Pyruvate dehydrogenase (PDH) occupies a central node of intermediary metabolism, converting pyruvate to acetyl-CoA, thus committing carbon derived from glucose to an aerobic fate rather than an anaerobic one. Rapidly proliferating tissues, including human tumors, use PDH to generate energy and macromolecular precursors. However, evidence supports the benefits of constraining maximal PDH activity under certain contexts, including hypoxia and oncogene-induced cell growth. Although PDH is one of the most widely studied enzyme complexes in mammals, its requirement for cell growth is unknown. In this study, we directly addressed whether PDH is required for mammalian cells to proliferate.PDHA1 gene encoding an essential subunit of the PDH complex and characterized the effects on intermediary metabolism and cell proliferation using a combination of stable isotope tracing and growth assays. Surprisingly, rapidly dividing cells tolerated loss of PDH activity without major effects on proliferative rates in complete medium. PDH suppression increased reliance on extracellular lipids, and in some cell lines, reducing lipid availability uncovered a modest growth defect that could be completely reversed by providing exogenous-free fatty acids. PDH suppression also shifted the source of lipogenic acetyl-CoA from glucose to glutamine, and this compensatory pathway required a net reductive isocitrate dehydrogenase (IDH) flux to produce a source of glutamine-derived acetyl-CoA for fatty acids. By deleting the cytosolic isoform of IDH (IDH1), the enhanced contribution of glutamine to the lipogenic acetyl-CoA pool during PDHA1 suppression was eliminated, and growth was modestly suppressed.We genetically suppressed expression of the Although PDH suppression substantially alters central carbon metabolism, the data indicate that rapid cell proliferation occurs independently of PDH activity. Our findings reveal that this central enzyme is essentially dispensable for growth and proliferation of both primary cells and established cell lines. We also identify the compensatory mechanisms that are activated under PDH deficiency, namely scavenging of extracellular lipids and lipogenic acetyl-CoA production from reductive glutamine metabolism through IDH1.The online version of this article (doi:10.1186/s40170-015-0134-4) contains supplementary material, which is available to authorized users. This phenomenon has been called aerobic glycolysis  because it occurs even when enough oxygen is present to support normal mitochondrial function. Evidence indicates that aerobic glycolysis supports cell survival and growth in numerous ways, including providing substrate for macromolecular synthesis glucose or 4-mM [U-13C]glutamine, in DMEM supplemented with 5 % dialyzed FBS and allowed to proliferate for 24 h. Metabolites were extracted using the Bligh-Dyer method glucose  or [U-14C]glutamine  in DMEM supplemented with 5 % tetracycline-reduced FBS and allowed to proliferate for 24 h, then lipids were extracted  glucose or [U-13C]glutamine were used to simultaneously fit the same network model to estimate intracellular fluxes. To ensure that a global minimum of fluxes was identified, flux estimations were initiated from random values and repeated a minimum of 50 times. A chi-square test was applied to test goodness-of-fit, and accurate 95 % confidence intervals were calculated by assessing the sensitivity of the sum of squared residuals to flux parameter variations [Steady state metabolic fluxes were calculated by combining extracellular flux rates, growth rates, and  package , which a package , 35. We riations .PDHA1 transcript. Induction of either of two hairpins greatly reduced PDH E1α protein levels . PDHA1 silencing reduced the presence of glucose-derived carbon in total lipids and in all fractionated classes of polar and non-polar lipids  and established mouse embryonic fibroblasts (MEFs) from male embryos transgenic for UBC-Cre-ER and hemizygous for the floxed PDHA1 allele. Deletion of exon 8 is thought to impair the interaction between the E1α subunit and the rest of the complex, dramatically reducing PDH activity [PDHA1 exon 8 in culture  were analyzed by Isotopomer network compartmental analysis (INCA), a form of metabolic flux analysis (MFA) that enables quantitation of many fluxes interacting with central carbon metabolism and fatty-acid synthesis [13C distributions, is described . These studies underline the plasticity of cellular metabolism with future studies being directed at ascertaining their relevance in vivo.


Genome-scale metabolic models usually contain inconsistencies that manifest as blocked reactions and gap metabolites. With the purpose to detect recurrent inconsistencies in metabolic models, a large-scale analysis was performed using a previously published dataset of 130 genome-scale models. The results showed that a large number of reactions (~22%) are blocked in all the models where they are present. To unravel the nature of such inconsistencies a metamodel was construed by joining the 130 models in a single network. This metamodel was manually curated using the unconnected modules approach, and then, it was used as a reference network to perform a gap-filling on each individual genome-scale model. Finally, a set of 36 models that had not been considered during the construction of the metamodel was used, as a proof of concept, to extend the metamodel with new biochemical information, and to assess its impact on gap-filling results. The analysis performed on the metamodel allowed to conclude: 1) the recurrent inconsistencies found in the models were already present in the metabolic database used during the reconstructions process; 2) the presence of inconsistencies in a metabolic database can be propagated to the reconstructed models; 3) there are reactions not manifested as blocked which are active as a consequence of some classes of artifacts, and; 4) the results of an automatic gap-filling are highly dependent on the consistency and completeness of the metamodel or metabolic database used as the reference network. In conclusion the consistency analysis should be applied to metabolic databases in order to detect and fill gaps as well as to detect and remove artifacts and redundant information. Metabolic reconstruction is the computational process that aims to elucidate the biochemical network of reactions and metabolites which defines the cell metabolism of a certain organism ,2. Sincein-silico representation of a metabolic network [Although the objective of a metabolic reconstruction may be to create an organism's specific metabolic database, in many cases the final goal is to develop a genome-scale metabolic model (GSM), that is to say, an  network . A GSM c network ,15. Geno network ,17. More network ,19 and tIn general, inconsistencies will appear as holes in the structure of the network. These holes might indicate either global or organism specific gaps in biological knowledge. Global gaps are reflected in the existence of metabolites with an unknown biochemical fate , as wellglobal networks or metamodels [The resolution of inconsistencies in GSMs is known as network curation. This is a decision- making process where wrongly annotated reactions are removed and candidate reactions are included for the purpose of solving model gaps. The prediction of candidate reactions for filling gaps is referred to as the gap-filling problem ,24. Sevetamodels .metamodel through the CBM approach can lead to the detection of structural inconsistencies, as well as coupling relations [The analysis of a elations , such aselations . Remarkaelations , althougelations .The aim of the large-scale analysis proposed in this paper is to detect both the recurrent errors in the automatic reconstruction process as well the sources of these inconsistencies, and to assess the impact of the metamodel completeness and consistency in the gap-filling process. To this end, a dataset of 130 GSMs of bacteria reconstructed using the Model SEED pipeline  was selefastcore algorithm [i.e. without manual curation). A comparative analysis was performed between both versions of each GSM to investigate the impact of perform gap-filling using an inconsistent reference network. Finally, a set of models of certain organisms not considered during the construction of the metamodel was used, as a proof of concept, to extend the metamodel with new biochemical information, and asses its impact on the gap-filling results.A consistency analysis was performed on the metamodel using the unconnected modules approach . The detlgorithm . MoreoveNmxn. This matrix, where rows and columns correspond to metabolites and reactions respectively, represents the structure of the network [J indexes can be partitioned into two disjoint subsets: 1) the set JINT of biochemical reactions that take place inside the cell, as well the transport reactions that operate between the cell and the surrounding medium; 2) the set of exchange fluxes JEX, which are auxiliary variables used to represent the rate at which the metabolites that are allowed to cross the system boundary are consumed/produced [Any biochemical network such as cellular metabolism can be represented by its corresponding stoichiometric matrix  network . Moreoveproduced .v is the vector of reaction fluxes, or flux distribution. Second, the thermodynamic constraints, which ensure that the irreversible reactions take non-negative flux values.Irr is the set of the irreversible reaction indexes. Besides, lower and upper bounds are imposed over each reaction to represent additional constraints, such as the maximum capacity of an enzyme and also to model the surrounding environment of a metabolic system, i.e. by constraining the exchange fluxes JEX:βi and αi correspond to the lower and upper bound of reaction i, respectively.The structural properties of such networks may be assessed through the CBM approach. CBM relies on the use of constraints with the aim of reducing the system's functional states, to those that are physiologically more relevant ,46. Two Definition: Any non-trivial vector v feasible with respect to Eqs (t to Eqs  and 2)  DefinitiThe set of all possible flux distribution spans the so-called flux space:i.e. reactions which cannot display a steady-state flux other than zero, and gap metabolites, i.e. nodes in the network through which there can be no steady state flow [N and a set of irreversible reactions Irr, structural inconsistencies are defined as follows:An important step in the reconstruction of a metabolic model is to check the consistency of the network definition. In general terms, the structural inconsistencies of a metabolic model may manifest as blocked reactions, ate flow . FormallDefinition: a reaction j is defined as blocked if for every possible flux distribution v the corresponding flux value vj = 0.Definition: a metabolite is defined as a gap if all the reactions in which it participates are blocked.Moreover, the relation between blocked reactions and gap metabolites can be unambiguously established by means of the unconnected modules , as follDefinition: an unconnected module (UM) is defined as a connected bipartite sub-graph of blocked reactions connected through gap metabolites.Definition: a metabolic model with a stoichiometric matrix N and a set of irreversible reactions Irr is said to be flux consistent if it does not contain blocked reactions nor gap metabolites.https://github.com/migp11/consistency-analysis/. The scripts allow consistency analysis to be performed on any model, computing blocked reactions, gap-metabolites and the set of unconnected modules. Moreover, the code allows gap-filling to performed, based on fastcore algorithm.Constraint-based analysis was performed using the python-based toolbox COBRApy . LP and Methanosarcina barkeri str. Fusaro) and 1 eukaryote (Ostreococcus tauri). Since this paper focuses on the analysis of bacterial metabolism, the two models corresponding to the archaea and the eukaryote organisms were excluded from the analysis. A total of 27 of the remaining 193 models corresponded to older versions of some of the models, and therefore they were also excluded from the dataset in order to reduce redundancies.The Model SEED currently includes 236 publicly available models . A totalAfter these filtering steps, a dataset of 166 bacterial GSMs from a wide taxonomic range was obtained. The 166 selected models included a subset of 130 GSMs which corresponded to the dataset first published by Henry et al., albeit with slight differences which are detailed at the end of this section see also , and inchttp://www.theseed.org). Moreover, when retrieving the models corresponding to the dataset previously published by Henry et. al [T. crunogena XCL-2, was not available; however, by using the species name a model with a different ID was found (Seed317025.3), and this model was used to replace the unavailable model. Finally, the models were grouped according to taxonomic range, using the color schema employed in the Actinobacteria (light green) and the Bacteroidete (dark blue) groups respectively, had been grouped with the Gammaproteobacteria (yellow). Additionally, when the biomass equations of the models were compared, it was found that some models share the same formulation. There are a total of 157 biomass equation and the following organisms share a common equation: M. genitalium G-37 (Opt243273.1), M. pulmonis UAB CTIP (Opt272635.1); S. typhimurium LT2 (Opt99287.1), E. coli K12 (Opt83333.1), V. cholerae O1 biovar eltor str. N16961 (Opt243277.1); S. frigidimarina NCIMB 400 (Seed318167.13), S. halifaxensis HAW-EB4 (Seed458817.7), S. woodyi ATCC 51908 (Seed392500.5), S. amazonensis SB2B (Seed326297.9), S. pealeana ATCC 700345 (Seed398579.6), S. sediminis HAW-EB3 (Seed425104.6), Shewanella sp. MR-4 (Seed60480.18)  was allowed to be drained from the system in an independent way through demand fluxes; second, each reaction corresponding to a biomass equation was removed. Artificial variables (i.e. exchange and demand fluxes) were not considered for analysis of the coupling relation.Flux coupling analysis was computed following the algorithm previously described . Moreovefastcore algorithm used to perform the gap-filling on the GSM was re-implemented in Python programming language according to [https://github.com/migp11/consistency-analysis/. The inputs of the algorithms are a metamodel also referred as a consistent global network, a set of penalties, and an inconsistent model. The output is a consistent version of the model which includes a minimal set of new reactions needed to solve the inconsistencies. The algorithms is an iterative procedure that at each step solves linear programs at each step, in order to identify a set of gap-filling reactions that should be added to the model in order to solve a subset of blocked reactions.The rding to , and is et al. [Escherichia coli K12 (Opt83333.1) whereas the highest ~47% was found in Thermus thermophilus HB8 (Seed300852.3). Despite this wide range it is still possible to appreciate a trend between the number of blocked reactions and the total number of reactions in a GSM, as previously reported by the authors [Using the dataset previously published by Henry et al. , composeet al. . This is authors . This tradenosylcobalamin biosynthesis and heme biosynthesis), the automatic inference of the siroheme biosynthetic pathway shown to be far from trivial.The situation described above can be illustrated by the case of the biosynthesis of siroheme , a prostE. coli and B. subtilis .Finally, 480 reactions (~22%) were found blocked in every model where they are present, as depicted by the points on the main diagonal of The detection of always blocked reactions indicates the existence of recurrent inconsistencies within the reconstruction process see . These imetamodel was constructed by joining the 130 GSMs used in the previous section into a single network. The resulting metamodel, referred as MM130.0, contains a total of 2195 reactions, 1811 metabolites and 370 exchange fluxes , together with the never blocked (608) were found to be active in MM130.0. Furthermore, the 417 reactions found blocked in MM130.0 are a subset of the 480 always blocked reactions. In the same way, the 520 gap metabolites found in MM130.0 are a subset of the 570 metabolites always gap. This indicates that 63 out of 480 always blocked reactions and 50 gap metabolites previously classified as always gap were “restored” as a consequence of the metamodel construction.A consistency analysis was conducted on MM130.0. The result showed that the metamodel contains 417 blocked reactions and 520 gap metabolites (431 intracellular / 89 extracellular) grouped into 229 UMs see . As expein-silico flux modes that violate the principle of energy conservation and thus do not have any physical meaning [In order to understand how this spontaneous connectivity restoring occurred, we mapped these 63 reactions and 50 metabolites onto a bipartite graph, which resulted in 18 connected components see . Further meaning ,56. A cli.e. by considering the set of EC numbers) the three UMs decrease dramatically in size. It is worth noting that the curation of such pathways is particularly difficult. On the other hand, 179 UMs were composed of a single reaction, many of which were unconnected transporters. Within these two extremes, the third group of UMs included a significant number of biological pathways, as well as artifacts. As a consequence of this diversity, the curation of the UMs included in this group usually did not have a trivial solution. Thus, each UM was manually curated according to the procedure described in the Methods section.The size distribution of the 229 UMs found in MM130.0 indicates the presence of three different groups. The three biggest UMs included a total of 99 reactions involved in the biosynthesis of membrane lipids and teichoic acids. Interestingly, since lipids and teichoic acids are elongated by iterative reactions, if the corresponding reactions are considered as enzyme activities  allows the elucidation of the topological and flux connectivity features of a metabolic network . These f subsets ,35,60), e.g. directionally coupled → fully coupled) as a consequence of adding reactions. The only case where the coupling between reactions can become stricter occurs when a certain reaction i is found as blocked in a model, and then becomes active as a result of adding a new reaction j. This special case was considered in the Construction and curation of the metamodel section. On the other hand, when one or more reactions are removed from a consistent network there are different possible outcomes: 1) the couplings between the remaining reactions are not affected; 2) the coupling between some pairs of non-blocked reactions becomes stricter; 3) one or more reactions become blocked. Thus, based on the results commented above, the coupling structure of a metamodel can be used to detect missing reactions in any model that held to be a subnetwork of the metamodel.These results are a consequence of the mathematical properties of the coupling relations, which have previously been studied by Marashi and Bockmayr . The maiFCA was performed on the curated metamodel MM130.1 in order to detect all the coupling relations existing between the reactions in the network. The analysis was conducted on a modified version of model where the constant biomass composition imposed by the stoichiometry of the biomass equation was relaxed see  section.e.g. the biosynthesis of cofactors and some amino acids.The size of the FCSs varies between 2 to 34 reactions with a mean size of ~3 reactions. The biggest FCS is composed of reactions involved in core oligosaccharide biosynthesis, the major component of the outer membrane of Gram-negative bacteria. Other larger FCSs (> 10 reactions) were also involved in the biosynthesis of cell envelope components such as different membrane lipids and peptidoglycan. However, FCSs of a similar size involved in other biological processes were also found, The initial metamodel (MM130.0) and its curated version (MM130.1) were used alternatively as the reference network to perform a gap-filling on each individual GSM. In this way, the comparison between models gap-filled with different metamodels can help to assess the impact of the metamodel consistency and completeness on the gap-filling of a GSM.fastcore algorithm to allow the inclusion of a vector of linear weightings, as previously described [metablocked was removed from individual GSMs before the application of fastcore. The number of metablocked reactions is 417 and 161 for MM130.0 and MM130.1, respectively. Furthermore, the coupling information obtained from each metamodel version was used to assist the curation process. Finally, the set of weights used in each GSM was individually computed in the pre-processing step. The overall curation process was divided into 5 steps , T. pallidum and B. burgdorferi B31 (brown dots). These five organisms are known pathogens and possess the smallest genomes of the dataset . New organisms not considered during the construction of MM130.1 may contain reactions and compounds, or even previously unconsidered new metabolic pathways. Consequently, a metamodel will eventually need to be extended or updated. Thus, in order to assess how extending a metamodel affects the performance of gap-filling, 36 GSMs which had not been considered in the construction of MM130.1 were used to extend the metamodel ; and 2) the differences between both versions with respect to the gap-filled reactions.In order to assess the impact of the metamodel extension on the gap-filling of individual models, the process described in the previous section (Gap-filling of 130 GSMs) was repeated, but using MM166.1 as the reference network instead. Moreover, the gap-filling procedure was also applied to the additional 36 GSMs using the two metamodels (MM130.1 and MM166.1) as the reference networks. As a result two consistent versions of each of the 166 modes were obtained. In order to compare the two curated versions of each GSM two factors were considered: 1) the efficacy of the gap-filling algorithm  is clearly expected. However, this factor does not provide information about the degree of similarity between the gap-filling solutions obtained for each metamodel. Thus, the two versions of each curated model were compared to quantify the degree of similarity between them, in terms of the reactions they contain, using the Jaccard index. The Jaccard index, defined as the total number of elements in the intersection over the number of elements within the union of two sets, was calculated for each pair of models considering only the subsets of gap-filling reactions, i.e. the reactions added to solve the inconsistent ones.The mean efficacies for the models curated with MM130.1 and MM166.0 were ~0.87 and ~0.93, respectively for the 130 models, and 0.90 and 0.99 for the 36 additional models see . The incThe mean value of the Jaccard index of the 130 models was ~0.71, and the same mean value was obtained for 36 models, which means that on average each pair of curated versions shares, approximately 85% of the new reactions see . Surprisgammaproteobacteria, which includes E. coli.The consistency analysis performed on a dataset of 130 GSMs of different bacteria showed that most of the models have at least 25% of their reactions blocked. The results also showed that the reconstruction of a non-model organism tends to become easier when the GSM of a phylogenetically closer organism exists, as previously discussed . In the E. coli K12 (Opt83333.1) with a value of ~19%. The same measure was also evaluated for the last version of the manually reconstructed GSM of E. coli K12, named iJO1366 , and the result showed that 10% of its reaction were blocked. The difference found was expected, since iJO1366 has been extensively manually curated, whereas Opt83333.1 was automatically reconstructed. On the other hand, T. thermophilus (Seed300852.3) was shown to be the model with the highest percentage of blocked reactions (~47%). As in the case of E. coli, this measure was compared against the value obtained for a recently published GSM of T. thermophilus, named iTT548 [As expected, the model with the lowest percentage of blocked reactions was the one corresponding to d iTT548 , where ~i.e. “always blocked”). This showed a remarkable number of network inconsistencies at the level of the metabolic database used as a reference during the reconstruction process. When these reactions were grouped by subsystem, 25% were found to be involved in the biosynthesis of cell wall components as well as membrane lipids  are blocked in each GSM where they are present ; second, the detection and resolution of incomplete pathways by the addition of the corresponding missing reactions, e.g. the pimelic acid biosynthesis (i.e. the first stage of biotin biosynthesis); third, the detection and resolution of global deadend metabolites such as the cases of S-adenosyl-4-methylthio-2-oxobutanoate and of some biomass components not previously included in the biomass reaction of any GSM. The curated metamodel MM130.1 can be used as a reference network for the curation of any model generated using the SEED. In this way, different algorithms and weights can be tested for the curation of a particular model. Additionally, the metamodel presented here can be modified or extended to adjust to particular situation such as the case of organisms with highly reduced genomes.The detection of recurrent inconsistencies motivated a global consistency analysis, Many gap-filling algorithms have been developed by focusing on the structure of the objective function. However, the possible impact of the reference network consistency, which affects the gap-filling process, has received little or no attention. Therefore, a gap-filling was performed on the whole dataset to evaluate the impact of the metamodel completeness and consistency, using alternatively MM130.0 and its curated version MM130.1. When the reaction content was compared within each pair of curated GSMs, in 125 of the cases the version gap-filled with MM130.1 contained 85% or more of the reactions present in the version gap-filled with MM130.0. Strikingly, in five models the percentage of inclusion varies between 65–80%, which indicates a remarkable difference between the two versions. Thus, it can be concluded that in some cases the result of an automatic gap-filling can be highly dependent on the metamodel used as the reference. In particular, the divergence was found to be greater for the smaller models. Since, these organisms correspond to obligate parasite and symbionts, their metabolisms tend to lack many biosynthetic capabilities and thus, they should import a great number of metabolites from the surrounding environment. Furthermore, the possibility of a metabolic complementation between parasites or symbionts and their hosts may result in the exchange of metabolites not commonly included in growth media. Thus solving such situation requires a manual inspection of individual UMs to evaluate the possibility of adding unknown transporters and the corresponding exchanges fluxes . As a coM. genitalium G-37 (Opt243273.1) contained 292 reactions, of which 118 were blocked, whereas both gap-filled versions included more than 500 reactions. The manually reconstructed model of M. genitalium G-37 iPS189 [Finally, the gap-filling results showed that in many cases the number of orphan gap-filling reactions included to solve gaps significantly exceeds the number of gaps. This result is independent of the metamodel version used, and suggests that in many situations blocked reactions can be artifacts and should be removed from the model instead of adding new reactions to solve what at first looked like a gap. For example, the initial GSM of 7 iPS189  containsP. difficile). Nevertheless, this new information was enough to affect the outcome of the gap-filling process, as has been shown  the incorrect assignment of an enzymatic activity to certain coding sequences. The presence of type 1 and 2 errors will produce the absence, or the wrong inclusion, of some reactions in the GSM, respectively. Thus, gaps in a GSM caused by distinct types of errors will require a differential treatment. In the case of type 1, missing reactions should be gap-filled. However, in the case of type 2 errors, the wrong added reactions should be removed. Since both types of errors will manifest as blocked reactions and gap metabolites, we argue that the problem resides in how to differentiate, in an automatic fashion, between the blocked reactions that have to be gap-filled (in order to restore their connectivity) and the erroneous reactions that should be removed. As shown in this paper the distinction between these types of errors is far from trivial, and not considering them will result in the overestimation of the reaction content of an organism.The reconstruction of a GSM depends, to a great extent, on the quality of the genome annotation. Thus, errors in the annotation will lead to the presence of inconsistencies in the model formulation. In this context, in principle there are two different types of annotation error: 1) the absence of certain functional annotations, Although there have been considerable advances in the automatic reconstruction of GSMs, the outputted models still contain many structural inconsistencies, as the results presented have shown. Furthermore, the detection of recurrent inconsistencies manifested as metablocked reactions indicates that gaps may already be present in the metamodel or the metabolic database used to perform the reconstructions. As a consequence, we argue that consistency analysis, such as the one presented in this paper, should be applied to metabolic databases in order to detect and fill gaps as well as to remove artifacts and redundant information.S1 FigThe diagram represents the set of unconnected modules obtained for MM130.0, together with other artifacts detected, and set of reactions added during the curation process. White nodes correspond to blocked reaction solved; green nodes correspond to the reactions added during the curation; red nodes indicate the set reaction that were removed from the metamodel (metablocked).(SVG)Click here for additional data file.S2 Figin-silico flux modes that violate the principle of energy conservation. In b) the cases of in-to-out linear pathways are shown  the sub-graphs the representing cycles which correspond to (PNG)Click here for additional data file.S3 FigThe diagram represents the flux coupling graph associated to MM130.1 as previously described. Grey and red nodes represent single reactions and full coupled sets of reactions respectively. Directed arrows indicate the presence of directional coupling between the pair of nodes.(PNG)Click here for additional data file.S4 FigIn a) and b) the number of reactions in the curated GSM against the number of reactions in the original GSM are shown (including metablocked reactions), using MM130.0 and MM130.1 respectively.(PNG)Click here for additional data file.S1 FileCompressed ZIP file including both curated metamodels (MM130.1 and MM166.1) in SBML format.(ZIP)Click here for additional data file.S1 TableThe table contains two sections. In A) the 130 GSMs used in the present paper are listed, including a detailed description of the models as well as the main results of the consistency. In B) the mapping between the version of the models used herein and those used in the original publication . In C) t(XLSX)Click here for additional data file.S2 TableThe table contains five sections. In A) the set of 2195 reactions included in at least one GSM. Each row corresponds to a reaction and includes the reaction's attributes together with the number of models which include the reaction, the number of models where it is blocked and the calculated blocked frequency. Sections B), C) and D) presents the reactions (grouped by subsystems) classified as “never blocked”, “sometimes blocked” and “always blocked”, respectively.(XLSX)Click here for additional data file.S3 TableThe table contains five sections. Section A) includes the complete set of reactions and their description. Additionally, two columns were added to indicate if the reaction was added or removed during the manual curation, and a third column to indicate the unconnected module ID associated to those reaction first found blocked. In a similar fashion, sections B) and C) described the set of exchanges fluxes and metabolites of the metamodel respectively. In D) the 157 biomass equations are presented, indicating the models which have that biomass composition. In E) the list of new biomass compounds found are shown. In F) and G) the new 226 reaction and 113 metabolites, respectively, found in the set of 36 GSM that was used for the metamodel extension.(XLSX)Click here for additional data file.S4 TableThe table contains three sections. The results of the gap-filling performed using MM130.0 and MM130.1 are depicted in sections A) and B) respectively. In section C) the results of the comparative analysis performed on each pair of gap-filled GSM are shown. In D) the results of the gap-filling performed on the dataset of 130 GSMs using MM166.1 are shown. In E) the results of the gap-filling performed on the dataset of 36 GSMs using MM130.1 MM166.1 are shown. In F) the comparative analysis of the gap-filling results obtained using MM130.1 and MM166.1 are shown.(XLSX)Click here for additional data file.


E. coli, and then we assess how accurately we can predict the original growth conditions from the phenotypes. Prediction is carried out via regularized multinomial regression. Our analysis provides several important physiological and statistical insights. First, we show that by analyzing metabolic end products we can consistently predict growth conditions. Second, prediction is reliable even in the presence of small amounts of impurities. Third, flux through a relatively small number of reactions per growth source (∼10) is sufficient for accurate prediction. Fourth, combining the predictions from two separate models, one trained only on carbon sources and one only on nitrogen sources, performs better than models trained to perform joint prediction. Finally, that separate predictions perform better than a more sophisticated joint prediction scheme suggests that carbon and nitrogen utilization pathways, despite jointly affecting cellular growth, may be fairly decoupled in terms of their dependence on specific assortments of molecular precursors.A widely studied problem in systems biology is to predict bacterial phenotype from growth conditions, using mechanistic models such as flux balance analysis (FBA). However, the inverse prediction of growth conditions from phenotype is rarely considered. Here we develop a computational framework to carry out this inverse prediction on a computational model of bacterial metabolism. We use FBA to calculate bacterial phenotypes from growth conditions in  In such cases, one might want to predict the bacterial growth conditions from the measured bacterial physiology.Research into metabolism and physiology generally tries to uncover how an organism's internal state is determined by the environment to which the organism is exposed. For example, one might ask which genes are up or downregulated as microbes are grown on different nutrient sources Do we expect physiology, and in particular the internal metabolic fluxes, to be predictive of the current environment? On the one hand, one could envision a scenario where an organism can only assume a small number of distinct metabolic states, and many diverse environments elicit the same physiological response. In other words, the mapping from environment to metabolism is many-to-one. Under this scenario, metabolism would not be particularly predictive of environment. On the other hand, each environment might elicit an entirely different metabolic response, i.e., the mapping from environment to metabolism is one-to-one. Under this scenario, organismal physiology can be considered an accurate reflection of the specific environment the organism resides in, and the environment can be predicted accurately from the metabolic state. In reality, we can expect the mapping between environment and metabolism to fall somewhere between these two extremes. While there are probably many different metabolic states an organism can assume, there will also be distinct environments that create similar metabolic responses.Metabolic modeling approaches generally ask the forward question, i.e., how can we calculate the metabolic state as a function of the environment. For example, flux balance approaches calculate the metabolic fluxes in an organism as a function of input fluxes and the organism's metabolic network in-silico model of E. coli can predict the organism's simulated growth environment. We first calculated metabolic fluxes via FBA for a variety of environmental growth conditions. We then developed statistical models to predict the particular growth conditions for a particular solution of the flux balance equation, using internal metabolic fluxes as input. We found that prediction is possible with surprisingly low error rates, even if a moderate amount of impurity is present in the simulated growth media. We further found that carbon and nitrogen metabolisms seem to be largely decoupled (prediction accuracy of a given carbon source does not strongly depend on the presence of particular nitrogen sources and vice versa) and that most carbon and nitrogen sources can be identified reliably from a small number of predictive fluxes.Here, we asked whether the internal metabolic fluxes in an in-silico model of E. coli encode the growth substrates. Are there distinct metabolic states that reflect specific growth conditions? We addressed this question using the following strategy  simexchange reactions, which simply take up a molecule of a specific metabolite and place it into cell. Any metabolic flux model contains a substantial number of such exchange reactions. Within a cell, the metabolites are transferred via transport reactions. Clearly, predicting environmental growth conditions from fluxes through these exchange or transport reactions would be trivial, and it would not be a reflection of what information the internal metabolic state of the cell holds about the external environment. To address this issue, we discarded all transport and exchange reactions in our regression analysis. In our model  plus a small quantity of randomly chosen other metabolites. We varied the number of metabolites serving as impurities to evaluate how sensitive the regression model was to the amount of chemical noise present in the environment. Impurities were selected at random from a set of 174 carbon and 78 nitrogen sources used previously with the k-means clustering of fluxes obtained for all 174 carbon and 78 nitrogen sources (see online data repository). We simulated fluxes for environments containing all pairwise combinations of the seven carbon and seven nitrogen sources, plus impurities. For each amount of impurity and training data-set size, we generated 100 replicates of each pairwise combination, for a total of 4900 sets of flux values . At 10 C/N, a number of carbon sources are predicted as either acetate or pyruvate . A closeIn a direct comparison, however, the separate prediction models always outperfomed the joint prediction models . The per−1 hr−1 that is generally used for carbon and nitrogen sources in FBA studies. To determine to what extent our results depended on this choice, we artificially increased the uptake rates of the carbon source to a maximum of 1000 mmol gDW−1 hr−1 while keeping the nitrogen source at the normal rate, and vice versa. These simulations can be considered as conditions of excess carbon  or excess nitrogen . Next, we looked into understanding the role of excess resources on prediction results. Above, we used the conventional maximum uptake rate of 20 mmol gDWnormal uptake rates for both sources. It seems that the more one source becomes available in excess, the more separate prediction outperforms joint prediction.When predicting growth conditions from the final fluxes, we obtained similar results as before, i.e., individual prediction performed better than joint prediction. For an artificially high uptake rate for nitrogen but with a normal uptake rate for carbon sources, the misclassification rate with separate prediction was 10%, while the misclassification rate with joint prediction is 26%, at an amount of impurities of 1 C/N and with a training data size of ∼2450 replicates. Separately predicting carbon resulted in 151 mispredictions compared to 109 mispredictions for nitrogen. In combination, there were 250 mispredictions using separately trained models. Joint prediction resulted in 638 mispredictions. Similarly, for artificially high uptake rates for carbon sources and normal uptake rates for nitrogen sources, the misclassification rate under separate prediction was 3.8% while the misclassification rate under joint prediction was 14%. Joint prediction resulted in 324 mispredictions. Separate prediction resulted in a combined misprediction from C and N sources of 94 mispredictions . Clearly, prediction rates were better for separate prediction compared to joint prediction even with larger training data sizes, which was not the case for Since individual prediction seemed to work well, we next tested whether we could use this approach to predict growth conditions chosen from the comprehensive list of 174 carbon and 78 nitrogen sources. Joint prediction in this case was infeasible, since we would have had to train a model to distinguish between All the results presented so far were obtained with a simple maximization of the biomass reaction. FBA can also be carried out with different optimization functions, and the equilibrium fluxes that are found will depend on the specific optimization function chosen. To confirm whether our approach would work under different optimization schemes, we carried out additional simulations in which we maximized biomass and then subsequently minimized the absolute sum of fluxes, holding the maximal biomass value constant. Then we performed the regression analysis as described above. We carried out this analysis for the case of 7 distinct C and 7 distinct N growth substrates, 10 C/N impurities, and individual prediction of C and N sources. We found a combined misclassification rate of 23%, relative to 15% using only the biomass maximization. , the misclassification rate remained unchanged when we eliminated any of the other 99 reactions before model fitting. PGI catalyzes a reaction that produces fructose-6-P from glucose-6-P, and knock-out of the PGI gene causes diminished growth rate Finally, we asked whether we could predict growth substrates simply on the basis of flux through the entry points of the metabolites into the metabolic network, i.e., based on first set of reactions past transport. For the 7 C and 7 N substrates we considered, there are 38 such post-transport reactions . Thus, wNext, we wanted to determine how the prediction would perform on previously unseen carbon or nitrogen sources. We first obtained simulated flux measurements using maltose as the carbon source and using either of the seven nitrogen sources used earlier. We generated simulated flux data for 100 replicates and at impurity numbers of 1 C/N and 20 C/N. This resulted in 700 observations. After eliminating replicates with very low biomass see , 695 andFor 20 C/N impurities, there were 699 viable flux measurements. At this amount of chemical noise, maltose was predicted as glucose 68% of the time, while the correct nitrogen source was predicted 81% of the time. For both low and high numbers of impurities, individual predictions seem to outperform joint prediction. Further, separate prediction is more likely to correctly predict all the known growth sources while predicting the unknown ones to their nearest known compound.Next, we did simulations to test how an unseen nitrogen source gets predicted with the above models. For this, we used cytosine as a nitrogen source and either of the 7 carbon sources used earlier. Note that cytosine is one of the 4 bases founds in DNA and RNA. We used 2 numbers of impurities, 1 C/N and 20 C/N, and we generated 100 replicates for each case for testing. At 1 C/N, there were 602 viable flux measurements, i.e., for these measurements biomass was greater than the threshold used in this study. Interestingly, all 98 non-viable flux measurements were for Cytosine + Acetate sources. For the viable flux measurements, only 5 carbon sources were wrongly predicted (∼0.01% misclassification). Interestingly, in all cases, the nitrogen source cytosine was predicted as ammonia. This result may be due to a reaction that directly liberates the exocyclic amine of cytosine as ammonia.At 20 C/N impurities, all the 700 flux measurements were viable (biomass greater than threshold). In this case, 27 carbon sources were incorrectly predicted (∼0.04% misclassification rate). The nitrogen source cytosine is predicted as ammonia in 78.8% of cases and as adenine in all other cases.E. coli metabolic network model for 7 carbon and 7 nitrogen sources. Then, we divided the data into training and test sets and employed machine learning with a generalized linear framework to train a model to predict growth conditions. We found that even in growth environments contaminated with other nutrient sources, we could make reliable predictions regarding the primary composition of the growth media. Our prediction technique worked well on pairwise combinations of carbon and nitrogen sources, and it could also extrapolate to previously unseen metabolites.We have developed a method for making predictions regarding bacterial growth conditions from known simulated metabolic fluxes. We generated fluxes using the complete It was surprising to us that given the same number of observations in the training set, separate prediction of nutrients always performed better than joint prediction. There are two likely explanations for this result. First, making joint predictions requires discriminating between 49 different pairwise combinations. By contrast making individual predictions only requires discriminating 7 different conditions in two different sets. Thus, one possible explanation for the lack of predictive power is that we simply did not have the appropriate level of training data. Indeed adjusting the amount of training data appears to have a dramatic effect on joint prediction in particular . On the E. coli metabolism. Namely, as the environmental chemical noise increases from 1 C/N to 10 C/N, our model increasingly predicts acetate and pyruvate as the default carbon sources. Due to its centrality in terms of energy and precursor-molecule production, for any input growth source the reactions that lead to the TCA cycle or the reactions within the TCA cycle should have some reasonable amount of reaction flux. In other words, acetate and pyruvate as default nutrient sources may not be so surprising when one considers their central role in the TCA cycle—which is essentially the center of bacterial metabolism.Although the background chemical noise can have a dramatic affect on model accuracy, the misclassification rate remained acceptably low even with 10 randomly picked C/N impurities. The addition of these impurities revealed one interesting and unexpected physiological hypothesis about the To verify that the observed default carbon-source misclassification was not an artifact of nutrient limitation (carbon versus nitrogen), we increased the uptake rates of carbon source artificially high while keeping nitrogen source at normal uptake and vice versa. This ensures limiting conditions for one source and non-limiting for the other. These simulations did not alter our earlier conclusion that separate prediction performs better than joint prediction.In addition to these simulations, we carried out three further analyses. First, instead of using all the metabolic reactions in the iAF1260 model, we used only the post-transport reactions in the regression model, as the earlier analysis had suggested that the key reactions for a growth substrate seemed often to be at the substrate's entry point into the metabolic network. However, this approach lead to poorer predictions than did the approach of initially using all metabolic reactions in the model and letting the LASSO technique select the predictive ones. This finding confirms that the growth substrates are non-trivially encoded in the internal fluxes of the metabolic network. Second, instead of using equal numbers of carbon and nitrogen impurities, we also considered using only carbon or only nitrogen impurities. When only carbon (or nitrogen) impurities were present, prediction of nitrogen (or carbon) sources had higher sensitivity than when there was a mixture of C/N impurities. Finally, we considered an alternative optimization protocol where we minimized the absolute sum of fluxes on the FBA solution obtained by maximizing biomass. Under this protocol, prediction accuracy was somewhat lowered relative to our default protocol. However, prediction remained possible at accuracies way above random guessing.Our regression model had a relatively large feature space (1442 reactions) compared to the number of observations used to train the model (∼480 to ∼2450). Therefore, efficient feature reduction was crucial to obtain reliable models. We prevented over-fitting during feature selection by employing regularized regression via the LASSO in principle to make inferences about the growth environment. Our results indicate that this is indeed the case, though it remains to be tested how well our results carry over to experimental systems.Our work is conceptually related to the work by Brandes et al. One shortcoming of our statistical approach to predicting growth conditions is that it cannot predict previously unseen nutrients, i.e., carbon or nitrogen sources that were not used in the training data set. Nevertheless, we found that our regression model made reasonable choices, such as predicting the previously unseen maltose (a disaccharide consisting of two glucose molecules) as glucose. In this context, it is comforting that separate prediction generally outperformed joint prediction, since separate prediction was much more robust to previously unseen nutrients. In particular, a previously unseen carbon source did not substantially negatively affect prediction of a previously seen nitrogen source and vice versa.Throughout this work, we have used basic flux balance analysis to predict the bacterial phenotype. In principle, one could use more realistic models that integrate regulatory information and/or signalling-pathway information with flux balance analysis techniques E. coli network. In addition, our results indicate that for most input metabolites at least one predictive reaction commonly occurs near its entry point into central metabolism. Finally, we found that the number of reaction fluxes required to make accurate predictions is relatively small.We have found that predicting growth conditions from simulated metabolic flux data is a computationally tractable problem. Of note, our data indicate that separately predicting carbon and nitrogen sources performs better than jointly predicting them from paired input. Although this result is to some extent influenced by the volume of training data, it very likely reflects the structure of the metabolic reactions in the −1 hr−1. But for 5 reactions, i.e., ATPM, CAT, FHL, SPODM, SPODMpp, the upper bound is set to 50 mmol gDW−1 hr−1. The lower bound for the majority of reactions (nearly 1800) is set to 0 mmol gDW−1 hr−1, which means that the flux cannot flow in the direction opposite to that specified in the model (irreversibility constraint). A set non-growth associated maintenance (NGAM) of 8.39 mmol gDW−1 hr−1 is used for the ATPM reaction (ATP maintenance). The lower bounds of some exchange reactions is set to non-zero values, i.e., these reactions by default are meant to uptake ions, carbon and nitrogen sources, and so on. We used the default oxygen uptake rate (−18.5 mmol gDW−1 hr−1) in the iAF1260 model, but we changed the lower bounds of glucose and ammonia to zero, except when we used these compounds as carbon or nitrogen sources.We carried out flux balance analysis (FBA) using the COBRA toolbox optimizeCbModel in the COBRA toolbox, using default parameters. We considered all solutions with a biomass flux below a threshold of 0.558 to be inviable. The choice of this threshold value is explained in subsection “Impurities” below.After setting up the constraints on transport fluxes as described in the previous paragraph, we carried out FBA using biomass as the objective function. FBA finds fluxes that are consistent with the given constraints and that maximize the objective function. The FBA was performed with the function optimizeCbModel , where model is the iAF1260 model with biomass reaction as optimization function.To understand if the choice of objective function affects the prediction of growth substrates, we also carried out simulations with an additional level of constraints. The additional constraint we imposed was minimization of the absolute sum of fluxes on the solution obtained from prior biomass maximization. This analysis was carried out using the function k-means clustering of steady-state fluxes obtained using all pair-wise combinations of the 174 carbon and 78 nitrogen sources. Of the 7 carbon sources chosen, none resulted in any growth when used as a growth condition in the absence of a nitrogen source. By contrast, all nitrogen sources except ammonia yielded growth when supplied in the absence of a carbon source. Note that all of these remaining nitrogen sources do contain carbon atoms, thus additional supply of carbon was not strictly necessary for growth on these substrates.We initially carried out simulations on 49 growth conditions consisting of all pairwise combinations of 7 carbon and 7 nitrogen sources . The com−1 hr−1. This lower bound is commonly used in many studies For any given growth environment we simulated, we set the lower bound of the exchange reactions corresponding to the carbon and nitrogen sources present to −20 mmol gDW−1 hr−1 while keeping the lower bounds of nitrogen sources at −20 mmol gDW−1 hr−1 and vice versa.For conditions with excess carbon or nitrogen, we increased the maximum uptake rate of one source while keeping the other one fixed. Thus, we changed the lower bounds (uptake rate) of carbon sources to −1000 mmol gDWFinally, we also carried out simulations on all pairwise combinations of all 174 carbon and 78 nitrogen sources previously used in Feist et al −1 hr−1. Note that we generated the flux data for a pairwise combination of 1 carbon and 1 nitrogen source along with the background impurities as described above. We also did additional simulations where we used only C or only N impurities. The bounds on the uptake rates for these impurities was the same as before.To make the simulation scenario more challenging and more realistic, we incorporated different numbers of impurities  to the simulated growth media. For this, we used a subset of the 174 carbon and 78 nitrogen sources, previously used in Feist et. al For all the results described above, we used a biomass threshold to filter out non-viable flux measurements. We calculated this threshold value using biomass measurements at the lowest number of impurities (1 C/N), using all pairwise combinations of the 7 carbon and 7 nitrogen sources chosen for the first analysis, and with the largest training dataset size (∼2450 replicates). We recorded the biomass values for all these simulations, and used as lower threshold of viability three standard deviations below the mean, which came out to 0.558.We predicted growth conditions using regularized multinomial logistic regression, as implemented in the GLMNET package cv.glmnet in the GLMNET package. When using this function, we set family equal to “multinomial”. The cross-validation procedure yielded the λ value that had the lowest misclassification rate under cross-validation  as well as the regression coefficients at that λ. We then used the fitted models to calculate the misclassification rate on the test set, using the function predict. We repeated this step to calculate the misclassification rates at different numbers of impurities  and different training data sizes .After filtering for biomass, for each number of impurities, we used half of the dataset as test set. We used subsets of the remaining half as training sets . On the training sets we fitted regularized regression models via 3-fold cross validation, using the function −6 on the magnitude of all flux values. Absolute flux values below the threshold were set to zero before fitting the LASSO model.To guarantee that the LASSO model would converge, we imposed a minimum threshold of 10https://github.com/clauswilke/Ecoli_FBA_input_prediction.All raw data and analysis scripts are available online in the form of a git repository at S1 FigureScatter plot showing varying uptake amounts of C/N sources when carbon is unlimited. We increased the upper bounds of the carbon sources and plotted the uptake amounts of carbon and nitrogen sources. The color coding reflects whether separate prediction could predict the carbon and nitrogen sources correctly for each replicate. Green: both C and N source are correctly predicted; blue: only N source is correctly predicted; purple: only C source is correctly predicted; red: neither source is correctly predicted.(EPS)Click here for additional data file.S2 FigureScatter plot showing varying uptake amounts of C/N sources when nitrogen is unlimited. We increased the upper bounds of the nitrogen sources and plotted the uptake amounts of carbon and nitrogen sources. The color coding reflects whether separate prediction could predict the carbon and nitrogen sources correctly for each replicate. Green: both C and N source are correctly predicted; blue: only N source is correctly predicted; purple: only C source is correctly predicted; red: neither source is correctly predicted.(EPS)Click here for additional data file.S3 FigureProbability of misclassification, for FBA with and without minimization of absolute fluxes. For each heat map, the actual C or N source is plotted along the x-axis and the predicted one is plotted along the y-axis. The gray level of squares indicates the fraction of times a given C or N source was predicted, with white corresponding to 0% and black corresponding to 100%.  Predictions performed on fluxes whose absolute values were not minimized (default throughout this work).  Predictions performed on fluxes whose absolute values were minimized. In all cases, we added 10 C/N impurities to the growth environment.(EPS)Click here for additional data file.S1 TableKey reactions identified to discriminate carbon sources. These reactions were identified from a model trained to only predict carbon sources (separate prediction). The model was trained on a data set obtained with 1 C/N impurity and with training data-set size of ∼2450 observations.(XLSX)Click here for additional data file.S2 TableKey reactions identified to discriminate nitrogen sources. These reactions were identified from a model trained to only predict carbon sources (separate prediction). The model was trained on a data set obtained with 1 C/N impurity and with training data-set size of ∼2450 observations.(XLSX)Click here for additional data file.


Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae  Metabolic modeling is a powerful tool for bioprocesses to understand, predict and optimize the synthesis of intracellular molecules of interest To overcome these hurdles, a commonly used hypothesis is the balanced-growth hypothesis, also called the Quasi-Steady-State Approximation (QSSA). Internal metabolites are assumed not to accumulate inside the microorganisms, which turns out to be a reasonable hypothesis for most of the microorganisms growing under constant conditions. This implies that every substrate uptake leads to microbial growth and products excretion. Thanks to this hypothesis, intracellular models are simplified and thus depend only on the stoichiometry of the network, the reaction reversibility and the uptake rate of the substrates.Most of the metabolic modeling and analysis frameworks rely on the balanced-growth hypothesis. These frameworks include Flux Balance Analysis (FBA) However, the balanced-growth hypothesis is unreasonable for microorganisms undergoing permanent environmental fluctuations. Indeed, in this case, the everlasting dynamics of intracellular accumulation and reuse play a key role in the cell metabolism. This is the case for phototrophic microalgae submitted to day/night cycles, which use photons to fix inorganic carbon during the day using photosynthesis. These promising organisms are seen as good candidates for production of third-generation biofuels thanks to their higher productivity compared to classical biofuels Microalgae store energy and carbon during the day so as to support growth and maintenance during the night, because of their autotrophic metabolism and the synchronization of their circadian cycle on the daily light Tisochrysis lutea) in order to illustrate it on a realistic example, where simulation results are compared to experimental data. Finally, assumptions of the present approach and their implications are discussed in a last section along with the perspectives of the present work and the future possible applications.The aim of the present paper is to present DRUM , a new metabolic modeling framework, which allows to model dynamically intracellular processes where accumulation of metabolites plays a significant role. In a first section, the modeling approach and its mathematical translation are described. Then the approach is applied successfully to the carbon metabolic network of a unicellular microalgae  system:A (AC), are not under the quasi-steady-state constraint. They are allowed to accumulate and thus can behave dynamically, which provides the dynamics to the whole network  the presence of metabolic pathways corresponding to metabolic functions ii) the presence of group of reactions regulated together iii) the presence of different compartments in a cell . Groups of reactions are thus determined taking into account these intracellular mechanisms. It is to be noted that some intracellular reactions can thus belong to several group of reactions. Mathematically, this is represented by redundant columns in the stoichiometric matrix K. The remaining metabolites (A) interconnecting the sub-networks formed using these rules are usually either situated at a branching point between several pathways or are end-products of metabolic pathways (e.g: macromolecules).The QSSA for sub-networks relies on K into sub-matrices SNiK formed of grouped reactions: i composed of i) incoming and outgoing metabolites SNiS and SNiP allowed to accumulate and ii) intermediate metabolites SNiC at quasi-steady state. SNiS and SNiP are either substrates S, products P, biomass B or intracellular metabolites A allowed to accumulate.The sub-networks correspond mathematically to a partitioning of the stoichiometric matrix Each sub-network is assumed to be in a quasi-steady-state: SNiE is the matrix of elementary flux modes of sub-network iSN and SNiα is the weight vector of the elementary flux modes. SNiα can be interpreted as the kinetics of the macroscopic reactions described by the stoichiometric matrix Under these assumptions and using elementary flux mode analysis By grouping all the sub-networks, the following system is obtained:A are authorized to accumulate. Any other metabolite jC∈C∖A are assumed not to accumulate. Thus: Only metabolites jC∈C∖A have simple dynamics. Hence a reduced dynamic model is obtained, defined by the metabolites vector En the number of macroscopic reactions:A) is allowed. Only the kinetics α of the resulting macroscopic reactions need to be determined. Classical kinetics found in literature are mass-action, power-law, Michaelis-Menten, Hill, cybernetic kinetics α are determined, all the metabolic fluxes can be computed using: System (7) is a simplified version of (1) with the same structure but of much lower dimension, where accumulation of some internal metabolites  can then only be determined thanks to a mass-balance on each chemical element:Z correspond to a chemical element  and B(t) correspond to the concentrations of A and B at time t, and Z(t)X correspond to the concentration of chemical element Z in total biomass X at time t.In the DRUM approach, particular attention has to be drawn to the definition of biomass To sum up, the DRUM approach is based on the following methodology, which is decomposed into a 4-step process :Find in the literature or build the metabolic network of the microorganism under study.Group metabolic reactions into sub-networks assumed to follow the QSSA.Reduce each sub-network to a set of macroscopic reaction using elementary modes analysis.Define kinetics for macroscopic reactions obtained and deduce an ODE system.For sake of pedagogy, in the next section, the DRUM approach is illustrated on the carbon metabolism of unicellular microalgae.Isochrysis affinis galbana  under day/night cycle was used Tisochrysis lutea2). The following measurements were performed: nitrates, particulate carbon and nitrogen, chlorophyll, total carbohydrates and neutral lipid concentrations To assess DRUM, experimental data of a continuous culture of Tisochrysis lutea has not been sequenced yet, no genome-scale metabolic network reconstruction was possible. Using the metabolic network of eukaryotic microalgae available  photosynthesis, ii) upper part of glycolysis iii) carbohydrate synthesis iv) lower part of glycolysis, v) lipids synthesis, vi) biomass synthesis. Then, each sub-network was reduced to macroscopic reactions thanks to elementary flux mode analysis efmtool was used Metabolic reactions were grouped by metabolic functions, taking into account cell compartments and metabolic pathways. Six sub-networks were obtained  correspoIn the following sections, the formation and reduction of each sub-network is developed. The results are summarized in Photosynthesis allows phototrophic organisms to generate cell energy and incorporate carbon autotrophically. The process takes place in the chloroplast and is decomposed into two steps commonly called the light and dark steps. The light step consists in the generation of cell energy  from water and photons, producing oxygen (R1). Thanks to the energy of the light step, the dark step incorporates carbon dioxide through Calvin cycle producing one 3 carbon sugar (3-phosphoglycerate written G3P). Then G3P is transformed in glyceraldehyde 3-phosphate (GAP) and transported to the cytosol of the cell (R14).As both the dark and light step of photosynthesis takes place in the chloroplast and they both have the same metabolic function (to incorporate inorganic carbon), the reactions of the two steps were grouped into a sub-network and assumed at quasi-steady state. Elementary flux mode analysis yielded only one Elementary Flux Mode (EFM) , giving As GAP is the end-product of photosynthesis and is situated at the center of glycolysis, glycolysis was split according to GAP into two sub-networks: lower glycolysis and upper glycolysis. In addition, dividing glycolysis into two parts is meaningful since upper glycolysis and lower glycolysis have different metabolic goals. Indeed, upper glycolysis synthesizes glucose 6-phosphate (G6P) to produce reductive power (NADPH) or to produce carbon storage compounds (carbohydrates), whereas lower glycolysis produces phosphenolpyruvate (PEP), which is then invested either in lipids synthesis or in the citric acid cycle to generate precursor metabolites for protein, DNA, RNA, chlorophyll and biomass synthesis.G6P, instead of glucose, was chosen as the output of upper glycolysis because G6P is at a branching point between two metabolic pathways with different metabolic functions: carbon storage through the synthesis of carbohydrates and synthesis of NADPH reducing power through the pentose phosphate pathway.Metabolic reactions of upper glycolysis were grouped and assumed at steady-state. Elementary flux mode analysis resulted in 3 macroscopic reactions . ReactioLower glycolysis is a cascading set of reactions which generates the key metabolite phosphoenolpyruvate (PEP) and energy cofactors  from GAP. Lower glycolysis was cut at PEP instead of acetyl-coA (AcCoA) because of the presence of the anaplerotic reactions , converting oxaloacetate into PEP and vice-versa.Lower glycolysis was assumed at steady state. One macroscopic reaction (MR5) was obtained with Elementary Flux Mode analysis . StoichiCarbohydrates (CARB) are complex sugars stored in the cell. They are formed from 6-carbon sugars (here G6P) by reverse glycolysis. All the reactions participating to carbohydrate synthesis were grouped and assumed to be in quasi-steady state. One reversible macroscopic reaction (MR6) was obtained by reduction thanks to elementary flux mode analysis .Lipids include a broad group of different macromolecules present in a cell. They contain at least one hydrophobic part and are constituted of long carbon chains linked to a sugar by an ether bound. In microalgae, only Triacylglycerols (TAGs) can be transformed into biofuels All the reactions participating in lipids synthesis were grouped and assumed at quasi-steady state. One reversible macroscopic reaction (MR7) for the synthesis of PAs was obtained with elementary flux mode analysis . Stoichi2 and conversely some carbon atoms are gained when consuming lipids.The macroscopic reaction obtained satisfies balance of the cofactors. For example 2 ADP yield 2 ATP, and 29.3 NADPH yield 29.3 NADP. Interestingly, when lipids are synthesized, some carbon atoms are lost through the production of COProtein, DNA, RNA and chlorophyll are necessary to synthesize biomass. Hence, all their synthesis reactions were grouped into a sub-network and assumed at quasi-steady state. Reactions for PA synthesis were not included because a dedicated sub-network is already present in the model. Therefore the biomass synthesis sub-network includes citric acid cycle, oxidative phosphorylation, pentose phosphate pathway, N and S assimilation, amino acids synthesis and nucleotide synthesis. Citric acid cycle takes place in the mitochondrion and transforms PEP into many precursor monomers for nitrogen assimilation, nucleotide and amino acids synthesis. For each run of the cycle, energy cofactors are generated  and can be breathed into ATP thanks to oxidative phosphorylation. ATP is then reinvested into amino acids and nucleotide synthesis, necessary for DNA, RNA, protein and chlorophyll synthesis. Finally, reductive power (NADPH) necessary for nucleotide and amino acids synthesis is synthesized through the pentose phosphate pathway.2. A principal component analysis on the EFMs revealed that the difference was mainly due to two metabolic functions  that could be performed following different pathways, some less energy-efficient than others explaining the difference of CO2 production  composed of substrate S, metabolites authorized to accumulate A and functional biomass B; K' is the reduced stoichiometric matrix (16×8) and α is the kinetics vector (8×1)  .B corresponds to functional biomass. Total biomass, in terms of particulate carbon and nitrogen, is computed using the following formulae:AC and BC correspond to the number of carbon atoms per molecule of A and B, AN and BN correspond to the number of nitrogen atom per molecule of A and B, A(t) and B(t) correspond to the concentration of A and B at time t, and C(t)X and N(t)X correspond to the concentration of carbon and nitrogen in total biomass X. As carbon and nitrogen biomass were measured experimentally, we simulated carbon and nitrogen content of the biomass. However, other chemical elements can be easily computed using the formula above. No additional parameters would be necessary as the above formula only uses chemical element composition and concentrations of A and B. Chemical element composition for A and B is available in section 1.5 of the As explained in section 2, biomass 2 dissolved concentration), estimation of maintenance and hence cofactors balance is difficult to perform. We thus decided not to consider the balance of energetic cofactors, and we did not describe their fate .Here, only the core metabolic network of a unicellular autotrophic microalgae was represented. It does not take into account energy necessary for mechanisms not represented by the network, like for instance the turnover of macromolecules and other so-called futile cycles. As it is clearly documented in the literature The dynamic model has 10 degrees of freedom, each degree represented by a parameter that needs to be calibrated. To estimate parameters, we minimized the squared-error between simulation and experimental measurements (taken as an average of the duplicates) using the following formula:fminsearch under Scilab (http://www.scilab.org)) was used. To reduce the risk of finding a local minima, several optimizations were performed with random initial parameters set. Then the set fitting the best experimental data was chosen. As very few data were available, all data were used to estimate model parameters. Results of parameter identification are presented in To minimize the error, the Nelder-Mead algorithm Model simulation reproduces accurately experimental data see . In partThe model predicts a minimum of carbon storage (lipids and carbohydrates) one hour and a half after sunrise (13h37 and 13h17), when light intensity is sufficient to catch up with carbon loss through respiration. In a similar way, the maximum is reached three hours before sunset (20h50 and 21h02), when light intensity is insufficient to catch up with carbon loss through respiration . Total cContrary to carbon storage, functional biomass carbon quota increases three hours before sunset until two hours after dawn, taking carbon from the lipids and carbohydrates pool . Most ofTotal biomass can be visualized in terms of particulate carbon and nitrogen . Carbon Tisochrysis lutea stops incorporating nitrates as soon as the night starts. This time period corresponds to the period where cells divide In the model, nitrogen content has exactly the same trend as functional biomass, since functional biomass is the only intracellular metabolite with nitrogen. It can be observed that there is slight delay in the uptake of nitrogen between the model and experimental data. In experimental data, the minimum is at sunrise and the maximum at sunset, meaning that Finally, it is interesting to look at the evolution of PEP, G6P and GAP concentrations predicted by the model. First, their concentrations are sufficiently low in terms of carbon, showing that carbon storage is mainly done with lipids and carbohydrates. However, their concentrations over time are not constant, and are particularly different between day and night. Indeed, their concentrations are much higher during the day than during the night, giving certain flexibility to the metabolic network when environmental conditions changes rapidly (here light). The ability of metabolic network to face permanent fluctuating environmental conditions consolidates one of the advantages of the DRUM approach. Such flexibility is acquired through certain metabolites, which can accumulate and therefore act as buffers. This could not be achieved with a steady-state assumption.The main assumption of the DRUM approach is the quasi-steady state assumption on sub-networks of the metabolic network. This assumption is supported by the idea of cell function and cell compartment, often associated to co-regulation and substrate channeling.Indeed, in a cell, metabolic pathways composed of grouped reactions regulated together are omnipresent. These reactions are often synchronous: intermediate metabolites produced by a reaction are nearly immediately consumed by the next reaction in the cascade. This implies a quasi-steady state for the intermediate metabolites. Many examples of such pathways can be found in literature. One of the most illustrative ones is reactions in cascade where the first reaction of the pathway is submitted to feedback inhibition by the end-product of the last reaction Chlamydomonas reinhardtiiIn addition, spatial and molecule crowding are not negligible phenomena in a cell. When not taken into account, they imply that any intracellular metabolite can be consumed in any reactions of the cell, even if the reaction occurs at a far loci or in a different compartment where the molecule cannot be transported to and needs to be resynthesized. This often leads to erroneous metabolic flux distributions when using flux balance analysis and to a combinatorial explosion of the number elementary flux modes representing the metabolic network. For example, in the case of the metabolic network of An extreme illustration of space phenomena supporting our quasi-state assumption is substrate channeling, where an intermediate metabolite is, instead of being released in the solution, passed from enzyme to enzyme so as to avoid any loss to competing pathways Even if regulation, substrate channeling and reactions loci in the cell are not always well-known, we assumed that QSSA is a biologically reasonable assumption for a group of reactions taking place in the same compartment, synthesizing a same pathway end-product or fulfilling a similar metabolic function. QSSA on sub-network is a mild way to relax the balanced growth hypothesis, without constraining the full network anymore. In most cases, the main sub-networks will be the same, defined on metabolic functions: upper glycolysis, lower glycolysis, TCA cycle, Calvin cycle (for photoautotrophs), macromolecules synthesis.It is very important to keep in mind that the DRUM approach does not only split the initial network into sub-networks, but it also duplicates some reactions that take place simultaneously at different part of the cell within different functions. This point is very important in order to keep a sound meaning to the reduced networks derived from the EFM analysis.A allowed to accumulate are thus end-products of metabolic pathways  or situated at a branching point between several pathways.Network splitting into groups of reactions is performed on the basis of the above-mentioned criteria. However, these intracellular mechanisms are not always well known. Hence, it is difficult to split the network only taking into account experimentally proved report of these phenomena on the microorganism studied. To overcome this hurdle, network splitting was also performed thanks to educated guesses using the topology of the metabolic network, the known metabolic functions of some groups of reactions, the experimentally known accumulating metabolites  and the key topological place of some metabolites. The metabolites Tisochrysis Lutea, the presence of the chloroplast compartment was used to assume QSSA for photosynthesis. For the rest of the metabolic network, reactions were grouped according to known metabolic functions: carbohydrate synthesis, upper glycolysis, lower glycolysis, lipids synthesis, biomass synthesis. The accumulated metabolites GAP, PEP, G6P were chosen because situated at branching points of several metabolic pathways. Indeed, GAP, the output of photosynthesis, is situated at the middle of glycolysis and is also an output of the pentose phosphate pathway. G6P is situated at the branching point between carbohydrates synthesis and the pentose phosphate pathway. Finally, PEP is situated at the branching point between lipids synthesis, the TCA cycle for precursor metabolites necessary for biomass synthesis and the anaplerotic reactions.In the case of Tisochrysis lutea metabolic network was performed by trial and errors with different possible decompositions. Several possible configurations were tested and the best one was kept. For example, the metabolic network was cut, instead of glyceraldehyde 3-phosphate (GAP) at glycerone-phosphate (DHAP) and instead of phosphoenolpyruvate (PEP) at pyruvate (PYR). To cut at PEP seemed a better choice to fit functional biomass data, but cutting at DHAP did not influence the results since DHAP and GAP are interchangeable metabolites (‘DHAP <–> GAP’ (EC 5.3.1.1)). Whether the network should be cut at GAP or DHAP could only be answered with additional experimental measurements.However, the choice of the decomposition is not totally straightforward. The splitting of In a general way, only few decompositions work, but some have close performances. Only experimental data will allow favoring one from the other. Still, the presence of these equivalent decompositions is beneficial since it points out the dynamic measurement of metabolites to make so as to discriminate the best model.The method, in its first developmental stage, is not automatic yet. However, systematic network splitting techniques could be developed. For example, the network could be split according to the metabolites participating in more than a threshold number of metabolic reactions efmtoolOnce network splitting into sub-networks was performed, network reduction is straightforward as it consists in computing Elementary Flux Modes (EFMs) for each sub-network and reducing them to macroscopic reactions by keeping only the transport reaction of incoming and outgoing metabolites. This can be performed automatically using softwares like However there is an exponential explosion of the number of Elementary Flux Modes (EFMs) when the number of reactions increases, which implies an exponential explosion of the kinetics parameters to estimate. This could make the approach intractable and annihilate the advantage of DRUM compared to a full kinetics model when using large sub-networks resulting for example from the splitting of a genome-scale metabolic network. To overcome this difficulty, small sub-networks should be favored and there are available methods to reduce the number of EFMs such as the use of experimental data Tisochyris lutea, the biomass synthesis sub-network is composed of 105 reactions. The calculation of the EFMs resulted in 24 macroscopic reactions. Note that the number of macroscopic reactions is already lower than the number of reactions of the original sub-network. For a further reduction, we kept the EFM with best PEP/CO2 yield when normalized by unit of biomass synthesis flux, which was the same as optimizing biomass growth since we minimized carbon loss through oxidative phosphorylation.In the case of Tisochrysis lutea, DRUM reduces the number of EFM from 18776 for the whole network down to 11. This implies a low number of degrees of freedom (10 parameters) compared to the other methods  catalyze the intracellular reactions and hence growth.Biomass B. We assumed that macromolecules catalyzing growth such as proteins do not accumulate and end up in biomass B, which we rename functional biomass B. This relies on the assumption that storage compounds of a cell does not have any other metabolic functions than to store chemical elements  so as to supply energy and chemical elements demands to continue growth when these resources are no longer available in the environment. The term αB in (7) is thus still meaningful, since functional biomass B catalyzes growth as the term vB does in (1). An estimation of the total actual biomass can then be obtained by summing up functional biomass B and the storage terms A  in microalgae For metabolic models, only static flux predictions under constant light were made, where lipids and carbohydrates were at a constant ratio in biomass In relation to the existing microalgae models DRUM, the new framework proposed in this paper, allowed for the first time to predict dynamically at the same time the macroscopic scale of the bioprocess  exploit the Gene-Enzyme-Reaction relationship to predict the effect of the deletion of one or several genes on the growth and/or on product synthesis The first level consists in targeting metabolic functions represented by the macroscopic reactions deduced from the EFMs of each sub-networks. Deleting a metabolic function is hence equivalent to delete a macroscopic reaction. In a practical way, as EFMs are minimal metabolic behaviors of the cell The second level is the deletion of a reaction in the metabolic network. This could yield the same result as deleting one metabolic function, yet it could also imply accumulation of a previously non-accumulating metabolite hence modifying the decomposition of the sub-networks. It could also imply obtaining different EFMs and hence different macroscopic reactions (e.g.: stoichiometric coefficients). This could require a new decomposition and reduction of the sub-networks, and new kinetics to postulate and parameters to estimate.Tisochrysis lutea, the goal of our microalgae model was to better apprehend the carbon metabolism of microalgae in day/night cycles. It is clear that such a model has many direct implications for metabolic engineering with microalgae. The fact that cells can store very high amounts of lipids with a daily pattern has clear consequences on the harvesting period (section 3.4). It also indicates the paths and the enzymes to be targeted in order to more efficiently accumulate lipids. For example, we can target the carbohydrates production (MR6) and simulate de novo the model to see whether it has an impact on lipids accumulation. The results suggests, as expected, that the carbohydrates storage pool diminished quickly at the expense of the lipids and functional biomass pool  reveals two distinct metabolic behaviors.(TIF)Click here for additional data file.Figure S2Principal component analysis of the elementary flux modes obtained from the biomass synthesis sub-network. The difference in the PEP/CO2 yield is mainly due to two metabolic functions (incorporation of nitrogen (x-axis) and alanine synthesis (y-axis)) that can be performed thanks to different pathways, some less energy-efficient than others explaining the difference in CO2 production.(TIF)Click here for additional data file.Figure S3Predicted photosynthetic quotient during a day/night cycle. The quotient varies between 1.29 and 1.60, depending on the light intensity, which agrees with the typical range of 1.0–1.8 for algae (TIF)Click here for additional data file.Figure S4Metabolic fluxes of the core network at midday (18 h).(PNG)Click here for additional data file.Figure S5Comparison of the wild type and MR6-deficient in silico models. The two models were then simulated for 48 h, one with kcarb = 0 h−1.mM B−1, the other one with kcarb = 70.00 h−1.mM B−1. The dilution rate and the incoming substrate concentrations were set at 1 days−1 and 4.018 mgN.L−1.(PNG)Click here for additional data file.File S1Detailed metabolic network reconstruction process of Tisochrysis lutea; list of reactions and metabolites; analysis of the whole metabolic network; list of sub-networks; list of macroscopic reactions obtained for the biomass synthesis sub-network.(PDF)Click here for additional data file.File S2Scilab script of the day/night cycle model of Tisochrysis Lutea.(SCE)Click here for additional data file.File S3Experimental data of continuous cultures of Tisochrysis Lutea.(XLS)Click here for additional data file.Video S1Predicted metabolic fluxes between sub-networks during a 24 h day/night cycle.(MP4)Click here for additional data file.