Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field. Cell metabolism represents all the biochemical reactions occurring within the cell. Those reactions provide the supply of precursors for biosynthetic purposes, energy for anabolic reactions, signaling metabolites and general maintenance processes. In order to maintain the cell homeostasis and ensure the availability of all the necessary components, metabolism is highly regulated by different mechanisms involving allostery, enzyme abundance, and post-translational modifications. Metabolic network complexity provides plasticity and robustness to the cell in response to perturbations, leading to a challenge for researchers to understand and predict the molecular mechanisms governing cell behavior.Development of high-throughput technologies has provided researchers with the capability to analyze and quantify an increasing amount and variety of biochemical constituents in the living cells, the so-called omics data. These omics technologies enable the identification and quantification of biological molecules  connecting the genotype with the phenotype. Due to the close relationship between metabolism and cellular phenotype, the development of the high-throughput technologies for metabolomics has been particularly important in the study of a large number of biological processes.Thus, the increasing amount of data provided by high-throughput platforms together with the complexity of metabolic networks makes it implausible to assess the overall behavior of metabolism from the individual properties of its components. Therefore, the study of cell metabolism behavior as a whole must be approached from a holistic perspective in order to extract relevant biological knowledge from the increasing amount of omics data by instead the so-called data-driven approaches. In this sense, metabolomics in combination with computational methods has the potential to unravel how cell metabolism is modulated in response to endogenous or exogenous perturbations such as genetic mutations or changes in the environmental conditions. A number of methods have been developed to analyze the increasing amount of omics data, the so-called data-driven approaches. These methods are extremely useful to define patterns or correlations between metabolic species and/or between groups/conditions. However, these correlations do not necessarily imply causality, which makes it difficult, if not impossible, to infer specific molecular mechanisms associated with a given phenotype. In this sense, incorporating prior information, such as network structure, component interactions, or physico-chemical properties enhances the predictive capabilities of the analysis and enables the identification of the mechanisms governing the system’s behavior. This information is typically incorporated in the form of a computational model. Models can describe cellular functions organized into hierarchical levels that are tightly controlled by dynamic and intricate gene regulatory mechanisms, signaling pathways and metabolic control . The results of these regulations and the network topology make metabolic networks highly non-linear and complex systems. Thus, model-driven methods are required to cope with this complexity in order to unveil the molecular mechanisms responsible for changes in metabolite concentrations as well as the emergent properties  of metabolic systems arising from its intrinsic structure.Based on how the metabolic network is formalized, two main modelling approaches can be considered: (i) constraint-based approaches that incorporate the reactions’ stoichiometry and thermodynamic information to infer metabolic flux distributions and predict complex metabolic phenotypes; and (ii) kinetic models that simulate changes in metabolite concentrations over time by incorporating biochemical network stoichiometry, mechanistic reaction rate laws, kinetic parameters and enzyme concentrations. These approaches are complementary and can be used jointly to explain emergent properties, show hidden patterns, and build new hypotheses. In this review, we will describe the current state of the art of model-driven methods to integrate omics data, with special focus on metabolic data. Furthermore, we will look into the examples of metabolomics data integration, strengths, and limitations of such approaches, as well as the successful case studies. In brief, constraint-based modelling incorporates information about reaction stoichiometry and thermodynamics , while kConstraint-based modelling is one of the most widely used family of methods to study metabolism . It alloGiven a vector describing the flux of each reaction  ,14,15 isTo explore alternative and suboptimal solutions as well as study the network flexibility, a variant of FBA, flux variability analysis (FVA) , can be While FBA with the objective of maximizing growth results in reasonable solutions for wild-type cells, it does not so for (unevolved) gene knockout mutants. While in principle wild-type cells optimize their growth, unevolved cells with knockouts do not. Since homeostasis governs metabolic reprogramming ,25, we cEscherichia. coli throughout batch cultivations in different conditions [For problems which cannot be addressed by traditional stoichiometric methods, such as —changing concentrations over time and/or changing steady states, —dynamic methods were proposed. The idea behind them is to solve multiple constraint-based problems, each at a different time point, assuming steady state at each of them, which allows the modelling of metabolic changes over time. This approach, called dynamic FBA (dFBA), was originally proposed by Varma and Palsson to predict the metabolism of nditions . In this review, we described constrained-based methods that are necessary to understand state-of-the-art approaches of metabolomics data integration. To obtain more information about the variability of approaches of constraint-based methods, we refer the readers to the review by Lewis et al. . We alsoA different way of approaching the analysis of metabolic networks is the elementary flux modes (EFM) analysis ,36. EFMsAmong the major limitations of constraint-based models in their classical implementation is that they rely only on fluxes and stoichiometry and not metabolite concentration. Thus, under the steady state assumption, fluxes occur irrespective of the metabolite pools—so it is neither possible to incorporate nor predict concentrations in the system. The choice of objective function and the applicability of the steady state assumption have an important impact on the final solution . AnotherMetabolic flux analysis (MFA)  is a wid2 secretion rate, or the growth rate. stMFA is based on minimizing the difference between the experimental and simulated secretion and uptake rates. Given stoichiometric constraints and measured fluxes, least square regression is performed. However, secretion and uptake rates are usually insufficient to resolve all the reaction fluxes in the model. Further, small-scale models are typically used, and therefore the reduction in genome-scale models is needed. Similar to dFBA [Stoichiometric MFA (stMFA) ,45 does  to dFBA , the dyn13C-MFA [13C-MFA is based on minimizing the difference between the experimental and simulated secretion, uptake rates and isotopic-labelling pattern. This more detailed metabolic information allows 13C-MFA to infer metabolic reaction fluxes, which otherwise could not be resolved, such as cycles, bifurcations or the source of NADPH production. Thus, when such a part of the metabolism is of interest, researchers should consider adding isotope labelling to their experiments. However, this implies more complexity in terms of experimental design and data analysis [Another technique is 13C-MFA ,48, wheranalysis ,49.There are different ways to approach labeling experiments, depending on the molecules/reactions of interest and the required resolution. Methods range from measuring the labeling patterns of distinct sets of metabolites, e.g., central carbon metabolism intermediates , protein13C)glucose and (13C6)glucose, or different labelled substrates, such as (13C6)glucose and (13C6)glutamine [It might not be possible to resolve the more complex metabolic architectures by a single labeling experiment and may require parallel setups with differentially labeled tracers, for example, a mixture of different tracers of a single substrate, such as  harbors distinct advantages in certain aspects. For instance, by taking time-dependent labeling of metabolites into account, metabolite pool sizes and reversible exchange fluxes can be estimated. This allows for comparison with (or inclusion of) metabolomics data ,57.The above-described methods use the same formalism as constraint-based models: linear combinations of reaction fluxes and the steady state assumption. Notably, this approach (minimization of the difference between observed and modelled fluxes and isotopic pattern) can be applied in the kinetic modelling framework and such an application was demonstrated ,60,61,62For detailed information about MFA and a family of different MFA methods, we refer to this review  and protKinetic modelling describes the changes in metabolite concentrations given an initial condition by representing the metabolic network as a system of differential equations, most commonly ordinary differential equations. The fate of each metabolite is described by an ordinary differential equation that consists of a rate equation for each reaction that either consumes or produces the metabolite. Solutions for such systems yield the concentration of metabolites at each time point, and make it possible to evaluate the evolution of fluxes and metabolites over time. The equations for the reaction rates are functions of the enzyme concentrations, kinetic parameters, and metabolite concentrations. Kinetic modelling describes not only the stoichiometric relation between substrate and products but also the enzymatic mechanisms and different levels of regulation , which makes these methods suitable for the integration of multiple omics data types.While constraint-based models are suitable to predict the state of the system, they do not answer how it is achieved. Further, it is not always possible to assume that the system is in a steady state. Since kinetic models describe the enzymatic mechanisms underlying a given metabolic reaction, this approach enables the incorporation of allosteric regulations, where the enzyme activity is affected by the binding of a small molecule to a site other than the enzyme’s active site . AllosteKinetic modelling approaches have been widely applied in a variety of cases, such as inferring metabolite kinetics from experimental data ,69,70,71Researchers are working on solutions to address current limitations, such as kinetic parameter paucity and small-scale preference. One possible approach to address the lack of kinetic parameters and/or uncertainty in the given kinetic parameters, and as a consequence in predictions, is to use ensemble modelling . Among cIn ensemble modelling, the predictions of multiple models are combined in order to create a feasible solution space that encompasses all of them. The topology of a network and its steady state flux are used to infer the metabolic flux distributions. As much information as is available about the mechanism of enzymatic reactions in the model is included to keep the ensemble biologically feasible. The steady state flux can be determined experimentally, taken from literature, if available, or estimated based on the exchange fluxes of the system. An ensemble of models is created, spanning the range of thermodynamically allowed kinetic parameters, each reaching the same steady state flux and metabolite concentrations. Flux changes due to enzyme perturbation can be used to refine the analysis and reduce the number of models in the ensemble .Numerous approaches have been developed to integrate metabolomics data into mechanistic models, such as kinetic or constraint-based models. These computational tools allow researchers to obtain new insights into metabolism regulation. From a mathematical point of view, we can describe two main types of data integration: variable constraints  and parameter fitting . From a problem statement point of view, researchers can infer intracellular fluxes from the experimental data, estimate flux changes that lead to a specific phenotype, or find the parameters of the system  to predict or describe another metabolic state . In this13C isotopes as a carbon source. The substrate is processed by the cell and converted into labeled products and intermediates. By measuring these products and intermediates, distinct labeling patterns are revealed, from which the fluxes through the reactions can be inferred [13C-MFA extends this idea to the systems biology approach. Together with previous knowledge about the cell metabolism, the data is integrated via 13C-MFA methods to infer a metabolic flux profile that is consistent with the experimental measurements. 13C-MFA integrates the prior information in the form of a network topology and carbon rearrangements to find the steady state that best satisfies the stoichiometric and mass-balance constraints, as well as the experimentally measured isotopic-labelling pattern. This is usually referred to as “fluxomics” in literature. 13C-MFA is now a gold standard in resolving flux distributions. 13C-MFA has been extensively used in different biological fields, such as metabolic engineering, cancer research, physiology, biochemistry, and plant sciences, both in prokaryotic and eukaryotic systems. A major goal of metabolic research is to explain how metabolic networks are rewired and regulated in response to a given perturbation. Unlike proteins, transcripts, and metabolites, fluxes cannot be measured directly—they can only be estimated. Labelling experiments have been extensively used to determine flux values (relative or absolute) and pathway usage . To acquinferred . The dyninferred . 13C-MFA13C-MFA was used in cancer cell culture research to show drug vulnerabilities and lead to possible treatment targets and combinations [13C-MFA was also applied to study cell metabolism in biotechnological processes. As an example, Pereira et al. used 13C-MFA to study the metabolic response of industrially relevant Chinese Hamster Ovary (CHO) cells to change the media composition in order to decrease the production of toxic ammonia as a byproduct of the fermentation [13C-MFA to identify metabolic reprogramming associated with high antibody productivity in CHO cells [13C-glucose were used to estimate the flux distribution and showed differences in cellular respiration between those two cell types. In addition, model-driven strategies were used to support other findings in a study that suggest differences between metabolic features of cancer stem cells and epithelial–mesenchymal transition phenotypes. Each of the phenotypes can be linked to optimal cell proliferation and sustaining specific cell phenotypes. This study provides an example of how isotope-labelling data can be used with kinetic models to determine the intracellular fluxes. Labeling metabolomics in combination with kinetic modelling can also be used to infer the intracellular metabolic network topology in order to study physico-chemical phenomena such as channeling [inations . 13C-MFAentation . TempletHO cells . AguilarHO cells . Experimanneling  or crowdanneling . However13C-MFA are small scale, genome-scale models have been introduced recently. One of such approaches was introduced by Martin and coworkers [13C labeling data. They assumed that the flux flows from the central carbon metabolism to the peripheral parts of metabolism and does not flow back. 13C-MFA is then used to infer the flux distribution in central carbon metabolism, which is used as a constraint to predict the flux distribution in peripheral metabolism. One advantage of this approach is that it does not require any strong evolutionary or physiological assumption, such as the maximization of the cell growth rate or ATP production. Another example is the work by Gopalakrishnan and Maranas [13C-MFA to a genome-scale model. This study highlighted the variation in flux values that is introduced by selecting models of different sizes. The authors point out that even though using genome-scale models should be preferable, it is impractical due to the increase in computational time associated with a higher number of variables. McCloskey et al. [13C-labelled metabolomics to constrain a model that describes 537 reactions and 429 metabolites, and showed a significant increase in the number of calculated fluxes. This included measurements for metabolic intermediates in central carbon metabolism and cofactors of peripheral metabolism. The authors also used this approach to study the evolution of gene knockout strains of E. coli and find how the cells adapt to gene loss [While in general the models used in oworkers  who prop Maranas , where ty et al.  used 13Cene loss . 13C-MFA is proven to be a valuable approach to determine flux distributions. However, it still remains a challenge for many systems, especially those with slow labelling dynamics, multiple compartments, and different carbon sources. An assessment of the measurement uncertainty of this method has also highlighted: (i) the importance of improving the model used to reduce its structural error, and (ii) that suitable certified matrix reference material is lacking for isotopologue analysis [13C-MFA is used to determine flux values, but provides no mechanistic explanation for observed events. analysis . FinallyConcentration data at a single point of time can be used to constrain a model by defining steady state concentrations, thermodynamics and, accordingly, reaction directionality or flux cue changes for multiple condition experiments.To integrate single-point intracellular metabolomics into a kinetic model, one can utilize the steady state assumption, where the model is simulated until the system reaches a steady state that should describe the observed concentrations. Kinetic modelling can integrate metabolite concentration values, metabolic fluxes, enzyme amounts and/or kinetic parameters . Metabolomics experiments provide metabolite concentrations that can be used to either find the kinetic parameters given the known fluxes, or to infer the metabolic fluxes given the kinetic parameters known from the literature.For instance, the kinetic parameter inference approach  was used to build personalized kinetic models of red blood cells based on patients’ metabolomics data . AssuminS. cerevisiae with knockouts in the sphingolipid biosynthesis. They used this data to validate their approach to predict knockout targets. The authors propose using this method for cell factory design and characterization of unknown mutations in personalized medicine.One of the main challenges in the interpretation of metabolomics data is to trace back the changes that led to the observed phenotype. To address this issue directly with modelling, Savoglidis et al.  proposedSacaromyces cerevisiae in various environmental conditions and were able to characterize the changes in different parts of the metabolism.Integrating metabolomics data from single-point experiments is challenging since constraint-based models only utilize flux information. The approaches mentioned so far require either strong assumptions or measurements of at least two time points to infer the metabolic fluxes. Nevertheless, different approaches have been proposed to incorporate single measurements. For instance, Mo et al.  used exoE. coli genome-scale model as an integration platform to calculate the Gibbs free energy of the metabolic reactions in different E. coli strains. They showed significant differences in reaction thermodynamics, among them such drastic changes that led to reversing the reaction directionality. That enabled a more accurate characterization of the strains, making them good candidates for biotechnological applications. In another paper [E. coli in anaerobic and aerobic conditions. They integrated metabolomics data as a way of estimating thermodynamics in a genome-scale model, which allowed them to find inconsistencies between the model and the data. With this analysis, the authors were able to highlight the importance of enzyme promiscuity and the usage of alternative pathways and pathway directionality for microbial growth. In a study using elementary flux modes, Gerstl et al. [Methods assessing the thermodynamics of the system also allow the integration of single-point absolute metabolite concentrations into models. Metabolite concentrations can be used to calculate the Gibbs energy of the reaction according to the equation: methods  and the  methods ,95, this methods . Additio methods  used an er paper , researcl et al.  introducA larger number of approaches have been developed to integrate metabolomics from time-course experiments compared to single-point metabolomics. In this section, examples of both intracellular and extracellular metabolomics time-series data integration will be discussed.Exometabolomics from time-series experiments is one of the most commonly experimental data type integrated into both kinetic and constraint-based models. Exometabolomics refers to the metabolomics of the cell milieu, such as the culture media, the natural environment of the microorganisms, or the extracellular fluid. From an experimental point of view, this approach has less technical requirements than the assessment of intracellular metabolites. In addition, extracellular metabolite concentrations are integrated over time and produce a more intensive signal . Such inWhen there are distinct metabolic states throughout the time-series experiment , it is necessary to split the data into distinct phases and construct models separately to study the different metabolic behaviors in each phase . DynamicHowever, label-free metabolomics-based MFA has limitations. For instance, it cannot resolve the source of NADPH production in the cell. Hence, it requires us to make additional assumptions, such as cofactor balances or leaving out reactions that are believed to carry no flux. Still, this approach narrows down the number of possible solutions significantly and is relatively easy to apply.An alternative approach is to use calculated fluxes to constrain the model for FBA. FBA will also use the assumption of metabolic optimality and give a single solution (or narrowed down solution for FVA). Aurich and coworkers  used thiE. coli on glucose in a batch fermentation, where acetate is initially secreted and subsequently consumed. With the use of dFBA, researchers were able to predict fluxes during diauxic growth on glucose and acetate by imposing additional constraints on the maximum oxygen uptake level, including the secretion and later reutilization of acetate [Dynamic FBA was proposed to incorporate the rate of change of flux constraints from measured concentrations in a time-course experiment . Similar acetate .M-DFBA and R-DFBA incorporate the MOMA and ROOM algorithms into dFBA. MOMA and ROOM were proposed to study the fluxes of knockout phenotypes. M-DFBA and R-DFBA were thus used to smooth flux transitions over time. Kleessen and Nikoloski  showed aTo incorporate time-series of both intracellular and extracellular metabolomics data, a number of dynamic FBA variations have been proposed. Among them are MetDFBA , TREM-FlE. coli to a peroxide pulse [E. coli reserves the pentose phosphate pathway flux capacity during normal growth in order to perform a rapid response for oxidative stress.Kinetic models, which describe the changes of metabolite concentrations over time, are innately appropriate to integrate time-course metabolomics. As an example, Christodoulou et al. performed a time-series intracellular metabolomics experiment to study the metabolic response of de pulse . To furtAnother example is the work of Nishino et al. , where tIntegrating different types of omics data is the most promising, yet challenging, goal. It has the potential to incorporate enzyme regulation occurring at different levels, such as gene regulation or signaling pathways, and show the cross-talk between them. In this section, some of the most successful methods developed in the field will be discussed.S. cerevisiae grown in a chemostat [S. cerevisiae. They showed that regulation occurs not only within pathways but also between pathways.Hackett et al. collected omics data  for 25 different steady state conditions for hemostat . They deThe same dataset from Hackett and colleagues was also analyzed by St John et al. . In thisUntangling complex interactions between signaling and metabolism is one of the most important goals of metabolic modelling. Such a possibility was demonstrated by Yugi and coworkers . In theiE. coli with different gene knockouts. Kleessen et al. [Chlamydomonas strain to rapamycin treatment. Covert et al. [A number of approaches aim to estimate the flux distribution without using labelled data. To address that, Yizhak et al.  proposedn et al.  proposedn et al.  in whicht et al.  also proMetabolomics and transcriptomics data can also be used to impose constraints on constraint-based genome-scale metabolic models. GIM3E is an example of such an algorithm . The GIMSalvy and Hatzimanikatis  publisheThe modelling approaches described so far treat a whole cell population as a homogeneous single-cell type group of cells. While this is a simple yet powerful approach that allows obtaining numerous findings, it is challenging to study systems where such assumptions do not hold. Examples of such systems are (a) interactions within communities of microorganisms in different environments, (b) cross-talk between cells in a normal tissue, (c) heterogeneous tumors, (d) interactions between tissues and organs, (e) interactions within the microbiome, (f) interactions between the microbiome and an organism, etc. In order to study these biological systems, novel approaches capable of capturing the underlying interaction between different cell types are required. The interest in these topics is driving the rise in the development of multicellular, multitissue, and community modelling techniques and software. The necessity to work with different cell types increases the size and complexity of the models. Strategies for building community metabolic models are usually the following (1) multispecies dynamic modelling that accounts for kinetics of nutrient uptake and metabolite production by individual species; (2) compartmentalized network modelling, where species are treated as compartments in the model, and generally used for prediction of cross-species metabolic interactions; (3) mixed-bag network modelling, where the community is treated as a superorganism (cell). These strategies are typically used to uncover environment-community interactions . Yet, cuMature metabolic modelling standards and practices are the foundation for successful data integration processes . ResearcDynamic constraint-based methods are suitable for integration of large-scale models, since they do not rely on kinetic parameters that are often hard to obtain. dFBA was one of the first methods to be used in metabolomics data integration for community modelling. Hanemaaijer and coworkers applied dFBA to study a synthetic anaerobic co-culture of Clostridium acetobutylicum and Wolinella succinogenes , and sho13C-MFA is a gold standard to infer flux distributions and has been extensively applied to mono-cultures during the past two decades. Yet, there are only a handful of 13C-MFA examples for microorganism communities. Ghosh et al. demonstrated a peptide-based alternative to the standard amino acid-based 13C-MFA [13C-MFA to infer the metabolic flux profile of a co-culture system of two E. coli knockout strains. They did not use physical separation nor genetic labelling to perform the measurements. Rather, the fluxes were inferred via pooled distribution of isotopes in co-culture. While the peptide-based approach is capable of resolving fluxes in larger and more diverse communities, the total biomass labelling approach is suitable for closely related species, and in theory should be capable of finer resolutions, since peptides inherently contain less flux information than amino acids.Inference of fluxes is crucial for the understanding of metabolism and its regulation. In addition, it facilitates the development of kinetic models that allow researchers to characterize the system and its regulation.  13C-MFA . This me 13C-MFA  combinedConstraint-based modelling has been used to model whole organisms, multitissue and multicellular models of plants and animals to elucidate the interactions between the different cell types within a tissue and higher levels of interactions ,137,138.13C-MFA was applied at an organism level in humans [Recently, n humans . The autn humans  and MFA The technical capability provided by different high-throughput platforms to analyze and quantify an increasing number of molecular entities existing within a living cell opens up opportunities for novel discoveries and scientific findings in metabolic research ,144,145.Stoichiometric models have the advantage of scaling well for large-scale problems, since they require little prior information. In this review, we have discussed several techniques and examples to integrate metabolomics data in order to study cell metabolisms. In general, kinetic models are more suitable for well-known metabolic systems, which on the other hand reduce their scope to models of small and medium size. Kinetic models are also suitable to predict the state of the systems and they can deal with allostery and regulation. On the other hand, constraint-based modelling is usually more suitable when using large-scale models with scarce knowledge about the system. We refer to the specialized article for the details of usage of mechanistic models . The typThe application of such models supports the systematic overview of the metabolism by applying physico-chemical principles to metabolic pathways. Kinetic models can innately encode different types of information and various types of omics data from first principles. Kinetic models, especially large scale, are not easy to parametrize due to the lack of kinetic parameters describing the in vivo behavior or because they are not fully characterized and not applicable for case-specific studies. Accurate inference of large-scale kinetic models from experimental data is the most promising technique, yet needs a significant amount of data points and efficient computational approaches as well as computational power. The combined application of both kinetic models and constraint-based models in the study of biological systems would allow taking advantage of their complementary features in a synergistic manner with the potential to overcome existing setbacks. The combination of the methods can be achieved in different ways, from modelling different parts of the metabolism with either kinetic modelling or constraint-based modelling ,121   and The Systems biology already provides insights into the mechanisms that govern metabolism in different biological fields. By routinely using mechanistic models to integrate and interpret metabolomics data, it will be possible to shed more light into the complex network of interactions in the metabolism.


Haemophilus influenzae in 1999, the GSM models have been reconstructed for various organisms including human and mouse. There are two important strategies for generating a GSM model: in the bottom-up approach, individual genomic and biochemical components are integrated to build a GSM model. Alternatively, the orthology-based strategy uses a previously reconstructed model of a reference organism to infer a GSM model of a target organism. Following the update and development of the metabolic network of reference organism, the model of the target organism can also be updated to eliminate defects. Here, we presented iMM1865 model as an orthology-based reconstruction of a GSM model for Mus musculus based on the last flux-consistent version of the human metabolic network, Recon3D. We proposed two versions of the new mouse model, iMM1865 and min-iMM1865, with the same number of gene-associated reactions but different subsets of non-gene-associated reactions. A third extended but flux-inconsistent model (iMM3254) was also created based on the extended version of Recon3D. Compared to the previously published mouse models, both versions of iMM1865 include more comprehensive annotations of metabolites and reactions with no dead-end metabolites and blocked reactions. We evaluated functionality of the models using 431 metabolic objective functions. iMM1865 and min-iMM1865 passed 93% and 87% of the tests, respectively, while iMM1415 and MMR (another available mouse GSM) passed 80% and 84% of the tests, respectively. Three versions of tissue-specific embryo heart models were also reconstructed from each of iMM1865 and min-iMM1865 using mCADRE algorithm with different thresholds on expression-based scores. The ability of corresponding GSM and embryo heart models to predict essential genes was assessed across experimentally derived lethal and viable gene sets. Our analysis revealed that tissue-specific models render much better predictions than GSM models.Since the first in silico generation of a genome-scale metabolic (GSM) model for  For each enzyme-associated reaction in a GSM model, a gene-protein-reaction (GPR) rule describes the relationship between necessary genes encoding the enzyme that catalyses this reaction3. These GPR associations enable GSM models to be used for prediction of phenotypic consequences of genetic perturbations4. For multicellular organisms, these rules allow integration of gene or protein expression data with a GSM model and reconstruction of cell- and tissue-specific models5. Also, GPR rules are a fundamental component of a GSM model of a reference organism to reconstruct new GSM models of another target organism by homologous gene mapping6.A genome-scale metabolic (GSM) model is a comprehensive model for metabolism of an organism that includes all known chemical reactions and their corresponding associated genes3. The first step is to automatically generate a draft reconstruction based on extracting metabolic function from the genome annotation and biochemical reaction data within related databases such as KEGG7, BioCyc8, and BRENDA9. The second step is to manually curate the draft reconstruction using literature information. In the final step, evaluation process is performed to examine the model for mass and charge balances, existence of dead-end metabolites and blocked reactions, and passing functional metabolic tasks1. The two last steps are iterated until the resulting model becomes as gap-free and consistent as possible. Based on this approach, the first comprehensive GSM models of human, Recon110 and Edinburgh Human Metabolic Network (EHMN)11, were generated by different groups in 2007. To date, various human models have been presented to improve these primary models. The most recent of these networks are the other versions of Recon including Recon2.0212, and Recon3D13, and also recent versions of Human Metabolic Reaction (HMR) models; HMR114 and HMR215. In the case of mouse models, Quek and Nielsen16 created a compartmentalized mouse model from available online metabolic databases. Their model contains 2037 reactions, 2110 metabolites and 1399 genes. Two years later Selvarasu et al.17 extended an older model by including additional information on GPR associations and improving the network connectivity in many biosynthetic pathways. The resulting model contains 1494 reactions, 1162 metabolites and 724 genes. Both these models only include three compartments  while more modern models have additional compartments including the Golgi apparatus, lysosome, nucleus, endoplasmic reticulum and peroxisome. In a large-scale generation of computational models, the Path2Models project also generated a mouse model that is an automatic compilation of available database information. This model includes 5607 reactions and 2693 metabolites without any compartmentalization18.To reconstruct GSM models, a traditional approach is a bottom-up method that integrates individual genomic and biochemical components to achieve a consistent model20. The prerequisite is that the genomic sequence of a target organism shares a high degree of homology with its reference organism. Genes in the GSM of the reference organism could, therefore, be replaced by corresponding target organism orthologues. Several mammalian metabolic networks have been generated from different versions of human models as a reference21. Two existing mouse models, iMM141521 and MMR19, were generated from human models of Recon1 and HMR2.0, respectively. Upon the release of a more recent version of reference GSM, corresponding target GSM models could be revisited and reconstructed once again.In parallel to the bottom-up approach, the orthology-based method infers a genome-scale metabolic network of a target organism based on a previously reconstructed GSM of another reference organism22, INIT23, tINIT24 mCADRE25, FASTCORE26 have been developed. The constraint-based analysis of tissue-specific models has been widely applied to predict the metabolic phenotypes resulting from genetic and environmental perturbations and to identify potential biomarkers and drug targets31.Due to the metabolic differences between diverse mammalian tissues, a GSM model is applied to generate tissue-specific models via integration of multi-omics data. For this purpose, several algorithms such as GIMME13, to reconstruct a new and comprehensive metabolic model for mouse (Mus musculus). The orthology-based approach was adopted to map human genomic data of Recon3D to mouse. Two versions of the model were presented, both of which involving 1865 genes. A minimalist version, denoted as min-iMM1865, with a restriction on inclusion of non-gene-associated reactions, involves 8829 reactions, and the maximal version, denoted as iMM1865, involves 10612 reactions. Both models were validated against a set of 431 metabolic objective functions and used to construct a context-specific model of mouse embryo heart tissue based on expression array data and the metabolic Context-specificity Assessed by Deterministic Reaction Evaluation (mCADRE) algorithm25. Gene essentiality simulations were also used as another assessment of the predictive capabilities of reconstructed models. An extended mouse model denoted iMM3254 was also created from the extended version of Recon3D. Though it contains many dead-end and blocked components, it can be helpful in future reconstruction attempts.In this study, we took the advantages of the most recent human metabolic model, Recon3DAn overview of the adopted protocol for reconstruction of new mouse models is depicted in Fig. The well-known human GSM models are compared in Table Human genes in Recon3D were mapped to corresponding mouse orthologues by automatic application programming interface (API) programming complemented with a manual search of databases (see Supplementary Table-S1). The HomoloGene NCBI database and the orthologues reported in NCBI Gene records were searched by E-Utilities interface. This resulted in 1804 mouse orthologues out of 1884 Recon3D genes. The remaining 80 human genes were manually searched in KEGG orthology (KO) and Ensemble databases. This reduced the number of Recon3D human genes without any mouse orthologues to 43 (including 15 pseudogenes). For those human genes that were mapped to more than one mouse orthologues in HomoloGene database, further assessment was conducted by searching other databases (see Supplementary Table-S1).Based on orthology relations between human and mouse genes, the set of Recon3D gene-product-reaction (GPR) rules were compiled to their corresponding logical expressions for the mouse model. Moreover, the existence or absence of mouse orthologues for human genes was interpreted as Boolean true/false values to divide Recon3D reactions into three different sets; 4662 non-gene-associated reactions, 5922 gene-associated reactions available in both human and mouse (GAHM set) and 16 gene-associated reactions in human (GAH set). An automatic gene orthology search provides no evidence for existence of a GAH set in the mouse model. However, this might be a result of a lack of information in Recon3D or searched databases. Accordingly, further databases and literature searches were performed before the final decision on each of these reactions.GAH1 subset consists of five reactions. The GPR rules of these reactions in Recon3D and their genes were revised and the reactions were kept in mouse model after repeating the orthologue mapping. For example, the reaction “2-Hydroxyphytanoyl Coenzyme A Lyase” (BIGG ID: HPCLx_1) in the fatty acid oxidation subsystem is associated with a single gene (Entrez gene ID: 26062) in Recon3D which was found to be a pseudogene and thus was not matched to any mouse orthologues. By correcting the association to a corresponding functional human gene (Entrez gene ID: 26061) and mapping it to the related mouse gene (Entrez gene ID: 56794) the reaction was decided to be present in both human and mouse .SLC25A6, Entrez gene ID: 293) which corresponds to an ATP/ADP mitochondrial antiporter protein with no reported GTP/GDP transport activity. It should be noted that the same reaction corresponds to a multi-pass membrane protein in yeast . Unlike mammalian cells, in yeast cells, GTP is synthesized only outside the mitochondrial matrix in cytosol, so GTP/GDP transporter is necessary to regulate the level of these substances in yeast mitochondria33. On the other hand, the yeast GGC1 gene has no reported human and mouse orthologue .It was decided that all three reactions in the GAH2 subset were to be removed from both human and mouse models. Because Recon3D model was still consistent after removal of these reactions (i.e. no reaction became blocked), they were not included in resulting mouse models. For example, the reaction “Mitochondrial GTP/GDP exchange carrier” (BIGG ID: R0801) is assigned to a single gene in Recon3D  in Recon3D. The gene products involved in “Blood Group Synthesis” and “Glycosphingolipid” subsystems. The other remained human-specific reaction is retinyl ester hydrolase (BIGG ID: RETH) involved in “Vitamin A Metabolism” that catalyses the hydrolysis of retinyl ester to all-trans-retinol (vitamin A) plus a fatty acyl group35. The Recon3D gene associated  with this reaction is PNPLA4 (Entrez gene ID: 8228) without any mouse orthologue in searched databases. However, since the consistency of Recon3D is influenced after removal of these human-specific reactions, they were kept as non-gene-associated reactions in subsequent steps of reconstruction  fucosyltransferase genes . Among these, only four reactions were considered as mouse-specific while there was no strong evidence in literature or other databases for others.36. The Glue gene (Entrez gene ID: 268756) of mouse encodes L-gulonolactone oxidase. Human cells are not able to perform this reaction and produce vitamin C due to an absence of Glue orthologue38  encodes this enzyme but Human TDH gene is an expressed pseudogene that encodes non-functional protein40  catalysed by L-gulonolactone oxidase is the final step of the ascorbate biosynthetic pathwaysee Fig. .Figure 241. Cytidine monophosphate-N-acetylneuraminic acid hydroxylase enzyme catalyses both of them which is encoded by the Cmah mouse gene (Entrez gene ID: 12763). The human CMAH gene differs from mouse Cmah by a deletion in a region corresponding to exon six of the mouse gene that causes an inactive hydrolase enzyme in human42. After addition of the last two reactions, it is required to also add four new metabolites including CMP-N-glycoloylneuraminate (BIGG ID: cmpglna), N-glycoloylneuraminate (BIGG ID: HC01115), ferricytochrome b5 (BIGG ID: ficytb5), and ferrocytochrome b5 (BIGG ID: focytb5)  and “CMP-N-acetylneuraminate, ferrocytochrome-b5:oxygen oxidoreductase” (KEGG ID: R01115), are involved in aminosugar metabolism pathway see Fig. 41. Cytidsee Fig. .Two different strategies were adopted that led to a maximal, larger mouse model and a minimal, smaller one. From a methodological point of view, one cannot prefer any of these with respect to the other but, as will be discussed later, these minimal and maximal models exhibit different levels of predictive capabilities in different contexts. Two sets of core and non-core reactions were defined. The core set includes all gene-associated reactions that should be available in both minimal and maximal models since there are well-known genomic evidence for these reactions formulated in their GPR rules. As can be seen in Fig. In the minimal reconstruction approach, an initial draft was created from the core set of reactions. The core draft was then extended by adding a minimum number of non-core but necessary reactions to create a flux-consistent model (see Supplementary Table-S3). This goal was achieved by applying the fastGapFill algorithm which by design guarantees the minimalism of a resulting model. The initial minimal GSM mouse model which includes 8829 reactions and 5200 metabolites, will be referred to as min-iMM1865. On the other hand, the maximal approach combines both sets of core and non-core reactions to create a GSM model of 10612 reactions and 5839 metabolites, denoted as iMM1865. It should be noted that by excluding mouse-specific components both min-iMM1865 and iMM1865 inherit flux-consistency of the reference human model. The mouse-specific reactions in both models were also kept consistent by some additional sink reactions.21.Since mice show high biochemical similarities with humans, the same metabolic functions can be used to test the functionality of mouse metabolic models. Similar validation strategies have been used in previous studies13. These functional tests were divided into two groups; 347 of them were metabolite conversion tests (MCTs) and 84 of them were reaction optimization tests (ROTs). In each MCT, the conversion of source metabolites to target metabolites, through one or multiple reactions, was tested under a RPMI1640 medium43 (see Methods section). For MCTs, iMM1865 and min-iMM1865 passed 322 and 312 tests, respectively, while iMM1415 and MMR passed 315 and 309 tests, respectively. In iMM1865, 19 tests failed because of missing source or target metabolites in the model. These numbers were 26, 1 and 29 for min-iMM1865, iMM1415 and MMR, respectively. Since most of failures in two iMM1865 versions were due to lack of source or target metabolites, we repeated the comparison with a list of tests whose participating metabolites are present in both versions of iMM1865. For this list (321 tests), iMM1865, min-iMM1865, iMM1415 and MMR passed 315, 312, 295 and 286 tests, respectively. For ROTs, iMM1865 and min-iMM1865 passed 79 and 62 tests compared to iMM1415 and MMR which passed 32 and 53 tests, respectively. Absence of some reactions leads to failure of 4, 16, 17 and 28 ROTs in iMM1865, min-iMM1865, iMM1415 and MMR, respectively. Among 68 tests, objective reactions were present in both versions of the presented models: iMM1865, min-iMM1865, iMM1415 and MMR passed 67, 62, 32 and 51 tests, respectively. The results clearly demonstrate considerable improvements of two versions of iMM1865 models compared to iMM1415 (see Supplementary Table-S4 for details).Both versions of iMM1865 were evaluated against 431 metabolic objective functions which were developed to validate the functionality of Recon3D+/NADH and cellular GTP pool, respectively. These reactions carry flux in both iMM1865 versions but not in MMR and/or iMM1415 models. Furthermore, the MMR model, in contrast to the iMM1415 and iMM1865 models, has no information about enzyme complexes in corresponding GPR rules. For both versions of iMM1865 and iMM1415 models, distribution of reactions within subsystems is shown in Fig. Some features of iMM1865 and min-iMM1865 reconstructions are outlined in Table 44 and linear version of Minimization Of Metabolic Adjustment (lMOMA)45 methods were used to perform gene knock-out simulations for 62 lethal (see Supplementary Table-S6) and 120 viable (see Supplementary Table-S7) metabolic genes in iMM1865 and min-iMM1865, iMM1415 models under HAM media24. An essential gene is a gene whose deletion reduces biomass production to less than a significant fraction (30%) of its optimal value in a wild type model. Linear MOMA approach in min-iMM1865 has better compatibility with experimental results compared with the other simulations on genome-scale models  were binarized using the Affymetrix MAS5 detection call47. The mCADRE algorithm uses the binarized expression data in conjunction with network topology features to prune the global GSM model and reconstruct the embryo heart model. Based on different selected thresholds for expression-based score in mCADRE, we reconstructed three embryo heart models from each GSM model fraction 0% of itsUp to this point, both min-iMM1865 and iMM1865 are flux-consistent functional models suitable for many applications and simulations via constraint-based modelling. However, they do not reflect all of our knowledge about mouse metabolism. There are many more reactions in the extended version of Recon3D (Recon3D_VMH) and it might be interesting to know which of them can be mapped to the mouse. In this regard, we repeated the above mentioned orthology based procedure by starting from Recon3D_VMH to create an extended mouse model denoted as iMM3254. It contains 13543 reactions (7666 gene-associated), 8395 metabolites and 3254 genes. It is obvious that this model is a much more comprehensive but with 884 dead-end metabolites and 1569 blocked reactions. The functional tests also performed on this model. From 347 MCTs only five tests failed due to non-optimality. From 84 ROTs, three of them failed because corresponding reactions are not available in the model and another test failed due to non-optimality. In the light of ongoing increase in our knowledge about metabolism of human and mouse, iMM3254 can be a suitable starting point for future developments in creating better mouse models.Mus musculus metabolic model. In iMM1865 models, we replaced genes of human metabolic Recon3D with their corresponding Mus musculus orthologues. The difference between the two versions is the availability of non-gene-associated reactions in the final model. In the minimal version (min-iMM1865), the final model only consists of a small subset of these reactions which are essential for model consistency. In another approach, the maximal version of the model (iMM1865) was obtained by the inclusion of all non-gene-associated reactions. To avoid the new mouse models being just a pruned version of the reference model, mouse-specific reactions were also added to both reconstructed versions. The mouse-specific reactions were extracted through comparison of KEGG metabolic networks of human and mouse and also were searched by other biochemical databases and literature. These models have been validated using 431 metabolic objective functions which have been used to verify Recon3D13. The iMM1865 and min-iMM1865 models satisfied 401 and 374 of these tests, respectively, which is an improvement over the previously published mouse models, iMM1415 and MMR, that only passed 347 and 362 tests, respectively.In this study, we have prepared two versions of orthology-based reconstructed Moreover, two versions of iMM1865 have more comprehensive annotations of metabolite and reactions compared to iMM1415. Unlike iMM1415, iMM1865 covers reactions and metabolites that are involved in “Drug Metabolism” and “Peptide Metabolism” pathways. In addition, the reconstruction of lipid metabolism pathways is more complete in iMM1865 compared with iMM1415. Therefore, it is a more appropriate model to study mouse lipid metabolism. Two versions of iMM1865 models unlike iMM1415 do not have any dead-end metabolites and blocked reactions.In comparison with the other published mouse model MMR, iMM1865 models are flux consistent, without including any blocked reactions and dead-end metabolites. Also, the GPR rules of MMR model, unlike iMM1865 models, did not include any information related to enzyme complexes which is very important for mapping omics data to GSM models.We have used FBA and a linear version of MOMA to predict gene essentiality in iMM1865, min-iMM1865 and iMM1415. The essentialities of mouse metabolic genes were predicted based on a significant reduction of growth rate. For this purpose, we have simulated gene knock-out analysis for the experimentally reported data including a list of lethal and viable genes. The best prediction was for the min-iMM1865 model with the lMOMA method. Since the experimental data were phenotypes resulting from knock-outs of genes in mouse embryo, we also repeated the simulations for embryonic tissue-specific models. We reconstructed embryo heart models from iMM1865, min-iMM1865 and iMM1415 using mCADRE algorithm. Our findings suggest that tissue-specific models have better predictions than GSM models. The perturbation caused by deletion of a gene in a GSM model could be damped due to the existence of alternative pathways or isozymes while these pathways or isozymes might be inactive or absent in the tissue-specific model resulting in better agreement with gene essentiality experiments.To date, the two versions of iMM1865 are the most comprehensive consistent models of mouse metabolism. Different types of context-specific models can be reconstructed using integration of multi-omics data into these GSM models. These models allow prediction of behaviour of the organism in response to environmental and genetic perturbations. Since mouse is a model organism for human biology, these models can be used to identify candidate metabolic biomarkers and drug effects for diseases such as cancer and complex metabolic disorders.48. They were reconstructed from Recon3D as the largest reported human metabolic model without blocked reactions. Recon3D consists of gene-associated and non-gene-associated reactions. For every gene-associated reaction, relationships between genes and reaction are represented by a Gene-Protein-Reaction (GPR) logical rule. To reconstruct mouse genome-scale metabolic network from Recon3D, human genes in the GPR rules were replaced with mouse orthologues. HomoloGene and orthologues mouse records in NCBI’s Gene database were used for identification of mouse orthologous. Entrez Programming Utilities (E-utilities) provide the programmatic access to these databases. If a search found no match, KEGG orthology and Ensemble databases were searched for missing orthologous genes. Gene-associated reactions of Recon3D that are affected by missing orthologues genes were further investigated in other biochemical databases and literature and categorized into three groups. Mouse-specific reactions were determined using a comparison of human and mouse metabolic KEGG pathways and literature reviews. The KEGG API50 was used to obtain human and mouse biochemical pathways.Two versions of iMM1865 were reconstructed using COBRA toolbox v3.051 to select a minimum set of these reactions. The fastGapFill function is a COBRA toolbox extension to find candidate missing reactions from reference databases such as KEGG for a desired metabolic model. Herein, we have applied this function to identify missing reactions in the set of core reactions from a set of non-core reactions. In the second strategy, all non-gene-associated reactions were added to the set of core reactions and also included in the final model. All models generated in this study can be found in supplemental data as SBML files.We have defined all mouse gene-associated reactions as a set of core reactions and all non-mouse gene-associated reactions as a set of non-core reactions. Two strategies were applied for the addition of non-core reactions to the set of core reactions in order to reconstruct final genome-scale models. In the first strategy, only non-gene-associated reactions that are essential for carrying flux over core reactions were added to the core set. We used fastGapFill algorithm52 was performed to determine reactions with zero flux. fastFVA is an implementation to perform more efficiently the flux variability analysis (FVA)53 which calculates the minimum and maximum ranges of fluxes through each reaction in the metabolic model. To evaluate the functionality of the reconstructed models, we used 431 metabolic functional tests previously introduced for validating Recon3D13. These tests can be categorized into two groups; metabolite conversion tests (MCTs) and reaction optimization tests (ROTs). In the first group, conversion of some metabolites (source metabolites) to some other metabolites (target metabolites) was tested under RPMI1640 medium43. Source metabolites can be converted to target metabolites through one or multiple reaction steps; for example, for the conversion test of glucose to pyruvate, a series of reactions involved in glycolysis pathway must be included in a model to break down glucose to pyruvate. To test this function, first, reactions were added (if not available) to represent a source of glucose and consumption of pyruvate, while all uptake reactions except those for RPMI1640 medium were set to be closed. Then, the ability of pyruvate production through glucose was checked by maximizing the flux through pyruvate demand reaction. In the second group, ROTs, a reaction was checked for its availability and ability to carry non-zero flux under specific conditions; for example, we analysed the model for maximum production of ATP from glucose under aerobic conditions. First, we closed all exchange reactions of organic compounds except glucose and then maximized ATP maintenance reaction (ATPM) as an objective reaction. It should be noted that under aerobic conditions, Oxygen uptake is allowed while its uptake will be prevented under anaerobic conditions. There are three types of failure for MCTs and ROTs. The MCT will fail when i) the source or target metabolites do not exist in the model, ii) the optimal solution of the test objective does not exist, or iii) the value of the test objective is almost zero. The ROT will fail if i) the test reaction does not exist in the model, ii) optimal solution does not exist for the test reaction as an objective, iii) the value of the test objective is almost zero.During the draft reconstruction process, fastFVA54. The data consists of 139 samples derived from healthy hearts at different embryonic stages using GPL1261 platform. Prior to data binarization, we performed pre-processing to identify and remove outlier samples. The Pearson correlation coefficient (PCC) was calculated between every pair of samples. The following standard score formula was used to determine outlier samples:55s is standard deviation. Samples with two and more standard deviation values above or below the total mean were detected as outliers and removed. The process of outlier detection was repeated until all samples with divergent gene expression pattern were ruled out. Finally, 119 microarray samples were used to generate embryo heart model (see Supplementary Table-S8).To reconstruct a tissue-specific metabolic model using mCADRE, we downloaded raw gene expression microarray profiling data from gene expression omnibus (GEO) database47 in affy package of BioConductor to flag each gene as “Present”, “Marginal”, and “Absent” (P/M/A). For gene binarization, “Present”, “Marginal”, and “Absent” calls replaced with 1, 0, and 0, respectively. For genes with multiple probe sets, the maximum expression value was used.The Affymetrix GPL1261 platform has 45101 probe sets that map to 21603 unique genes. A binary matrix represents the state of expression of each gene in a particular sample. We used “mas5call” algorithm24 during the model building process. If removal of a reaction reduced the objective value of biomass reaction less than 80% of the value of the GSM model, the reaction would remain in the final tissue-specific model. Similar to checkModelFunction and checkModelConsistency built-in functions, checkBiomassProduction function was also checked in every iteration.The mCADRE algorithm categorizes GSM reactions into two sets, core and non-core set reactions, using an expression-based score. The reaction expression-based score was determined by the frequency of expressed state of genes that were associated with a desired reaction across expression profiles of the selected tissue. The binarized expression data was used to calculate the frequency of expressed states of each gene. A reaction with a high expression-based score has strong evidence to be active in the desired tissue. The core set reactions have an expressed-based score at or above the fixed selected threshold. The non-core set reactions were ranked based on expressed-based and connectivity-based scores. The connectivity-based score for each reaction is a parameter of network topology that estimates connectivity of all its adjacent reactions. In this study, due to the unavailability of reaction biological evidence data, the confidence score was ignored to rank non-core reactions. The mCADRE algorithm sequentially removes ordered non-core reactions from the GSM model. At each iteration of the algorithm, the functionality of the model for key metabolites produced from glucose as well as model consistency were checked. A reaction was eliminated if it did not affect the functionality and consistency of the model. In this study, a new function was added to mCADRE in order to test biomass production under HAM media56. This report identified 410 homozygote lethal genes and 1143 homozygote viable genes. The number of 62 metabolic lethal genes (see Supplementary Table-S6) and 120 metabolic viable genes (see Supplementary Table-S7) which were also available in the reconstructed models were selected to validate prediction capabilities of the models.The embryo’s phenotypes resulting from 1751 unique gene knock-outs were reported in 201644 problem was formulated to find a flux distribution that maximizes biomass production in gene knock-out model under HAM media27.27.The FBA45 is another approach to predict phenotypic consequences of genetic perturbation in a metabolic network. MOMA can be used to identify the closest sub-optimal flux distribution following a perturbation to an optimal wild-type solution. A linear version of MOMA is formulated as follows:singleGeneDeletion function in COBRA toolbox was applied for gene knock-out simulation. Three methods consist of FBA, quadratic version of MOMA approach, and a linear version of MOMA (lMOMA) were implemented in singleGeneDeletion function to perform single gene deletion analysis.The method of the Minimization of Metabolic Adjustment (MOMA)Results of gene knock-out prediction fall into four groups: True Positives (TP), True Negatives (TN), False Positives (FP), and False Negatives (FN). TP means a lethal gene was correctly predicted as an essential gene. TN indicates a viable gene was correctly predicted as a non-essential gene by the model. FP means the model incorrectly predicted a viable gene as an essential gene. Finally, FN indicates the model incorrectly predicted a lethal gene as a non-essential gene. Using sensitivity and specificity, the performance of gene knock-out simulation tests was evaluated. The sensitivity of a test calculates the proportion of actual essential genes that are correctly predicted. The specificity of a test reflects the proportion of actual non-essential genes that are correctly predicted. The mathematical representation of sensitivity and specificity are as follows:Supplementary Note.Supplementary Data 1.Supplementary Data 2.Supplementary Data 3.Supplementary Data 4.Supplementary Data 5.Supplementary Data 6.Supplementary Data 7.Supplementary Data 8.Supplementary Data 9.Supplementary Table-S1.Supplementary Table-S2.Supplementary Table-S3.Supplementary Table-S4.Supplementary Table-S5.Supplementary Table-S6.Supplementary Table-S7.Supplementary Table-S8.


To aid the strain selection and design process, we used stoichiometric modelling  and the Escherichia coli (E.coli) core stoichiometric model to investigate the network-wide effect of butanol and butanol precursor production pathways differing in energy and electron demand on product yield. An FBA-based co-factor balance assessment (CBA) algorithm was developed to track and categorise how ATP and NAD(P)H pools are affected in the presence of a new pathway. CBA was compared to the balance calculations proposed by Dugar et al. (Nature Biotechnol. 29 (12), 1074–1078). Predicted solutions were compromised by excessively underdetermined systems, displaying greater flexibility in the range of reaction fluxes than experimentally measured by 13C-metabolic flux analysis (MFA) and the appearance of unrealistic futile co-factor cycles. With the assumption that futile cycles are tightly regulated in reality, the FBA models were manually constrained in a step-wise manner. Solutions with minimal futile cycling diverted surplus energy and electrons towards biomass formation. As an alternative, the use of loopless FBA or constraining the models with measured flux ranges were tried but did not prevent futile co-factor cycles. The results highlight the need to account for co-factor imbalance and confirm that better-balanced pathways with minimal diversion of surplus towards biomass formation present the highest theoretical yield. The analysis also suggests that ATP and NAD(P)H balancing cannot be assessed in isolation from each other, or even from the balance of additional co-factors such as AMP and ADP. We conclude that, through revealing the source of co-factor imbalance CBA can facilitate pathway and host selection when designing new biocatalysts for implementation by metabolic engineering.In the growing field of metabolic engineering, where cells are treated as ‘factories’ that synthesize industrial compounds, it is essential to consider the ability of the cells’ native metabolism to accommodate the demands of synthetic pathways, as these pathways will alter the homeostasis of cellular energy and electron metabolism. From the breakdown of substrate, microorganisms activate and reduce key co-factors such as ATP and NAD(P)H, which subsequently need to be hydrolysed and oxidized, respectively, in order to restore cellular balance. A balanced supply and consumption of such co-factors, here termed  The chemicals industry is a major contributor to greenhouse gas emissions and desperately requires more sustainable alternatives. Genetically engineered microorganisms can be used as ‘bio-factories’ to manufacture chemicals, replacing those currently sourced from fossil fuels or unsustainable tropical plant agriculture. However, due to the complexity of biology, the features that render one bio-factory design more efficient than others are difficult to identify. Computational modelling of such designs can enable the selection of optimally performing designs, but it remains challenging as biology is complex and not fully understood. Microorganisms require energy for their own growth and maintenance, but also to convert molecules into desired target products. The supply and consumption of such energy is through co-factors, and the balance of such co-factors influences the performance of the engineered bio-factories. This study developed a computer-aided approach for quantification of the co-factor balance of bio-factories. Using the chemical n-butanol as a case study, our study explores the impact of variant bio-factory designs with differing co-factor balance on the potential efficiency of biomanufacturing. We provide insights into the relative balance of different designs and provide a computational framework to select the best-performing designs. The record will include editor decision letters (with reviews) 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.Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.Thank you again for your submission. 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,Anders WallqvistAssociate EditorPLOS Computational BiologyJason PapinEditor-in-ChiefPLOS Computational Biology***********************While the data underlying the figures are available, the Python function for the co-factor balance assessment is missing. As this code and analysis is the main contributions of this study, we would propose that this be made available the reader.Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: In this paper, de Arroyo Garcia and Jones explore how cell metabolism can limit the yield of synthetic metabolic pathways. In the growing field of metabolic engineering, were cells are treated as potential “factories” to synthesize industrial compounds, it is important to consider the capability of the cells native metabolism to “mesh” with the demands of synthetic pathways, as these pathways will alter the homeostasis of cellular energy charge and redox.The methodology is centered on the use of flux balance analysis, but with extensive manual curation of the reaction constraints. Throughout, various pathways to n-butanol, a non-native product in E. coli, are considered based on how their NADPH and ATP demands are met by the cell, and what the true pathway yields would be. The main technical novelty is a new script for tracking and categorizing how cellular ATP and NADPH are affected (produced or consumed) in the presence of the new pathway.The concept is not altogether novel, as pointed out by the authors they are following concepts laid out by Dugar and Stephanopoulos 2011. However, this approach is useful, in that it uses a core metabolic model instead of a pathway in isolation. The authors are thorough as well, they systematically “hunt” and constrain futile cycles as well as key reactions that appear to be bounded when analyzing experimental MFA data of knockout strains. This latter addition is interesting, as the MFA data suggest that cellular metabolism is not as flexible in adapting to knockouts as it appears from stoichiometric metabolic models. As a result, the limitations of FBA are systematically revealed and addressed in order to arrive at a more accurate prediction of a pathway’s actual yield.Overall the paper is well conceived and well-written. It is somewhat specific to butanol, but there is a variety of butanol pathways considered that allow somewhat general conclusions to be drawn about expected pathway yields based on ATP and NADPH usages. The technical novelty is a bit lacking.Specific points that could be addressed to improve the manuscript:The authors use FBA with product maximization, and then record rates through various ATP and NADPH reactions. FBA gives one particular flux distribution out of many, would it have been better to use FVA here instead?Authors use product as cellular objective and then tabulate fluxes of ATP and NADPH-related reactions. However, there may be more realistic ways to estimate how the cell would respond to new pathways. The MOMA technique  is another way to estimate fluxes after network perturbation, such as addition of a biosynthetic pathway, while biomass remains the cellular objective. The authors could consider such alternative methods for comparison, to see if similar ATP and NADPH-consuming rates arise. Perhaps MOMA where a certain flux into production pathway is used as a constraint.In Abstract and Introduction, authors refer to “flexibility” of computational predictions. Later in the manuscript it is clear they mean possible flux patterns to reach the same objective (FVA). I recommend defining what is meant by flexibility (perhaps plasticity?) as early as possible (preferably in Abstract).The authors use various butanol pathways as case studies, and also attempt to generalize findings about the predicted yields of pathways with certain ATP and NADPH demands. The reliance on MFA data from multiple mutants could limit the approach to be only available for E. coli or yeast as host strains, but these are likely still useful to get an idea of how a synthetic pathway could be limited in different hosts.From the review file and SI, it was not clear if all scripts and models have been made publicly available. Missing are the different models and the Python scripts used to perform CBA. I encourage the authors to provide those.Looking at table 1, NADPH and NADH are lumped together when it comes to pathway requirements. How is this translated in the model? Is there one reaction for each cofactor? Please clarify.Fig. 1 Could be helpful to have enzyme abbreviation directly on the figureFig. 2 A) What does the thickness of the arrows mean? Is it proportional to the flux amplitude? If yes, please state under which condition CBA was performed, with WT or one of the “engineered” models ?B) Same as A), few flux values a represented but it is not clear where they come fromFig. 2 and Fig.3 NADPH waste: In fig.2 caption, it says “waste category may also include reactions..” What are these other reactions?l.248 “Under aerobic conditions, solutions for the engineered models showed no biomass accumulation” Was it also the case in aerobic conditions ?l.257  If PDH is the major contributor of NADPH waste for ButOH-0, ButOH-1 and tpcBuOH, what is the major contributor of NADPH consumed in the NADPH waste?Also related to this point, maybe the authors can expand on why the NADPH waste is 0 in BUTYR  versus non-zero in BUTAL. After all, these two models are one reaction consuming ATP apartl.355 constraining both lower and upper boundaries?l.377 “After cycle detection,..” What is the cutoff value here to decide that this particular set of reactions is now actually a futile cycle?l.403 “BuOH-1 appears to be the most balanced..” most balanced in term of what metric? Redox balance? It would seem that the model having no flux towards biomass instead is actually the most balance redox-wiseRelated to the above point, have the authors tried to include an artificial NADPH and/or an ATP sink reaction in the model to see how imbalanced the redox state is? It would be interesting to see if these reactions would have a non-zero flux in the model making no biomass for instance. It could also be used as a metric to determine redox imbalance in each model.l.427 Same as above artificial sink reaction could prove that. If you add an ATP sink reaction, how does the CBA analysis of NADPH vary and vice versal.501 and paragraph. I think this is an unfair comparison between 13C-MFA and FVA variability. First, knocking-out a single gene would not probably push the reactions of the network to their maximal range as this is the case in silico. Secondly, this is certainly not the case with FBA as it predicts a long-term flux distribution (after many generations). Whereas the 13C-MFA data obtained from Havekorn et al. will provide flux data that should instead be compared to MOMA .Fig.7 Great results to guide pathway engineering (on a pure stochiometric aspect). From this figure, it seems it would be possible to determine an “optimal” ATP/NADPH ratio for each product. I would also suggest to add a marker showing where each model stand in each sub-plotl.607 Can the authors hypothesize on why no solutions exist for ATP produced >2 in Fig. 7 G & H. Since product is set as objective function, does this mean that no solution exist? It would be good to indicate that there is no flux solution (leave the area blank) rather than implying no flux to product.Reviewer #2: The authors had a very interesting idea to explore cofactor balance and its relation to maximizing the production of compounds. The authors leveraged FBA, CBA, FBA, and MFA to interrogate the Ecoli core and 8 addition engineered models with different combinations of pathways that leads to the biosynthesis of butanol. Each model had a different demand for ATP and NAD(P)H and the authors looked at how those change in redox demand effected flux distribution and yield under aerobic and anaerobic conditions. I think the idea is interesting, however there are some concerns associated with the analysis.1) The comparison between WT and engineered strains is not a fair comparison due to the difference in objective functions. Would the results change if all of the engineered trains were constrained to the growth rate of the WT, and then maximizing the production of butanol?2) FVA not conducted across all engineered strains. Single FBA/CBA flux distributions were used to draw conclusions about how redox demand effects the over flux distribution of the network. However, many other solutions exist that yield the same objective value, the singular solution that the author presented and analyzed will change based on the algorithm and solver that was used to solve the linear programming problem. Although the yields may be correct, the CBA may yield an incomplete picture. How much did the cofactor contributions change if FVA was performed?3) NADPH and NADH are analyzed interchangeably, however pathways such as pentose phosphate replenishes NADPH and can contribute to the cofactor analysis.Reviewer #3: This paper proposes a procedure to analyse the impact of metabolic engineering on the balance of co-factors, and use it to evaluate alternative metabolic engineering designs.The results are interesting and the paper is well written.However, the several computational procedures could be presented with more mathematical details:1) In Section 4.2, I do not undersand why max vobjective is set equal to vobjective,lb . What is vobjective,lb?2) Still in section 4.2, the models are unconstrained (except for the stoichiometry and irreversibility of course): what is the number of degrees of freedom of the different models?3) the text often mentions the "excessive flexibility of FBA". I think that this statement sounds a bit too strong, and vague at the same time. Per se, FBA is an excellent tool, all depends on the degrees of freedom of the problems under considerations.Additional information or measurements will help reduce the underdeterminacy of the problem (which is a better concept than the flexibility of a method).4) Is the CBA protocol available to the community as a Python function?5) In FVA, why 99% of the maximal value of the objective function, and not 100%?6) In section 4.4, C-13 labelling experiments by Haverkorn et al. (which is reference 44 and not 46) are used to constrain the models. Afterwards, it is refered as the "Rijsewijk dataset" which is unclear.Could the authors elaborate on the fact that this dataset is appropriate to create constraints in their study?The use of the flux values to create min-max bounds seems to be a big assumption.What are the remaining degrees of freedom after the implementation of these constraints?7) Figures 3 and 5 would be easier to interpret if the same scales were used in the graphs.Reviewer #4: General comments:The authors presented analyses on the cofactor balance of different production pathways for butanol and its precursors. The authors also organized the analysis steps into a workflow. By examining the energy or redox wastage the authors claimed that those flux distributions are not biologically realistic and made efforts to block such wastage like ATP hydrolysis and redox sinks and futile cycles in particular ways to find solutions in which energy and redox either go into products or growth, to predict more realistic yields. The assumption is based on previous studies that have suggested that when growth is the only major sink of energy and redox surplus, more materials  will be consumed by growth too and result in an overall lower yield.Specific comments:Though the analysis does generate some useful insight and results, and based on an assumption that is valid to a certain extent. There are major concern from the reviewer’s point of view.Major commentsAlthough many observations and computations are solid, how the authors present their arguments or assumptions/hypotheses seem biased and not objectively based. And it does not represent a proper way of interpreting computational results.1.1. One example is to directly take a certain type of FBA solutions (pFBA here) and use the flux values for intracellular reactions as the predictor and then draw conclusions from that. For example in section 2.4, the authors just take the values predicted for ATPM returned by the particular pFBA solution and claimed FBA predicted ATP wastage. The underlying philosophy of constraint-based modeling is that when we have more constraints from biochemical principles, like mass balance and reaction directionality, we can narrow down the range of phenotypes. But we should be always aware that since the system is mostly way underdetermined, we should never simply take a certain flux value and draw conclusions from that. A better way is to look at the FVA range, which the authors actually did. And from Table S1, FBA actually did not preclude solutions with minimum ATPM only . This is actually consistent with what the authors found. They were able to fix ATPM value and still get max. yields the same as before. The authors can present the FVA ranges and then say that they include metabolic flux distributions that represent energy and redox wastage but should not simply take a particular solution from FBA and say it predicted wastage since no wastage does lie within the prediction of FBA. It just did not exclude wastage prediction.1.2. Following the last comment, lines 192 – 194 claims ‘Five out of eight models surprisingly had the same theoretical maxima under aerobic conditions achieved through considerable adjustments to the network flux distributions’.But the authors looked at only one solution using pFBA for each model. The possibilities that there are other solutions that are more similar to each other given the same yields cannot be ruled out. The authors should claim that only if they have tried to, for example, add the maximum yields as constraints and minimize the difference  between all models and still see that they are significantly different.Also, from Table S2, only BuOH-0, BuOH-1 have the same max. of 10 mol/10 mol glucose, while tpcBuOH, BuOH-2 and fasBuOH have lower yield. Did the author include also CROT, BUTYR and BUTAL which produce different end products (though they are precursors of butanol)? But still they are not quite comparable especially they involve cofactors that directly impact the final yield.2. Line 303 asks “Is bacterial metabolism that flexible”? The authors did not directly answer this but from the analyses afterward it is pretty apparent that their answer was ‘NO’. But the reviewer does not see very strong evidence about that. The reviewer hopes that this is a misunderstanding originating from how the authors interpret the flux distributions from FBA. From the text later, the reviewer could see that the authors argued that it is not possibly that flexible because there is energy and redox surplus that go into wastage sink or futile cycles which are not biologically realistic. The authors argue that they should go into growth. So growth must accompany the product formation. Well, that should be obvious enough for most metabolic engineers. No growth no nothing no matter the product generates energy or redox surplus. But mostly metabolic engineers look at theoretical yield because we hope that the pathway can be active under the condition of growth or after growth. So under growing conditions, is that possible for the bacteria to include very different pathways with different cofactor balance profiles to the product formation? The reviewer tends to say yes. Just that the absolute fluxes through the pathways could be different depending on how well it is coupled to growth. Even not under growth conditions, the reviewer does not see the reason why those pathways are necessarily not feasible. Since they are engineering pathways anyway, there could be engineering efforts to further improve that. For example there have been work to introduce ATPase activity to consume ATP in resting cells and observed enhanced fluxes.3. The argument in Lines 336 – 342 for “FBA having more flexibility than what would be expected in reality” seems highly speculative. Is the ‘flexibility’ that the authors were referring to the same as the ‘flexibility’ that ref. 27 ? It seems that in that article restoring the ‘flexibility’ is something desirable for the cells while here the authors were saying such flexibility was not realistic. There seemed to be some misinterpretation without proper definition. By the way the reference for ref. 27 needs fixing.4. Lines 345-346 are misleading. Since the authors only used the E. coli core model, which does not have glycerol in the model, of course the solutions cannot resort to glycerol production. And it is just very intuitive that FBA will simply not produce biomass to consume the energy or redox in excess. Biomass production competes cellular resource with the pathways for producing many compounds because in addition to energy or redox, biomass production involves the synthesis of many metabolites and producing any biomass will very probably reduce the maximum yield of butanol, contradicting to the assumption of optimal yield when the authors ran pFBA.5. Section 2.7 comparing the ranges from FBA and MFA could be over-/mis-interpretation of data. Metabolic fluxes are almost never directly measured (not that the reviewer knows). Flux ratios between pathways are usually first measured (this point included the assumption of which pathways to include) and then fitted into a stoichiometric model . Therefore the observation that MFA flux ranges are narrower than FBA ranges by direct comparison are not necessarily valid because the models used to interpret the data or do predictions are different, which impact the results a lot (or at least to an unknown extent). Though I think the authors’ conclusion of MFA narrowing down FBA ranges must be correct, the reason is simply because MFA flux ratios give additional information that an FBA model does not have by default. But comparing directly this way without any elaboration gives a biased understanding. Did the authors examine carefully the original stoichiometric model used for fitting the flux data and check that it still largely applies to the E. coli core model? Or just fit the data into the current model to check potential range?Besides the interpretation of computation results, there are some major concerns in the computation methods used.https://bmcsystbiol.biomedcentral.com/articles/10.1186/1752-0509-3-117) to address this issue. Basically one should find the ‘cofactor turnover’ range by minimizing and maximizing the sum of all cofactor score (as defined by the authors) to fully describe the flux through a cofactor. Similarly, for the energy and redox balance profile breakdown, one should minimizing and maximizing the sum of all cofactor score across reactions belong to a particular category and present a range. Simply comparing one particular flux distribution from each model is not representative.6.1. Related to the first point, the CBA algorithm only analyzed a particular solution from FBA. It is not a systematic analysis. There was a previous study introducing a technique called flux-sum analysis  does go into ‘NADH target’ (-ve). Is that a proper definition of waste?7.1. The procedure to eliminate futile cycles described in lines 372 to 384 is problematic. Bounding the fluxes with the values from the wild-type flux distribution, which was obtained by maximizing biomass production, will probably make the predicted fluxes look like the growth metabolism. This also potentially excludes other reactions that can be used but not active under the condition of maximum biomass production.https://www.nature.com/articles/s41598-019-38836-9) for an example. Basically you just equations (6) - (10) in the method section7.2. There are well-established techniques to add constraints to exclude all futile cycles while not excluding any feasible flux distributions without futile cycles. For example, adding integer cuts iteratively instead of adding bounds on specific reactions. More systematically, one can use the loopless FBA formulation . The formulation usually blocks completely balanced cycles which has delta G = 0. For the purpose here, one can simply calculate the null space which excludes the cofactors of interest  and use the same formulation accordingly. Then all cycles whose net effect are consumption or production of the cofactors will be prohibited in the solution. See the Methods section in Ng et al., Scientific Report, 2019  and futile cycles which are tightly regulated. So the authors developed a method to first check the RANGE of energy and redox balance profile  to see if a pathway has energy or redox surplus. Then formulate an optimization method based on loopless FBA for predicting pathways and theoretical yields in the absence of unconstrained high wastage flux and futile cycles. For the MFA constraint added, the best would be to add the originally derived flux ratios as constraints. If not possible at least the assumptions or applicability should be carefully studied and discussed. The reviewer would appreciate in the more general and systematic effort to find out pathways that couple growth to energy and redox surplus to have a more realistic yield and pathway prediction.Minor comments:- Please include the gene/reaction names in Figure 1. It should not difficult to explicitly show and name all eight different routes with good use of colors. Or beside the main figure, add thumbnail versions of all different pathways without the detailed names but simply arrows for the particular routes- Refer to Tables S2 and S3 for the FBA-calculated yields between line 185 and line 188.- What does the % yields between lines 185 and 188 mean? They are neither weight nor carbon yield. If it is simply molar ratio of butanol to glucose, that should not be reported as a percentage. Like probably no one will say the theoretical yield of glycolysis from glucose to pyruvate is 200% just because 1 mol of glucose yields 2 mol of pyruvate. The reviewer suggests using carbon yield instead, i.e., 1 mol glucose to 1 mol butanol means 66.67% carbon/carbon yield. The same goes for Figure 3A.- Line 279: please state the reaction name and ID corresponding to Tables S4 or S5.- Line 291: which figure the authors were referring to? Figure 3B or 3C, ATP or NADH?- Lines 293 and 295: it reads incorrect to the reviewer to call PFL and PDH the same/identical reaction. In particular for these two reactions. The analysis can be made more relevant by turning on PFL only in anaerobic conditions, which is a consensus on PFL activity.- Section 2.3 is not well-oriented. Not until the very last sentence only the reviewer can get the message that the authors were trying to assess how practical/biologically realistic the solutions from pFBA are. Please include a topic sentence telling what the authors want to examine and what they did before going deep into the details. For example, saying the following in the beginning of that paragraph will orient the readers much better (a pretty arbitrary construction that does not seems right): ‘Since realistic bacterial metabolism usually exhibits only a limited flexibility [if that is the assumption the authors have], we examined the plasticity in the FBA solutions for different pathways to determine if they together fit into a realistic description of bacterial metabolism.’- The text in lines 312  and 324  and the data in Table S2  seem to be contradictory.- The math and the algorithm are not clearly presented in the Methods section (4.2) and not in Figure 8. For example, CFS = co-factor stoich. x flux should be written using the standard symbols which have already been introduced in the FBA section, for example:o CFS_i,j = S_{i,j}v_j for cofactor i in reaction j.https://bmcsystbiol.biomedcentral.com/articles/10.1186/1752-0509-3-117o CFS_i = \\sum_{reactin j, if CFS_i,j > 0} CFS_i,j, or simply \\sum_{j} abs/2 as in the flux-sum analysis paper defined . 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  digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. 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For instructions, please see  23 Jun 2020AttachmentPLOS rebuttal letter.docxSubmitted filename: Click here for additional data file. 6 Jul 2020Dear Dr Jones,We are pleased to inform you that your manuscript 'In silico  co-factor balance estimation using constraint-based modelling informs metabolic engineering in Escherichia coli' has been provisionally accepted for publication in PLOS Computational Biology.Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. 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It is my opinion that the article is improved by the additional data and revised text. There is now more clarity in describing motivation, methodology, and results. All of the technical questions have been addressed.Reviewer #2: Very interesting work, great job!**********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?). 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  1223-442824 | ploscompbiol.org | @PLOSCompBiolPLOS Computational Biology | Carlyle House, Carlyle Road, Cambridge CB4 3DN | United Kingdom