A horizontal comparison was performed for the five networks/sub-networks: TRN, sACL, sMM, sTC, sTL from five aspects: (1) Total number of ExPas and the P/R ratios; (2) ExPa length distribution and L/R ratios; (3) Reaction participation rates; (4) Correlated reaction sets and adjacent ratios; (5) Inter-connectivity of ExPas.ExPa analysis were applied to two new models, the Reactions in TTN represent actual biochemical reactions like those in MN, and thus, ExPas in TTN characterize the steady-states of the corresponding biological systems. In contrast, columns in TRN represent the transcriptional regulatory rules and coefficents only reflect the qualitative information describing the presence or absence of the corresponding components rather than the quantitative information describing reaction stoichiometries as in TTN and MN. Therefore, an ExPa in TRN characterizes a specific transcriptional regulatory state, namely which transcriptional regulatory rules are activated and which genes are expressed in a specific environmental state.ExPa analysis emphasizes the functional and systemic properties of biologcial process as ExPas are systemically independent functional units. The total number of ExPas and the P/R ratios characterize the flexibility of the networks/sub-networks. ExPa length corresponds to the reaction steps needed to form a steady state, therefore showing a close relation to network complexity. Crosstalk enables the analysis of pathway redundancy and network determinacy. Comparisons from these aspects indicate that MN is more flexible but less deterministic than TRN and TTN. Environmental cues affect transcriptional regulation, which controls the following transcription and translation processes. Then the resulting gene products (enzymes) enter the metabolic system to catalyze the corresponding reactions. It is necessary for a cell to respond accurately to the environment and produce the required enzymes. MN is more robust to environmental changes, which reflects the struggle of a cell to achieve an alternative steady-state to provide substance support for TRN and TTN and maintain life.The distributions of reaction participation in the five networks/sub-networks are similar except that there are more reactions participating in more than 10% ExPas in sACL and sMM. Only a small percent of the reactions participate in a large number of ExPas, which indicates the phenotypic potentials of TRN, TTN and MN are affected greatly by a small number of important reactions. Evaluations on the representatives show that reactions with high participation rates often play an important role in certain biological processes. These reactions are the relatively weak part of the networks because a large number of ExPas will be destroyed when these reactions become invalid, which may cause the loss of various functions. These reactions may be used as drug targets and further direct the design of new drugs.CoSets were identified via the calculation of reaction participation. Besides the expected topological connections, the topologically unconnected reactions in a CoSet may indicate the information of transcriptional coregulation in MN. However, most Cosets of TRN and TTN are trivial, and thus have few chances to be a clue giving novel information like in MN.E.coli TRN model which we studied in the paper has 776 components whose availability  constitute the environmental condition, including environmental stimuli, transcription factors or proteins. It is impossible to enumerate all the possible conditions due to "combination explosion" without mentioning the calculation of the ExPas under each condition. However, using the approach we proposed, it took only about 45 seconds to computing the whole ExPa set on a PC with four 3.2-GHz Intel(R) XEON processors and 16GB RAM . We believe that this approach could be helpful for readers who are also interested in the ExPas of TRNs.Last but not least, an improved approach was introduced to calculate the ExPas on TRN models. Compared to the existing method, the biggest advantage of ours is the high efficiency in calculating all the extreme pathways of a TRN, especially for the one which may work under huge amount of environmental conditions. For example, the This study presents the first horizontal comparison among the E.coli TRN, MN and TTN through ExPa analysis. The results show that ExPa also has biological meanings in TRN and TTN. Different properties of ExPas reflect the biological nature of each biological process. Along with the the increase of reconstructed models on TRNs and TTNs as well as the development of new methods, ExPa analysis may reveal more biological properties and get larger space of application in the medical and biochemical fields.The COBRA framework stoichiometrically represents a biochemical network as a matrix where e system .Given the reversibility of reactions, an internal reversible reaction can be divided into a forward and a backward sub-reactions, each taking a non-negative flux. The model's solution space is now a convex polyhedral cone in high-dimensional space ,40, whic,41. All For a given network, the ExPa set has the following properties: (1) It is unique; (2) Each ExPa uses fewest reactions to form a function unit; (3) It is systemically independent which means an ExPa cannot be represented by a nonnegative linear combination of other ExPas ,43.expa' [E.coli MN and TTN models were divided into small sub-networks using the method proposed in [ExPas were calculated using an open source tool 'expa' . The E.cposed in .A TRN is composed of a set of transcriptional regulatory rules which describe cells' transcriptional responses to environmental signals. A regulatory network matrix of a TRN . It was  protein ,45. DiffFor example, given a toy TRN with three regulatory rules:where A, B, C and D are four metabolites enacting as signalling stimuli.The corresponding converses are:The matrix In order to calculate all the ExPas of the TRN, all the environmental states, namely all possible tal cues . Therefon environmental inputs expa' [The gist of the method is to improve Gianchandani's method by employing two columns instead of one to delineate the presence and absence of a unique envionment cue respectively, by which a new environment matrix l 'expa' .Notably, some infeasible steady states employing contradictory inputs may be involved in the right null space of Figures Algorithm 1.Given Data: // // // // Result: For to do End forFor to doIf do            Else if do    If do                    Else if                     End if        End if    End forAlgorithm 1: Procedure of normalizing In a normalized ExPa Here we prove that Statement 1: each ExPa in Proof: given Algorithm 2):Data: // // // // Result: // For to do End forFor to doIf do            Else if             End if    End forAlgorithm 2: Procedure of transforming For roven in ,  and G′Statement 2: each feasible ExPa in Proof: Since any environmental cue is impossible to be both present and absent in a specific environment, Algorithm 2, a legal From statements (1) and (2), we conclude that ExPas fall into three classes, in which class III stands for internal reaction cycles with no exchange flux . Class ICOBRA: Constraint-based Reconstruction and Analysis; MN: Metabolic Network: ExPa: Extreme Pathway; TRN: Transcriptinal Regulatory Network; TTN: Transcriptional and Translational Network; sACL: The subnetwork of Amino acid, arbohydrate and Lipid metabolism; sMM: The subnetowrk of Membrane and Murein metabolism; sTC: The subnetwork of Transcription in the TTN; sTL: The subnetwork of Translation in the TTN; ORF: Open Reading Frame; P/R: the Number-based Ratios of ExPa to Reaction; L/R: the Ratio of Average ExPa Length to Reaction Number; RPR: the Reaction Participation Rate; TCF: Transcription Factor; CRP: C-reactive Protein; PDH: Pyruvate Dehydrogenase; ACP: Acyl-carrier Protein; IF: Initiation Factor; 70SIC: 70S Initiation Complex; rib_30_IF1_IF3: 30S Ribosomal Subunit/IF1/IF3 Complex; rib_50_inact: 50S Ribosomal Subunit; CoSet: Correlated Reaction Set.The authors declare that they have no competing interests.YX conceived and designed the study, participated in drafting and revising the manuscript. YZ carried out the analysis and drafted the manuscript. LW interpreted the results biologically. FW supervised the study, participated in its design and to revise the manuscript. All authors read and approved the final manuscript.


Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention.Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution.We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems.The online version of this article (doi:10.1186/s12918-016-0259-2) contains supplementary material, which is available to authorized users. Mathematical models of cellular metabolism are a complementary tool to experimentation for analyzing and engineering metabolic function. Over the past several decades, flux balance analysis (FBA) based on stoichiometric descriptions of cellular metabolism has emerged as the dominant approach for microbial metabolic modeling. FBA involves the formulation of stoichiometric equations describing the metabolic network followed by linear program solution of the underdetermined linear equation system subject to an assumed cellular objective such as growth rate maximization . The advClassical FBA methods assume time invariant and spatially homogeneous extracellular conditions and generate steady-state predictions consistent with well-mixed, continuous cultures . Most mi2 concentrations decrease as the gas flows up the column due to cellular consumption [In contrast to the dynamic case, the development of metabolic models that account for spatially varying environments has received little attention. Such problems are very common in natural and engineered microbial systems. For example, naturally occurring microbial biofilms typically exhibit strong spatial gradients due to differential nutrient availability at the biofilm boundaries . Spatialsumption . The incsumption –13, lattsumption , 15 and sumption . These mz for simplicity. Additional modeling assumptions include that constant gas and liquid phase volume fractions and velocities, constant gas–liquid mass transfer coefficients, constant cell and metabolite diffusion coefficients, and cell incompressibility. The last assumption allows a simple convection term to be used in the species mass balance equations. While cell compressibility could be included in the model if necessary, we expect that this effect would negligible under the low velocity liquid flows encountered in the examples consider here as well as in most practical applications.The class of spatiotemporal metabolic models considered below is sufficiently general to encompass a wide variety of potential applications including microbial communities with interacting species and multiphase systems in which the liquid and gas phases move relative to each other. The framework is based on the standard dynamic flux balance modeling assumption that the intracellular metabolism is much faster than the extracellular dynamics, which we do not believe is any more restrictive when the environment exhibits spatial variations. Furthermore, we assume that spatial variations occur only in a single direction Under these assumptions, a general set of model equations can be written as,i-th microbial species where Xi is the biomass concentration, μi is the growth rate obtained from the genome-scale metabolic model, μdi is the death rate, uL is the liquid phase velocity, DiX is the cellular diffusion coefficient that accounts for cell motility. The second equation represents a mass balance on the j-th liquid phase metabolite where vij is the net flux of metabolite j into the liquid phase from species i, DjL is the liquid-phase metabolite diffusion coefficient, kj is the gas–liquid mass transfer coefficient, and Mj* is saturation concentration in the liquid phase calculated from the associated gas-phase concentration using Henry’s law. The net flux vij is calculated as the difference between the synthesis rate obtained from the genome-scale metabolic model and the uptake rate calculated from Michaelis-Menten type kinetic expressions [j-th gas phase component where uG is the gas phase velocity, DjG is the gas-phase diffusion coefficient.The first equation represents a mass balances on the ressions , 18. TheBoundary conditions for these equations are problem specific and can account for the supply/removal of liquid and/or gas phase components at the domain boundaries. Although not discussed here, the general model formulation can be extended to include a moving boundary as would be required for biofilm expansion. In the Appendix, two examples of formulated spatiotemporal metabolic models are presented: 1) a bubble column reactor for bacterial conversion of synthesis gas to ethanol; and (2) a bacterial biofilm associated with chronic wound infections. For the most part, these two models adhere to the general set of equations presented above. However, the species mass balance equation for the biofilm model  with embedded linear programs. The efficient and stable solution of such models is a challenging problem at the forefront of microbial metabolic modeling. Our solution approach is based on spatial discretization such that the PDEs are converted into a large set of ordinary differential equations (ODEs) in time with embedded LPs. The spatial domain is discretized with Our approach for solving such large discretized models involves the use of DFBAlab , a MATLADFBAlab is a modified MATLAB implementation of our previously developed simulator . DFBAlabMinimize infeasibilities: If the first objective is equal to zero, the LP is feasible and all other objectives are consistent with the solution of the original FBA LP; otherwise, the objective is positive. If the original FBA LP is infeasible, the reformulated Phase I lexicographic LP still returns values for growth rate and exchange fluxes allowing the integration process to continue. This objective can be integrated to obtain a penalty function. This penalty function can provide useful insights on why and under what conditions the FBA model becomes infeasible.Maximize growth rate: this is the traditional FBA objective.n fluxes appearing in the right hand side of the ODEs, the vector-valued objective will require at most n + 2 elements to obtain a unique right-hand side.Maximize/minimize all of the exchange fluxes appearing in the right-hand side of the ODEs. Each one of these objectives involves a linear combination of fluxes that can be minimized or maximized as appropriate. If there are More specifically, DFBAlab reformulates the FBA LP as a Phase I lexicographic LP to obtain all information required by the right-hand side of the ODEs as a unique vector-valued solution with the following order of objectives:i-th species in a bubble column reactor:DFBAlab is designed to solve ODE systems; however, it provides a flexible framework that enables the solution of PDE models if the equations can be transformed into ODEs. Consider the following equation that describes the biomass concentration of the j in the spatial domain and each species i:This PDE can be easily converted into an ODE by discretizing the spatial domain. If a simple backward difference formula is used to approximate the convection term, then the following set of ODEs is obtained for each point L is the length of the spatial domain, ΔL = L/n and n is the number of discretization points. In addition, Xi,0 = Xfeed = 0 and the outlet biomass concentration of the bubble column reactor is Xi,n. A more detailed explanation for the single species case can be found in Fig. i and the secretion exchange fluxes vij were set equal to zero whenever DFBAlab detected that the LP for the i-th species was infeasible. This situation occurred when local nutrient uptake rates were insufficient to meet the non-growth ATP maintenance requirements. While this approach had the potential to make the right-hand side of the ODEs discontinuous, we found that DFBAlab had little problem integrating through such points because the growth rates and byproduct secretion rates tended to be very small immediately prior to an infeasibility occurring.where From a biological perspective, the additional objectives involving the exchange fluxes represent lower level cellular strategies than the main objective of growth rate maximization. The choice of these objectives is problem dependent and requires assumptions about the cellular metabolism. We typically assume that the cell regulation machinery is configured to maximize substrate uptake fluxes and minimize byproduct secretion fluxes, which is consistent with the main objective by maximizing the input of carbon containing and electron accepting metabolites and minimizing the output of carbon wasting byproducts. While DFBAlab requires specification of these lower level objectives, they impact the lexicographic optimization only when alternative optima occur. Our experiences with the two examples discussed in the following sections and other problems solved with DFBAlab is that the ordering of these objectives has a negligible impact on spatiotemporal model solutions because alternative optima typically occur only for short periods of simulation time. In other words, DFBAlab allows the integrator to reliably transition across short periods where alternative optima exist.https://yoric.mit.edu/dfbalab. Any entity desiring permission to incorporate this software or a work based on the software into commercial products or otherwise use it for commercial purposes should contact Dr. Paul Barton (pib@mit.edu). Simulation codes for the synthesis gas bubble column reactor and bacterial biofilm models can be obtained from www.ecs.umass.edu/che/henson_group/downloads.html.All simulations were performed with MATLAB 8.5 (R2015a) using DFAlab for dynamic flux balance model solution and Gurobi 6.0 for linear program solution. DFBAlab is freely available for both education and non-profit research purposes from 2/CO/CO2) by specialized CO fermenting microbes. Because syngas can be produced relatively cheaply from a wide variety of biomass feedstocks [2 concentrations decrease as the gas flows up the column due to cellular consumption, the column can have strong spatial gradients that affect cellular growth and product synthesis. The development of model-based techniques for simulating and optimizing these complex multiphase reactors is important to advance syngas fermentation technology.An emerging route for the large-scale production of renewable fuels and chemicals is direct fermentation of waste gas streams and synthesis gas  and 600 LPs (6 per point). Despite the substantial computational complexity of this discretized model, we found that a typical 1000 h dynamic simulation for determining a steady-state solution required only about 8 min running DFBAlab and MATLAB version 7.11 on a Dell XPS laptop with Intel Core i7-2760QM processor and 8 GB RAM. Time and spatially resolved predictions obtained for reactor startup with a simulation time of 250 h are shown in Fig. 2 concentrations decreased along the length of the reactor due to gas consumption, while the biomass, acetate and ethanol concentrations increased along the reactor due to liquid flow. The synthesis of CO2 was negligible under these nominal operating conditions. Because the feed gas was relatively rich in CO, the H2 conversion was 62 % while the CO conversion was only 29 %. As a result of H2 being depleted in the first half of the reactor, considerable acetate was produced in the second half of the reactor and the liquid product stream exiting the top of the column contained more acetate than ethanol (ethanol fraction ~40 %). While we are not aware of any published experimental studies that describe the startup dynamics of syngas bubble columns, our model could be a powerful tool for predicting and optimization reactor startup.Our first goal was to investigate the efficiency of DFBAlab for simulating startup of the bubble column reactor with N = 100 node points were sufficient to obtain nearly converged solutions, we performed dynamic simulations for reactor startup with different N values and compared the resulting steady-state solutions obtained at t = 1000 h  and computational time (~8 min per simulation). All remaining simulations were performed with N = 100.To demonstrate that 0 h Fig. . While c2 mixture to a 50/50 CO/H2 mixture. The column exhibited similar dynamics for this H2 rich feed, as the biomass concentration still required approximately 200 h to reach steady state  conversions compared to the nominal case. Our predictions were in qualitative agreement with published experimental studies [Next we performed a dynamic simulation with the CO gas–liquid mass transfer coefficient changed from the nominal value  packing . Consist studies , 29, 30 Pseudomonas growing as biofilms on a complex mixture of wound exudate [Chronic, non-healing wounds are a growing medical challenge associated with diabetes and obesity . These w exudate , 33. Bac exudate . Carbon  exudate , 36. TheP. aeruginosa [P. aeruginosa, we constrained the D-alanine secretion flux to zero such that the only byproducts were acetate and succinate. While other byproducts could be secreted in different biofilm microenvironments, we did not attempt to determine or model other byproducts due to our focus on cellular growth. The spatiotemporal metabolic model was comprised of 5 PDEs for the liquid-phase concentrations of P. aeruginosa biomass, glucose, oxygen, acetate and succinate  and 250 LPs (5 per point). A 1000 h dynamic simulation for determining a steady-state solution required about 15 min on our Dell XPS laptop. This computation time was substantially greater than the 8 min required to simulate the bubble column reactor model over the same time period despite the larger size of the discretized column model . While we hypothesize that the increased computation times obtained with the biofilm model were attributable to the diffusion dominated behavior, these results demonstrate the need to better understand the computational complexity of these large-scale ODE/LP systems.We performed a dynamic simulation for a biofilm thickness of 50 μm with Figure To explore the impact of biofilm thickness on physiology and to further evaluate our modeling framework, we performed a dynamic simulation for a 100 μm thick biofilm Fig. . This th2 was from air at the top of the biofilm, blood plasma has low O2 levels [z = 0 for the O2 mass balance , the main differences from the nominal case were that more biomass was produced near the interface and lower succinate levels were generated throughout the biofilm. When succinate consumption also was introduced (“Succinate Consume”), then biomass was preferentially accumulated at the top of the biofilm due to succinate oxidation, resulting in a less dense region located in the middle. This prediction was consistent with the known physiology of nutrient limited biofilms [Finally we performed a dynamic simulation to investigate the effects of putative succinate reassimilation on biofilm physiology. The thickness was specified as 100 μm and Obiofilms . SuccinaMany natural and engineered microbial systems exist in non-homogeneous environments that require metabolic models that account for both temporal and spatial variations. Our spatiotemporal metabolic modeling framework involves combining genome-scale metabolic reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in the extracellular environment. The PDE model is spatially discretized and the resulting system of ODEs with embedded LPs is integrated using DFBAlab , a MATLAThe datasets supporting the results of this article are included within the article and its additional file.