Altered metabolism is associated with many human diseases. Human genome-scale metabolic models (GEMs) were reconstructed within systems biology to study the biochemistry occurring in human cells. However, the complexity of these networks hinders a consistent and concise physiological representation. We present here redHUMAN, a workflow for reconstructing reduced models that focus on parts of the metabolism relevant to a specific physiology using the recently established methods redGEM and lumpGEM. The reductions include the thermodynamic properties of compounds and reactions guaranteeing the consistency of predictions with the bioenergetics of the cell. We introduce a method (redGEMX) to incorporate the pathways used by cells to adapt to the medium. We provide the thermodynamic curation of the human GEMs Recon2 and Recon3D and we apply the redHUMAN workflow to derive leukemia-specific reduced models. The reduced models are powerful platforms for studying metabolic differences between phenotypes, such as diseased and healthy cells. The complexity of genome-scale metabolic networks (GEMs) hinders their application in specific physiological contexts. Here, the authors introduce a framework to reduce thermodynamically curated GEMs to the subnetworks of interest and demonstrate its application by deriving leukemia-specific models. Understanding the metabolic mechanisms that underlie this reprogramming guides the discovery of new drug targets and the design of new therapies. To this effect, tremendous efforts are now being made to use the large amounts of now-available multi-omics experimental data to gain insight into the metabolic alterations occurring in different phenotypes. Unfortunately, current mathematical models can be too complex for this analysis, rendering them too cumbersome to employ for many systems biology studies.An altered metabolism is a hallmark of several human diseases, such as cancer, diabetes, obesity, Alzheimer’s, and cardiovascular disorders5 and are valuable tools for studying metabolism7. The mathematical representation of GEMs through the stoichiometric matrix7 is amenable to methods such as flux balance analysis (FBA)8 and thermodynamic-based flux balance analysis (TFA)13, which ensure that the modeled metabolic reactions retain feasible concentrations and their directionalities obey the rules of thermodynamics, to predict reaction rates and metabolite concentrations when optimizing for a cellular function, such as growth, energy maintenance, or a specific metabolic task. Additionally, GEMs can be used for gene essentiality14, drug off-target analysis15, metabolic engineering18, and the derivation of kinetic models22.In the field of systems biology, genome-scale metabolic models (GEMs) integrate available omics data with genome sequences to provide an improved mechanistic understanding of the intracellular metabolism of an organism. GEMs have been reconstructed for a large diversity of organisms spanning from bacteria to mammals24. Since then, the scientific community has been working to develop high-quality human GEMs, including HMR 2.025, Recon 226, Recon 2.227, and Recon 3D28. The human GEMs used for the analysis in this article are Recon 2 and Recon 3D. Recon 2 is composed of 7440 reactions with 4821 of them associated to 2140 genes, and 2499 unique metabolites across seven compartments: cytosol, mitochondria, peroxisome, Golgi apparatus, endoplasmic reticulum, nucleus, and lysosome. Recon 3D is the latest consensus human GEM. It is an improved more comprehensive version of the previous GEMs consisting of 10,600 reactions, with 5938 of them associated with 2248 genes, and 2797 unique metabolites compartmentalized as Recon 2 with an additional compartment for the mitochondria intermembrane space.The first human GEM was reconstructed in 200729, for healthy and diseased cells31, and for cells growing under diverse extracellular conditions. Some examples of such methods are (1) GIMME32, mCADRE33, and tINIT34 to reconstruct tissue-specific models based on omics data and a set of tasks or a specific objective function; (2) redGEM–lumpGEM36 to reconstruct models around a specific set of subsystems of interest for the study; and (3) iMM38 to characterize the extracellular medium and the metabolites that are essential for growth under each condition. Context-specific metabolic models have been extensively used to understand the differences in metabolism between cancer cells and their healthy counterparts45.Human GEMs reconstruct the metabolic reactions occurring in several human cell types. However, a given cell type only leverages a portion of these reactions. This motivates the development of methods to generate context-specific metabolic models that can be used to study the differences in metabolism for different cell typesIn this article, we present redHUMAN, a workflow to reconstruct thermodynamic-curated reductions of the human GEMs Recon 2 and Recon 3D. We integrate the thermodynamic properties of the metabolites and reactions into the GEMs and use redGEM–lumpGEM to reconstruct reduced models around specific subsystems. Furthermore, we introduce redGEMX, a method to identify the pathways required to connect the extracellular compounds to a core network. redGEMX guarantees that the reduced models have all the feasible pathways that consume and produce the components of the extracellular environment of the cell. Finally, we use metabolic data for leukemia as an example of how to integrate experimental data to derive disease- and tissue-specific metabolic models.In order to generate reduced models from human GEMs, we developed redHUMAN, a six-step workflow that can be applied to any GEM or desired model system. The overall workflow is briefly described here and shown in Fig. − group). We observed that as the number of metabolites increases from Recon 2 to Recon 3D, the percentage of thermodynamic coverage increases as well. This is due to the improved annotation of the metabolite structures in Recon 3D. Using the thermodynamic properties of the compounds as constraints (see “Methods”), we estimated the Gibbs free energy for 51.3% of the 7440 reactions present in Recon 2 and 61.6% of the 10,600 reactions in Recon 3D. These constraints ensured that the reactions in the computed flux distributions operated in thermodynamically feasible directions.We first determine the directionality of the chemical reactions of the network, which is directly associated with their corresponding Gibbs free energy. The Gibbs free energy of a reaction can be estimated from the thermodynamic properties of its reactants and products. Therefore, we curated the GEMs Recon 2 and Recon 3D (see “Methods”) and integrated the thermodynamic properties for 52.4% of the 2499 unique metabolites from Recon 2 and 67.5% of the 2797 unique metabolites from Recon 3D Fig. . Three m49. Consequently, the core subsystems for our models were glycolysis, pentose phosphate pathway, citric acid cycle, oxidative phosphorylation, glutamate metabolism, serine metabolism, urea cycle, and reactive oxygen species detoxification. We have estimated the thermodynamic properties for the metabolites and the reactions in these initial subsystems. In the case of Recon 2, we provide an estimate for the Gibbs free energy of formation for 236 metabolites  and the Gibbs free energy of reaction for 143 reactions . In the case of Recon 3D, we provide estimated values of the thermodynamic properties for 288 metabolites (97.6%) and for 183 reactions (91.0%).A proper metabolic model contains the pathways that are essential for the survival of the cell as well as the pathways that are informative of a specific metabolic behavior. In this work, we were interested in the metabolism of cancer cells. Thus, we selected as core subsystems: (a) the central carbon pathways that provide the energy, redox potential, and biomass precursors, and (b) the subsystems that have been reported to be altered in cancer cellsSubsequently, to reconstruct the core network we pairwise connected the chosen subsystems using redGEM (see “Methods”). The algorithm first performed an intra-expansion of the initial subsystems. In this process, each initial subsystem was expanded to include additional reactions from the GEM whose reactants and products belong to that subsystem. These reactions can be assigned to different subsystems in the GEM which are not any of the initial subsystems and the core network would miss these additional reactions if we had considered the formal definition of the initial subsystems. The initial core subsystems of Recon 2 contained a total of 180 reactions. After the intra-expansion, 135 reactions from 21 subsystems were added. Examples of these added reactions included three from pyruvate metabolism that interconvert acetyl-CoA, acetate, malate, and pyruvate, which are all metabolites that participate in the citric acid cycle subsystem. For Recon 3D, 171 reactions from 24 subsystems were added to the 211 reactions from the initial core subsystems.D  between pairs of metabolites from the subsystems. Our final models included the connections for degree D = 1, that is, all the reactions that in one step connect two metabolites (excluding cofactors) belonging to any of the initial subsystems. A degree D = 1 was enough to pairwise connect all the initial subsystems , and Recon 3D simulated growth in a medium with glucose, the nine essential amino acids, the same inorganics as Recon 2, and one of the two essential fatty acids . The presence of the two essential fatty acids in the iMM of Recon 3D is a consequence of the improvement of the lipid metabolism28, where the essential fatty acids participate in the synthesis of phospholipids. This demonstrates how the algorithms and workflow can be used to compare and validate updated model reconstructions for the same organisms or between different organisms.Cells adapt their metabolism to the available nutrients in their extracellular environment. Consequently, a correct definition of the medium in the metabolic model is fundamental for an adequate representation of the intracellular metabolism. Given the complexity of the extracellular medium, it is particularly important to identify and classify the essentiality of the medium components and the pathways used for their metabolism. To this end, we curated the representation of the interactions of the cell with its environment into the human GEMs. First, we did not allow the exchange of intracellular metabolites lacking associated transport reactions or transport molecules containing P, CoA, or ACP (acyl carrier protein). Secondly, we allowed the synthesis of generic fatty acids from palmitate, with reactions from Recon 2 and Recon 3D . This algorithm finds the pathways from the GEM that are needed to connect the extracellular metabolites to the core network defined by redGEM. In this work, we considered a complex medium composition of 34 metabolites Fig. , and redl-histidine which affects many aspects of human physiology, including cognition functions and allergic reactions. The classical pathway to metabolize l-histidine consists of four steps that sequentially convert it into urocanate, 4-imidazole-5-propanoate, N-formimidoyl-l-glutamate, and ultimately, l-glutamate50. Interestingly, the resulting redGEMX subnetwork for l-histidine uses this classical pathway to connect it to the Recon 2 core metabolites l-glutamate and 4-aminobutanoate, both from the subsystem glutamate metabolism. The subnetwork is composed of 22 reactions, and it contains not only the classical pathway but also all the additional reactions required to balance the cofactors and by-products  to connect l-histidine to the core network of Recon 2. The alternatives emerge from the existence of different transport reactions for the extracellular metabolites. In the case of Recon 3D, l-histidine is connected to the core network using 20 reactions, and there exist two pathways of minimum size. The subnetworks connect l-histidine to the Recon 3D core metabolites l-glutamate, 5-10-methylenetetrahydrofolate, 2-oxoglutarate, and pyruvate using the classical pathway to metabolize l-histidine. The different topology of the Recon 2 and Recon 3D networks manifests in differences in the pathways used to metabolize and synthesize the compounds, thus, it is important to characterize which are the pathways used in the models. Following this approach, we added the reactions that compose all the alternative subnetworks of minimum size to the core networks to connect the 26 extracellular metabolites . Similarly to redGEMX, lumpGEM generates subnetworks that account for the synthesis, degradation, and balancing of all the by-products and cofactors required by the main pathway. The alternative subnetworks generated with lumpGEM can assess the flexibility of the cells to use alternative pathways to produce the BBBs, which can lead to survival in different conditions and drug resistance. Using lumpGEM, we calculated all the alternative subnetworks (set of reactions) of minimum size to capture the flexibility of the network for the biosynthesis of the BBBs , cholesterol, and the phospholipids and sphingolipids. The core network of Recon 2 contains a reaction that produces l-cysteine, however, the core network of Recon 3D requires two reactions to produce it. The subnetworks that produce dTTP have the same size in both models, but a different number of alternatives. The subnetworks to produce the purine nucleotides have one more reaction and more alternatives in Recon 3D. Cholesterol is another BBB whose subnetworks agree in size for both models, but Recon 3D has more alternatives than Recon 2. The explosion of alternatives in Recon 3D is due to the parallel description of the synthesis of cholesterol in three compartments, namely cytosol, peroxisome, and endoplasmic reticulum. The differences in the lumped reactions for the phospholipids and sphingolipids between both models are due to the introduction of the essential fatty acid in their synthesis in Recon 3D.The subnetworks generated with lumpGEM have the same size and number of alternatives in both Recon models for most of the BBBs, indicating that both models have the same level of flexibility for synthesizing the BBBs, with the exception of 54 for the synthesis of phosphatidylserine comprises four steps, wherein glycerol 3-phosphate is converted to lysophosphatidic acid, phosphatidic acid, CDP-diacylglycerol, and phosphatidylserine. In Recon 2, the subnetwork generated with lumpGEM for the synthesis of phosphatidylserine was composed of eight reactions. It included the KEGG pathway with the exception of the CDP-diacylglycerol intermediate, which was not connected to phosphatidylserine in the GEMs. Instead, phosphatidylserine was produced directly from phosphatidic acid by attaching serine. Additionally, the subnetwork contained the reactions required to generate from acetyl-CoA the fatty acids that would attach to glycerol 3-phosphate and to lysophosphatidic acid, which are important to consider for the final synthesis of phosphatidylserine. All the reactions involved in the synthesis of phosphatidylserine were lumped together in one reaction.As an example of the subnetworks that produce the BBBs, we show the synthesis of the phospholipid phosphatidylserine Fig. . The sta52.For Recon 3D, the phosphatidylserine synthesis subnetwork was generated with the same eight reactions, but in this case, four alternative subnetworks existed Fig. , indicatThe analysis performed with lumpGEM allows to characterize and classify the metabolic pathways and their alternatives, leading to an in-depth understanding of the flexibility of metabolism. In the context of GEMs, such detailed analysis of the subnetworks is often a difficult task due to their large size and interconnectivity.By applying the redHUMAN workflow, we reconstructed four reduced metabolic models for human metabolism Table . Two of 34. The four models captured 45 of the 57 tasks, including rephosphorylation of nucleoside triphosphates, uptake of essential amino acids, de novo synthesis of nucleotides, key intermediates and cholesterol, oxidative phosphorylation, oxidative decarboxylation, and growth  the model reconstruction, specifically the definition of the biomass, or (2) the reduction properties, that is, the subsystems included in the reduction and the representation of parts of the network as lumped reactions. To recover these tasks such that they are captured by the model, the following actions should be performed: the synthesis of proteins from amino acids and vitamin and co-factor metabolism can be recovered by modifying the biomass to account for their synthesis and utilization; the inclusion of lipid metabolism subsystems can recover the beta oxidation of fatty acids; and finally, the utilization of inositol can be recovered by adding the explicit reactions that compose the subnetworks, as it was found to be hidden in the lumped reactions of phosphatidyl-inositol. This demonstrates that redHUMAN allows to build reduced models consistent not only with the GEM but also with the metabolic tasks, and these models are suitable for targeted modifications and expansions.55. Additionally, we limited the maximal growth to the doubling time reported for leukemia cells, which is 0.035 h−1, and we constrained according to literature values the maximum uptake rate of oxygen to 2 mmol·gDW−1·h−1 40 and the ATP maintenance to 1.07 mmol·gDW−1·h−1 56  for the corresponding leukemia cell lines. We have identified that, in the four models presented in this study, over 99% of the enzymes with gene associations  are expressed in the NCI60 leukemia cell lines  on the common reactions between the GEM and the reduced model. The top 20 reactions whose rate ranges changed the most in absolute value included reactions from glycolysis, the pentose phosphate pathway, folate metabolism, and nucleotide interconversion among others Fig. . For real-glutamate 5-semialdehyde dehydratase (from arginine metabolism) and l-glutamate 5-semialdehyde:NAD+ oxidoreductase (from urea cycle) are bidirectional when flux variability is performed without thermodynamics and become unidirectional when their thermodynamic information is taken into account. Therefore, integrating thermodynamic information reduces the space of reaction directionality and the physiological solution space, and it eliminates thermodynamic infeasible reactions, excluding some pathways.redHUMAN helps to navigate large human genome-scale metabolic models to explore and classify the metabolic pathways that cells use to function and survive under specific conditions. The thermodynamic curation performed in the genome-scale models guarantees that the reactions obey the laws of thermodynamics, discarding possible pathways that would not be compatible with the bioenergetics of the cell. As an example of how thermodynamics reduces the space of solutions to the thermodynamically feasible pathways, we analyzed the flux variability with and without thermodynamic constraints in the Recon 3D reduced model that has all the alternative lumped reactions of minimum size (Smin). The reactions The leukemia-specific models generated in this study are powerful tools to analyze how the metabolic pathways are altered with respect to other cancer cells or normal cells. In particular, we can analyze how leukemia cells utilize the nutrients available in the microenvironment to biosynthesize the precursors required for growth and cellular functionality. As an example, we identified the minimal number of reactions that are required for the synthesis of phosphatidyl-serine in the reduced Recon 3D model with all the alternative lumped reactions of minimum size. We found that at least 76 reactions should be active for the production of phosphatidyl-serine including the interactions with the extracellular medium, i.e., for some alternatives the uptake of glucose, histidine, linoleic acid, oxygen, and phosphate, and the secretion of succinate, ammonia, carbon dioxide, and water. The main pathways active within the subnetwork of 76 reactions are glycolysis, the citric acid cycle, serine metabolism, and the electron transport chain. This type of analysis will enlighten our knowledge on how cells adapt their metabolism to the microenvironment allowing researchers to hypothesize how and why the cancer cells change their expression profile to adapt and survive.For a better understanding of the altered metabolisms that accompany many human diseases, we have herein presented a workflow to generate reduced models for common human GEMs that can reduce the complexity of these systems to the relevant processes to be studied, making detailed in silico analyses of metabolic changes possible.59 in redHUMAN allows to integrate endo- and exo-metabolomics in the models, constraining the concentration of the metabolites according to physiological data. The size of the model is directly related to the percentage of metabolites that need to be measured. Therefore, the continuous expansion in the size of genome-scale models increases the demand of larger sets of metabolomics, and such data are not always available. In addition, there is a community effort to expand constraint-based models to include information on enzyme abundancy relating the metabolic fluxes with enzymatic data and allowing to integrate transcriptomics and proteomics data into the models. These data are currently limited, but they can be continuously updated and integrated as they become available61.During the last years, there has been an increased generation of metabolomics data that better study what is happening in the physiology of cell metabolism compared to other omics data. This has created a need to expand the classical constraint-based modeling methods to include metabolomics information. Our thermodynamic formulation and application of TFA62. The main difficulty with these methods is the large amount of data required to fully characterize the initial set of reactions or core reactions. The lack of data could lead to unconnected parts and the impossibility to include reactions that could be important for the specific physiology, affecting the final model and the predictions.Moreover, most of the existing methods to build context-specific models are data-driven, that is, the reduced models are extracted from a GEM by considering only the enzymes associated to highly expressed data, or literature-based pathways. Then, they include additional reactions that are required to simulate growth and cellular functions62, tINIT34, mCADRE33, uFBA63, GECKO64, ETFL65, TEX-FBA66, and IOMA67.redHUMAN reconstructs reduced models considering only the pathways of interest and their stoichiometric connectivity. The reduced models are built unbiased from the data, guaranteeing thermodynamic feasibility and consistency with the GEM and the metabolic tasks. The reduced models can then be used to construct context-specific models by integrating omics data, accommodating to also integrate partial data without sacrificing reactions from the network. Overall, the reduced size of the new models and their conceptual organization overcomes some of the main challenges in building genome-scale context-specific models as for example, the barrier of data network coverage. The reduced models generated with redHUMAN are powerful representations of the specific parts of the network, and they have promising applications as they are suitable to use with existing methods including MBABased on our results, we propose the following approach to using these models as tools to explain and compare phenotypes. First, generate a reduced model around a desired set of subsystems and for a defined extracellular medium, and check that the model captures the metabolic tasks. Subsequently, build physiology-specific models by integrating experimental data into the reduced models. Then, test the consistency of the reduced network with respect to its parent GEM. Finally, integrate different sets of omics data, including expression, to compare different physiologies, such as diseased vs healthy or within several types of cancers. This approach will help to better investigate the alterations in metabolism that occur as diseases develop and progress. Moreover, the same procedure can be used to analyze systematically and consistently metabolic models for the same organism and to compare metabolic models of different organisms, enhancing our understanding of their similarities and differences.68.Throughout this paper, we have considered a specific set of subsystems, a specific medium, and the biomass definition from the GEMs. In the future, the reduced models could be further expanded to include other pathways, a more complex medium, or more biomass components. To introduce new subsystems or pathways into the core network, redGEM should be run to find the pairwise connections between the added pathways and the rest of the core. For an expansion of the medium, redGEMX would find the connections necessary for using the new extracellular metabolites. In a similar manner, a further curation of the biomass reaction could increase the number of BBBs, requiring lumpGEM to be run to find the biosynthesis pathways for those compounds. If a higher consistency was required between the GEM and the corresponding reduction, we could find the reactions missing in the reduced model to satisfy that condition. Moreover, we have selected a set of metabolic tasks to test the generated reduced model based on the definition within the original GEM. However, these sets of tasks can be expanded or redefined according to the needs of the specific studies, which can be based on expert knowledge or experimental data, as done in ref. Furthermore, in this study, we have used metabolomics, proteomics, and growth data from the NCI60 cell lines to define a generic physiology for leukemia cells. The core networks of the reduced models are structurally the same across growth conditions and depend only on the structure of the corresponding GEMs. Therefore, these generic models are robust to variations in growth or data for the same physiology, and thus data for individual leukemia cell lines can be used without changing the workflow. However, if there are important differences in the data, for example across different physiological conditions, the authors suggest running the lumpGEM workflow with data integration and generate alternative subnetworks and lumped reactions, which in turn will capture the different flux profiles for each physiological state.Overall, our analysis demonstrates how redHUMAN facilitates the characterization of differences in metabolic pathways across models and phenotypes.The thermodynamic curation of the human GEMs Recon 2 and Recon 3D aims to include thermodynamic information, i.e., the Gibbs free energy of formation for the compounds and the corresponding error for the estimation, into the model. The workflow to obtain this information is as follows.http://www.metanetx.org)69 to annotate the compounds of the GEMs with identifiers from SEED70, KEGG54, CHEBI71, and HMDB72. We then used Marvin  to transform the compound structures  into their major protonation states at pH 7 and to generate MDL Molfiles. We used the MDL Molfiles and the Group Contribution Method to estimate the standard Gibbs free energy of the formation of the compounds as well as the error of the estimation59.We first used MetaNetX  problem that incorporates the thermodynamic constraints to the original FBA problem. The Gibbs free energy of the elemental and charge balanced reactions is calculated as a function of the standard transformed Gibbs free energy of formation (depending on pH and ionic strength) and the concentrations of the products and reactants.TFA estimates the feasible flux and concentration space according to the laws of thermodynamicsm metabolites and n reactions, the Gibbs free energy,i is:ni,j is the stoichiometric coefficient of compound j in reaction i; j; xj is the concentration of the compound j, R is the ideal gas constant, T is the temperature. In this case, T = 298 K.Considering a network with The value of the Gibbs free energy determines the directionality of the corresponding reaction and the thermodynamically feasible pathways. With this formulation, we included the concentrations of the metabolites as variables in the mathematical formulation. TFA allows the integration of metabolomics data into the model.38. iMM identifies the minimum number of boundary reactions (uptakes and secretions) that need to be active. The method defines new binary variables in the TFA problem that represent the state of each boundary reaction, active or inactive. New constraints link the new binary variables to the corresponding reaction rates such that if the reaction is inactive, then it should not carry flux. The objective of the problem is to maximize the number of inactive reactions.iMM is formulated as a MILP problem that introduces new variables and constraints to the TFA problem to find the minimum set of extracellular metabolites necessary to simulate growth or a specific metabolic task with the GEMm metabolites and n reactions, the mathematical formulation of the iMM problem is the following:nb is the total number of boundary reactions in the model, zk are new binary variables for all the boundary reactions, S is the stoichiometric matrix, v are the net fluxes for all the reactions and M is a big constant  and C is an arbitrary large number. In this case, if k is active.Assuming a network with The redGEM, redGEMX, and lumpGEM algorithms seek to generate systematic reductions of the GEMs starting from chosen subsystems , based on the studied physiology and the specific parts of the metabolism that are of interest.35 that extracts the reactions that pairwise-connect the initial subsystems from the GEM, generating a connected network named the core network.redGEM is a published algorithm35 for further details). For example, for a degree equal to 2, it will connect the metabolites from the starting subsystem that are one and two reactions away in the GEM.The inputs for redGEM are (i) the GEM, (ii) the starting subsystems or an initial set of reactions, (iii) the extracellular medium metabolites, (iv) a list with the GEM cofactor pairs, and (v) the desired degree of connectivity. The algorithm then performs an expansion (by graph search) of the starting subsystems by finding the reactions that pairwise-connect the subsystems up to the selected degree  nor (b).Classify the extracellular metabolites of the GEM into 3 classes:Those that belong to the inter-connected subsystems network (core-reactions),those that do not belong to the inter-connected subsystems network (non-core reactions).Classify the reactions from the GEM into 2 classes:Block the flux through the reactions in the GEM that involve only extracellular metabolites.Block the flux through the boundary reactions of other metabolites in the GEM (1c). Steps (3) and (4) guarantee that the subnetwork reaches the core network.Force the uptake of a medium metabolite  and minimize the number of non-core reactions (2b) required to connect this extracellular metabolite to any core metabolite participating in a core reaction (2a). Note that the subnetwork will contain any reaction required to balance the by-products secreted by the subnetwork and/or the core network.The redGEMX method involves five steps:(i)Consider the TFA problem of the model that we want to reduce.(ii)zi for each non-core reaction (2b). Non-core reactions are denoted as Rnc.Create binary variables (iii)bF and bR are the binary variables for the forward and reverse fluxes of all the reactions (coupled to the TFA constraints); when zi = 1, the corresponding reaction is inactive.Generate a constraint that controls the flux for each non-core reaction:(iv)Build the following MILP problem for each extracellular medium metabolite (1a)veM,j is the flux of the jth extracellular medium metabolite (1a), and c is a small number.The redGEMX is a MILP problem that is formulated as follows:36 that generates elementally balanced lumped reactions for the synthesis of the biomass building blocks (BBBs). Using a MILP formulation, lumpGEM identifies the smallest subnetwork (minimum number of reactions from the GEM) required to produce each BBB from metabolites that belong to the core network using reactions from the GEM that are not part of the core. With this formulation, we can identify all the alternative subnetworks  for the synthesis of each BBB (one by one). lumpGEM generates, for each BBB, an overall lumped reaction by adding all the reactions that constitute each subnetwork (see ref. 36 for further details). Note here, different subnetworks can give rise to the same overall lumped reaction. This implies that although we produce all the alternative subnetworks with their associated lumped reactions, only the unique lumped reactions will be added to the final reduction.lumpGEM is a published algorithm73 has been used to draw the subnetworks in the figures.The simulations of this article have been done with Matlab 2017b and CPLEX 12.7.1. EscherFurther information on research design is available in the Supplementary InformationSupplementary Data 1Supplementary Data 2Supplementary Data 3Reporting SummaryDescription of Additional Supplementary Files


Recent studies have enabled the incorporation of thermodynamics and metabolomics data to improve the predictive capabilities of these approaches. However, an in-depth comparison and evaluation of these methods is lacking. This study presents a thorough analysis of two different in silico methods tested against experimental data (metabolomics and 13C-MFA) for the mesophile Escherichia coli. In particular, a modified version of the recently published matTFA toolbox was created, providing a broader range of physicochemical parameters. Validating against experimental data allowed the determination of the best physicochemical parameters to perform the TFA . An analysis of flux pattern changes in the central carbon metabolism between 13C-MFA and TFA highlighted the limited capabilities of both approaches for elucidating the anaplerotic fluxes. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA. Finally, this study emphasised the need for standardisation in the fluxomics community: novel approaches are frequently released but a thorough comparison with currently accepted methods is not always performed.Metabolic engineering in the post-genomic era is characterised by the development of new methods for metabolomics and fluxomics, supported by the integration of genetic engineering tools and mathematical modelling. Particularly, constraint-based stoichiometric models have been widely studied: (i) flux balance analysis (FBA) ( Biotechnology has benefitted from the development of high throughput methods characterising living systems at different levels (e.g. concerning genes or proteins), allowing the industrial production of chemical commodities. Recently, focus has been placed on determining reaction rates (or metabolic fluxes) in the metabolic network of certain microorganisms, in order to identify bottlenecks hindering their exploitation. Two main approaches are commonly used, termed metabolic flux analysis (MFA) and flux balance analysis (FBA), based on measuring and estimating fluxes, respectively. While the influence of thermodynamics in living systems was accepted several decades ago, its application to study biochemical networks has only recently been enabled. In this sense, a multitude of different approaches constraining well-established modelling methods with thermodynamics has been suggested. However, physicochemical parameters are generally not properly adjusted to the experimental conditions, which might affect their predictive capabilities. In this study, we have explored the reliability of currently available tools by investigating the impact of varying said parameters in the simulation of metabolic fluxes and metabolite concentration values. Additionally, our in-depth analysis allowed us to highlight limitations and potential solutions that should be considered in future studies. Metabolic engineering aims to improve microbial strains by considering comprehensive metabolic pathways in their entirety rather than overexpressing a single gene . To imprC) is assumed, so that the stoichiometric matrix (S) (including the stoichiometric coefficients of metabolites in each reaction of the metabolic network) constrains the set of metabolic fluxes (υ) [This systematic framework exploits information regarding the metabolic state, which comprises the metabolome (complete set of low-molecular-weight metabolites <1.5 kDa)) and the fluxome  [ kDa) anduxes (υ) :dCdt=S×YX/S, equal to the ratio growth rate/substrate uptake rate), maximisation of ATP yield, and minimisation of sum of fluxes, which have been suggested to compete in the regulation of bacterial metabolism [13C-MFA) [13C-MFA is considered to be the gold standard in fluxomics [Two main approaches to solve this equation can be found: (i) flux balance analysis (FBA), normally applied to large models   or (ii) tabolism . Hence, tabolism . In contluxomics . Howeverluxomics ) limit i13C-MFA assume most reactions to be reversible [a priori chosen objective function [13C-MFA they are determined by the MIDs [rG′ and ΔrG′o are the Gibbs free energies of reactions (the latter referring to adjusted standard conditions), Q and keq are the ratio of products to reactant concentrations or activities (the latter at equilibrium) and (J+/J−) is the relative forward-to-backward flux [The set of constraints characterising stoichiometric modelling approaches  is insufversible : in the function ), whereathe MIDs . The fluthe MIDs ) links tard flux .rG′ bounds leads to biased results [YX/S) and simulates metabolomics data [in silico metabolite concentration values [Four main approaches exploiting thermodynamics data can be highlighted: (i) energy balance analysis (EBA), where pre-selecting Δ results , (ii) ne results , (iii) m results , and  are considered, (ii) salinity (S) is not taken into account when calculating parameter A, and (iii) Gibbs free energy values are adjusted for ionic strength (I) using the extended Debye-Hückel equation , where  < 0.1 M .t, I and S) on the predictive capabilities of TFA under mesophilic growth conditions. In order to do so, a modified matTFA was developed by increasing the number of parameters and parameter values that were originally considered [13C-MFA and metabolomics data was performed. In particular, flux pattern changes between in vivo and in silico fluxes in the central carbon metabolism were analysed, with a focus on the anaplerotic reactions. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA.This study was based on determining the impact of varying and adjusting the physicochemical parameters : iJO1366, which has proven to predict phenotypes in a wide range of growth conditions [C with minimal medium and a fixed specific growth rate (μ) of 0.20 h-1. The experimental glucose uptake rate (2.93 mmol gDCW-1 h-1) was used as a constraint, leaving the default lower and upper bounds for transport reactions. Maximisation of the biomass yield was selected as the objective function, and no flux value was forced through the biomass reactions (vbiomass). Directionalities of resulting flux values from TFA were compared on a reaction-by-reaction case against in vivo fluxes from 13C-MFA, for which a mapping and directionality correction step was needed . Analyses were performed using the COBRA toolbox [The original matTFA toolbox uses unique values for t and I , and S it and I , the com toolbox  in MATLAI affects the Gibbs energy of formation, an adjustment from the reference state  . In the (ΔfGj′o)  and othe(ΔfGj′o) ,28 the e < 0.1 M Eq 3). T. TI affe-1/2L1/2 ,32. Mod- < 0.5 M .I, where NH(j) is the number of hydrogen atoms in species j, R is the gas constant, T is the absolute temperature and zj refers to the charge of the species [C, but the lack of measured changes in enthalpy (ΔHo) for all the metabolites prevents from doing so [C to 37°C were assumed to be small, as shown elsewhere [A is normally assumed to be constant [F), vacuum permittivity (ε0), gas constant (R) and Avogadro’s constant (NA)), and the second is the temperature (T in K and t in °C), and salinity (S) dependent functions to calculate the density (ρsw) [sw) [Both formulas include terms correcting the pH and  species . Applyindoing so . Hence, lsewhere . The parconstant or calculconstant ,26, and constant was also  term in  includesty (ρsw) and the rsw) [sw) for seawaA (mol-1/2kg1/2) and B (mol-1/2L1/2) is achieved by assuming 1 kg = 1 L. In this study, an expression for seawater . Since different factor combinations converged into the same set of solutions, tests were characterised at the fluxomics and metabolomics levels by considering either the full set of values, or the subset with an experimental counterpart.Mesophilic growth conditions for inations  were tes13C-MFA flux values (r) was performed, as shown in [Results yielding feasible solutions were also compared against x values  and expex values , respectshown in . In ordeshown in . Finallycurrency [side [pool [The constraining capacity of metabolites is not uniform, and depends on their connectivity in the network ,46. To fcurrency , side [4cy [side or pool [de [pool metabolitG, defined as a pair G = , where the vertices (or nodes) V are the metabolites, and the edges E the reactions connecting them. The stoichiometric matrix was converted into an adjacency matrix using an in-house script . This s6 tests (iJO1366 [-1 h-1), reaching a μ ≈ 0.28 h-1  for all FBA and TFA tests. Overall, 26/64 tests were unsuccessful (no cell growth), and the remaining 38/64 converged into common optimal solutions  by calcI (M) was the top one for all responses except for TFA (full), where it equalized t (°C) at 95.7% and was second to the adjustment method. In all cases, using either default concentrations values for AMP, ADP and ATP , or experimental data made no difference. As a result, tests only differing in this factor showed the same correlations with experimental data (The importance of each factor was assessed by means of decision trees (CART in Minitab 19) . Brieflytal data .r ≈ 0.02, whereas for TFA it varied within the range from 0.90 to 0.95. A reaction-by-reaction comparison of flux directionalities in central metabolism showed inherent differences between 13C-MFA and FBA/TFA, as discussed in the last section of this study. At the metabolomics level, it ranged from 0.08 to 0.18  and degradation during extraction [Regarding the metabolomics level, the 9 non-redundant solutions were subjected to a similar analysis. Likewise, only 46/972 metabolites had a variance among tests greater than zero , out of traction –63. SinccalcDGspecies.m). In addition, Gibbs free energy values are relaxed when no feasible solution is found, so the constraining power of experimental metabolite concentration values is reduced [Thermus thermophilus, a potential non-model metabolic engineering platform [Other limitations refer to the design of the tool itself. This method does not consider other complex phenomena affecting the thermodynamic feasibility of metabolic pathways, such as Mg complexation with metabolites, or compound dissociation into more than two protonated species ,20(as shplatform ), recentplatform .Successful tests converged into 5 solutions at the fluxomics level , which aPageRank scores were calculated, allowing to identify metabolites in the top 50% for which experimental data was available . OverallE. coli, where the former also plays a role as nitrogen donor in the biosynthesis of nucleic acids [+, NADH, CO2, menaquinol-8, menaquinone-8 and D-lactate. All but the latter were classified as side compounds for this study , D-fructose-6-phosphate and glyceraldehyde 3-phosphate (not quantified). Both L-glutamate and 2-oxoglutarate participate in the assimilation of nitrogen in ic acids . The latic acids . Accordiic acids , where tic acids ). In parexcluded ), since E. coli, concentration values for NAD(P)H oscillate along the cell cycle [The impact of the inherent dynamics (cell cycle and cell ageing) has been pointed out as a source of metabolic heterogeneity in clonal microbial populations . In a chll cycle , and ATPll cycle . From a ll cycle . Particull cycle , and nicin vivo and in silico fluxes in the central carbon metabolism were analysed, with a particular focus on the anaplerotic reactions. The ‘anaplerotic node’ , PYK and PPS (between phosphoenolpyruvate and pyruvate), ME1 and ME2   , and fin and PPS , which cin silico flux distributions are the result of optimising the system according to the chosen objective function. Accordingly, when maximising the biomass production (which requires ATP), FBA and TFA promote pathways that reduce wasting ATP in the optimal solution [E. coli grown on glucose has proven that both PPC and PPCK (which constitute a futile cycle) are active and play a role in metabolic regulations [13C-MFA.On the other hand, solution . For insulations . Howeverulations ). In thiulations . FBA/TFAEven though flux pattern changes between predicted and experimentally determined intracellular fluxes were present, TFA offered a reliable prediction of intracellular fluxes . This ovIn addition, the nonlinear dependency of the anaplerotic fluxes on the growth rate has been reported in the literature, limiting the reliability of conclusions from experiments using single dilution rates ,71. Partin vivo fluxomics data (r ≈ 0.9) was high enough to enable the analyses on the impact of varying the physicochemical parameters in the predictive capabilities. Studying flux pattern changes on a reaction-by-reaction basis also allowed to confirm previously reported limitations from both 13C-MFA and FBA/TFA with regards to the anaplerotic node [Consequently, it was assumed that the high correlation coefficient achieved for TFA against tic node ,69,75. TThis study showed that the predictive capabilities of TFA can be potentially improved by using physicochemical parameters closer to the experimental conditions and adequate equations. In addition, we proposed a method based on centrality measures to identify important metabolites allowing to further constrain the TFA. In contrast to previous attempts, our strategy is not limited by the size of the network and is computationally cheap. Therefore, a preliminary TFA could be considered when designing a metabolomics protocol to maximise the constraining power of the experimental concentration values. Overall, our study stressed the necessity of performing an in-depth assessment of available methods in the fluxomics field. For instance, interesting published potential solutions to known problems (e.g. elucidation of the anaplerotic fluxes) should be integrated with the widely used approaches. This should increase the degree of standardisation in the community, allowing to cross-validate novel strategies and improving the reliability of the simulated data.S1 Appendix(DOCX)Click here for additional data file.S1 Dataset(XLSX)Click here for additional data file.S2 Dataset(XLSX)Click here for additional data file.S3 Dataset(XLSX)Click here for additional data file.S4 Dataset(XLSX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.


Campylobacter jejuni, the most frequent cause of food-borne bacterial gastroenteritis, is a fastidious organism when grown in the laboratory. Oxygen is required for growth, despite the presence of the metabolic mechanism for anaerobic respiration. Amino acid auxotrophies are variably reported and energy metabolism can occur through several electron donor/acceptor combinations. Overall, the picture is one of a flexible, but vulnerable metabolism. To understand Campylobacter metabolism, we have constructed a fully curated, metabolic model for the reference organism M1 (our variant is M1cam) and validated it through laboratory experiments. Our results show that M1cam is auxotrophic for methionine, niacinamide, and pantothenate. There are complete biosynthesis pathways for all amino acids except methionine and it can produce energy, but not biomass, in the absence of oxygen. M1cam will grow in DMEM/F-12 defined media but not in the previously published Campylobacter specific defined media tested. Using the model, we identified potential auxotrophies and substrates that may improve growth. With this information, we designed simple defined media containing inorganic salts, the auxotrophic substrates, L-methionine, niacinamide, and pantothenate, pyruvate and additional amino acids L-cysteine, L-serine, and L-glutamine for growth enhancement. Our defined media supports a 1.75-fold higher growth rate than Brucella broth after 48 h at 37°C and sustains the growth of other Campylobacter jejuni strains. This media can be used to design reproducible assays that can help in better understanding the adaptation, stress resistance, and the virulence mechanisms of this pathogen. We have shown that with a well-curated metabolic model it is possible to design a media to grow this fastidious organism. This has implications for the investigation of new Campylobacter species defined through metagenomics, such as C. infans. Campylobacter, the leading cause of acute bacterial gastroenteritis, is Gram-negative, microaerophilic, spiral-shaped, highly motile bacteria , a temperature of 37°C or 42°C, with complex media containing blood, peptone, meat, or yeast extract ; in addition to the ability to utilize O2 as an electron acceptor, nitrate, nitrite, and fumarate have also been described as alternatives. Campylobacter spp. would therefore appear to have the potential to carry out anaerobic respiration  describe the metabolic interactions of an organism with its environment, based on a reaction network ultimately inferred from enzymes encoded by the genome. Their analyses enable an investigation of metabolic behavior of the whole system, rather than individual reactions and pathways, and can be used to identify mechanistic links between cellular genotype and metabolic phenotype.Over the last two decades, GSMs have become a valuable tool to analyze cellular behavior under different biological conditions, to design drug targets, to investigate metabolic interactions in microbial communities, and to design defined growth media reversibility. Such information can usually be obtained from a number of on-line databases including databases such as BioCyc  metabolites, otherwise they are referred to as internal metabolites. Reactions that only involve internal metabolites are therefore internal reactions, while those which involve internal and external metabolites are transport reactions. Although gene annotation with regard to enzymes is usually well-defined, annotation of transporters tends to be less comprehensive. Experimental investigations involving growth on defined media thus proves a useful independent method to infer the presence of transport processes, as well as providing useful data for subsequent analyses of the model.In addition to defining the properties of internal reactions, it is, for all practical purposes, necessary to identify the properties of transport processes, representing the consumption and production of compounds in the assumed environment. Compounds present in the environment are referred to as Despite the fundamental importance of online databases, any reconstruction based solely upon these is likely to exhibit a number of problems, the most common of which are: missing gene-protein-reaction (GPR) associations, inconsistent naming of metabolites, and reaction identifiers, incorrect reaction stoichiometries, and reversibility, which propagates to the draft model. Thus, in order to represent a realistic representation of a given organism, an initial draft model will require refinement and curation by the user. The curation process usually begins with correcting reaction stoichiometries and reversibility to ensure that the model follows the law of mass and energy conservation, followed by checking consistency of identifiers, and identifying missing reactions by “gap-filling.” Such gap-filling may often lead to an updated gene annotation. One area of metabolism that requires special attention is the electron transport chain, to ensure that translocated protons are correctly assigned to their location in the cell or the environment.Usually, large-scale metabolic models such as GSMs, are analyzed using constraint based linear programming (LP) approaches  with experimental validation. In doing so we define new, chemically defined, media compositions that will serve as a basis for further modeling and experimental studies of this organism.The aim of this study is to explore Campylobacter jejuni M1cam (https://www.ncbi.nlm.nih.gov/nuccore/CP012149). Genes were predicted and annotated, and used to construct a strain specific Pathway/Genome database (PGDB) for Campylobacter jejuni M1cam. This was used as the basis for the model which was structured in a modular fashion as described by Poolman et al. , as described by Thiele et al. , nitrogen (N), phosphorus (P), and sulfur (S), iron (Fe), sodium (Na), oxygen (O), proton (H), and charge. Metabolites with unknown atomic compositions or generic compounds and reactions involved with such metabolites were replaced, where possible, by balanced reactions with known atomic composition of metabolites. For example, reactions involved with generic compounds  were replaced with specific metabolites and the stoichiometric coefficient balanced on both sides of the reaction. Reactions involved with non-metabolic species  were excluded from the model. Similarly, reactions were corrected for reversibility so that the model is not able to generate energy (in the form of ATP and NAD(P)H) in absence of a mass flux through the system. Thus, the model is ensured to follow the laws of mass and energy conservation, and is free from stoichiometric inconsistencies  flux values (including transporters), subject to the constraints: Nv = 0 (steady-state assumption), vi..j = bi..j defines flux in biomass transporters, as described in section 2.1.2, vk..l defines fluxes in the reactions importing media components, as described in section 2.1.2, vATPase = A defines flux in a hypothetical ATPase reaction in order to account for a growth and non-growth associated maintenance cost and vOtx ≤ Otxmax defines a maximum microaerophilic O2 consumption rate. A was assigned a value of 16 mmol/g DW/hr   set to zero, one at a time. Failure to obtain a solution was taken as demonstrating auxotrophy with respect to the component whose transporter was thus constrained.Substrate auxotrophies were determined, using the model, by repeatedly attempting to solve Equation (1) with individual media transporters (Campylobacter spp. was successfully cultured in the DMEM/F-12 medium (section 2.4), the initial model could not account for the production of all biomass components from these nutrients. These components were identified by modifying Equation (1) to account for the production of a single biomass component, sequentially. Additional reactions were then identified by their presence in other Campylobacter spp. specific biochemical databases in Biocyc and KEGG, literature surveys, and with reference to BLAST  was modified to represent Brucella broth was purchased from Sigma-Aldrich  and Brucella agar from BD . Gibco Dulbecco's Modified Eagle Medium/Nutrient Mixture F-12 (DMEM/F-12) media with no added phenol red, was purchased from Thermo Fisher Scientific . All chemicals were of commercial analytical grade and obtained from Sigma-Aldrich. All solutions, except amino acids and vitamins, were made every week, sterile filtered , and kept at −4°C until needed. Amino acids and vitamins were prepared immediately before use.Campylobacter jejuni M1 has a published genome sequence .The other 7 strains, selected from different clades, according to Champion et al.  and Stab2 [v/v], 5% CO2 [v/v], 85% N2 [v/v]), using an anaerobic cabinet and gas supply , on Brucella broth agar plates, for 48 h at 37°C, except those tested in the Department of Veterinary Medicine, Cambridge University, which were grown at 42°C using a gas mix of hydrogen , also using an anaerobic cabinet and gas supply .All strains were grown under microaerophilic conditions  OD600 of approximately 0.004 in Brucella broth, incubated with shaking (180 rpm) using the same temperature and gas supply indicated previously, to an OD600nm of 0.6 (approximately 2.8 × 109 CFU/ml). Cultures with OD600 different to 0.6 were standardized to that value using sterile PBS. After 20 h, 1.7 mL of this culture was collected, washed twice and resuspended in 1.7 mL of sterile PBS. Each one of the media tested in our study was inoculated in triplicate at 1% (100 μL in 10 mL of media), using Campylobacter jejuni washed cells. Cultures were then incubated microaerobically for 48 h with shaking (180 rpm), under the same temperature and gas conditions stated above, and growth was assessed daily, measuring OD600 in triplicate of each of the technical replicates, using a plate reader . For this purpose, cultures were sampled in a class II cabinet and returned immediately to the anaerobic cabinet. All experiments performed in this study were repeated three times, each time using a new starting culture, prepared from glycerol stock, and with freshly made simple defined media.All Campylobacter jejuni M1cam genomic DNA for WGS was extracted using Maxwell® RSC Cultured Cells DNA Kit. DNA extracts were converted into a Nextera library for sequencing on an Illumina NextSeq 500 platform and genomes were assembled using Velvet de-novo genomic assembler and then subjected to multi-locus sequence typing (MLST).To confirm the identity of the experimental organisms, typical cellular morphology was checked using x1000 bright field microscopy of carbol fuchsin stained cultures and whole genome sequencing (WGS) was performed on selected isolates. Campylobacter jejuni M1cam  to confirm auxotrophy of the compounds tested. If no growth was obtained, experiments were repeated, to confirm results.Campylobacter jejuni M1cam in the defined media given by Guccione et al. ] and adjusted to pH 7 using 1M NaOH or 1M HCl solutions. To maintain sterility, work was carried out in a class II microbiological safety cabinet, and 10 mL of media was filtered into each of the four 50 mL sterile cell culture flasks , closed with their filter caps and kept at 37°C until inoculation. Maintaining media at 37°C until inoculation proved to be very important to obtain reproducible results. Finally, in order to compare our results with previously published defined media, we also tested growth of e et al.  and Alaze et al. .Campylobacter jejuni M1cam PGDB comprised of 228 pathways with a total 1,366 reactions, including 22 transport reactions, and 1,009 compounds. There were 291 reactions without any assigned gene and were inferred from pathway prediction algorithm. This also included reactions that were essential for biomass productions in the model. There were also genes that encoded metabolic enzymes but were not associated with reactions. The reason for the missing GPR association was mainly: (i) information necessary to attribute a particular reaction to specific gene was missing in the annotated file (ii) though the gene product had been annotated it was not detected by the Pathologic software. Reactions, particularly those inferred as essential for biomass production, without any gene association were revisited to establish GPR relation (see 2.1.1) where possible. https://data.quadram.ac.uk/dipali.singh/CJM1cam_DB/.The automatically generated The curated model consists of 994 reactions. The number is less than that of the initial draft model generated from the PGDB due to removal of reactions involved with non-metabolic species and those of unknown atomic composition, as described in 2.1.3. 76% of reactions in the model have gene associations, 6% are spontaneous, while the remainder are inferred by the gap filling algorithm or added after careful curation. The model includes 115 transporters, 968 internal metabolites and 93 external metabolites, summarized in 4 and CO2 were among the excreted by-products. The model is able to account for ATP generation under anaerobic conditions through oxidative phosphorylation, using nitrate or fumarate electron acceptors. However, it is not able to generate biomass in the absence of O2.The solution to Equation (1), with DMEM/F-12 media, has a total of 326 reactions, including transporters. There are 165 essential for biomass production: removal of any one of these results in Equation (1) having no feasible solution. The solution has no net import flux of amino acids, leucine, arginine, histidine, valine, asparagine, phenylalanine, alanine, threonine, tyrosine, tryptophan, and lysine . There was, however, notable net import of pyruvate, as a carbon source, and the amino acids, aspartate, serine, glutamine, and proline; Acetate, succinate, NHmethionine, pantothenate and niacinamide  were identified as auxotrophic. The pathways for the de-novo biosynthesis of these metabolites were absent in the PGDB and thus the model. These included homoserine O-succinyltransferase and methionine synthase from the methionine biosynthesis pathway, 3-methyl-2-oxobutanoate hydroxymethyltrasferase, pantothenate synthetase, and 2-oxopantoate reductase from the pantothenate biosynthesis pathway, and nicotinate-nucleotide diphosphorylase and quinolinate synthetase from the niacinamide biosynthesis pathway.Out of the 33 organic substrates tested in the model, 30 substrates were identified as non-essential. The remaining three substrates, The model analysis suggests that growth can be supported with a medium containing only pyruvate, methionine, pantothenate, and niacinamide . Furthermore, the fact that aspartate, serine, glutamine, and proline were imported in excess, relative to that required by the biomass composition, suggests that the presence of these compounds in the media would enhance growth.C. jejuni M1cam. The removal of methionine, pantothenate and niacinamide from the DMEM/F-12 media , pantothenate, and niacinamide  supported growth of 12 media  resultedAs part of the media development, the concentration of sodium pyruvate, as a carbon source, was increased from 0.5 to 10 mM. In addition, the concentrations of auxotrophic substrates, niacinamide and pantothenate, were optimized to 33.1 and 9.4 μM, respectively . The inoThus, four simple defined media compositions were defined, where all four included the auxotrophic substrates, methionine, pantothenate, and niacinamide along with pyruvate as a carbon source, and with different combinations of non-essential but growth-improving organic substrates, presented in Campylobacter jejuni M1cam. Although each of MM1 and MM2 had a similar effect on growth of Campylobacter jejuni M1cam, MM1 was selected as final defined media, as it had a higher starting pH and required less NaOH to reach pH 7.The best results, in terms of growth, were obtained when cysteine, serine, and glutamine or glutamate where present  S containing amino acids, methionine, and cysteine.The modeling and experimental results presented here, indicate that k et al. . On the Campylobacter jejuni M1cam is the derivative of the human isolate Campylobacter jejuni M1 and is epidemiologically related to poultry strains  cluster lies in the hypervariable region  and pyruvate as the carbon source, contains amino acids cysteine, serine, and glutamate/glutamine. The latter amino acids, though not essential for growth, had a significant growth promoting effect on Campylobacter jejuni M1cam under our experimental condition. Similar, reports have been shown for strains 81176 and NCTC11168 where substrates, though not essential, had to be added to improve growth (Alazzam et al., Campylobacter. Although pyruvate transporters have not been identified, pyruvate has been shown to be used as an exogenous carbon source when present in growth medium (Mendz et al., C. jejuni M1cam. It should be noted that the media designed in this study was optimized to maximize the growth of C. jejuni M1cam. Further tests will be needed to optimize the growth of other strains, however it is clear that the designed media MM1 can support the growth of a variety of strains under different conditions.Our media, apart from Campylobacter jejuni M1Cam, we have built and analyzed a strain specific genome-scale model of this organism. The analysis allowed us to identify specific auxotrophies, as well as compounds which are preferentially consumed, and this allowed us to develop a new media suitable for the study of M1Cam and other Campylobacter spp. strains. The model analysis also replicated the apparently paradoxical, but widely reported observation, that although Campylobacter spp. can operate the electron transport chain in the absence of oxygen, oxygen is nonetheless essential for growth. Experimentally confirming all aspects of our model results, in particular the generation of metabolic by-products in the media, was beyond the scope of the current contribution. However, we believe the experimental and modeling results we have presented here, when taken together, provide a solid foundation upon which to build further investigations of Campylobacter jejuni M1cam and related organisms.By adopting a systems-biology approach and using a newly annotated genome of https://data.quadram.ac.uk/dipali.singh/CJM1cam_MM/, https://data.quadram.ac.uk/dipali.singh/CJM1cam_DB/. Additionally, Pathway/Genome database generated in this study is available from Pathway Tool Registry.The datasets generated for this study can be found in the NT and DS designed and supervised research plans with input from JW. DS constructed the biochemical database and genome-scale metabolic model. NT performed experiments for minimal media design with input from BP. LC performed gene predictions and annotations. ES and FN tested minimal media designed in this work in other strains. BD performed sequence analysis. MP and DS analyzed GSM and together with NT wrote the paper with revision from JW. All authors contributed to the article and approved the submitted version.SequenceAnalysis.co.uk and was paid to perform this work. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.LC is the director of


Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes. Our findings point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the constraints imposed by the network structure at steady state. Since reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering.Biological networks across scales exhibit hierarchical organization that may constrain network function. Yet, understanding how these hierarchies arise due to the operational constraint of the networks and whether they impose limits to molecular phenotypes remains elusive. Here we show that metabolic networks include a hierarchy of reactions based on a natural flux ordering that holds for every steady state. We find that the hierarchy of reactions is reflected in experimental measurements of transcript, protein and flux levels of  E. coli, which we call the flux order relation. Specifically, we identify pairs of reactions in which one reaction always carries a higher flux than the other at steady state. Hence, the flux order relation creates a hierarchical organization of metabolism. We show that the flux order relation is reflected in experimental data sets of fluxes, gene expression, protein levels, and enzyme catalytic constants. Our results point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the flux order relation.Metabolism results from the activity of thousands of biochemical reactions, which create, transform and recycle all chemicals, i.e., metabolites, required by life. Metabolic reactions depend on enzymes—proteins acting as biological catalyzers—to proceed, which effectively links metabolism to other layers in the organization of cellular physiology, such as transcription and translation. These reactions do not operate in isolation but interact in a metabolic network due to the metabolites they share. The joint action of the reactions imposes constraints on the reaction fluxes denoting rates of conversion between metabolites. Here, we identify one such constraint imposed by the metabolic network of  Hierarchical organization has been recognized as a salient feature of biological networks, spanning from the molecular to the ecosystem scale –6. BioloMoreover, hierarchies that rely on pairwise relationships between components often consider operational principles in conjunction with the network structure. For instance, mass-balance and steady state constraints also induce hierarchies based on asymmetric, pairwise relations among reactions . One sucE. coli Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors investigate the broad field that biological networks across scales exhibit hierarchical organization that may constrain network function. They find that metabolic networks show a hierarchy of reactions based on a natural flux ordering that holds for every steady state, even reflected in experimental measurements of transcript, protein and flux levels of Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes.This is nice and well documented here both by the formal analysis as well as the public experimental data used for validation of these findings and a nice analysis.Comments:--What should be discussed somewhat more is the direct implications of the results and possible explanations:Certainly, there is some input from resource partitioning and there is fine-tuning of enzyme levels in E. coli and of course it has to respect the constraints imposed by the network structure at steady state.However, all this may even more be the result of other more general factors, in particular the evolution of enzyme networks or just the result of fitness optimization, in particular as E.coli is metabolically so active and broad.--I agree that reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, however, it would be good if the authors can show a nice concrete example on how the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering, for instance in plants.Again, there is no doubt that you can do metabolic engineering by constraint-based modelling, but it would be good if the authors can clarify how then the insight in the natural flux ordering presents then a handle to do something novel which is not already obvious from e.g. calculating the flux modes according to standard techniques.Reviewer #2: In their manuscript "flux-based hierarchical organization ..." the authors propose a new method for computing a hierarchy among metabolic reactions.Employing the framework of steady-state fluxes obtained via LP from genome-scale metabolic models, the criterion for ranking reactions is flux ordering. The authors compare the resulting hierarchy with categories derived from metabolic pathways, with flux measurements and with regulatory information.I find the manuscript suitable for PLOS CB. However, I have a few concerns and comments, which the authors should address.(1) From my perspective the literature around the hierarchical organization of metabolic systems  should be cited on a broader level. For example in  the distribution of gene attributes across hierarchical levels has been studied . Also, as the authors point out in the introduction, the hierarchical organization of metabolic systems can be assessed on the level of metabolites, as well as on the level of reactions. Examples for the former, which the authors may consider to cite are: , . Regarding the comparison with transcriptional regulation, I regard the findings from  to be highly relevant. The authors should compare their results with the 'determined' and 'non-determined' categories from this paper.(2) I was surprised that the authors do not discuss the fact that metabolic fluxes follow a power-law distribution . Doesn't this already imply a hierarchical organization?(3) How do the authors motivate their choice of iJO1366 as the genome-scale metabolic model? Wouldn't the more recent model iML1515 from  been a more plausible choice?(4) In Section 2.2 the authors study the distribution of pathways across the hierarchical levels. Maybe I missed this point, but shouldn't these percentages be compared to a null model of shuffled macrosystem labels, in order to eliminate (level and system) size effects?(5) I have not understood the argument in Section 2.5.1 regarding the potential artifcact due to the empirical focus of flux data on the metabolic core. Wouldn't the appropriate test for this be to evaluate the flux order graph obtained from the E. coli 'metabolic core model' from ?(6) Given the scope of comparisons in Sections 2.5.2, I would recommend a correction for multiple testing for the p-values reported here.(7) I might have misunderstood the analysis strategy of the authors here, but when they say 'a reaction is connected to another by a directional edge if it carries a greater of equal flux in any steady state', do they mean 'any steady state compatible with the minimum flux through the biomass reaction' or do they literally mean any vertex of the flux polytope? I suppose it is the former. In this case, however, the results will depend strongly on the choice of this minimal flux to be 95 percent of the maximally feasible biomass production rate . If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  and your responses to reviewer comments. If eligible, we will contact you to opt in or out[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Christoph KaletaAssociate EditorPLOS Computational BiologyJason PapinEditor-in-ChiefPLOS Computational Biology***********************ploscompbiol@plos.org immediately:A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact [LINK]Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors revised their manuscript thoroughly, one question remains:"as discussed in Section 2.7, the difference is that essential reactions which are also flux-ordered affect flux through the biomass reaction in a continuous manner, while essential reactions which are not flux-ordered affect biomass production in a binary  manner. Hence, identifying essential reactions which are flux-ordered with the biomass reaction could allow fine tuning of reaction flux to control biomass production."This is fair enough, but please discuss why not identifying the essential reactions just by looking at those modes which drop out if an enzyme is inhibited does not do a similar good job . I would even think that this method is simpler and allows easy to quantify the more important enzymes (as blocking these inhibits a higher number of modes).--So as mentioned already regarding the previous version of the manuscript, please make still a bit clearer, best by looking at this remaining comment, why and where your approach is preferable to classical elementary mode analysis and what you really gain by using this more complex method of yours.Reviewer #2: The revised version of the manuscript "Flux-based hierarchical organization of Escherichia coli's metabolic network" (PCOMPBIOL-D-19-01496R1) is, from my perspective, a substantial improvement.I agree with their assessment that the results of Shlomi et al. (2007) cannot be directly compared with their findings.Regarding the work by Almaas et al. 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However, this decision is the responsibility of the authors (they explain quite clearly what they are doing).The point about the dependence of the results on the choice of the minimal flux has been addressed properly by the authors, as have been the other (mostly minor) remarks I had.Summarizing, I have no objection against acceptance of the manuscript .**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Computational Biologydata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: Yes**********what does this mean?). 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Methylocella silvestris is a facultative aerobic methanotrophic bacterium which uses not only methane, but also other alkanes such as ethane and propane, as carbon and energy sources. Its high metabolic versatility, together with the availability of tools for its genetic engineering, make it a very promising platform for metabolic engineering and industrial biotechnology using natural gas as substrate.M. silvestris is presented. The model has been used to predict the ability of M. silvestris to grow on 12 different substrates, the growth phenotype of two deletion mutants (ΔICL and ΔMS), and biomass yield on methane and ethanol. The model, together with phenotypic characterization of the deletion mutants, revealed that M. silvestris uses the glyoxylate shuttle for the assimilation of C1 and C2 substrates, which is unique in contrast to published reports of other methanotrophs. Two alternative pathways for propane metabolism have been identified and validated experimentally using enzyme activity tests and constructing a deletion mutant (Δ1641), which enabled the identification of acetol as one of the intermediates of propane assimilation via 2-propanol. The model was also used to integrate proteomic data and to identify key enzymes responsible for the adaptation of M. silvestris to different substrates.The first Genome Scale Metabolic Model for M. silvestris, such as its use of the glyoxylate shuttle for the assimilation of one and two carbon compounds and the existence of two parallel metabolic pathways for propane assimilation. This model, together with the fact that tools for its genetic engineering already exist, paves the way for the use of M. silvestris as a platform for metabolic engineering and industrial exploitation of methanotrophs.The model has been used to elucidate key metabolic features of  The draMethylocella model and those in 2 previously reconstructed models of type II methanotrophs (Methylocystis hirsuta and Methylocystis parvus) [Figure  parvus) , 16, as Methylocella silvestris is provided as Additional file Methylocella silvestris contains those catalyzed by the enzymes isocitrate lyase  and malate synthase , which form the glyoxylate shunt, allowing the use of ethanol and acetate as sole carbon sources. Other type II methanotrophs such as Methylocystis sp. SB2 and Methylocystis hirsuta [Methylocella silvestris) and have very low specific growth rates . The roMethylocella silvestris and absent in both of the Methylocystis species considered, we predicted 6-phosphogluconate and its derivatives 6-phosphogluconate-1–5-lactone and 2-keto-3-deoxy-6-phosphogluconate, which are involved in the Entner-Doutdoroff pathway. Other specific metabolites are 4-hydroxy-2-oxovalerate and 2-keto-4-pentenoate, which are linked to the presence of a 2-keto-4-pentenoate hydratase .Among the metabolites specific to Methylocella, compared to other methanotrophs, is characterized by its metabolic versatility and the high variety of substrates on which it can grow. In particular, its use of alkanes such as ethane and propane [ propane  is of grMethylocella silvestris . The predicted metabolic fluxes are 0.78 and 0.71 mmol h−1 g-DW−1 for ICL and MS. Enzymatic activities are reported in nmol min−1 mg-Protein−1. Thus, to compare the predicted metabolic fluxes with the results of enzyme activity tests, we need to transform grams of dry weight into milligrams of protein. Assuming that half of the total biomass corresponds to proteins, the predicted in-vivo activities of these enzymes are equivalent to 26 and 24 nmol min−1 mg-Protein−1. The predicted activity of ICL is close to the measured activity (26 versus 23 nmol min−1 mg-Protein−1), whilst the measured activity of MS is one order higher than the minimal activity necessary to support the observed growth rate (424 versus 24 nmol min−1 mg-Protein−1).In order to confirm the activity of these enzymes, enzyme assays were carried out with extracts of acetate grown tris see . The meaM. silvestris were constructed  and “PrMO2” (yielding 2-propanol). Even if some cross activity is possible, the reaction “PrMO” has been annotated as catalyzed by the enzyme PrMO, while the reaction “PrMO2” has been annotated as catalyzed by the enzyme sMMO. Both monooxygenation reactions are coupled to the consumption of an oxygen molecule and the oxidation of an NADH equivalent. bstrates . Growth M. silvestris contains eight genes predicted to encode NAD(P)-dependent alcohol dehydrogenases (ADHs), as well as a pyrroloquinoline quinone (PQQ)-containing methanol dehydrogenase (Msil_0471) and a PQQ-containing ADH with 73% identity to xoxF from Methylobacterium extorquens (Msil_1587). For modelling purposes, it is essential to elucidate if the oxidation of 1-propanol and 2-propanol, to propanal and acetone respectively, is coupled to NAD(P)H generation, or coupled to transfer of electrons to PQQ, which are further transferred to cytochrome-c, with proton extrusion [The genome of xtrusion . OxidatiMethylocella silvestris can grow on both acetone and propanal (the oxidation products of 2-propanol and 1-propanol). The genome revealed the presence of genes encoding a putative pathway from propanal to methylmalonyl-CoA, composed of four reactions with two putative enzymes for each of them , which confirmed its relation to propane utilization. More interestingly, when growing on propane, the Δ1641 strain started accumulating acetol in its growth medium . The mutant strain also lost its ability to grow on 2-propanol and acetone, which confirms the involvement of Msil_1641 in the downstream degradation pathway of acetone. Based on the evidence alone (and its annotation by RAST as a NAD associated oxidoreductase), it was assumed that Msil_1641 catalyzes the oxidation of acetol to 2-oxopropanal with concomitant NADH production. The oxidation of acetone to acetol was proposed to be catalyzed by two putative cytochrome P450 oxidoreductases represented in the genome (Msil_0731 and Msil_1926). Similar enzymes have shown to catalyze this reaction in rabbit [The genome annotation did not reveal all the enzymes catalyzing the reactions involved in the downstream metabolism of acetone. Both 2-propanol and acetone accumulated in the culture broth, during growth on propane, which suggests a kinetic bottleneck downstream of acetone. The RAST annotation shows the presence of three putative hydroxyacylglutathione hydrolases  and three putative lactoylglutathione lyases . These reactions would allow the transformation of 2-oxopropanal into lactate, which could be further metabolized via its transformation into pyruvate by a putative lactate dehydrogenase present in the genome . However, the enzymes involved in the transformation of acetone to 2-oxopropanal remain to be elucidated. Proteomics has revealed strong overexpression of the gene Msil_1641, induced by propane. This gene has been annotated as a glucose-methanol-choline oxidoreductase, which does not suggest any specific association with propane degradation, therefore its role in M. silvestris, one of them, via 1-propanol, transforms propane into methylmalonyl-CoA, while a second pathway, via 2-propanol, transforms propane into lactate. Both pathways co-exist simultaneously and the metabolic flux going through each of them depends on the ratio between 1-propanol and 2-propanol produced by PrMO and sMMO [−1 and specific production rates of 2-propanol, acetone and acetol of respectively: 0.188, 0.075 and 0.152 mmol h−1 g-DW−1. This rate of 0.152 mmol h−1 g-DW−1 was assumed to be equal to the rate of acetol oxidation to 2-oxopropanal in the wild type.There are two alternative pathways for propane degradation in and sMMO . Deletio−1, produced 2-propanol and acetone at 0.189 and 0.073 mmol h−1 g-DW−1 respectively (with no acetol accumulation in the medium). These experimental values, as well as the acetol oxidation rate of 0.153 mmol h−1 g-DW−1, inferred from the behaviour of Δ1641, were imposed as constraints in the metabolic model. Propane uptake rate was minimized, leading to a prediction of 0.67 mmol h−1 g-DW−1. This corresponds to a biomass yield on propane equal to 25 g-DW mol−1, which is very close to the experimental yield measured for the wild type of 24 ± 2 g-DW mol−1 [The wild type, which showed a growth rate on propane of 0.0174 ± 0.0002 hMethylocella silvestris have been obtained for growth on methane, succinate and propane [Proteomic data for  propane . The proThe reconstructed model was used to calculate correlation coefficients between the predicted metabolic fluxes in each to the three experimental conditions and the enzyme abundances. This allows to identify metabolic reactions whose predicted fluxes correlate with the abundances of the enzymes catalyzing them . Using the terminology of Metabolic Control Analysis (MCA) , some enp values were obtained for each of the metabolic enzymes detected in the proteome. The p-vales were corrected for multiple testing and a false discovery rate of 0.05 was set as a cutoff. Nine proteins passed this threshold, among them the three subunits of PrMO, which are expressed only in presence of propane. Two other enzymes were expressed only under growth on propane, those were the previously discussed oxidoreductase coded by the gene Msil_1641, and the methylmalonyl-CoA mutase coded by Msil_3785. The identified enzymes included also two enzymes of the serine cycle, namely phosphoenolpyruvate carboxylase (Msil_1718) and serine-glyoxylate aminotransferase (Msil_1714), which show their highest expression levels during growth on methane. 3-oxoacyl-synthase (Msil_2205) and inorganic pyrophosphatase (Msil_1025) showed their highest expression and metabolic flux during growth on succinate, followed by growth on propane and methane.These enzymes are responsible for the transcriptional adaptation of the cell to different carbon sources. Model predictions were carried out by setting specific growth rates to their experimental values and minimizing the carbon source uptake rate. In the case of propane, the fluxes in the pathway via lactate (discussed in the previous section), were also constrained to their experimental values. Pearson correlation coefficients and p value resulting from the correlation. Figure Figure Methylocella. The model captures the metabolic versatility of the strain and is able to reflect its ability to grow on a broad range of substrates as well as to predict quantitatively its biomass yields on methane and ethanol. The model also predicts the phenotypes of two deletion mutants, ΔICL and ΔMS, and could explain the reliance of M. silvestris on the glyoxylate shunt for growth on C1 substrates. This feature makes M. silvestris different from other type II methanotrophs and should be taken in account for the design of future metabolic engineering strategies. Regarding the ability of M. silvestris to grow on propane, two alternative pathways have been identified. Experimental evidence suggests that both pathways operate in parallel. One of the pathways proceeds through methylmalonyl-CoA while the other proceeds through lactate. The existence of 2 independent pathways for propane assimilation makes M. silvestris a potential platform to synthesize compounds using propane as a carbon and energy source. For example, the deletion of lactate dehydrogenase can be expected to disrupt the second pathway and to result in lactate accumulation, while energy and biomass could still be obtained via the first pathway. Alternatively, the second pathway could be disrupted downstream of methylmalonyl-CoA and its metabolic flux deviated to compounds having methylmalonyl-CoA as precursor, while the cell could still use the pathway via lactate to obtain energy and biomass precursors.In this work we present the first GSMM of an organism of the genus Methylocella silvestris BL2 was obtained from the Joint Genome Institute (JGI) (DSM 15510). After annotation with RAST [The genome of ith RAST  a draft ith RAST . The genJGI) DSM 510. Afteith RAST . The genhttps://github.com/SergioBordel/ModelsMethanotrophsThe reconstructed GSMM in SBML format (Methylocella.xml), together with tab separated files containing metabolites (Methylocella_metabolites.txt) and reactions (Methylocella_reactions.txt) and a file containing the top connected metabolites in the model (MethylocellaMets.txt), as well as the RAST annotation in Excel format (Methylocella.xls), can be downloaded from 2 (6 mM), phenylhydrazine HCl (4 mM) L-Cysteine HCl (12 mM) protein (50—200 µg) and was initiated with DL-isocitrate  (8 mM). Increase in absorbance at 324 nm, due to the accumulation of glyoxylate phenylhydrazone, was recorded against reactions containing water instead of isocitrate. After a lag of approximately 1–2 min, the reaction was linear for at least 10 min. Rates were calculated using ε324 for glyoxylate phenylhydrazone of 1.7 × 104 M−1 cm−1. Malate synthase was assayed by following the decrease in absorbance at 232 nm due to the breakage of the acetyl-CoA thio-ester bond in the presence of glyoxylate. Reactions (1 ml) contained Tris buffer pH 8.0 , MgCl2 (3.4 mM), acetyl-CoA  (0.05 mM) and protein (100 µg). Absorbance was measured for 5 min before and after addition of glyoxylate . Without substrate, change in absorbance was less than 0.0008 min−1. Rates were calculated using ε232 for acetyl-CoA of 4.5 × 103 M−1 cm−1. Alcohol dehydrogenase (experiments on propane) was assayed as previously described [Isocitrate lyase and malate synthase (experiments on acetate) were assayed following the method of Dixon and Kornberg , adaptedum salt)  mM. IncrUnmarked deletion mutants of isocitrate lysase, malate synthase and Msil_1641 were constructed by double homologous recombination, followed by removal of the antibiotic cassette, as previously described . UpstreaMethylocella silvestris BL2 and the three marker-free deletion mutants, were grown in 120 ml serum vials, sealed with rubber stoppers, on dilute nitrate mineral salts medium (DNMS) as previously described [escribed . For culescribed , 10 min) and 3 μl of the supernatant injected into an Agilent 7890A gas chromatograph fitted with an HP-PLOT Q column . Biomass was calculated from optical density (OD540), measured with a Shimadzu UV-1800 spectrophotometer, based on the conversion factor 1 OD ml unit = 0.25 mg dry weight. Methane was measured using a Porapak Q column (Supelco).Methane, ethanol and biomass concentrations were monitored over time and the yields were calculating by plotting the produced biomass versus the consumed substrate and obtaining the slope (before reaching limitation by nitrogen). Methane was added to cultures by injection through the rubber stopper to a headspace concentration of 10% v/v, and monitored by gas chromatography (GC) . The iniAdditional file 1: FS1. List of unique reactions and unique metabolites in the model of M. Sylvestris.Additional file 2: FS2. Gene annotation obtained using RAST.Additional file 3: FS3. Equivalence between gene annotations.