Constraint-based modeling is a widely used and powerful methodology to assess the metabolic phenotypes and capabilities of an organism. The starting point and cornerstone of all such modeling is a genome-scale metabolic network reconstruction. The creation, further development, and application of such networks is a growing field of research thanks to a plethora of readily accessible computational tools. While the majority of studies are focused on single-species analyses, typically of a microbe, the computational study of communities of organisms is gaining attention. Similarly, reconstructions that are unified for a multi-cellular organism have gained in popularity. Consequently, the rapid generation of genome-scale metabolic reconstructed networks is crucial. While multiple web-based or stand-alone tools are available for automated network reconstruction, there is, however, currently no publicly available tool that allows the swift assembly of draft reconstructions of community metabolic networks and consolidated metabolic networks for a specified list of organisms.Here, we present AutoKEGGRec, an automated tool that creates first draft metabolic network reconstructions of single organisms, community reconstructions based on a list of organisms, and finally a consolidated reconstruction for a list of organisms or strains. AutoKEGGRec is developed in Matlab and works seamlessly with the COBRA Toolbox v3, and it is based on only using the KEGG database as external input. The generated first draft reconstructions are stored in SBML files and consist of all reactions for a KEGG organism ID and corresponding linked genes. This provides a comprehensive starting point for further refinement and curation using the host of COBRA toolbox functions or other preferred tools. Through the data structures created, the tool also facilitates a comparative analysis of metabolic content in any given number of organisms present in the KEGG database.AutoKEGGRec provides a first step in a metabolic network reconstruction process, filling a gap for tools creating community and consolidated metabolic networks. Based only on KEGG data as external input, the generated reconstructions consist of data with a directly traceable foundation and pedigree. With AutoKEGGRec, this kind of modeling is made accessible to a wider part of the genome-scale metabolic analysis community.The online version of this article (10.1186/s12859-018-2472-z) contains supplementary material, which is available to authorized users. Bacillus, Clostridium, Escherichia, Pseudomonas, and Salmonella, the Eukaryota Homo sapiens, and Saccharomyces, and the Archaea Methanosarcina, to name just a few. While many of these reconstructions were created years ago, they are still a helpful and reliable source when constructing a new genome-scale metabolic model (GEM) for another species, or to extend the knowledge of an existing reconstruction. However, the metabolic networks are often reconstructed using quite different methodologies and approaches with a wide variety of annotation conventions. Consequently, the comparison of genome-scale reconstructions is not straightforward when the interest is in identifying how much a set of reconstructed networks actually differ in biological content. This challenge needs to be addressed by the modeling community in order to avoid unnecessary repetition of arduous reconstruction work [Genome-scale metabolic modeling has gained a sharp increase in popularity in recent years. Currently, there exist more than 160 well curated metabolic network reconstructions [ion work , 3.For manipulating and curating these model metabolic networks, different tools exist. Most notable is the COBRA Toolbox , an openThe development of tools to aid and assist in the reconstruction of GEMs has recently been an area of active research –15. For Some of the tools, such as ModelSeed , MicrobeOf the tools mentioned above, CarveMe  has a noMEMOSys  is a staThe aforementioned reconstruction tools have various strengths, thus offering the modeling community a strong base to create and curate single organism FDRs suitable to a user’s needs. In addition to these, more specialized tools exist, such as KEGG2SBML , which tHowever, as is well known within the field, even when using one of the tools capable of automatically generating FDRs, it is a necessity to use a host of other tools or software packages in a manual-curation process to optimize a reconstruction’s prediction accuracy : It has In general, it is also necessary to manually add and adjust transport reactions, their presence automatically surmised from experimental evidence of uptake rates, cytosolic activity, or template reconstructions. Finally, the biomass composition function is notoriously difficult to assess correctly, as the biomass composition might be subtly different for two related strains in the same medium, but drastically different for the same strain in two different media . While tThere is an increasing interest in the modeling of microbial communities, both due to the fact that it is becoming more and more tractable from a technical standpoint, and because of the mounting evidence for the importance of microbiomes in ecology , industrHowever, constructing GEMs for a microbial community is an arduous and time-consuming process: It is not simply a case of twice the organisms resulting in twice the work. As the number of organisms increases, the complexity of the potential interactions also increases exponentially. In order to save time and effort to make the task more tractable, it is therefore imperative to supply researchers with a set of tools that allow the efficient automation of, at least, parts of this reconstruction process. This is a topic of research and development receiving much attention at current conferences.As a contribution to fill this capability gap, we created a pipeline within the COBRA Toolbox in Matlab named AutoKEGGRec that only uses the Kyoto Encyclopedia of Genes and Genomes (KEGG) database –28 as exAutoKEGGRec is easy to use, and there is no need for conversion of model files to work with supported SBML versions and requirements of the COBRA toolbox. Specifically, AutoKEGGRec allows the construction of a large number of draft reconstruction networks, as well as the direct assembly of community reconstructions. In the process of assembling these reconstructions, the AutoKEGGRec function also constructs a consolidated draft metabolic network consisting of a union of all metabolic reactions in the query organisms. Note that analyses may be performed on the consolidated network and other data structures generated by the function.E. coli K-12 strains with the KEGG IDs eco, ecj, ecd, ebw, and ecok and explain the overall design of the pipeline. A user Manual [Additional file AutoKEGGRec is designed in Matlab 2017b, hereafter referred to as Matlab, and uses functions within the COBRA Toolbox v3.0, hereafter referred to as COBRA toolbox/COBRA. Since AutoKEGGRec uses existing COBRA toolbox functions for saving the models, the generated data structures containing the reconstructed model work seamlessly with all COBRA functions. In the following, we will illustrate functions of AutoKEGGRec by using a set of query organisms consisting of the five Designed to be a fast tool that is easy to use, AutoKEGGRec facilitates the rapid assembly of draft models from KEGG annotations for one or several query organisms. Internally, it’s designed for efficiency of operation, first minimizing the number of queries sent to the KEGG servers during data collection stage and, subject to this, minimizing the number of operations needed to assemble the draft model from the collected data. Intended to fit into the COBRA toolbox as a function, AutoKEGGRec requires no further installation or setup. While not necessary for its intended operation, it is directly amenable to be modified by each user as required since it is provided as a Matlab function. Figure OrgRxnGen-flag  or n , the reactions are not included in the reconstruction. If the “Remark” field contains the strings “Generic”, “General”, or “General reaction”, these reactions are also omitted. Additionally, the compound information stored within KEGG occasionally note whether a compound is generic, and lists exact mass. When mass is set to 0 for a compound, this signifies it as a generic compound, and reactions that contain it are omitted from the reconstruction.All the reactions in the draft metabolic network(s) are filtered to avoid redundant or poorly defined reactions (step (4)). For example, if the “Comment”-field in KEGG contains “Remark” and the reaction equation contains OmittedData option flag. These reactions are marked with a new rxnAttention field which explains why AutoKEGGRec omitted them from the reconstruction. This allows the user to first identify omitted reactions relevant to their project, followed by a curation step before they are potentially included.Omitted reactions are, for the sake of transparency and potential utility, stored within an additional Matlab structure, which is accessible for the user using the createModel function in the COBRA toolbox, the consolidated-type draft reaction network is created based on KEGG genome annotation and linked reactions. The GPR (gene-protein-reaction) rules are added based on the ORG matrix, and the model is annotated according to the KEGG information for the reactions and components. This includes compound names, reaction names, and compound KEGG IDs, to name just a few.In generating an FDR, AutoKEGGRec will add the complete reaction annotations: where possible, annotation fields supported by COBRA are used, but some new fields are, by necessity, created to store the information. Using the SingleModels option flag is provided. These draft models are generated by first making multiple copies of the consolidated model (one for each organism), before removing reactions not specifically present in each organism. The community model is generated using the COBRA createModel function with the complete list of reactions as input. Here, each organism appears as a separate compartment since AutoKEGGRec will add the organism’s KEGG ID to all of its compounds.AutoKEGGRec will generate individual draft network reconstructions for each of the listed organisms when the Since the resulting output is a Matlab structure variable, the user only needs to define a single output variable independent of the number or combination of optional input flags.OrgRxnGen, GenePlot and Histogram may be used without generating a reconstruction, only providing the information listed for these flags  matrix, that matches organisms to reactions. Thus, the OR matrix describes a bipartite graph representing the reactome of each query organism as given by KEGG from the OR matrix, a complete list of every reaction present in at least one of the query organisms is assembled, allowing further KEGG queries to be conducted only for these reactions. Also, AutoKEGGRec constructs the Organisms-Reactions-Genes (ORG) matrix using data in the OR matrix.E. coli K-12 to illustrate the organization of information. Here, each row corresponds to a KEGG reaction ID, and empty rows indicate that the particular reaction ID is not present in any of the organisms . In this example, a value of five in the Sum column and a value of unity in the Total column shows that the reaction is present in all E. coli K-12 strains. The genes associated with each reaction in the organisms are separated with, an “OR”-relationship. The number of genes per reaction is summarized in the “Genes” column; if the value varies between the organisms, a list of the different values are reported.Table The pipeline uses only KEGG organism IDs as input.G instead of C, are not included in the reconstruction even if there is no alternative reaction.Glycan reactions are mostly removed. Since some of the glycans also have compound numbers within KEGG, these are still included in the first draft reconstruction. Reactions containing only glycans, i.e. KEGG metabolite IDs starting with n or m of a compound C are not included by AutoKEGGRec: The constraint-based modeling is based on a steady-state or semi-steady-state approximation, and there is no consensus in the field for how one handles polymerization reactions. The user may edit these reactions to allow their inclusion in a reconstruction.Polymer reactions or non-specific reactions dealing with an of amount createModel. Even though KEGG includes a few transport reactions for some organisms, these are not explicitly marked.There is no assignment of reactions to different compartments. All reactions and compounds are placed in the default compartment “cytosol” by the COBRA function Genes are linked to reactions. In the case of more than one gene associated with a reaction, the genes are linked together with “OR”-relationships since KEGG does not specify how the gene-products interact. Consequently, the user must manually curate these relations, providing the correct “AND” or “OR” relations between genes.C00017) or “DNA” (C00039), but also more specific compounds like “DNA adenine” (C00821).Reactions with massless compounds are omitted. This step is necessary to maintain a mass balance within the reconstruction. Some of these reactions contain compounds like “protein” , and 3 reactions were excluded from the FDR because of potentially being polymerization reactions. AutoKEGGRec evaluates the 1626 compounds of the remaining 1604 reactions, to identify generic (mass-less) compounds. In the example case of the E. coli K-12 strains this is true for 390 compounds, which is about 23.98%. These compounds participate in 378 reactions, which increases the number of omitted reactions to 519 (29.74%), and leaves the FDR with 1226 high quality reactions. All the mentioned reactions are detailed in the output data structure generated by the omittedData option flag, the omitted compounds and the saved KEGG annotations are stored as well, examples of outputs of the omitted data are shown in the Manual.The number of omitted reactions for the five mentioned C06136 and C06135, leading to an alternative reaction in the KEGG reaction universe using only these C compound names as C-named KEGG compounds is used in the FDR generated by AutoKEGGrec. This particular reaction, however, contains the compound C06136, which is, according to the KEGG compound annotation, a generic compound with the formula C45H79N2O23R, and for that reason has no mass. While assembling this important compound information, such compounds are identified and the reaction will be marked in the “RxnAttention” field with “This reactions contains a generic compound or a compound without mass in KEGG”, so that these omitted reactions are easy do identify. These compounds are stored within the Matlab structure for omitted data so that the user can quickly access the compounds in questions, identify the reason for omission, and decide if and how the user wants to implement the compound/reaction into the (curated) reconstruction. Note that the field “RxnAttention” will be found within the model for included reactions for careful inspection, shown in the next example, as well as within the omitted reactions.As an example use of our proposed model field “RxnAttention”, 10 reactions were marked in the generated FDR. One such reaction is C compound KEGG ID, e.g. in the reaction There are examples of glycan molecules which do not have a exact_mass or mol_mass listed in KEGG, but only mass. However since there is a specific mass given which allows the user to manually check the reactions for mass consistency, AutoKEGGRec includes these compounds.It is added to the FDR because of a lack of alternative reactions, and will be marked in the “rxnAttention” annotation field. We encourage users to carefully inspect reactions with this tag that stay within the reconstruction. Additionally, we note that some glycan compounds do not have and E. coli strains stored in KEGG by their KEGG organism ID could be joined into one consolidated model, offering the user the union of the E. coli reaction networks available in KEGG along with corresponding gene links. Even unrelated organisms could be added to include their reactions, pathways, and related gene names.AutoKEGGRec has no intrinsic limit on the number of query organisms, all 65 eco, to the published E. coli models iAF1260 [E. coli K-12 MG1566 with the ID 511145.180. Comparing the quality of different GEMs is a complicated issue, not least in part due to differences in namespace, making alignment of different metabolic networks difficult.Directly investigating the correspondence between the AutoKEGGRec FDRs and experimental data would make little sense, as the tool’s purpose is not to make a complete model capable of producing biomass. However, in order to give an idea of the amount of remaining work for any modeler employing the tool, we chose to compare the AutoKEGGRec FDR, created using the KEGG ID  iAF1260  and iJO1 iAF1260 , as welleco, the FDR generated in AutoKEGGRec, is of comparable quality to the manually curated models iAF1260 and iJO1366. This speaks to the quality of KEGG, as well as FDRs generated using AutoKEGGRec.Since two of the models are manually curated and the third is made from a template, they contain biomass and transport reactions. As AutoKEGGRec reconstructions do not, such reactions have been removed before comparison. That way the pure reaction networks can be compared to that of the KEGG-based reconstruction generated by AutoKEGGRec. The results can be seen in Table AutoKEGGRec is an easy-to-use tool for the rapid assembly of first-draft reconstructions for genome-scale metabolic modeling including as much data as possible. While there exists a selection of tools and toolkits that aid in the assembly and refinement of first-draft GEMs, these tend to be stand-alone and/or online, both of which, especially in combination with small development teams in temporary academic positions, may cause any number of issues due to lack of support. These tools mostly create single-organism FDRs, as most are not designed for or allow the creation of community or generic/consolidated models.Any automatic reconstruction necessitates steps such as gap-filling, mass and charge balance for reactions, reaction reversibility corrections, and adjustment of exchange, ATP maintenance and biomass reactions. These steps being mostly automated might appear as a convenience, but it is important to note that these tools often make implicit assumptions in the course of the reconstruction work without marking them as such. This is done in order to achieve functional models, i.e. models that are capable of producing the constituents of a biomass reaction, but, importantly, there are usually many ways of achieving this, and which way is chosen matters for the correctness and quality of the model, making control and traceability of the process an important issue. Many such educated guesses are based on template models or common knowledge, such as the inclusion of seemingly universally essential cofactors  in the bBiomass reactions in particular are known to be fickle with regards to cofactor coefficients . This maTo varying degrees, these published tools automate the generation of first draft reconstructions, and greatly facilitate the reconstruction of GEMs. AutoKEGGRec, however, is not intended to automatically generate a first draft model with all requisite transport reactions and a biomass function. Since all information is based only on KEGG, every detail is eminently traceable, which may be of particular interest to modelers, as many “new” models are based on previous models, and may therefore inherit previous poor annotations and assumptions. The intent is to generate an unbiased and clean FDR of the metabolic network based only on the genome annotation in KEGG.It is implemented as a Matlab function fully integrated with the COBRA toolbox, with its open, community-maintained and state-of-the-art suite of tools for model curation and manipulation. Additionally, AutoKEGGRec contains the complete annotation for all reactions and compounds offered by KEGG, putting more information right at the modeler’s fingertips than what is offered by most other comparable reconstruction tools.In its rapid assembly of a draft reconstruction, AutoKEGGRec mostly covers the currently automatable parts of the first stage in the protocol to generate high-quality genome-scale metabolic reconstructions . AdditioWhile the reconstruction of microbial consortia remains an immature method, AutoKEGGRec can help speed up the process. Further work in assembling the reconstruction is still expected to rise steadily with the number of organisms, as not only does each separate organism’s metabolic network needs to be curated, but also the interactions between the different networks and their global effect on the environment. However, due to the chosen naming convention for compartments within the community models, transport reactions can easily be added simultaneously for multiple organisms if necessary.Here we present AutoKEGGRec, a fast tool to be used within the COBRA toolbox in Matlab that is able to create single organism, community, and consolidated first draft reconstructions based on the KEGG database. Unlike most other available tools, AutoKEGGRec is designed from the ground up to allow for community and consolidated metabolic network reconstructions. Also, being based only on data from KEGG, it has a clear and transparent data ancestry.AutoKEGGRec does not provide a fully functioning model since elements such as a biomass function, ATP maintenance function, and most transport reactions for the given organism(s) are not included. The addition of these elements would require estimations and guesswork beyond the data available in KEGG at present. However, AutoKEGGRec does provide a very well annotated first draft reconstruction based on all data available in KEGG. As with reconstructed networks generated with any software package, the user should perform additional experiments, and add biomass function(s), ATP maintenance, and relevant import reactions to further enhance the reconstruction; all tasks which may be performed using existing functions in the COBRA toolbox. Consequently, AutoKEGGRec fills an important niche for the modeling community with its reliable and rapid generation of well annotated single, community, and consolidated FDRs within the COBRA toolbox environment based only on the clear, high-quality, and freely accessible data in KEGG.Project name: AutoKEGGRecOperating system(s): Any which can run MatlabProgramming language: MatlabOther requirements: Matlab, COBRA Toolbox version 3.0 or newerLicense: MatlabAny restrictions to use by non-academics: Licence needed for MatlabAn internet connection is required.Availability: AutoKEGGRec will be submitted to be part of the COBRA toolbox. Additionally, the software is included as supplementary file, and is also freely available for download at https://www.ntnu.edu/almaaslab and https://github.com/emikar/AutoKEGGRec. AutoKEGGRec was developed and tested on Matlab  and the COBRA toolbox v3.0.Additional file 1User manual for AutoKEGGRec. (PDF 5258 kb)Additional file 2The Matlab file for AutoKEGGRec. (M 83 kb)


We then used this model to characterize the response of the liver’s energy metabolism to a controlled perturbation in diet. Transcriptomics data were collected from the livers of Sprague Dawley rats at 4 or 14 days of being subjected to 15%, 30%, or 60% diet restriction. These data were integrated with the iRatLiver model to generate condition-specific metabolic models, allowing us to explore network differences under each condition. We observed different pathway usage between early and late time points. Network analysis identified several highly connected “hub” genes  that showed differing trends between early and late time points. Taken together, our results suggest that the liver’s response varied with short- and long-term diet restriction. More broadly, we anticipate that the iRatLiver model can be exploited further to study metabolic changes in the liver under other conditions such as drug treatment, infection, and disease.Mapping network analysis in cells and tissues can provide insights into metabolic adaptations to changes in external environment, pathological conditions, and nutrient deprivation. Here, we reconstructed a genome-scale metabolic network of the rat liver that will allow for exploration of systems-level physiology. The resulting  Homeostatic regulation in hepatocytes involves many metabolic processes spanning interconnected pathways, requiring a systems approach to provide mechanistic insight. GEnome-scale metabolic Models (GEMs) provide one such systems biology framework for the quantitative interrogation of metabolic capabilities across diverse conditions3. GEMs detail the connectivity of the metabolic network through reaction stoichiometries, allowing for systems-level computation of reaction fluxes in response to genetic or environmental perturbations5.Metabolic adaptation is critical for the ability of cells to maintain homeostasis following a physiological change. One of the more important organs for regulating homeostasis is the liver, which plays a primary role in detoxification, protein synthesis, and nutrient regulation8. Notably, the integration of transcriptomics data has allowed for the construction of condition-specific models12. The global human metabolic network reconstruction15 paved the way for the use of GEMs to explore clinical applications and resulted in many cell- and tissue-specific GEMs18. Several of these tissue-specific models have been used to study human physiology22 and pharmacological targets25. The hepatocyte has been the focus of several cell-specific modeling efforts. In 2010, two GEMs of the human hepatocyte were published simultaneously27 to understand diverse physiological liver functions; one of these models26 was later used to simulate metabolic phenotypes resulting from inborn errors of metabolism28. A later GEM, iHepatocytes23, was used to predict serine deficiency in patients with non-alcoholic fatty liver disease and to identify genes that are potential therapeutic targets for treatment of non-alcoholic steatohepatitis29.The scope of GEMs has been iteratively expanded to include additional pathways and physiological information, including various -omics data30 and to model aspects of human physiology30. Studying these diverse metabolic processes of the liver provides important insights into the physiological response to pharmacological interventions31. One of the well-studied physiological responses in the liver is due to a change in nutritional status, such as over-fed or starvation conditions34. During a well-fed state, the liver stores excess glucose as glycogen, which is then converted back to glucose during glucose deprivation. Understanding the metabolic regulatory responses to such perturbations in various physiological models represents an important open area of research.While these cell-specific models have been used to understand pathophysiology in humans, the limitations associated with perturbation experiments in humans have limited their utility in translation research. Thus, organisms like Sprague Dawley rats (Rattus norvegicus) – small in size, easy to handle, high rate of reproduction, and similar physiology to humans – have been used as a primary model organism to study toxicologyin silico investigation of the metabolic effects of different diet-restriction patterns as interpreted through our reconstruction of a liver-specific GEM of the rat (iRatLiver). We generated genome-wide transcriptomics data of the rat liver to assess the response to different feeding patterns. These data were then integrated with iRatLiver to generate condition-specific models that were used to simulate changes in metabolic pathway usage as a result of the dietary changes. More broadly, we anticipate that this model can be a useful resource for toxicological and biomedical research, with its comparability back to the human reconstructions.Here, we present the 35. Because we are ultimately interested in studying human physiology, we used an existing GEM of the human liver16 as a starting point for the homology-based reconstruction of rat liver metabolism; see Methods for details regarding the reconstruction process. The resulting model, iRatLiver, comprises 1882 reactions, 1448 metabolites, 994 genes, 7 compartments , and 82 metabolic subsystems  as previously reported16  and corion Fig. ).Figure 51. Further, the diet-restricted samples for days 4 and 14 clustered separately, indicating that the expression profile was also influenced by the duration of the diet restriction. We observed high variance in the group 5 rats (60% diet restriction), suggesting that there was a less uniform adaptive response. Ultimately, these results indicated that the underlying expression profile of the liver varied as a function of time.We then filtered the gene expression data to the set of metabolic genes to examine the effects of diet restriction on liver metabolism. We performed principal component analysis (PCA) on the normalized expression values of the metabolic genes, observing distinct clusters for the different experimental groups Fig. . The con12 and E-flux52); the two algorithms take different approaches to integrating the expression data with the GEM, resulting in models with differing structure (see Methods). The resulting condition-specific models  allowed for the exploration of how metabolic fluxes and pathway usage were altered under nutrient deprivation.Analysis of the raw transcriptomics data provided a snapshot of biological processes that might be regulated in various conditions, but our goal herein was to obtain a holistic view of how the metabolic network changed as a result of diet restriction. Thus, we integrated the transcriptomics data into the iRatLiver model using previously published methods 54, showing that various metabolic subsystems cluster together  on the 55, such as L-lactate dehydrogenase (LDH_L) malate dehydrogenase (MDH), succinate dehydrogenase (SUCD1m), and phosphoribosylpyrophosphate synthetase (PRPPS), showed variations in fluxes across conditions55. Under starvation conditions, iRatLiver correctly predicts the synthesis of glucose through gluconeogenesis, the conversion of lactate to pyruvate (by LDH_L) to oxaloacetate in the mitochondria. The accumulation of TCA cycle intermediates in hepatocytes due to gene deletion is responsible for hepatic steatosis in dietary restricted state56. In addition to these behaviors, the iRatLiver model also predicted alterations in phosphoribosylpyrophosphate synthetase (PRPPS) under fasting conditions.Upon deeper analysis of these subsystems, we observed that the distribution of reaction fluxes varied between conditions Fig. . SeveralHsd11b1), hydroxysteroid (17-beta) dehydrogenase , and aldo-keto reductase family 1 (Akr1c19). These genes are involved in various biological processes such as glucocorticoid biosynthesis, cholesterol biosynthetic process, fatty acid biosynthesis process, oxidation-reduction process as well as response to nutrient levels. This observation suggests that hormone regulation is another important physiological change that occurs during diet restriction.We also examined the regulation of hormones, one of the main functions of the liver, and the subsequent effect on various physiological functions in the system during diet restriction. Several genes in steroid metabolism were altered based on our metabolic analysis, namely hydroxysteroid 11-beta dehydrogenase 1  to be pyruvate kinase , hydroxyacyl-CoA dehydrogenase (Hadha), transketolase and transketolase-like protein , phosphoglucomutase (Pgm1), triosephosphate isomerase (Tpi1), and enolase (Eno3). We calculated the node degree distribution (the number of connections the node has to other nodes in the network) and edge betweenness (the number of shortest paths that go through an edge in the network) for the network. The edge betweenness for glycerol kinase (Gk) and glyceraldehyde-3-phosphate dehydrogenase (Gapdh) was highest, indicating that many paths in the network traverse by this edge.To test this hypothesis, we constructed a protein expression network in which genes are nodes and interactions are edges  and used it to study diet restriction in rats. We used the iRatLiver model to compute changes in the network-level metabolic flux state of the system due to alterations in the nutritional status of 50 Sprague Dawley rats. We have provided evidence that this 55, an observation supported by our results herein.First, upon diet restriction, the liver maintains homeostasis through regulation of metabolic activity across the metabolic network. We observed that several key pathways – central carbon metabolism, fatty acid degradation, purine metabolism, and propanoate metabolism – are responsible for the regulation of systems-level function under the diet restriction. Hepatocytes can use glucose and/or fatty acids as metabolic fuels, and selection of these depends on hormonal regulation and nutrient levels. In fasting or nutrient starvation conditions, hepatocytes predominantly depend on oxidation of fatty acids for energy supplyPrps1, Prps1l1, Prps2) was previously reported to be affected by amino acid depletion59, while mutations in Prps1 have been associated with hyperuricemia, hyperuricosuria, hypotonia, and ataxia and gain-of-function mutation results in PRS-1 superactivity60. Our investigation of differential pathway usage under diet restriction therefore warrants further study to better characterize genetic factors that influence the varied metabolic shifts observed here in short- and long-term diet restriction.Second, the liver’s response varied with respect to short- and long-term diet restriction. The survival of rats subjected to severely restricted diet indicates that the organism is able to alter its metabolism to maintain required energy levels. Through integration of gene expression data with the iRatLiver model, we were able to identify the genes and pathways responsible for the metabolic shifts that allowed the organisms to adapt to changing environmental conditions. We investigated reactions involved in carbohydrate metabolism  and observed changes in the flux through phosphoribosylpyrophosphate synthetase (PRPPS) in fasting conditions. PRPPS  is a key enzyme in pentose phosphate pathway and governs carbon flow. Akt is known to regulate Tkt activity, and it has been reported that caloric restriction causes downregulation of the PI3K/Akt/mTOR pathway, ultimately affecting amino acid, carbohydrate and purine metabolism61. Thus, we conclude that these pathways are affected under the conditions studied here. Similarly, Pgm1 (Phosphoglucomutase) –involved in the interconversion of glucose-1-phosphate and glucose-6-phosphate – has been connected to the regulation of glycogen content during nutritional stress in the system62. In humans, Pgm1 plays a role in balancing cellular demand during nutrient depletion, thus helping cell proliferation. Both Pgm1 and Tkt (identified here as hub nodes) have been implicated in cancer cell proliferation and have been studied as possible therapeutic targets62. Thus, it is possible that a network approach such as the one presented here could be used in pharmaceutical studies for the identification of potential drug targets.Third, network models have the potential to provide important insights into complex liver functions. The construction of an interaction network allowed for the identification of key genes such as In this study, we used a systems approach to interrogate energy metabolism in the rat liver in a metabolic network model context. Through the integration of transcriptomics data, we generated condition-specific models that were used to compute pathway usage under different diet-restricted conditions. Our results suggest that the construction of a detailed transcriptional regulatory network of the rat liver would lead to further important insights into the effects of diet restriction, such as genes that are switched on or off during those stress conditions. We anticipate that the iRatLiver model presented here, which we are making freely available to the scientific community, will also prove useful to others in studying important physiological and biomedical questions related to obesity, aging, and pharmacology.16) for the construction of iRatLiver model. The liverCADRE model displayed improved metabolic functionality and was useful in predicting biological outcomes. The liverCADRE model consisted of 1763 reactions, 1402 metabolites, 994 unique genes and 80 subsystems16. Following the established protocol for reconstructing metabolic networks35, we identified homologous genes between human and rat using Ensembl (GRCh37)63 and Homologene64 and replaced these human genes with the corresponding Rattus norvegicus genes.We used a previously published tissue-specific GEM of the human liver 16 and iRatLiver model and found differences in vitamin B2, vitamin C, squalene and cholesterol synthesis, fatty acid oxidation, tryptophan as well as pentose phosphate pathway.The resulting draft reconstruction consisted of 1843 reactions, 1477 metabolites, and 988 unique genes. We then added reactions belonging to cholesterol metabolism, tryptophan metabolism, glycolysis, tyrosine metabolism and others using information from the human Recon 2 model37. Second, we performed a previously used array of tests to ensure the model could compute basic functionality of the liver16. Specifically, we tested the model’s ability to perform gluconeogenesis, triglyceride synthesis, amino acid degradation, and ammonia and ethanol detoxification  was provided either ad libitum (groups 1 and 2), reduced by 15% (group 3), reduced by 30% (group 4), or reduced by 60% (group 5). Reduction in food was calculated based on the average food consumption recorded for group 1 and 2 based on the previous 3 days. There were 10 rats per group; five rats per group were subjected to 4 days of dietary restriction (necropsy on day 5) and the remaining 5 per group were subjected to 14 days (euthanized on day 15). Groups 2–5 were fasted 8–12 hours overnight prior to necropsy. Standard clinical and anatomic pathology endpoints were collected and examined (not included in this study).We studied the effects of varying levels of nutrient deprivation on male Sprague Dawley rats, approximately 8–10 weeks of age, that were subjected to varying levels of dietary restriction Fig. ). Rats wRNA extraction from rat hepatocytes was carried out using Qiagen  RNeasy Mini kit and qiazol according to the manufacturer’s instructions to homogenize the tissues and chloroform for phase separation. Amplification was performed with Oligo dT primed RT using SSII, 2nd strand cDNA synthesis, cleanup via Qiagen MinElute. Synthesis of biotinylated cRNA using the Enzo  amp kit, cleanup of cRNA via Qiagen RNeasy Mini kit. Biotin-labeled aRNA products were hybridized to Affymetrix  GeneChip® Rat Genome 230 2.0 Arrays per manufacturer instructions provided on the product insert. Scans were carried out as per manufacturer instructions provided on the product insert. The scan files were processed using Expression Console (Affymetrix) for quality control and subsequent results were used in microarray data analysis.affy (version 1.38.1). The expression data was submitted in Gene Expression Omnibus (GEO)72 and the accession number for the data is GSE98621. A single Empirical Bayes model included in the Bioconductor package EBarrays (version 2.2.0) package, Lognormal-Normal-Modified-Variance (LNN-MV), was used to calculate differentially expressed genes. These analyses were conducted separately for each treatment group. The function crit.fun, setting FDR = 0.1, was used to calculate the minimum posterior probability required to deem a sequence representing a gene significant in each treatment group.All statistical analyses were executed using the R statistical computing platform (version 3.0.1). Expression data were normalized using the Robust Multi-Array Average method implemented in the Bioconductor package 57  as control. The number of DEGs in each condition are represented in Data see Data ).73, we implemented two different algorithms: Gene Inactivity Moderated by Metabolism and Expression (GIMME)12 and E-Flux52. The two algorithms make differing assumptions for the integration of transcriptomics data, resulting in differing outputs and interpretations of subsequently computed physiological states.To identify the metabolic changes taking place in the liver, we integrated transcriptomic data with the iRatLiver model. Among available methods for integrating omics data with metabolic model54 to normalize the average flux values and represented the values in clustergram in Fig. 74 and determined the robustness of metabolic model. The information related to altered subsystems can be extrapolated to further identify possible rewiring in the system leading to adaptation during diet-restricted state. The COBRA toolbox76 was implemented in MATLAB 2014a and academic licenses of Gurobi Optimizer v7.5 and IBM CPLEX v12.7.1 were used to solve LP and MILP problems in this study.The combination of these methods is helpful in identifying set of active reactions in condition of interest and capturing extent of flux changes and reshaping the flux cone considering the measurements of gene expression. Upon implementation of the algorithms, we computed the flux state (optimizing for growth rate) of each model separately; the reactions with zero flux were identified (reactions with a flux less than 1E-06 were denoted as carrying no flux). Reactions having non-zero fluxes were selected from the total set of reactions in the model. Only those reactions having measurable fluxes from both methods were considered active and subsequently used for analyzing reactions and determining which subsystems were perturbed under diet-restricted conditions. We considered absolute values of reaction fluxes and grouped the reactions based on their corresponding subsystems. For each subsystem, we calculated average values of reaction fluxes. Considering group 2  as control, we subtracted the average values calculated for each subsystem for diet-restricted conditions. Then we carried out an unbiased approach to identify subsystem differences between diet-restricted conditions. We used projective decomposition77. A P-value cutoff of 0.05 was considered statistically significant in all analyses.Fisher’s exact test followed by a correction of the p-values for multiple testing using Benjamini-Hochberg procedure was used for pathway-based enrichment of genes identified from metabolic analysis57 was used for extracting confident interactions (STRING combined score >0.7) between these genes/proteins of the specific organism. The genes are represented as nodes and the interaction between nodes is called an edge. The interactions were visualized using Cytoscape78. We used the NetworkAnalyzer application in Cytoscape to calculate node degree distribution and edge betweenness. Nodes with highest connections in the network are defined as ‘hub’ nodes. The number of shortest paths that go through an edge in the network determines the edge betweenness.The genes belonging to altered subsystems were used for network analysis. STRING v10.5Supplementary figure 1Data S1Data S3Data S2


Recent research has shown that many types of cancers take control of specific metabolic processes. We compiled metabolic networks corresponding to four healthy and cancer tissues, and analysed the healthy–cancer transition from the metabolic flux change perspective. We used a Probabilistic Minimum Dominating Set (PMDS) model, which identifies a minimum set of nodes that act as driver nodes and control the entire network. The combination of control theory with flux correlation analysis shows that flux correlations substantially increase in cancer states of breast, kidney and urothelial tissues, but not in lung. No change in the network topology between healthy and cancer networks was observed, but PMDS analysis shows that cancer states require fewer controllers than their corresponding healthy states. These results indicate that cancer metabolism is characterised by more streamlined flux distributions, which may be focused towards a reduced set of objectives and controlled by fewer regulatory elements. Metabolic rewiring is a feature of many cancers. Here, the authors combine control theory and flux correlation analysis to study the transition of healthy metabolic networks to cancer states, and find that cancer metabolism is characterized by more streamlined flux distributions. In particular, cancer pathogenesis has recently been closely associated to serine, glycine and one-carbon metabolism2. Preclinical analyses have shown that by adopting a specific diet that limits the amount of serine and glycine, tumour growth was severely inhibited.Metabolic pathways are essential chemical processes that catalyse complex reactions indispensable for development and life. Recent research has shown that many types of cancers take control of specific metabolic processes4. However, these approaches are not easily applicable to large systems since they rely on a kinetic model of the metabolic pathways. More recently, an approach was developed that uses flux couplings between metabolic reactions5. Flux couplings identify constrained relations between fluxes of different reactions, which arise from the network topology and mass conservation6. Five types of couplings were identified, namely directional, partial, full, anti and inhibitive couplings. The networks were analysed using a minimum dominating set (MDS) approach to identify potential driver nodes reactions5. The MDS approach was proposed by Nacher and Akutsu7 and has been used to analyse many biological systems and identify proteins associated to cancer12. However, the flux coupling approach uses a discrete definition of coupling between reactions and does not take into account the full range of possible flux distributions that the metabolic system is able to support. For example, two reactions are defined as anti-coupled if when one of them is inactive then the other carries a non-zero flux (in a non-zero steady state), but this definition does not take into account the relation between both fluxes in situations where both reactions are active.Understanding how metabolic networks are controlled is a challenging question though. Metabolic control analysis was originally developed to evaluate how metabolic fluxes depend on kinetic parameters of enzymatic reactions or metabolite concentrations. The level of control is quantified by calculating control or elasticity coefficients13, it can be obtained from the angles between the vectors forming an orthonormal basis of the null-space (or kernel) of the stoichiometric matrix defining the metabolic network. The cosine of this angle precisely represents Pearson’s correlation coefficient between the fluxes carried by a pair of reactions over all possible steady states of the system, and was therefore named reaction correlation coefficient. Hence, the reaction correlation coefficient ϕij of a pair of reactions i and j is a continuous value comprised between –1 and 1, where ϕij = 0 indicates that the fluxes of both reactions are completely independent, ϕij = 1 indicates that they are perfectly correlated and ϕij = −1 indicates that they are perfectly anti-correlated.Here, we argue that in order to investigate the distributed control of metabolic flux in large-scale metabolic networks, a different approach is needed. Coupling should be measured by a continuous value characterising the relations between reaction fluxes over all feasible steady states, instead of a set of binary values that represent particular subsets of steady states. In order to distinguish this continuous measure from previously used definitions of coupling, we hereon use the term correlation. Such a measure already exists: as demonstrated by Poolman et al.14. In this network representation, the nodes are interpreted as metabolic reactions and the weighted edges correspond to the probabilistic flux exchanged among reactions. The application of PMDS in the context of metabolic fluxes makes it possible to connect controllability theory with flux correlations.In this work, we compiled metabolic networks corresponding to four healthy and cancer tissues, namely breast, lung, kidney and urothelial cancer. This data allows us to analyse the transition from healthy to cancer states from the metabolic flux perspective Fig. . We firsFrequency distributions of all correlations in models of healthy and cancer cells corresponding to four different tissues were computed and the results are shown in Fig. The clustering degree in all networks shows, however, a similar local structure Table . This inWe also determined the degree distributions in all these networks and found that they are similar and adhere to the classical scale-free distribution observed in most biological networks, including metabolic networks Fig. . It is iHowever, the specificity of lung cancer appears in the fraction of nodes connected to the giant connected component Table . Breast,Θ (threshold probability). The results . Even with a moderate perturbation of 10%, the average PMDS fraction only marginally increased and the PMDS fraction in the healthy state always remained larger than in the corresponding cancer state  and pyruvate metabolism . The citrate cycle is significantly enriched in PMDS nodes in breast and renal tissues  but not in urothelial and lung; inositol phosphate metabolism was enriched in healthy breast (p = 0.03). Conversely, aminoacyl-tRNA biosynthesis was significantly depleted in PMDS nodes in all cancer and non-cancer networks , as well as N-glycan biosynthesis . Overall, the fact that a higher proportion of controller nodes are found in central metabolic pathways is consistent with expectations, since these pathways distribute fluxes towards other parts of the metabolic network, and this property is maintained between healthy and cancer cells. Additionally, these results confirm that each cancer type has distinctive characteristics in terms of pathways enriched in PMDS nodes, with lung cancer being more distinct than the three other types.In order to compare the controller and non-controller nodes from a perspective of biological significance, we analysed the distribution of PMDS and non-PMDS nodes among metabolic pathways from the KEGG database. Since we are using metabolic models, a comparison to metabolic pathways is more appropriate than for example the Gene Ontology, which contains other types of biological functions not included in the data. We found that some central metabolic pathways are enriched in PMDS nodes across cancer and non-cancer networks: these pathways include glycolysis  among reactions in lung cancer, the number of necessary reactions to be controlled in cancer does not largely change. More importantly, the metabolic flux space in cancer remains easier to control than that in healthy state.Nevertheless, specific differences in metabolic flux correlations were observed in lung cancer. These differences were also reflected in the number of reactions assembled in the main connected component of the network. Heterogeneity in metabolic pathway activity has been reported before, not only between different types of cancers25. The glutamine metabolic pathway is tightly interconnected with the mTOR signalling pathway, which promotes cell survival and is activated by glutamine efflux; this particular feature is being investigated for potential therapeutic applications26. The tyrosine kinase epidermal growth factor receptor (EGFR) is frequently mutated in non-small cell lung cancer and has strong interrelations to several metabolic pathways. It was shown that EGFR signalling promotes not only glucose consumption and lactate production, but also de novo pyrimidine synthesis, therefore it plays a major regulatory role on global metabolism27. Different KRAS mutations are also found in lung cancer, which do not have the same cellular activity. It was shown that they affect different metabolic pathways, with distinguishing effects in particular in the glutaminolysis and glutathione pathways28. These examples show that, in addition to strong metabolic effects shared with other types cancers such as aerobic glycolysis, lung cancers can also be characterised by original relations with metabolic pathways. The full extent of these relations is still poorly understood but is an active area of research towards new therapies25.The number of active correlations in lung cancer is twice as large as that number in breast cancer. Counterintuitively, the PMDS size of both lung and breast cancer is lower than that in the corresponding healthy state. This indicates that the size of the reaction control backbone of both lung and breast cancer is very similar. The increase in correlations observed in lung cancer, consistent with the already reported variability on cancer metabolism, might only perform peripheral metabolic functions without critical control roles. Glutamine metabolism is altered in many types of cancer cells, but the consumption of glutamine by lung cancer cells is higher than in other cancer typesS, whose elements are the stoichiometric coefficients of each metabolite in each reaction. The kernel matrix K is defined by vectors constituting a basis of the null-space of S, such that S KT = 0.The computation starts by constructing the stoichiometric matrix of the network, K is not unique. However, if the vectors of K form an orthonormal basis, which means K KT = I, then the angles θij between the row vectors of K are invariant. The reaction correlation coefficient ϕij is defined as the cosine of ϑij:ki and kj are the row vectors of K corresponding to reactions i and j respectively. As demonstrated in Poolman et al.13, ϕij represents the Pearson correlation coefficient between the fluxes carried by reactions i and j over all possible steady states of the system. The mathematical demonstration is based on introducing a random matrix R that contains all possible steady states, s being the number of steady states which can be arbitrarily large. Then the Pearson correlation r of this distribution is defined, and when s tends towards infinite it is shown that r tends towards a product of k vectors, which represents the cosine of the angle.In most cases, K using the null function in Matlab and verified that it meets the orthonormality condition for each metabolic network. After obtaining ϕij for each pair of reactions, the probability of failure between reactions i and j was defined as ρij = 1 − abs(ϕij).We calculated i and j (ρij) and integrate it into a probabilistic control model. We want each node (reaction) to be covered by multiple nodes in MDS so the probability that at least one edge (incoming flux) is active is at least Θ. This problem can be formulated as a probabilistic minimum dominated (PMDS) as follows. Let S be a dominating set, then we require S to satisfy:ρij indicates the probability of failure between reactions .Natural and engineered complex networks are composed of thousands of nodes and tens of thousands of links. These links representing regulatory interactions or transmission lines suffer from probabilistic failures. The flux correlation coefficient allows us to define the probability of failure between reactions The standard MDS problem is formalized by the following integer linear programming (ILP) problem:Minimisesubject to:V indicates the set of reaction nodes in the network and E denotes the set of undirected edges between reaction nodes. Then, inserting the probabilistic condition shown in Eqs entclass1pt{minimaMinimisesubject to:deg(j) denotes the degree of reaction node j. In the above expression, the first term j is included in the PMDS, the inequality needs to be hold. In the implementation of the ILP-based method, a small number (10−6) is added to where 5 and Gatto et al.29 Supplementary data. Then, flux correlation networks were constructed by computing the reaction correlation coefficients. To create healthy and cancer networks a threshold of 0.5 was used, which means that absolute correlations smaller than 0.5 were deleted, or conversely that failure probabilities higher than 0.5 were deleted; in the resulting networks, nodes represent reactions and two reactions are connected if their correlation is higher than 0.5. This means that we are considering the high flux correlation networks in our analysis.Genome-scale models representing human metabolic pathways in healthy and cancer states were compiled from Basler et al.Θ, we constructed 10 randomised networks by rewiring 1%, 5% and 10% of the edges, respectively. We used the rewire function from the R igraph package, together with the keeping_degseq function that preserves the original network’s degree distribution, in order to conserve the topological properties of the networks.For each tissue type and for each value of 30 in order to obtain the number of PMDS and non-PMDS nodes in each pathway, then two-tailed Fisher exact tests were conducted using R in order to determine significant enrichment or depletion.We analysed the distribution of PMDS and non-PMDS nodes across all metabolic pathways of the KEGG database in order to determine whether some pathways are significantly enriched or depleted in controller nodes. Enzyme Commission numbers associated to reactions were extracted from the raw metabolic models, then were mapped to PMDS and non-PMDS node lists in the same conditions as described above. These node lists were searched against KEGG pathways using the KEGG Mapper toolFurther information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


Escherichia coli. In the present study, it was revealed that culturing E. coli in the presence of phenol not only decreased growth rate, but also biomass yield. This suggests that phenol affects the carbon flow of the metabolism, but the mechanism is unknown. To investigate the effect of phenol on the flux distribution of central carbon metabolism, 13C-metabolic flux analysis (13C-MFA) was performed on cells grown under different phenol concentrations . 13C-MFA revealed that the TCA cycle flux reduced by 25% increased acetate production from acetyl-CoA by 30% in the presence of 0.1% phenol. This trend of flux changes was emphasized at a phenol concentration of 0.15%. Although the expression level of citrate synthase, which catalyzes the first reaction of the TCA cycle, does not change regardless of phenol concentrations, the in vitro enzyme activity assay shows that the reaction was inhibited by phenol. These results suggest that the TCA cycle flux decreased due to phenol inhibition of citrate synthase; therefore, ATP could not be sufficiently produced by respiration, and growth rate decreased. Furthermore, since carbon was lost as acetate due to overflow metabolism, the biomass yield became low in the presence of phenol.Phenol is an important chemical product that can be used in a wide variety of applications, and it is currently produced from fossil resources. Fermentation production of phenol from renewable biomass resources by microorganisms is highly desirable for sustainable development. However, phenol toxicity hampers phenol production in industrial microorganisms such as  Bacterium coli phenologenes, Pantoea agglomerans, and Clostridium tetanomorphum, catalyzes the conversion between tyrosine and phenol , phenol condition   is an effective approach to investigate the carbon flux distribution on central carbon metabolism (Various organic solvents are toxic to log Pow) . The log is 1.46 , and is olerance . Furtherolerance , and pheolerance . Becauseolerance , the cautabolism .E. coli under different phenol concentrations , and compared these flux distributions to identify the effect of phenol on the metabolism. To investigate the cause of the flux changes, the in vitro enzyme assay was performed and revealed that citrate synthase is strongly inhibited by phenol.In the present study, we cultured wild type E. coli strains used in this study are shown in gltA+, and Δpta strains were aerobically grown at 37°C overnight using 5 mL of M9 medium containing 4 g/L glucose in a test tube. For the gltA+ strain, 40 mg/mL histidine and 10 mg/mL Thiamine hydrochloride was supplemented to the M9 media in accordance with the previous report (The s report .660) of 0.05. Phenol was added to be 0, 0.04, 0.08, 0.1, 0.12, and 0.16% (v/v). The cultures were incubated at 37°C at 70 rpm using a TVS062CA incubator . The OD660 was measured every 5 min.To evaluate phenol toxicity using an automated optical density monitoring system, the preculture was inoculated into 5 mL of the same M9 medium in an L-shaped test tube at an initial optical density at 660 nm . Phenol was added to be 0 and 0.15% (v/v). For 13C-MFA, the cultures were performed using the same condition except that the glucose was replaced to [1-13C] glucose. Phenol was added to be 0, 0.1, and 0.15% (v/v). All cultures were performed in triplicate.For evaluating the fermentation profiles in flask scale, the preculture of wild type and Δ600 was measured using an UVmini-1240 UV-VIS spectrophotometer . The dry cell weight (DCW) was calculated using a conversion coefficient of 0.3 g/L/OD600 based on a previous report  was collected by centrifugation. After hydrolyzation, the proteinogenic amino acids were derivatized with tert-butyldimethylsilyl (tBDMS). The mass isotopomer distributions of amino acids were measured using a gas chromatography/mass spectrometer (GC/MS)  with a DB-5MS column . The mass isotopomer distributions were corrected for the presence of naturally occurring isotopes . The det13C-MFA based on previous analyses of E. coli. The elementary metabolites unit framework was used for modeling the carbon atom transitions  pathway, the anaplerotic pathway, and the glyoxylate shunt, was considered for nsitions . All reaimeasured and MIDisimulated are measured and simulated mass isotopomer distribution of ith amino acid, respectively. The standard deviation (SD) was set to 0.01 in GC/MS measurements . After removing the debris by centrifugation , the crude extract was used for citrate synthase activity measurement. The protein concentration of the crude extract was measured using a nanoDrop 2000 spectrophotometer . Citrate synthase activity was measured by Ellmann’s method, that detects the thiol group of CoA by a colorimetric reaction using 5′,5′-Dithiobis(2-nitrobenzoic acid) (DTNB) (To measure the citrate synthase activity of the ) (DTNB) . DTNB waE. coli citrate synthase in vitro reaction was examined using a sample obtained from a gltA overexpressing strain, JW0710-AM, from the ASKA library . At OD600 of approximately 0.3, 0.1 mM of isopropyl β-D-1-thiogalactopyranoside was added to induce gene expression. After 2 h, the cells were collected by centrifugation , and were washed by 5 mL of filter sterilized buffer containing 50 mM sodium phosphate, 200 mM NaCl, and a protease inhibitor tablet . To keep the plasmid overexpressing the gltA gene, 25 mg/L of chloramphenicol were added to the media. The obtained cell pellet was extracted by sonication and used for in vitro enzymatic assays in the same manner described above.Phenol inhibition of the  library . In precin vitro reaction was also evaluated using a sample obtained from wild type E. coli. PGI activity was measured as NADPH formation through a coupled reaction with glucose 6 phosphate dehydrogenase (G6PDH) , and 2 mM D-Fructose 6 phosphate, NADPH formation was measured by absorption at 340 nm. One unit (U) is defined as the amount of enzyme required to convert 1 μmol of substrate into product per minute per milligram protein.Phenol inhibition of glucose 6-phosphate isomerase (PGI)  (G6PDH) . After aE. coli BW25113 was cultured using a synthetic M9 medium with different phenol concentrations  in L-shaped test tubes. 660 at each phenol concentration. The specific growth rate decreased by 40% under 0.1% phenol, and by 84% under 0.16% phenol as compared to that without addition of phenol. A previous study has also reported that an increase in the phenol concentration of the culture led to a decrease in the growth rate of E. coli, and eventually cell growth was completely inhibited . The time courses of cell, glucose, and acetate concentrations in the culture broth are shown in 600 reached the maximum value of 4.7 at 9.3 h. Glucose consumption was the fastest among the three conditions, and was depleted by 8.3 h. Acetate concentration reached a maximum of 12.4 mM at 8.3 h, and was quickly consumed after glucose depletion. At 0.1% phenol, the maximum OD600 was 4.4 at 24.2 h. Glucose was consumed more slowly and was depleted by 10.4 h. Acetate concentration reached a maximum of 20.1 mM (1.6 times of that at 0% phenol) at 10.4 h, and then it was gently consumed. At 0.15% phenol, the maximum OD600 was significantly decreased to 2.6. Glucose consumption was the slowest and was depleted at 14 h. Acetate production was further enhanced to 34.5 mM at 24 h. No acetate consumption was observed after depletion of glucose. Furthermore, no ethanol, lactate, succinate, and formate productions were detected throughout the culture period under any conditions. The specific rates during the exponential growth phase are summarized in At 0% phenol, the ODpta strain which does not have phosphotransacetylase for acetate formation was cultured in the absence and presence of phenol . As a result of flux optimization, the RSS values of conditions with 0, 0.1, and 0.15% phenol were 92.1, 104.5, and 103.3, respectively . The 95% confidence interval of each flux, to explain the measured mass isotopomer distributions of amino acid, was also calculated. The best fitted flux distribution and the 95% confidence interval are shown in To identify the reaction in which the flux was changed depending on phenol concentrations, a -1 h-1. However, the fluxes of citrate synthase at 0.1 and 0.15% phenol were decreased to 0.5 and 0.4 mmol gDCW-1 h-1, respectively. This suggests that acetyl-CoA does not flow into the TCA cycle, therefore, increasing overflow from acetyl-CoA to acetate.Although no significant change was observed in the upstream pathways including glycolysis, the pentose phosphate pathway, and the ED pathway by phenol addition, a large change occurred in the downstream pathways including pyruvate metabolism and the TCA cycle. The flux distributions focused on the downstream pathways are shown in E. coli under glucose carbon source without phenol addition  were measured using an in vitro enzymatic assay. The specific activities of the crude cell extracts obtained from the cultures with 0, 0.1, and 0.15% phenol were 0.095 ± 0.007, 0.087 ± 0.009, and 0.100 ± 0.009 U, respectively. No significant difference was observed. This result suggests that the expression level of citrate synthase does not change among the culture conditions. Assuming 50% protein in the DCW, the citrate synthase activity (0.095 U) under the 0% phenol was calculated as 2.9 mmol/gDCW/h. In the 13C-MFA, the 95% confidence interval of this reaction was 3 to 4.5 mmol gDCW-1 h-1. Since the citrate synthase activity is almost consistent with the range of the flux, the in vitro enzyme assay results are reasonable.gltA overexpressing strain. The relative activities of citrate synthase to a phenol free condition were 59.8, 56.6, and 24.6% at phenol concentrations in the reaction mixture of 0.1, 0.15, and 0.3%, respectively  strain was cultured using the M9 medium with different phenol concentrations. Because the expression of citrate synthase is regulated by an IPTG inducible T5-lac promoter (660 at each phenol concentration. The decrease of cell growth was also observed in this overexpressing strain in the presence of phenol. Because the overexpression of citrate synthase caused a sever growth defect without phenol condition, fine-tuning of the expression level would be needed to alleviate the phenol stress.If the inhibition of citrate synthase by phenol is the cause of growth reduction, the overexpression would restore the growth in the presence of phenol. To evaluate the effect of citrate synthase overexpression on phenol tolerance, the citrate synthase overexpressing (promoter , 50 μM IE. coli from the viewpoint of metabolism. 13C-MFA showed an enhanced overflow of acetyl-CoA to acetate at phenol concentrations of 0.1 and 0.15%, indicating that the TCA cycle flux was significantly decreased. Further analysis based on measuring the specific enzyme activity in vitro revealed that citrate synthase, at the entrance reaction of the TCA cycle, was inhibited by phenol and led to the flux repression of this reaction.In the present study, we investigated in detail the cause of phenol toxicity in 13C-metabolic flux analysis can reveal how the flux changed on the metabolic pathways, but it does not provide the mechanism that caused this flux change. In addition, since it assumes a steady state condition, the flux change in a sequential pathway is found; however, it cannot identify which reaction in the pathway caused the flux change. The mechanism of flux changes must be discussed together with the knowledge about cellular systems, such as enzyme expression and reaction inhibition. For instance, the flux information alone cannot conclude whether the enhanced acetate production led to the decrease of the TCA cycle flux, or the decrease of the TCA cycle flux led to the enhanced acetate production. In E. coli, it is known that acetate synthesis occurs due to overflow metabolism (in vitro, it is considered that the overflow to acetate increased because the TCA cycle flux was repressed by phenol.tabolism . TherefoE. coli (E. coli grown with acetate as a carbon source, acetate is converted to acetyl-CoA and is catabolized via the glyoxylate shunt into the TCA cycle to avoid CO2 emission (How did the decrease of the TCA cycle flux occur in the presence of phenol? Because respiration and the TCA cycle are linked with NADH, damage to the respiratory chain may cause a decrease in the TCA cycle flux. If so, however, NADH will accumulate and lactate and ethanol will be produced in order to recycle NADH produced by glycolysis; like in anaerobic fermentation, these fermentation products were not detected in the culture broth analysis by HPLC. Furthermore, inhibition of the respiratory chain increases uptake of glucose in E. coli , but theE. coli . If α-keemission . TherefoE. coli, activity was evaluated by adding phenol to the in vitro reaction solution. As shown in in vivo. This enzyme assay result suggests that phenol affects the enzyme reaction level, and not the gene expression level. In the 13C-MFA results, since the citrate synthase flux is more severely inhibited to 11% at 0.15% phenol, it suggests that other factors are remained to decrease the TCA cycle flux. A comprehensive analysis of gene expression profiles might provide clues to identify the factors.Metabolic flux changes are caused by several factors, such as enzyme expression level, and reaction inhibition. Citrate synthase is an important enzyme that is regulated at the gene expression level by various transcription factors such as Cra, ArcAB, and Fnr . First, pta encoding phosphotransacetylase which catalyzes the acetate formation pathway was investigated (pta strain was observed in the presence of 0.15% phenol. Since the knockout mutant cannot discard the end product of glycolysis as acetate in the presence of phenol, excess intermediates would accumulate in the cell and inhibit the metabolic flow in glycolysis. As another hypothesis, post-translational modification of proteins by acetylation may have affected the metabolic behavior. Acetyl-phosphate, an intermediate in the acetate synthesis pathway, is an acetyl group donor for lysine acetylation of various proteins. It has been reported that the acetylation of isocitrate lyase affects the activity of glyoxylate shunt and transcription factor RcsB which related to an acid stress susceptibility (For decreasing the acetate overflow in the presence of phenol, a gene knockout of stigated . The phetibility .13C-MFA and enzyme assays reveal that the TCA cycle flux decreased due to phenol inhibition of citrate synthase; therefore, ATP could not be sufficiently produced by respiration, and growth rate decreased. Furthermore, since the carbon was lost as acetate due to overflow metabolism, the biomass yield became low in the presence of phenol. In the central carbon metabolism of E. coli, acetyl-CoA node is a branch point between the TCA cycle and acetate synthesis. The inhibition of citrate synthase by phenol blocks carbon flux into the TCA cycle and enhances the overflow into the acetate synthesis. Furthermore, since the acetyl-phosphate is an intermediate of acetate synthesis pathway, the accumulation may affect the TCA cycle flux through changes in enzyme activity and gene expression via protein acetylation. Investigations of the gene expression profiles and post-translational modifications on phenol stress would be necessary for further understanding the metabolic regulation. However, flux of upstream pathways such as glycolysis and the pentose phosphate pathway did not decrease. Phenol is synthesized via the aromatic amino acid synthesis pathway from phosphoenolpyruvate of glycolysis and erythrose 4-phosphate of the pentose phosphate pathway as precursors. So, although phenol has a negative effect on E. coli growth, phenol would not inhibit its own biosynthesis from glucose. Regarding phenol production by E. coli, then, it would be effective to separate the growth phase from the production phases, because the TCA cycle is not involved in phenol synthesis. The reaction for phenol synthesis should be suppressed during the growth phase, and should be induced after the cells are sufficiently grown.In the present study, SK, YT, and HS conceived the study. SK designed the study and performed all the experiments and computational analysis. YT designed the study and helped to do the experiments and computational analysis. HS designed and supervised the study. SK and YT drafted the manuscript. All authors contributed to preparing the final version of the manuscript and approved the manuscript to submit to this journal.The 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.


Escherichia coli diauxie is a fundamental example of metabolic adaptation, a phenomenon that is not yet completely understood. Further insight into this process can be achieved by integrating experimental and computational modeling methods. We present a dynamic metabolic modeling approach that captures diauxie as an emergent property of subpopulation dynamics in E. coli monocultures. Without fine-tuning the parameters of the E. coli core metabolic model, we achieved good agreement with published data. Our results suggest that single-organism metabolic models can only approximate the average metabolic state of a population, therefore offering a new perspective on the use of such modeling approaches. The open source modeling framework that we provide can be applied to model general subpopulation systems in more-complex environments and can be extended to include single-cell-level stochasticity. Escherichia coli, in which cells grow on glucose until its exhaustion and then transition to using previously secreted acetate. Here we tested different hypotheses concerning the nature of this transition by using dynamic metabolic modeling. To reach this goal, we developed an open source modeling framework integrating dynamic models  with structural models (metabolic networks) which can take into account the behavior of multiple subpopulations and smooth flux transitions between time points. We used this framework to model the diauxic shift, first with a single E. coli model whose metabolic state represents the overall population average and then with a community of two subpopulations, each growing exclusively on one carbon source (glucose or acetate). After introduction of an environment-dependent transition function that determined the balance between subpopulations, our model generated predictions that are in strong agreement with published data. Our results thus support recent experimental evidence that diauxie, rather than a coordinated metabolic shift, would be the emergent pattern of individual cells differentiating for optimal growth on different substrates. This work offers a new perspective on the use of dynamic metabolic modeling to investigate population heterogeneity dynamics. The proposed approach can easily be applied to other biological systems composed of metabolically distinct, interconverting subpopulations and could be extended to include single-cell-level stochasticity.Microbes have adapted to greatly variable environments in order to survive both short-term perturbations and permanent changes. A classical and yet still actively studied example of adaptation to dynamic environments is the diauxic shift of IMPORTANCEEscherichia coli diauxie is a fundamental example of metabolic adaptation, a phenomenon that is not yet completely understood. Further insight into this process can be achieved by integrating experimental and computational modeling methods. We present a dynamic metabolic modeling approach that captures diauxie as an emergent property of subpopulation dynamics in E. coli monocultures. Without fine-tuning the parameters of the E. coli core metabolic model, we achieved good agreement with published data. Our results suggest that single-organism metabolic models can only approximate the average metabolic state of a population, therefore offering a new perspective on the use of such modeling approaches. The open source modeling framework that we provide can be applied to model general subpopulation systems in more-complex environments and can be extended to include single-cell-level stochasticity. In natural environments, microorganisms are exposed to high fluctuations of nutrient and micronutrient availability and have therefore evolved adaptation strategies, both short term (to respond to temporary perturbations) and long term (to increase evolutionary fitness) . We stilit after updating of the external conditions according to the FBA solution at time it−1. Approaches to modeling of microbial communities with GEMs have been recently reviewed by Succurro and Ebenhöh . After imposition of the steady-state assumption and introduction of thermodynamic and biological boundaries for the metabolic fluxes (is (FBA) , 13 defiis (FBA)  and miniis (FBA) . In pFBAis (FBA) , allows  Ebenhöh .Escherichia coli in 1941 by Monod  rather than stochastic switching (where the two phenotypes would coexist from the beginning). Although stochastic mathematical models have been proposed to support those findings, metabolic modeling approaches are only considered suitable to describe homogeneous systems, with single-organism GEMs representing the average population metabolic state.FBA and dFBA have been applied to the study of one of the most basic examples of metabolic transitions: diauxie , 18, 19.by Monod , diauxieby Monod –23. Undementally , often wmentally . Single-mentally , eventuamentally . Kotte ementally  systematE. coli, with a single GEM growing aerobically first on glucose and then on the secreted acetate. Here we present a study of E. coli diauxic growth on these two carbon sources, with the bacterial population modeled either as having an average, unique metabolic state (standard FBA and dFBA approach) or as being composed of two E. coli populations adapted to one of the two carbon sources. We used a modeling approach that integrates ordinary differential equation (ODE) models with dFBA, extending methods typically applied to study the dynamics of multispecies communities to the investigation of emergent patterns from individual behavior in monocultures. We implemented three approaches: (i) we modeled a homogeneous and yet smooth shift, with a single E. coli GEM, by adapting the MOMA algorithm; (ii) we introduced the hypothesis of subpopulations growing on specific carbon sources and model population transition as a purely stochastic mechanism; and (iii) we introduced an environment-driven response. Our results suggest that diauxie, rather than being modeled as a coordinated metabolic shift, can be modeled as the emergent pattern resulting from subpopulations optimizing growth on different substrates in response to environmental changes. This is much in agreement with experimental evidence from, e.g., Kotte et al. . In the standard dFBA approach, a population is modeled with a unique GEM and fluxes instantaneously change to adapt to new environmental conditions. In reality, however, transcriptional changes and flux rerouting may cause delays which are not captured by existing algorithms. Furthermore, dFBA might predict metabolic states in which more carbon sources are simultaneously utilized, and it is not obvious that such an approach would correctly capture the complexity of a population diversifying into metabolically distinct subpopulations. Therefore, we modified the dFBA algorithm by taking advantage of optimization strategies previously developed for different biological issues and implemented novel concepts as well. In particular, we used either pFBA  homogeneous, smooth population shift; (ii) stochastic population shift; and (iii) environment-driven subpopulation differentiation. We observed that dFBA performed with both pFBA and MOMA predicted abrupt transitions from acetate catabolism to acetate anabolism and that condition-specific parameterizations were necessary to reproduce the different data. We then modeled two E. coli subpopulations growing exclusively on glucose or acetate. For this, we extended the standard dFBA approach to include the process of population shifts. We tested whether purely stochastic switches (ii) or, rather, responsive diversification (iii) could capture the diauxic behavior by modeling the population transitions either with constant rates (ii) or with a heuristic function dependent on carbon source concentrations (iii). We observed that only model iii could reproduce data from different experiments with a unique set of parameters. We did not find significant improvements using MOMA rather than pFBA within the same metabolic state, so the simpler pFBA implementation was used in the subpopulation simulations where each model was fixed into one metabolic configuration. Further details of the modeling approach are provided in Materials and Methods.We ran simulations with an open source modeling framework developed to model ecosystem dynamics. The models are ODE systems solved with integrating routines that at each integration step solve an FBA problem. We first validated the  Palsson  , glucose , and acetate . In E. coli growing on either glucose or acetate exponentially (data not shown) and compared the fluxes through the relevant reactions in E. coli growing on acetate to those in E. coli growing on glucose. E. coli model shifted from growth on glucose to growth on acetate. Enjalbert et al. , with t10.1128/mSystems.00230-18.2FIG S1E. coli modeled as a uniform population in batch (a and e) and fedbatch (b and f) conditions. Simulation  data are compared to data (squares) from Varma and Palsson  and simulation steps . (Right plots) Absolute distance between the flux data at simulation steps i and i + 1 for the reactions yielding the higher change, plotted against simulation time (lower x axis) and simulation steps . Notice the nonlinear relation between simulation time and simulation step data, originating from the variable integrator time step choice. Download FIG S2, PDF file, 0.3 MB.(Left plots) Euclidean distance between the flux solution vectors at simulation steps i and i + 1 plotted against simulation time  and simulation steps . (Right plots) Absolute distance between the flux data at simulation steps i and i + 1 for the reactions yielding the higher change, plotted against simulation time (lower x axis) and simulation steps . Notice the nonlinear relation between simulation time and simulation step data, originating from the variable integrator time step choice. Download FIG S3, PDF file, 0.1 MB.(Left plots) Euclidean distance between the flux solution vectors at simulation steps i and i + 1 plotted against simulation time  in the simulations. In red are highlighted the reactions found to carry higher fluxes after the switch to growth on acetate, in blue those carrying lower fluxes, and in gray those that did not change. The names of the reactions are color-coded in the same way but in accordance with the experimental results from Enjalbert et al.  model and the E. coli acetate (ECAc) model, were hence constrained to exclusively take up the corresponding carbon source. Two transition functions, dependent on acetate or glucose concentrations, were introduced to model cellular differentiation and cellular shift from one population to the other . We ran simulations to compare the different scenarios investigated experimentally by Enjalbert et al.  and glucose concentrations , only the simulation that included the population transition realistically reproduced the acetate consumption levels (R2 = 0.336 and R2 = 0.951 respectively) as well as a lag phase before culture crash. Neither of the simulations captured the eventual recovery of growth hinted at by the last data points. We reproduced two other results (where only biomass measurements were available) from Enjalbert et al. (Gl and ECAc) and the experimental setup accordingly. By modeling the population transition with the same constant rate, we were able to explain the biomass profile in the case where E. coli was grown on 15 mM glucose and, after glucose exhaustion, the acetate concentration was maintained at around 4 mM (R2 = 0.986), but not in the case where E. coli was grown on 15 mM glucose and 32 mM acetate and, after glucose exhaustion, the acetate concentration was maintained at the same high level (R2 = 0.727). We therefore introduced a dependency of the transition functions on the substrate concentration  that well captures all the experimental scenarios with a unique set of parameters (E. coli population starting with 95% ECGl and 5% ECAc describes well the biomass dynamics (R2 = 0.985) and matches the glucose exhaustion point, observed after around 4 h when acetate was maintained at 4 mM. Again, without fine-tuning the GEM simulation parameters, E. coli population starting with 75% ECGl and 25% ECAc reproduced the biomass measurements (R2 = 0.940) and the glucose exhaustion point after around 4 h also in the experimental setup with acetate maintained at 32 mM. The effect of adjusting the initial biomass ratios in the different experimental conditions is shown in Gl and 5% ECAc or 75% ECGl and 25% ECAc did not show strong differences, but further reducing the percentage of ECGl  to model t et al. . The init et al. , again uund 4 mM   growing on glucose only (a) or on glucose and (b) a low level of acetate or (c) a high level of acetate. Experimental data from Enjalbert et al. . The initial biomass value was taken from time point “GE—4hr” (a) or “GE—5hr” (b) in the data from Enjalbert et al. , any value of ϕ is allowed, but we report a subset here. Download Copyright © 2019 Succurro et al.2019Succurro et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the E. coli cultures required to achieve maximal growth after GE. In their switch experiments, they sampled at different time points “mother cultures” of E. coli cells growing under batch conditions on 15 mM glucose alone (“M9G” condition) or on 15 mM glucose and 32 mM acetate (“M9GA” condition) and reinoculated the sampled cells as “daughter cultures” into fresh medium exclusively containing glucose (M9G condition) or acetate (M9A condition). We replicated this experiment in silico by running first simulations under the M9G and M9GA conditions. For the M9G mother culture, we used the simulation of the mixed ECGl and ECAc population shown in Gl and 25% ECAc but without the feeding of additional acetate. The GE time points were about 4.6 h for M9G and 3.9 h for M9GA, consistent with the observations of Enjalbert et al. 0. (e to h) Effects of adjusting the transition parameters Kψ to values of 10 (e and f) and 30 (g and h) for the population ratio (top panel in the plots) and for the lag time (bottom panel in the plots) for daughter cultures sampled at different times with respect to the time of glucose exhaustion. Each point in panels e and g represents results from a daughter culture from the M9G mother culture, while each point in panels f and h represents results from the M9GA mother culture. Download FIG S8, PDF file, 0.2 MB.(a to d) Phase space of the lag time for typical daughter cultures from M9G mothers (a and b) and M9GA mothers (c and d) grown under M9G (a and c) or in M9A (b and d) conditions. When the glucose (acetate) value is zero, the transition ϕ (ψ) is in principle reduced to the noise component ϕCopyright © 2019 Succurro et al.2019Succurro et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the E. coli on glucose and acetate, aiming to test whether a dynamic metabolic modeling approach can capture diauxie in monocultures of E. coli as the observable emergent result of individual (subpopulation) behavior. To this end, we first developed a modeling framework to integrate dynamic models (ODE systems) with structural models (metabolic networks) and then performed simulations to reproduce published experimental results in silico.We have investigated a fundamental example of metabolic adaptation, namely, the diauxic growth of ad hoc changes of flux constraints. Indeed, we observed that a condition-specific fine-tuning of the constraint on acetate uptake could reproduce fairly well the growth dynamics of the different experiments (data not shown). However, the change of such a constraint from one experimental condition to another is not biologically justified. Although some extensions of the FBA approach such as FBA with molecular crowding  providet et al. . The useE. coli monocultures, solving the FBA problems either with pFBA  or with an adaptation of the MOMA algorithm. In the latter case, instead of minimizing the difference in flux distribution between a “wild-type” GEM and a modified one , we used the same concept to integrate the dFBA system while also imposing the following condition: at initial time it, the flux solution differs minimally from that at time it-1, where the time steps are set by the integration routine. In contrast to our expectations, however, this approach did not achieve smoother metabolic adjustments in the system in response to the changing external conditions. Instead, both implementations resulted in abrupt changes in the flux distributions following the shift from glucose to acetate metabolism  and the values for the maximal transition rate (20% h–1) were in good agreement with measured average protein turnover rates in E. coli cultures from the literature , we were able to capture all the experimental trends published by Enjalbert et al.  with theterature –33. Simuerature –, 25, 34,erature –, supportLactococcus lactis population (translating in practice to the rate at which the primary carbon source was consumed) played a significant role in determining the proportion of cells successfully transitioning to growth on the secondary carbon source. The connection between lag time and subpopulation distribution could in principle be exploited to estimate initial population distributions from lag time measurements. However, it is difficult to assess the robustness and reliability of such predictions with the currently available data, and further investigation, including experiments devoted to determination of initial conditions, is therefore required. An additional source of the discrepancies between our quantitative results and the experimental measurements could have been the experimental procedure itself. For example, abrupt changes in conditions, such as the reinoculation of daughter cultures into a different medium in the switch experiments, might select for additional adaptation strategies. Interestingly, we observed a dramatic improvement in the quantitative agreement between experiment and simulation by relaxing the condition imposing no growth for populations inoculated on the “wrong” carbon source (data not shown). By allowing the glucose-consuming population sampled from glucose mother cultures to growth more slowly on acetate, we mimicked a situation in which cells store resources and are able to survive a bit longer. On the other hand, allowing reduced growth on acetate (glucose) for the glucose consumer (acetate consumer) population that was exposed to both carbon sources in the mixed mother cultures could be a proxy for a memory effect. Bacterial cells do show memory effects in response to changes in environmental conditions  made it impossible to calibrate the initial model population. This could introduce a significant bias in the later sampling and determination of the subpopulation ratio, thus strongly influencing the quantification of the lag time, which is highly correlated with the population distribution . Solopovnditions , but morag phase . From tha priori knowledge that only two carbon sources would be available to E. coli, thus motivating the development of a two-subpopulation community, but in principle, an arbitrary number of subpopulations can be defined and more generic transition functions introduced. Further experiments, in particular, single-cell studies, could be designed to define and parameterize these transition functions. Thanks to the object-oriented (OO) design of the framework, it is relatively easy to introduce other functions regulating the constraints on specific reaction fluxes in the FBA problem. In this way, different hypotheses can be extensively tested to improve understanding of how to capture regulatory dynamics in dFBA. Notably, the methods developed in this framework to study population heterogeneity could then be transferred to other platforms that are more specific for microbial community modeling where different features are implemented . FinallThere is extensive experimental evidence that bacteria differentiate into subpopulations as a result of survival strategies , 27. SimS(m×n) is defined with the row and column dimensions corresponding to the numbers of metabolites m and reactions n respectively, the elements ijs being the stoichiometric coefficients of metabolite i taking part in reaction j. FBA defines and solves the following LP problem:j and u.b.j representing, respectively, a lower and upper bound on flux jv.In stoichiometric models, the stoichiometric matrix The steady-state assumption  gives a it-1 is used to compute the MOMA solution at time it as the minimally different solution that satisfies the objective function. Also in this case, the objective function is maximal flux through the biomass reaction. We use the MOMA implementation from COBRApy  to obtain the current reaction rates for https://www.python.org/) following the object-oriented programming (OOP) paradigm for efficiency and flexibility. The framework uses functionality from the following third-party packages: numpy  solely by the environmental conditions, and the lower bound of the exchange reactions  follows two simple Michaelis-Menten kinetics equations:We used a previously reported core version of coli GEM  downloadμv is the reaction rate of the biomass function (proxy for growth rate) in the FBA model, δ is the cell death rate, and ξfed-batch is a positive rate under fed-batch conditions and zero under batch conditions. Parameters and initial conditions are summarized in The ODE system is defined as follows:E. coli core models are loaded and defined as either a glucose consumer (ECGl) model or an acetate consumer (ECAc) model by switching off uptake of the other carbon source as follows:Two ζ · H(t − xt) is a heaviside function activated at time xt of glucose exhaustion in order to keep the acetate level constant, ψ and ϕ are functions that model the cellular shift from ECGl to ECAc and from ECAc to ECGl, respectively, and 0<ε<1 is a positive factor representing the transition efficiency. The ψ and ϕ functions are modeled as Hill functions with a noise offset as follows:n = 5. Indeed, the simulations seemed to work best for a transition function with a high degree of cooperativity, and the results are robust with respect to small deviations relative to this value. The other parameters and initial conditions, specific to the different simulations, are summarized in The ODE system is defined as follows:E. coli mixed-population model simulations are run as “mother cultures” as shown in Gl and ECAc used as the initial condition for the reinoculation simulations. The percentage of ECGl biomass at these time points is shown in X0 is the total initial E. coli biomass, X1 is the total E. coli biomass value at time t1 , and μmt et al. .Experimental data  from Enjalbert et al.  were kinhttps://github.com/QTB-HHU/daphne_ecoli-diauxie. The development version is hosted on https://gitlab.com/asuccurro/dfba-ode-framework, and people interested in contributing can request access by contacting A. Succurro (corresponding author).The version of the modeling framework used to obtain the results presented in this manuscript (v1.1) is publicly available with instructions to install and run simulations at