Yet, none of the existing computational approaches allows for a fully automated model extraction and determination of a flux distribution independent of user-defined parameters. Here we present RegrEx, a fully automated approach that relies solely on context-specific data and ℓ1-norm regularization to extract a context-specific model and to provide a flux distribution that maximizes its correlation to data. Moreover, the publically available implementation of RegrEx was used to extract 11 context-specific human models using publicly available RNAseq expression profiles, Recon1 and also Recon2, the most recent human metabolic model. The comparison of the performance of RegrEx and its contending alternatives demonstrates that the proposed method extracts models for which both the structure, i.e., reactions included, and the flux distributions are in concordance with the employed data. These findings are supported by validation and comparison of method performance on additional data not used in context-specific model extraction. Therefore, our study sets the ground for applications of other regularization techniques in large-scale metabolic modeling.Genome-scale metabolic models have proven highly valuable in investigating cell physiology. Recent advances include the development of methods to extract context-specific models capable of describing metabolism under more specific scenarios ( The findings from these analyses provide useful insights in metabolism, and may circumvent the drawbacks of estimating fluxes from labeling studies—still a computationally demanding undertaking [The investigation and understanding of cell metabolism has experienced a paradigm shift largely propelled by the development of high-throughput methods in the last two decades. As a result, the classical pathway-centered view have given way for a network-driven perspective, which considers the entire set of known interconnected biochemical reactions. This had led to the creation of genome-scale metabolic models (GEMs) for organisms from each of the three domains of life: archaea, bacteria and eukarya . While aertaking –4. Furthertaking ,6.contexts, only a subset of reactions is typically active. Therefore, the shift towards reconstructing context-specific models of cell metabolism has become necessary to provide more accurate and biologically meaningful insights. This is of particular importance when tackling the physiology of multicellular organisms, not only to better understand tissue- or cell-specific metabolism, but as a first step to reconstruct metabolic networks of an entire organism/body, where multiple specialized models are mutually interconnected [However, a metabolic network that includes all known biochemical reactions of an organism may not be realistic in a particular cellular scenario, since there is mounting evidence that cells adapt their metabolism to arising conditions, such as: external environment, developmental stage, cell type in multicellular organisms, or even during a pathological condition , to name only a few. In these different onnected ,8.Several methods have been proposed to determine context-specific networks, already comprehensively reviewed in . In gene3E [e.g., biomass production) is optimized through Flux Balance Analysis [GIMME  and GIM33E  form theAnalysis   which are most concordant with the associate data state. While iMAT uses data to pre-classify reactions of the GEM into active or inactive groups, INIT integrates data as a weighting factor for the binary variable. Moreover, INIT includes a set of key metabolites which must exhibit a small positive deviation from the steady state condition. In an extended version, tINIT [i.e., biochemical pathways) that must carry non-zero flux can be added as further constraints.The second group comprises iMAT  and INITn, tINIT , a set oi.e., all reactions in the model must be able to carry a non-zero flux in at least one of the allowed steady-state distributions). Unlike the methods in the previous two groups, these only extract a context-specific model and do not provide a respective flux distribution.The third group, composed of MBA , mCADRE With respect to another classification criterion, the first group belongs to the so-called biased methods  since the achieved solution depends on the definition of a metabolic function to be optimized. In contrast, the second and third group consist of unbiased methods since they are independent of a metabolic function . Howevera priori knowledge of a context-specific function and without any binarization or pre-classification of reactions in the process of data integration. This is of particular importance when a large number of context-specific models are to be extracted or, more relevant for not well-characterized organisms, for which no information regarding the context-specificity of reactions or metabolic function may be available in the existing databases or from detailed physiological studies. Here we present RegrEx, an approach based on regularized least squares optimization that fulfills these tasks of extracting context-specific models and providing a flux distribution in an automated and unbiased way.However, none of these methods allow fully automated model extraction and flux prediction, without using i.e., learning) high-dimensional functions from observations, as a means to reduce model complexity  and prevent overfitting to background noise. The latter has been shown to considerably improve prediction performance and model robustness. Several regularization methods have already been proposed, including: the Dantzig [n explanatory variables and m observations, where n≫m. This has been largely due to a better performance of the LASSO selector in feature selection  along with the simplicity of the operator, which facilitates its computation [Regularization is commonly applied when modeling  to find a best suited value with respect to a measure of performance . Regularization by means of the ℓ1-norm, as generalizations of LASSO, has been already applied in metabolic modeling; for instance, it has been used to reconstruct biochemical networks from time series data [The weighting parameter, λ, is usually determined by cross-validation, which offers an unbiased way , which is as close as possible to the experimental data, d . At the same time, it excludes the reactions irrelevant for the given context by shrinking their fluxes to zero. This is obtained by minimizing the squared Euclidean distance (second norm) between v and d, and exploiting the ability of the ℓ1-norm regularization to perform feature selection. This leads to the optimization problem, The Regularized Context-specific model Extraction method (RegrEx) aims at finding a feasible flux distribution, ϵ = d−v, considering only the subset of reactions to which data can be associated . We alsi.e., predominant direction of the two irreversible reactions) is part of the optimization problem and relies ultimately on maximizing similarity to data.Altogether, this resulted in a mixed integer quadratic program (MIQP) capturing the RegrEx method, As pointed out above, cross-validation is the canonical method to determine an optimal λ-value for a regression problem. However, this is not an appropriate method for RegrEx due to its particular characteristics, since consecutive sampling of the observations, in this case, would imply using only a subset of reactions of the original metabolic model to be in a steady-state. For this reason, we optimized λ selection by running the algorithm for a sequence of λ-values and taking the one that renders the highest Pearson product-moment correlation between fluxes and data. RegrEx was applied first over a coarse sequence of λ-values (λ step size of 0.1) until all reactions shrunk to zero. Then a second optimization was performed over a finer λ-sequence (λ step size of 0.01) centered on the region of maximum correlation found in the first optimization.i.e., 180 seconds, only caused a mean correlation increment between models of 0.0004, see We solved the MIQP of RegrEx using the Gurobi solver . To speeRegrEx was implemented in MATLAB, and the code is provided in i.e., organs or tissues) published online in the RNAseq Atlas [reduceModel function of the COBRA toolbox [To test RegrEx performance we selected, as a case study, the existent human metabolic network reconstructions, Recon 1 which haseq Atlas . To avoi toolbox . The expe.g., across tissues) between genes can be of several orders of magnitude. This may likely cause RegrEx to favor reactions whose associated genes have higher mean values across contexts, thus, reconstructing context-specific models in a biased manner. To correct for this bias, we normalized the expression value, t, of each gene, i, in context, j, to its maximum value across all considered contexts:The range of expression values typically varies between genes, especially in RNAseq-derived expression data, where differences in mean values  groups. The implementation provided in [−6 were considered active for a given context. In the case of FastCORE, we used the implementation provided in [th percentile; therefore, it uses the same set as the high-expressed group employed in iMAT.The existing iMAT implementation of the  toolbox  was usedvided in  was usedvided in  and obtahclust function of the package stats in the R environment, and by using the average linkage criterionThe Jaccard index was used to generate the similarity matrices comparing models extracted for different contexts, as well as models of the same context extracted by different methods. In this last case, the clustering dendrogram in i.e., the sum of each column of the distance matrix). Therefore, the respective z-score quantifies the extent to which a given context differs from the remaining.We z-normalized the sum of Jaccard similarities of each context to the remaining . This pre-processing improves RegrEx performance since the existence of blocked reactions in the GEM would lead to stoichiometric inconsistencies. We used RNAseq expression profiles for 11 human tissues as context-specific data [As a case study, we applied RegrEx to extract 11 context-specific human models, namely, adipose tissue, colon, heart, hypothalamus, kidney, liver, lung, ovary, skeletal muscle, spleen and testes, and to obtain the corresponding flux distributions. The starting GEM was the Recon 1 reconstruction , which wfic data . Althougfic data ,41, it s0), as a special case of the RegrEx method with λ = 0. We also included FastCORE in our comparison; however, since FastCORE only provides a context-specific model (i.e. set of active reactions), we only included it in comparisons at the structural level of the extracted models. In each case, we used the consistent part of Recon 1 and the same gene expression data from the RNAseq Atlas to provide unbiased and fair comparison.We compared RegrEx performance with other existing methods for context-specific model extraction and flux prediction. Namely, iMAT , the mete.g., RNAseq expression profiles) and flux values. For this reason, we also included Lee2012 in the comparative analysis. Nevertheless, RegrEx differs from Lee2012 in the inclusion of regularization and also in the treatment of reversible reactions: Lee2012 applies an iterative approach, where the optimization problem starts first with the subset of irreversible reactions, and reversible reactions are then added sequentially by solving additional optimization problems. This last step is time consuming because it involves two optimization problems per reversible reaction. In contrast, RegrEx selects direction of reversible reactions at once through the use of a binary variable, as explained in the Methods section, thus reducing the computational time. Moreover, RegrEx is unbiased with respect to the order in which the reversible reactions are added, which is a shortcoming not resolved in Lee2012.We would like to point out that Lee2012 was not originally developed to extract context-specific models. However, RegrEx has a form similar to that of Lee2012, which aims at improving flux prediction through minimizing the absolute distance between data  and the level of agreement between the correlation matrix of the expression data for each context and the Jaccard distance matrix of the extracted models (to quantify the distance between two models in terms of the set of active reactions). Second, we performed an independent validation of the extracted models by measuring their level of agreement with protein expression data taken from the Human Protein Atlas .i.e., the number of reactions included in an extracted model), Lee2012 generates models with the lowest mean cardinality (on average approximately 785 reactions per model) followed by RegrEx and RegrEx-λ0 . In contrast, FastCORE and iMAT result in markedly bigger models for the corresponding contexts . Each set of context-specific models extracted by a particular method has a core set of reactions shared by all contexts. In addition, each context has an exclusive set of reactions . In this sense, RegrEx extracted models have the smallest set of shared reactions, with 299 reactions, and the biggest set of total exclusive reactions , with 332 reactions. These two properties demonstrate that the models extracted by RegrEx are in fact more context-specific than the ones extracted by the other methods, which is confirmed by the mean Jaccard similarity between models. The Jaccard similarity is lowest in the case of RegrEx  in support of the previous claim. On the contrary, Lee2012 generates the greatest core set among the methods evaluated, with 509 shared reactions, and the smallest set of total exclusive reactions, amounting to 140 reactions, This, in turn, makes the Lee2012 models to be the least context-specific .The general characteristics of the extracted models by each method are summarized in data-orphan reactions, since their inclusion results in uncertainty (given the available data). On this line, we evaluated the aforementioned property by computing the data-orphan ratio  of each of the extracted models. RegrEx extracted models show the second lowest mean data-orphan ratio across all methods , only surpassed by Lee2012 , Notably, this is only valid when a regularized extraction is used, since in the case of RegrEx-λ0, the data-orphan ratio ranks to the second worst position, only surpassed by FastCORE, with mean orphan ratios of 0.47 and 0.50, respectively. The reduced data-orphan ratio indicates that RegrEx, although surpassed by Lee2012, is still capable of extracting compact models in which the number of data-orphan (uncertain) reactions is minimized.When extracting a context-specific model, there exists, in general, a subset of reactions of the original (unspecific) GEM whose fluxes are unbounded by data. This can be due to the absence of GPR rules , or simply because experimental data is missing for that reaction. In any case, it is of interest to minimize the number of included reactions without associated data, here called 0), or including the entirety or a majority of a predefined core set for a particular context, like in FastCORE and iMAT, respectively, which here was the same for both methods  and iMAT and FastCORE . The differences in total cardinality as well as mean cardinality per model can be explained by the two main objectives that the evaluated methods take; namely, minimizing the distance between data and flux values, like in the case of Lee2012 and RegrEx and are thus grouped together in the corresponding dendrogram of 0 and Lee2012 form another cluster, where models extracted by RegrEx and RegrEx-λ0 are grouped together, and the ones extracted by Lee2012 are closer to RegrEx-λ0.Indeed, this last grouping was reflected when we compared the similarity between models of the same context extracted by the different methods. Results were similar across all contexts, iMAT and FastCORE-derived models share many reactions, as indicated by the high Jaccard similarity index , followed by RegrEx-λ0 and Lee2012 . Moreover, iMAT results in the worst mean correlation value of -0.17 . However, this difference in correlation can be explained by the different approach followed by iMAT, since in this case the method does not aim at minimizing the distance between data and flux values.When inspecting the correlation between data values and predicted fluxes, RegrEx obtained the first position in the ranking  and Lee2012 (Rv = 0.69). This result support two claims: Firstly, although FastCORE does not provide fluxes and iMAT results in very poor correlation between flux and data values, they are still capable of capturing the general differences between contexts collected in the expression data. Secondly, RegrEx is also capable of capturing this differences but with a lower mean cardinality per extracted model. In other words, even with fewer reactions on average, the models extracted by RegrEx are still able to capture the main differences in active reactions contained in the gene expression data. This fact summarizes very well the purpose of regularization when learning models from experimental observations: remove variables (i.e. reactions) that are not important to explain the observations.To include FastCORE in the comparative analysis, we next inspected the similarity to data in a different manner: instead of considering the flux values, we now compare the set of active reactions per context. This criterion captures an aspect of the structure of the extracted metabolic networks. We used the sets of active reactions across different contexts and per method to compute the similarity matrix, using the Jaccard index. We then compared this similarity matrix with the corresponding correlation matrix of the gene expression values for all contexts by using the Rv coefficient. The level of agreement between these two matrices was indeed high for RegrEx, iMAT and FastCORE, as supported by Rv coefficient values of 0.9, 0.92 and 0.93, respectively; the level of agreement was markedly lower for RegrEx-λ0 and Lee2012 is again worse than the other methods, with a correlation value of 0.66 and 0.57, respectively. Interestingly, liver appears to be the most different context in terms of active reactions, and this is captured by all methods except for RegrEx-λ0. This is not surprising, since liver is well known to be the organ with greater metabolic capabilities.The previously reported values of the Rv coefficient quantify the overall agreement between both the similarity and correlation matrices. We next decomposed this result for each different context. To this end, we computed the z-scores (as detailed in Methods) for both matrices. In this sense, RegrEx performed better than iMAT and FastCORE in capturing the pattern showed by gene expression, as quantified by a correlation value of 0.92, between the z-score values of the extracted models and the ones of data, against a value of 0.88 and 0.89 for iMAT and FastCORE, respectively, see 0, since the only difference between the two approaches is the application of regularization and the inclusion of an optimization step to determine the optimal λ-value. Precisely the consideration of regularization allows RegrEx not only to extract more compact models, as commented before, but also to increase the correlation between data and flux values, reduce the data-orphan ratio, and greatly improve the general similarities and differences in the metabolic state of the different contexts, as showed by the RV coefficient and z-score values.To conclude this section, it is noteworthy to highlight the comparison of RegrEx performance with the one of its non-regularized version, RegrEx-λhigh, medium and low. To account for this, we evaluated whether models contained an enriched group of genes coding for proteins within the category of high expressed for the corresponding organ/tissue in comparison with the other two categories, as well as and an enrichment in genes from the medium expression value group in comparison to those from the low expression.We performed and independent test on the biological reliability of the extracted models by all evaluated methods. To this end, we compared the level of agreement of each model with protein expression profiles taken from the Human Protein Atlas  we had . The proi.e., the number of genes in high, medium and low across all organs/tissues, and applied the Mann-Whitmann-Wilconxon test on the obtained distributions to determine the statistical significance of their difference. This test was applied for each evaluated method. As observed in high and medium expressed genes since the p-values for all three comparisons, number of genes in the high group greater than in the medium, H>M, medium greater than low, M>L, and high greater than low, H>L, are below the significance threshold of 0.05. In the case of RegrEx-λ0 and iMAT, only two of the comparisons are significant, H>M and H>L, and M>L and H>L, respectively. Models in FastCORE are only enriched in high expressed genes in comparison to low expressed and none of the comparisons are significant in the case of Lee2012. These results add and additional experimental support to the extracted models by RegrEx and in a lesser extend the ones by RegrEx-λ0, iMAT and FastCORE, for two main reasons: the additional experimental data comes from a different (independent) database than the one used during the extraction, and relies on a lower hierarchical level in the causal chain controlling metabolic fluxes, namely, is based on protein expression rather than gene expression.To tests these hypotheses, we determined the number of genes of each group in each context, i.e., which are robust in flux capacity irrespective of the different contexts (note that this set of robust reactions must belong to the core set of shared reactions across contexts).The next step in evaluating RegrEx extracted models was to perform a functional analysis by determining which metabolic functions were important in each context. To this end, we calculated the flux capacity of every reaction in the models, given by the difference between the maximum and minimum corresponding flux value obtained per Flux Variability Analysis   is Transport, similar to the findings in . HoweverAs commented before, all context-specific models share a core set of 299 reactions in the case of RegrEx extracted models. If we consider the TNR in each metabolic category we obtain a distribution like the one displayed in Alternatively, to further evaluate the functional validity of the RegrEx extracted models, we used the previously calculated MFC to investigate the importance that a given subsystem had in each context. Furthermore, we ranked the subsystems according to the CV of the MFC value distribution of each subsystem across contexts. This implies that subsystems with a low CV are evenly represented among the different contexts, while with increasing CV, these subsystems tend to be more specific for certain contexts. For instance, all subsystems belonging to Central metabolism occupy top positions in the ranking, which is expected due to the fundamental role that these subsystems play in all cell types. The citric acid cycle is the first subsystem in the ranking with a CV value of 0.078. On the contrary, the pentose phosphate pathway is the subsystem in Central metabolism with a highest CV value of 0.21. However it can be considered low in the context of the entire ranking, and may be explained by the fact that, unlike the rest of subsystems in Central metabolism, the totality of its reactions in the core are non-robust, as mentioned before, see Lipid metabolism presents a middle level of specialization across the different contexts occupying middle positions in the ranking. Therefore, this finding implies that there are some tissues in which lipid metabolism is predominant. For instance, fatty acid metabolism is predominant in adipose tissue, liver and skeletal muscle. In addition, fatty acid oxidation and fatty acid activation are predominant in adipose tissue and skeletal muscle. This is consistent with known functions of these contexts, since the adipose tissue and liver are primary locations for fatty acid metabolism and the fatty acid oxidation provides the required energy supply for oxidative muscle contraction . We alsoi.e., these subsystems are only predicted to be active in a single context. This category consists of bile acid biosynthesis, biotin, riboflavin, vitamin B6, vitamin D, CYP, methionine and D-alanine metabolism  [The subsystems with largest CV value include those with extreme behavior, tabolism . We can tabolism . We wantactions) . After eRegrEx computational performance was also evaluated, and compared to the other methods. In all cases, with the exception of FastCORE, the Gurobi  solver w0), the computation is fixed to around 60 seconds per model extracted, this is due to the time limitation constraint imposed to the Gurobi solver, as discussed in Methods. When no time limit is imposed RegrEx gets the worst position among the evaluated methods, this may be due to the complexity inherent of solving an MIQP for a big network like the one of Recon 1. However, the sensitivity to time limit analysis suggests that the improvement obtained by increasing the time limit does not worth the extra time expended, even could be reduced to 30 seconds with a similar outcome . More specifically, the models obtained without employing regularization are less specific to each particular context, share a greater amount of reactions and contain less exclusive reactions in comparison to models for other contexts. This is supported by the higher mean Jaccard index over all pairs of compared context-specific models. In addition, the mean orphan ratio is higher if regularization is not used, implying that a greater number of reactions with non-associated experimental data is included and causing these models to be less compact. Finally the mean correlation values between predicted fluxes and data are also smaller in the non-regularized extraction. Altogether, these observations support the importance of including regularization to obtain a better performance in context-specific model extraction.We have presented RegrEx, a method to extract context-specific metabolic models and provide a flux distribution most in accordance with experimental data. RegrEx have generated context-specific flux distributions with the highest correlation values among the competing methods evaluated, as well as extracted compact models, enriched in reactions with high associated data values. Importantly, RegrEx performance is severely impaired when performing a non-regularized extraction , and the problem of lower coverage typically presented by protein profiles can be alleviated by jointly integrating gene expression data to fill the gaps with respect to data support. In addition, when there exist strong experimental evidence supporting the presence of a certain reaction in a given context, its lower bound can be set to an arbitrary positive value  thus forcing it to be included in the context-specific model. In a similar manner, when the evidence is for the presence of a metabolite, the sum of the reactions producing such metabolite could be constrained to ensure its inclusion, thus allowing integrating metabolomics data in a qualitative way.In the case study presented here, we have used gene expression profiles as experimental data. However, RegrEx can support other data sources; protein profiles can be easily integrated,  are deemed appropriate by the experimentalists.RegrEx can be easily used in MATLAB through the provided files. Moreover, no parameters need to be chosen by the user, since the only parameter, λ, is determined by RegrEx in an automated fashion. In this manner, the user only needs to provide a relevant (context-specific) data source(s) and the GEM from where the context-specific model is to be extracted, and the rest of the operating process is fully automated. Finally, RegrEx does not require any S1 FigThe importance of each metabolic category in each contexts is quantified using the total number of reactions (TNR) belonging to it and their mean flux capacity (MFC).(PDF)Click here for additional data file.S1 FileThe RegrEx code is provided for MATLAB. The 11 context-specific models are provided in the COBRA format (MATLAB structure), both for Recon 1 and Recon 2. The data set used in both cases is also provided.(ZIP)Click here for additional data file.S2 File(ZIP)Click here for additional data file.S1 Tablei.e., RegrEx without regularization), Lee2012, FastCORE and iMAT are collected in tables A, B, C, D and E, respectively. The abbreviations stand for the following: Card, denotes cardinality, #ExRxns., number of exclusive reactions, #Genes, number of genes, OrphRatio, data-orphan ratio, Cor, correlation between data and flux values, Res, mean residual value between fluxes and data, IJaccard, mean Jaccard index to any other context , and Lambda, represents the obtained optimum λ-value.Global characteristics of the models derived by RegrEx (with automated determination of λ), RegrEx-λ0 ((XLSX)Click here for additional data file.S2 TableHomo sapiens. The miscellaneous group “Others” contains subsystems of several different categories in the original KEGG classification. Metabolic categories are highlighted in bold.All metabolic subsystems from Recon1 present in the 11 RegrEx models were grouped in 8 broader categories, which are depicted in this table. This classification is based on the KEGG orthology for (XLSX)Click here for additional data file.S3 Tablei.e., with CV = 0, and the non-robust subset, which is composed by reactions with CV≠0. In this latter case, the reactions are ranked in descending CV value. Reactions highlighted in red in the non-robust subset belong to the pentose phosphate pathway.The 299 reactions of the shared core set are displayed along with the subsystem and metabolic category to which they belong, the mean flux capacity (MFC) of each reaction across contexts and the CV value of the previous MFC. The core set is partitioned into the robust subset, composed of reactions with the same flux capacity in all contexts, (XLSX)Click here for additional data file.S4 Tablei.e., reactions whose MFC value does not change across contexts, and the total number of reactions (#Rxns) are displayed for each subsystem. Subsystems presented in In this table, the subsystems are ranked in ascending order in terms of their CV value. The Recon 1 subsystem name is displayed along with the metabolic category to which each subsystem belongs, the mean flux capacity (MFC), the number of robust reactions (#RobustRxns), (XLSX)Click here for additional data file.S5 TableZ-score values of the associated expression data are displayed for the 8 subsystems with unique representation across contexts. The z-scores represent the deviations from the mean of the total sum of data values in each subsystem across contexts. The values highlighted in red correspond to the contexts where RegrEx uniquely assigns each subsystem. In all cases, these contexts present an extreme total sum of data values, as reflected in the highest z-score value as compared with the rest of the contexts.(XLSX)Click here for additional data file.S6 TableAll metabolic subsystems of Recon 2 represented in the 11 contexts are ranked according to their (increasing) CV value of the MFC across contexts. Subsystems highlighted in red correspond to subsystems of Recon 1 that were assigned by RegrEx to a single context.(XLSX)Click here for additional data file.


Systems biology has enabled the development of genome-scale metabolic models. However, analysing these models via flux balance analysis (FBA) cannot predict many evolutionary outcomes including adaptive diversification, whereby an ancestral lineage diverges to fill multiple niches. Here we combine Simulations predicted the adaptive diversification that occurred in one experimental population and generated hypotheses about the mechanisms that promoted coexistence of the diverged lineages. We experimentally tested and, on balance, verified these mechanisms, showing that diversification involved niche construction and character displacement through differential nutrient uptake and altered metabolic regulation.The evoFBA framework represents a promising new way to model biochemical evolution, one that can generate testable predictions about evolutionary and ecosystem-level outcomes.The online version of this article (doi:10.1186/s12862-016-0733-x) contains supplementary material, which is available to authorized users. The ability to predict evolution would be valuable not only for understanding such processes as adaptation and speciation –3, but aThe dynamics of evolutionary change reflect multiple processes and varying selective pressures that are influenced by many ecological, physical, and cellular constraints that may conflict with one another. Understanding whether and how these dynamics lead to the splitting and divergence of lineages is of central interest, as these processes represent the initial steps towards speciation. To this end, several theoretical studies have shown that cellular tradeoffs can promote lineage divergence –16. The Historically, the interplay between cellular tradeoffs and evolutionary and ecological dynamics has been analyzed using game theory and differential equation-based models that consider small or idealized metabolic systems , 14, 22.Flux Balance Analysis (FBA) has been developed to determine the optimal metabolic state of an organism, given knowledge of its biochemical network, biomass composition, and uptake flux rates . This ap2 “uptake” in that total, we seek to represent cellular limitations that can arise from many diverse processes, including redox cycling  is the concentration of the jth substrate in mmol/l, and Km is the half-saturation constant of the transporter in mmol/l. For simplicity, we arbitrarily set the initial Km values for all uptake reactions to 0.01 mmol/l. The vmax,j values were allowed to evolve by mutation (see next section below). The value of vj was then used as the uptake bound for the exchange reaction of each substrate when running FBA. For each simulated day, we evaluated each model using dynamic FBA j,t is the substrate concentration of the jth substrate at time t (mmol/l), BMi is the biomass of the ith model clone at time t (gDW/l), vj,i is the uptake rate of the jth substrate by the ith model genotype as computed by FBA (mmol/gDW/h), and V is the culture volume (l). To mimic the LTEE, we started each day’s culture with glucose at 0.1389 mmol/l. The culture was started with one model genotype  and oxygen were subject to mutation in evoFBA. The exchange rates for phosphate, ammonia, water, protons, and carbon dioxide had no limits, reflecting the fact that carbon is the growth-limiting factor in the LTEE.For the evoFBA simulations, we implemented the  E. coli . This moamic FBA  over thed by FBA . After uli model ) having d oxygen . The indE. coli in the LTEE  according to the number of cells produced in that step and those expected to contain a mutation (Nm(i)) as follows:Ni is the population size of model organism i. Ni was calculated from the biomass of model clone i divided by the mass of one cell in gDW; we used a mass of 600 fg/cell, which was reported previously for exponentially growing E. coli cells [Nm(i) was between 0 and 1, Nm(i) was used as a probability to determine whether or not a mutant was introduced; when Nm(i) was ≥1, a single mutant was always introduced.The point mutation rate of enotypes ) has beeneration . Directlli cells . When Nmvmax values. When a mutation occurred, one of the uptake reactions was chosen at random and the maximum rate for that reaction was changed as follows:vmax,m,new and vmax,m,old are the new and old rates for the mutated reaction m, and a is a random number from the uniform distribution over the interval . Each individual uptake rate was further constrained to lie between 0 and 40, such that the total uptake rate of 40 mmol/gDW/h was not violated. After any mutation, all other uptake reactions were updated as follows:k includes all uptake reactions except the mutated one. This adjustment ensures a constant total uptake flux across the membrane of 40 mmol/gDW/h. This mutation scheme generates strong tradeoffs between uptake reactions. The large effects of the mutations on reaction rates were chosen for computational speed of the evolutionary simulations; additional simulations with smaller maximum mutation steps produced qualitatively similar results  and dynamic FBA calculations using the COBRA toolbox . The MATE. coli, REL606 [The LTEE consists of 12 populations founded from the same ancestral strain of , REL606 , that ha, REL606  suppleme, REL606 , 50, 60.450nm every 10 min. Growth rates were computed from filtered OD data as dln(OD450)/dt over a sliding window of 1 h, using MATLAB. We report the mean of the three replicates. Filtering was performed by removing negative growth rates and mean growth rates that were more than 0.2 units above or below the immediately adjacent data points (outliers).Bacteria were grown in the same medium as used in the LTEE , except The ancestor, 6.5KS1, and 6.5KL4 clones were grown in DM250-glucose as described. Samples were taken at time 0 and every h for 9 h. After centrifugation to remove cells, we measured glucose and acetate concentrations in the supernatant using the Glucose Assay Kit  and Acetic Acid Assay Kit , respectively, following the manufacturers’ recommendations.We simulated the growth of the evoFBA model organisms with IDs 44490 and 12364 Fig. , and for2SO4, incubated at room temperature for 5 min, and passed through a 0.45-μm regenerated cellulose syringe filter . Samples were then analyzed on an Agilent 1260 Infinity HPLC system equipped with a Rezex ROA-Organic Acid (8 %) 300 × 7.8-mm column (Phenomenex) and a diode array detector. The analytical conditions were as follows: mobile phase, 5 mM H2SO4; flow rate, 0.6 ml/min; column temperature, 35 °C; injection volume, 50 μl; wavelength scan range, 190–400 nm; detection wavelength, 210 nm; and run time, 35 min. Concentrations of acetate and fumarate in the L-clone filtrates were determined from linear standard curves over the ranges of 0–10 mM and 0–100 μM, respectively, and with lower detection limits of 0.1 mM and 0.3 μM, respectively. Succinate, lactate, formate, propionate, and butyrate can also be separated under these analytical conditions with detection limits similar to acetate, but they were not detected in any samples.We analyzed by HPLC and GC-MS the metabolic by-products secreted by clone 6.5KL4 using filtrates from 24-h spent cultures of that clone in DM25- and DM250-glucose, both before and after growth of clone 6.5KS1. For HPLC, 1 ml of filtrate was acidified with 5 μl 1 M HGC-MS analysis of volatile compounds was performed using an Agilent GC HP6890 gas chromatograph equipped with a Varian CP-WAX 58 column , and coupled to an MSD5973 mass sensitive detector. The sample (600 μl) was cooled on ice, acidified with 50 μl 4 M HCl, and extracted with 0.375 g NaCl and 650 μl ice-cold ether. After vortexing three times for 10 s each, with 30 s cooling intervals, the sample was centrifuged for 5 min at 10,000 rpm and placed on ice for 5 min. The upper organic layer (2.5 μl) was then injected manually into the GC using an ice-cold syringe . The column was held at 40 °C for 1 min, ramped to 200 °C at a rate of 5 °C/min, and held for a further 3 min, giving a total run time of 36 min. The solvent delay for the MSD was 1.4 min and the mass scan range was set to 35–300 atomic mass units. The presence of acetate (retention time 12.2 min) in the L filtrate after growth in both DM25- and DM250-glucose was confirmed by this method. The estimated concentration from the DM250-glucose filtrate was 510 μM, which is close to the 480 μM detected by HPLC /OD450nm, where GFP is the fluorescence signal after subtracting the value for the empty plasmid and division by OD450nm standardizes the data with respect to cell biomass density. We show the mean values from three replicate experiments (Fig. We measured the activities of the promoters of four genes—st Table  given thst Table . We used fusions . Each ofr region . They wents Fig. .Table 1G


Synechosystis sp. 6803 as a host to its genome-scale model, and constructed a metabolic model of hybrid cells (SyHyMeP) using computerized analysis. Using this model provided a metabolic design that improves the theoretical yield of succinic acid, which is a useful compound.Designing optimal intracellular metabolism is essential for using microorganisms to produce useful compounds. Computerized calculations for flux balance analysis utilizing a genome-scale model have been performed for such designs. Many genome-scale models have been developed for different microorganisms. However, optimal designs of intracellular metabolism aimed at producing a useful compound often utilize metabolic reactions of only the host microbial cells. In the present study, we added reactions other than the metabolic reactions with Synechosystis sp. 6803. The theoretical yield of succinic acid production using a genome-scale model of these cells was 1.00 mol/mol-glucose, but use of the SyHyMeP model enabled a metabolic design with which a 33 % increase in theoretical yield is expected due to the introduction of isocitrate lyase, adding activations of endogenous tree reactions via D-glycerate in Synechosystis sp. 6803.Constructing the SyHyMeP model enabled new metabolic designs for producing useful compounds. In the present study, we developed a metabolic design that allowed for improved theoretical yield in the production of succinic acid during glycogen metabolism by The SyHyMeP model developed in this study has provided a new metabolic design that is not restricted only to the metabolic reactions of individual microbial cells. The concept of construction of this model requires only replacement of the genome-scale model of the host microbial cells and can thus be applied to various useful microorganisms for metabolic design to produce compounds.The online version of this article (doi:10.1186/s12934-016-0416-8) contains supplementary material, which is available to authorized users. Advances in the tools used to organize databases automatically and describe metabolic networks [Escherichia coli, Saccharomyces cerevisiae, and Corynebacterium glutamicum have enabled high-efficiency production of compounds such as succinic acid [C. glutamicum or S. cerevisiae are used to simulate metabolic design for cells capable of high productivity of useful compounds, it is impossible to automatically use metabolic reactions of the Entner-Doudoroff pathway of E. coli or other cells [E. coli as the host, the reaction pyruvic acid → oxaloacetic acid, which is catalyzed by pyruvate carboxylase in C. glutamicum, cannot be incorporated into the calculation [Designing optimal intracellular metabolism, as typified by metabolic engineering or synthetic biology, is essential when the aim is mass production of useful compounds by using microbial cells. One of the powerful tools for this design method is the use of genome-scale models (GSMs). In intracellular metabolic reactions, kinetics, of substrates and enzymes are involved, and various mathematical models that take these into consideration have been developed. However, the intracellular metabolism can be assumed to be in a steady state (pseudo-steady state) as long as the cells continue to be in the same environment. In other words, no change in the amount of intermediate metabolites occurs in the cell, and the metabolic flux in the cell can be predicted by mathematical calculation in the form of flux balance analysis (FBA). These computer-calculated prediction results successfully reflect the phenotype of the microbial cells in the actual experiment and have been reported to be highly accurate –3. Many networks  have alsnetworks –8. Usingnic acid , lactic nic acid , lycopennic acid , valine nic acid , vanillinic acid , and 1,4nic acid . In addinic acid –17. Howeer cells . Moreoveculation . Thus, iIn the present study, we developed a tool with which metabolic reactions that do not belong to a host microorganism can be automatically added to a GSM of that host and simulations can be run. With this tool, individual candidate reactions can be selected from the metabolic reactions in the Kyoto Encyclopedia of Genes and Genomes (KEGG) to construct a computerized metabolic model of a hybrid cell to prepare a new metabolic design with FBA. This tool has been named the Hybrid Metabolic Pathway design tool (HyMeP).Synechosystis sp. 6803 (SyHyMeP) and maximizing the theoretical yield of succinic acid production during glycogen metabolism. Synechosystis sp. 6803, which is a model cyanobacterial microorganism, is able to use carbon dioxide as a carbon source during photosynthesis and store glycogen. The complete genome was read in 1996 [http://www.energy.gov/), and, more importantly, it is a compound that is produced from non-fossil raw materials.Here, we propose an example of a metabolic design for constructing a HyMeP model for  in 1996 , and man in 1996 –27. Rese in 1996 –32, and  in 1996 . Major aSynechosystis sp. 6803 (SyHyMeP).Design of metabolic pathway for succinic acid production by extended GSM for Synechosystis sp. 6803 GSM (SyGSM) developed by Nogales et al. [Synechosystis sp. 6803.In the present study, we used the s et al. . MetabolR00479: Isocitrate → Succinate + GlyoxylateE. coli [C. glutamicum [E. coli and similar organisms has not been confirmed in Synechosystis sp. 6803. In fact, the reaction fumarate → succinate has not even been introduced in Synechosystis sp. 6803 [2 necessarily needs to be discharged. Introducing isocitrate lyase allows carbon to be consumed more sparingly, leading to succinic acid production, and is regarded as a preferred choice in the SyHyMeP as well. Synechosystis sp. 6803 does not have a complete TCA cycle, and according to the SyGSM, succinic acid needs to be generated from isocitrate by a GABA-mediated reaction. Introducing isocitrate lyase is therefore regarded as effective because succinic acid can be produced by skipping this relatively long pathway. Another compound that is produced along with isocitrate lyase, that is, glyoxylate, is preferably returned to the glycolytic system by three reactions carried out by Synechosystis sp. 6803 -Dihydroorotate + Fumarate → Orotate + SuccinateE. coli and other organisms. However, this may actually not be practical, because it requires that hydrogen peroxide, which is toxic to the cell, be generated within the cell.The SyGSM includes a reaction where orotate and hydrogen peroxide are combined as (S)-dihydroorotate; therefore, functionalizing both reactions would yield a reaction similar to that catalyzed by fumarate reductases of Synechosystis sp. 6803 besides the three reactions mentioned above, and thus, this design for succinate production is not thought to be realistic  and enables new metabolic designs. Thus, new metabolic designs pertaining to succinic acid production during glycogen metabolism in Synechosystis sp. 6803 have become possible. The optimal combination of metabolic reactions that could increase the yield of succinic acid production was when isocitrate lyase, represented by KEGG reaction number R00479, was introduced; in this case, three reactions were highly activated via intracellular glyceric acid. The theoretical yield for succinic acid at this time was 133. The HyMeP model proposed here was developed for Synechosystis sp. 6803, but the concept of construction of this model requires only replacing the GSM of host microbial cells, and thus can be applied to various microorganisms for developing metabolic designs to produce useful compounds. In other words, it is now possible to enable new metabolic designs that could not be designed with GSMs previously constructed for the metabolic reactions of individual microbial cells.In the present study, we designed the SyHyMeP, which automatically adds other metabolic reactions from the KEGG to the metabolic reaction model of Synechosystis sp. 6803 GSM (SyGSM) developed by Nogales et al. [2 from photosynthesis into the cells were set as 0, respectively. SyHyMeP was constructed by using the following procedure: Reactions included in the SyGSM were extracted from the metabolic reaction list provided by the KEGG (http://www.genome.jp/kegg/), and then the other reactions were set as a exSy_list. Inorganic compounds such as H2O and ATP and metabolites such as co-factors were excluded . FBA was performed with our original command line tool using OptFlux libraries, which use GLPK (GNU Linear Programming Kit) as a linear programming solver [For metabolic simulation, cytosolic glycogen was used as the sole carbon source, and the uptake rate was set to 100. Other external metabolites such as NHg solver .


Gluconacetobacter has been extensively characterized and is a model system for cellulose biosynthesis [Gluconacetobacter hansenii ATCC 23769 (GenBank number: CM000920 and taxonomy ID: 714995), has been completed and can be used to understand how this bacteria is able to produce cellulose. Bacterial cellulose has been used in the medical field as wound dressing and artificial skin material. Computational tools for predicting fluxes in biochemical networks are applied in the fields of integrated systems biology, bioinformatics, and genomics.Reconstruction and applications of genome scale metabolic models have truly influenced the field of systems biology ,2. Theseynthesis . Using hG. hansenii were used as the input for the Pathway Tools software, which can mapping genes to reactions in an automated manner. Moreover, a resource called Model SEED was used by creating a database of the organism. Then, to correct any mistakes and improve the reconstruction, the manual curation must be done using data from many different sources. An essential step is the addition of reactions which are not inferred from genome annotation and will decrease the number of dead-ends. The metabolic network file was loaded into MATLAB® using functions available in the COBRA toolbox. Moreover, a set of computational systems biology tools, written by our group called GEnSys (Genomic Engineering System), was applied to the network. The GEnSys comprises several modules that allow analysis and simulation of biochemical reaction networks, such as FBA  and MFA .The reconstruction process involves the following steps: (1) creation of a draft model; (2) manual curation; (3) conversion into a mathematical format; (4) identification and filling of gaps; and (5) simulation and visualization. The annotated data of the genome sequence of G. hansenii. Using the model in conjunction with constraint-based methods, we simulated the metabolic fluxes induced by three different environmental conditions to understand the effects of different carbons sources: glucose, glycerol and mannitol on cellulose production. We decided to maximize cellulose to evaluate the results. Also the maximum yield can be calculated for each carbon source. We summarized the biochemistry of each reaction in the G. hansenii model and we focused in the central pathways and cellulose biosynthesis to choose the reactions and metabolites in the core model. The core is a small scale model that can be used for testing and evaluating new constraint-based analysis methods, but still can be updated. This simplified model is representative and elevated our capability for understanding and predicting the cellular behavior of G. hansenii under any perturbations.In this work, we present an initial draft of genome-scale metabolic reconstruction and network analysis of


Seriola lalandi) by integrating the energetic cost of free‐ranging activity into a bioenergetics model. Accelerometry transmitters were used in conjunction with laboratory respirometry trials to estimate kingfish active metabolic rate in the wild. These field‐derived consumption rate estimates were compared with those estimated by two traditional bioenergetics methods. The first method derived routine swimming speed from fish morphology as an index of activity (a “morphometric” method), and the second considered activity as a fixed proportion of standard metabolic rate . The mean consumption rate for free‐ranging kingfish measured by accelerometry was 152 J·g−1·day−1, which lay between the estimates from the morphometric method (μ = 134 J·g−1·day−1) and the physiological method (μ = 181 J·g−1·day−1). Incorporating field‐derived activity values resulted in the smallest variance in log‐normally distributed consumption rates (σ = 0.31), compared with the morphometric (σ = 0.57) and physiological (σ = 0.78) methods. Incorporating field‐derived activity into bioenergetics models probably provided more realistic estimates of consumption rate compared with the traditional methods, which may further our understanding of trophic interactions that underpin ecosystem‐based fisheries management. The general methods used to estimate active metabolic rates of free‐ranging fish could be extended to examine ecological energetics and trophic interactions across aquatic and terrestrial ecosystems.Consumption is the basis of metabolic and trophic ecology and is used to assess an animal's trophic impact. The contribution of activity to an animal's energy budget is an important parameter when estimating consumption, yet activity is usually measured in captive animals. Developments in telemetry have allowed the energetic costs of activity to be measured for wild animals; however, wild activity is seldom incorporated into estimates of consumption rates. We calculated the consumption rate of a free‐ranging marine predator (yellowtail kingfish,  Assessing an organism's ecological requirements and constraints is central to predicting species distributions , as a study species. Little is known about the trophic ecology of kingfish, and consumption rate estimates will be useful for determining the trophic level of kingfish and associated trophic interactions. The field‐derived activity method was compared with two traditional bioenergetics methods to evaluate the contribution of field‐derived activity to consumption rate estimates.This study describes how measured activity rates in free‐ranging animals can be incorporated into bioenergetics models for estimating consumption rate. The method used laboratory calibrations and field activity data to estimate field metabolic rate, and then incorporated this into a bioenergetics model to estimate consumption rate. This method is presented using a marine pelagic predator, yellowtail kingfish −2) was determined by calculating the root mean square of triaxial acceleration (5 Hz) measured over a 20‐sec period. This calculation occurred onboard the tag with a single activity value acoustically transmitted within a random period of 50–100 sec .Estimating field metabolic rates required two steps, the first involved laboratory experiments to determine active metabolic rate, and the second step required sampling activity data from wild kingfish. Laboratory experiments were conducted to describe the relationship between activity (dynamic body acceleration), swimming speed, and metabolic rate. These experiments were necessary to measure active metabolic rate, and involved measuring the oxygen consumption rate of wild caught kingfish implanted with activity tags. Seven juvenile kingfish  were used in the calibration and all were captured at South Solitary Island, Australia . Fish were held in a flow‐through aquarium system at the National Marine Science Centre, Southern Cross University, Australia, maintained at 24 ± 1°C, and fed on a diet of fresh and frozen cephalopod and teleost food. Fish were internally tagged with an acoustic transmitter that measures activity  using standard surgical techniques  for 15 min at each speed. The respirometer was completely sealed from any sources of atmospheric air and dissolved oxygen concentrations were measured using a Hach oxygen meter . Oxygen consumption rate during each swimming trial was measured as a metric of metabolic rate. After each swimming trial, fresh seawater was flushed through the respirometer to return oxygen levels to ambient concentrations. If dissolved oxygen levels in the respirometer fell below 80% saturation during a swimming trial, the trial was paused and the respirometer flushed with fresh seawater. An acoustic hydrophone  was used to record the acoustic transmissions of activity data during each swimming trial. Fish were returned to the aquaria once swimming trials were completed.Fish were allowed to recover from surgery for a minimum of 5 days and were fasted for 12 h before being introduced to a Brett‐type swimming respirometer Brett  at 24 ± ” package  was expressed as a function of activity according to . An exponential form for equation e‐transforming MRA and using a linear mixed‐effects model of the form (eq. IDrand) was included as a random factor to account for correlation in measurements within individuals. Analysis of the laboratory trials also expressed mass‐specific oxygen consumption (MRS) as a function of swimming speed according to . Equation e‐transforming SMR and using a linear mixed‐effects model of the form MRA=sform eq. :(2)log(Mg to eq. :(3)MRS=rform eq. :(4)log(Mn = 7) after they were released at their site of capture, South Solitary Island. South Solitary Island had three established acoustic receivers, which were used to record the movements and activity of these seven kingfish from March to May 2013. Prior to release, these fish were given at least 14 days to recover from surgery to reduce any effects of tagging on fish behaviour. After release, the first 24 h of field data was not included in the analysis to reduce any potential behavioral bias associated with reacclimating to the natural environment. Hourly bottom temperature (mean 21 m depth) was recorded by temperature loggers attached to each acoustic receiver mooring. These temperatures were used to estimate the environmental temperature of kingfish during the monitoring period. Any acoustic transmissions recorded in temperatures outside the temperature range of the laboratory calibrations (24 ± 1°C) were excluded to avoid any uncertainty associated with the temperature dependence of the activity–metabolism relationship , AMR is the active metabolic rate (J·g−1·day−1), and G the energy allocated to fish growth  was calculated by converting field activity values to metabolic rate using the relationship derived from laboratory calibrations  and night periods . The mean hourly activity value within each period was converted to metabolic rate, based on equation s is the intercept, b the exponent of the derived relationship between metabolic rate and activity (eq. hd is the number of hours in the day period (0700–1800 h), hn is the number of hours in the night period (1900–0600 h), and Oxy is the oxy caloric coefficient of 14.14 J·mgO2−1 ions eq. . Field avity eq. ; Table 2G; J·g−1·day−1) was determined by , and Fj is the energy density of somatic tissue   was used due to similarities in ecology and trophic levels G=, Int is the intercept of the regression, Lc is a coefficient, SL is standard length (cm), Ac is a coefficient, and AR is aspect ratio of the caudal fin  using ImageJ software  of the seven experimental kingfish was used in equation 2 kg−1·h−1) using the relationship derived from laboratory calibrations in Table . AR is tMRS; eq. . This vaR; gO2 g−1·day−1) is  is the wet weight of the predator, Temp is a temperature dependence function (see below), and AM is an activity multiplier that scales standard metabolic rate to active metabolic rate  of the seven experimental kingfish was used in equation AM) was set at 2 to estimate the active metabolic rate of wild fish . In this study, T was the mean temperature from the sampling period at which acoustic transmissions were recorded. Within this sampling period, only temperatures within the boundary of the laboratory calibrations  is eq. :(9)R=RaWJohnston . The mea Winberg . The val Winberg , and is d as eq. :(10)TempA sensitivity analysis was undertaken to determine the relative effect of each parameter on consumption rate estimates and included all parameters in each of the three models . In this analysis, Monte Carlo simulations were used to select unique parameter values for each model run, where parameter values were randomly varied to be either the mean value or the mean value ±10%. Simulations were continued until the variance in consumption rate estimates stabilized . The random parameter values and model outputs were then standardized following Kleijnen  to allowThe variance, or uncertainty, of parameter values was incorporated into final consumption rate estimates for each of the three models using Monte Carlo simulations in MATLAB  with swimming speed  and log(r) had the greatest influence on consumption rates, respectively  and log(r)] are intercepts of the exponential equations to calculate metabolic rate from activity  had the greatest influence  and assimilation (A) were the only parameters in each model that were negatively related to consumption rates  and energetic density (Fj), and this was consistent across all three models.Sensitivity analyses identified a single parameter in each of the three models that had a dominant influence on consumption rate Fig. . For theely Fig. A, B. Thence Fig. C. Weighttes Fig. . The parμ = 181 J·g−1·day−1), followed by the accelerometry model (μ = 152 J·g−1·day−1) and then the morphometric model , compared with the morphometric (σ = 0.57) and physiological models  greater than the morphometric estimate (M = 119 J·g−1·day−1) and smaller than the physiological estimate (M = 178 J·g−1·day−1).Consumption rate estimates for kingfish were similar between all three models, with the physiological model having the highest estimate , log(r)]. This occurred despite the morphometric model including a large source of uncertainty from the multispecies empirical regression (eq. s) and log(r) parameters in the accelerometer and morphometric models indicates the significance of the functions used to derive active metabolic rate from activity (eq. s) and log(r) are the random intercepts that included real between‐individual variation in the laboratory calibrations. The between‐individual variation could have been examined by using whole‐animal metabolic rates instead of mass‐specific metabolic rates, which ultimately would have decreased the error of field metabolic rate estimates. However, insufficient field data for the experimental kingfish prevented the use of whole‐animal metabolic rates being used in consumption rate estimates.The distribution of estimated consumption rates in the accelerometry method had the smallest variance despite this method incorporating the variation of wild activity. This is surprising, given the real variation within and between wild individuals that was incorporated into the accelerometry method, and indicates the level of uncertainty inherent in the other methods. The sensitivity analyses revealed that the parameters associated with estimating metabolic rate had the largest influence on consumption rate estimates. For the accelerometry and morphometric models, the most influential parameters were the intercept of the linear models derived from the laboratory calibrations [log(sion eq. . The impvity eq.  and swimvity eq. . Log(s) Act) and metabolic rate (AMR) was best described by an exponential equation, as determined from AICc. The exponential form was surprising, given that a majority of studies have found a linear , a result that is biologically impossible. As the activity and AMR relationship (eq. dayAct) and night (nightAct) was within range of the activity values recorded in the laboratory calibrations. This ensured that the choice of the exponential form of equation The laboratory calibration that derived the relationship between activity (ship eq.  was beinQ10) had the greatest influence on consumption rate estimates in the physiology method. Temperature greatly influences metabolism and activity of animals, yet any scaling relationship between temperature and active metabolic rates remains unclear  and a comparable piscivorous predator, Arripis trutta (102 J·g−1·day−1; Hughes et al. K. pelamis (465 J·g−1·day−1; Essington A reliable understanding of the trophic demand of predators is needed for ecosystem‐based management. Within the framework of ecosystem‐based fisheries management, innovative methods are required to gain comprehensive information about trophic interactions. For example, the consumption rate estimates reported here have implications for the modeling of energy flow through ecosystems and provide a useful estimate for understanding kingfish production. Kingfish populations are exhibiting a poleward range shift (Robinson et al. None declared.


Acetogenic metabolism is considered one of the earliest modes of bacterial metabolism. A thorough understanding of various factors governing the metabolism, in particular energy conservation mechanisms, is critical for metabolic engineering of acetogens for targeted production of desired chemicals.The metabolic capabilities of acetogens to ferment a wide range of sugars, to grow autotrophically on HClostridium ljungdahlii, the first such model for an acetogen. This genome-scale model (iHN637) consisting of 637 genes, 785 reactions, and 698 metabolites captures all the major central metabolic and biosynthetic pathways, in particular pathways involved in carbon fixation and energy conservation. A combination of metabolic modeling, with physiological and transcriptomic data provided insights into autotrophic metabolism as well as aided the characterization of a nitrate reduction pathway in C. ljungdahlii. Analysis of the iHN637 metabolic model revealed that flavin based electron bifurcation played a key role in energy conservation during autotrophic growth and helped identify genes for some of the critical steps in this mechanism.Here, we present the genome-scale metabolic network of C. ljungdahlii to genetic perturbations under various growth conditions. Thus, the model will be instrumental in guiding metabolic engineering of C. ljungdahlii for the industrial production of biocommodities and biofuels.iHN637 represents a predictive model that recapitulates experimental data, and provides valuable insights into the metabolic response of  Their ability for autptrophy allows them also to grow on synthesis gas (H2/CO/CO2) by utilizing either H2/CO2 or CO alone. More recently, acetogens like Sporomusa ovata and Clostridium ljungdahlii have been shown to be capable of another form of autotrophic metabolism, called microbial electrosynthesis[Acetogenic microorganisms have unique metabolic capabilities that, if understood, could be harnessed to greatly increase strain engineering design options for microbial production of biofuels and biocommodities. Acetogens were discovered for their ability to autotrophically reduce CO pathway. In addiynthesis. These dynthesis.However, to efficiently engineer acetogens into platform strains and production hosts for chemicals at an industrial scale, a thorough understanding of the metabolic capabilities and aspects of energy conservation is a necessary prerequisite. The Wood-Ljungdahl pathway of carbon fixation employed by acetogens is believed to be one of the most ancient metabolic pathways. PhysiolConstraints based reconstruction and analysis (COBRA) has been a powerful technique for discovering and understanding new capabilities and content in microorganisms, as well as in guiding metabolic engineering efforts for targeted production. The COBClostridium ljungdahlii. We characterized the metabolic phenotypes of this bacterium under heterotrophic and autotrophic growth conditions. We further utilized physiological and transcriptomic data to elucidate novel biological capabilities and aspects of energy conservation during autotrophic metabolism of C. ljungdahlii.In this study, we reconstructed the first genome-scale metabolic network of an acetogen, C. ljungdahlii was reconstructed using a four-step integrative reconciliatory workflow involving four published models of related clostridia species and two draft models [C. ljungdahlii homologs in the other clostridia genomes. The reactions corresponding to these genes in the respective clostridia models were compiled and reconciled with the two draft models. The list of discrepancies pertaining to nomenclature between the different databases and gene-reaction associations was manually curated with the aid of biochemical literature and databases such as KEGG[The genome-scale metabolic network for  Figure . The firnotation using thnotation. In addirenckii)-17 using as KEGG and SEED as KEGG. Manual  as KEGG,20, whic2 and CO2 as well as just CO alone was feasible using the iHN637 reconstruction. The predicted growth rates and acetate production rates for each of these various substrates are provided in Table -1) was in good agreement with the experimentally measured growth rates (0.072 h-1). The simulated acetate production rate (2.7 mmol/gDWh) was also consistent with the measured value of 2.85 mmol/gDWh . iHN637 was successfully able to simulate heterotrophic growth on several of the known substrates  when nitrate was provided in ammonium-free medium. Specifically, the genes encoding for nitrate reductase, nitrite reductase, and the nitrate transporter were upregulated greater than 400-fold  activity and the subsequent formation of acetyl CoA through the acetyl-CoA synthase (ACS). It has been suggested that the CODH/ACS complex functions in a manner that CO resulting from CODH activity is kept as a bound metabolite in the complex to diminish thermodynamic barriers involved in this energy intensive process[C. ljungdahlii suggested that CO oxidation to CO2 is likely to be catalyzed by a different carbon monoxide dehydrogenase gene (CLJU c09090-09110) other than the ones encoded by the CODH/ACS complex. Taking these into consideration, the iHN637 reconstruction incorporates the CODH/ACS reaction as the net reaction of carbon monoxide dehydrogenase and acetyl CoA synthase activity, and associates the gene cluster CLJU c09090-09110 to the reaction representing CO oxidation to CO2. The methylenetetrahydrofolate dehydrogenase reaction catalyzed by the bifunctional FolCD (CLJU_c37630) was assumed to be NADPH-dependent based on sequence similarity with the corresponding enzyme in the acetogen Moorella thermoacetica[The fixation. Accordin branch. The key process. Furthermoacetica,27. The M. thermoacetica) and those that do not. Organisms such as Acetobacterium woodii have been shown to employ a sodium gradient as an energy conservation mechanism[C. ljungdahlii genome sequence has revealed that it falls into a third class of acetogens that neither uses respiratory cytochromes nor a sodium gradient for energy conservation[C. ljungdahlii reveals that electron bifurcation and proton translocating ferredoxin oxidation are critical mechanisms for energy conservation during autotrophic growth in C. ljungdahlii  was previously annotated as glutamate synthase. Another recent report describes a similar electron-bifurcating NADPH transhydrogenase activity in C. autoethanogenum and further indicates the presence of a homolog in C. ljungdahlii[An electron-bifurcating transhydrogenase (Nfn complex) that couples exergonic reduction of NADP with ferredoxin to drive the endergonic reduction of NADP with NADH had been characterized in  kluyveri. Recentlmoacetica. A homolungdahlii. As partne CLJU_c7240 was A. woodii genome revealed that the small subunit of the methylene-tetrahydrofolate reductase (MetV) can act as a flavoprotein that could aid in this proposed electron bifurcation, thereby indirectly establishing a proton gradient through the Rnf complex[A. woodii was identified next to the MetF gene in C. ljungdahlii and investigation of the intergenic spacing in the genome revealed a possible organization of MetV and MetF in the same operon (CLJU c37610 and CLJU c37620). Hence, an electron bifurcating methylene-tetrahydrofolate reductase reaction was included in the iHN637 reconstruction   gene. The cooS1 gene in Carboxydothermus hydrogenoformans is hypothesized to play a role in facilitating electron transfer through the hydrogenase[C. ljungdahlii has a similar role while growing on hydrogen. Importantly, transcriptome profiling during autotrophic growth revealed that the gene annotated as metV was co-transcribed along with metF, further validating the annotation and assignment of its function for electron bifurcation with metF . This is probably due to the fact that the Wood-Ljungdahl pathway is employed for fixation of CO2 using electrons obtained from fermenting sugars[C. ljungdahlii showed upregulation of the genes encoding the Wood-Ljungdahl pathway under autotrophic growth (4:1 CO:CO2)[2/H2 and the other being a condition rich in CO.Transcriptome profiling of rogenase. Hence i CO:CO2). This diC. ljungdahlii has revealed that flavin-based electron bifurcation is found to play a critical role in the essential reactions for autotrophic growth, thereby providing an explicit account of the requirement of reducing equivalents for the fixation of CO2 to acetyl CoA , which couples the exergonic reduction of NADH from H2 to drive the endergonic reduction of ferredoxin from H2 has been identified to perform this process in A. woodii[C. ljungdahlii  has both the NAD-specific and NADP-specific electron bifurcating hydrogenases associated to this gene cluster, with the NADP-specific one being set as the default.The genome-scale model of  Figure A. AnotheA. woodii,34. A houngdahlii. This reackA) was modeled under heterotrophic growth on fructose and autotrophic growth under the major constituents of syngas   under two different autotrophic growth conditions  that reflect the composition of syngas.When ethanol is the desired product from carbon fixation through the Wood-Ljungdahl pathway, 2 reducing equivalents in the form of NADH are required in addition to the 4 reducing equivalents  and 1 ATP  and the cofactor specificity of the bifurcating hydrogenase. When CO is the sole electron donor, all 6 required reducing equivalents are obtained solely in the form of low-potential reduced ferredoxin. Hence, flux is driven through the Rnf complex to get the necessary NADH for the Wood-Ljungdahl pathway and ethanol formation. Since the Rnf complex couples proton translocation with the oxidation of ferredoxin, this results in the formation of the required ATP to fix CO2 using the Wood-Ljungdahl pathway  to ensure that the reactions in the network were all elementally and charge balanced.The genome-scale metabolic network for database. This drbutylicum,15, C. trmocellum, and C. jerenckii) using tC. ljungdahlii was formulated using a previous template[B. subtilis and C. beijerenckii, was used[S. aureus was used due to similarity in terms of low G + C content[The Biomass Objective Functions for template. The prowas used,37. Howe content. It shou content.In silico simulations of gene knockout was carried out using the "singleGeneDeletion" function of the COBRA toolbox[The reconstructed metabolic network was represented in a mathematical format in a stoichiometric matrix S, where the rows correspond to the metabolites and columns correspond to the reactions in the network. Flux Balance Analysis simulations were carried out as described previously using th toolbox. The metClostridium ljungdahlii (ATCC 55383) was grown in 125 mL serum bottles under anaerobic conditions containing 100 mL of PETC medium (ATCC medium 1754) at 37°C. For growth experiments with nitrate, 1 mL of an anoxic NaNO3 stock solution (1 M) was added to the medium. Ammonium was omitted in some of the experiments from the medium containing nitrate. Growth was routinely determined by measurement of the OD600. Hydrogen and other gases in the cultures were quantified using gas chromatography as previously described[escribed. Concentescribed. Detectiescribed. The sumescribed. The proC. ljungdahlii was profiled under three different growth conditions: heterotrophically on fructose, heterotrophically on fructose with nitrate as the sole nitrogen source, and autotrophically on H2/CO2. For each of these conditions, total RNA was isolated from C. ljungdahlii cells growing in mid-log phase (OD600 of ~0.4 for both the heterotrophic conditions and an OD600 of ~0.09 for the autotrophic condition on H2/CO2) using the QIAGEN RNeasy Mini kit with on-column DNase I (QIAGEN) treatment. rRNA was subtracted from 2.5 μg of total RNA using the Gram-Positive Ribo-Zero rRNA removal kit (Epicentre). Then, paired-end, strand specific RNA sequencing (RNA-seq) was performed using the dUTP method[The transcriptome of P method,47 with C. ljungdahlii (RefSeq: NC_014328.) using Bowtie[The RNA-seq reads were aligned to the genome sequence of g Bowtie with twog Bowtie with appThe authors declare that they have no competing interest.HN, DRL, and KZ conceived and designed the study. HN, JN, and AE performed the reconstruction. MS and HL performed the experiments. HN carried out the simulations and analysis. HN and KZ wrote the manuscript. All authors have read and approved the manuscript.C. ljungdahlii grown on fructose. Shown are OD600, fructose, and acetate measurements. Error bars represent average of triplicate measurements. Physiological growth screen of Click here for fileC.ljungdahlii is simulated with and without nitrate grown on fructose.Flux distribution differences when Click here for fileC. ljungdahlii grown on fructose and autotrophically on H2/CO2.Differential expression of Click here for fileC. ljungdahlii during autotrophic growth on H2/CO2 showing cotranscription of MetF and MetV.RNA-seq reads from transcriptome profiling of Click here for fileModel 1. Metabolic network of C. ljungdahlii. The model file is preset with constraints to simulate heterotrophic growth on fructose. This file can be used with COBRA toolbox in MATLAB.Click here for fileModel 2. Metabolic network of C. ljungdahlii. The model file is preset with constraints to simulate autotrophic growth on H2/CO2. This file can be used with COBRA toolbox in MATLAB.Click here for file


In metabolic engineering, modification of metabolic networks is an important biotechnology and a challenging computational task. In the metabolic network modification, we should modify metabolic networks by newly adding enzymes or/and knocking-out genes to maximize the biomass production with minimum side-effect. In this mini-review, we briefly review constraint-based formalizations for Minimum Reaction Cut (MRC) problem where the minimum set of reactions is deleted so that the target compound becomes non-producible from the view point of the flux balance analysis (FBA), elementary mode (EM), and Boolean models. Minimum Reaction Insertion (MRI) problem where the minimum set of reactions is added so that the target compound newly becomes producible is also explained with a similar formalization approach. The relation between the accuracy of the models and the risk of overfitting is also discussed. Although much knowledge about metabolic networks is available in public databases and references, we often have to modify metabolic networks in various situations. For example, in metabolic engineering, we should modify metabolic networks by newly adding enzymes or/and knocking-out genes to maximize the biomass production with minimum side-effect. The former and latter correspond to adding and deleting chemical reactions, respectively, in a metabolic network. For another example, when we reconstruct a genome-scale metabolic network from a newly determined DNA sequence, the reconstructed metabolic network may need some modification to be consistent with the existing knowledge. Thus, in metabolic network modification, we often add or/and delete reactions so that specified constraints are satisfied.Minimum Reaction Cut (MRC) problem: delete the minimum set of reactions so that the target compound becomes non-producible, and (ii) Minimum Reaction Insertion (MRI) problem: add the minimum set of reactions so that the target compound newly becomes producible. It should be noted that, for most cases, a target compound can be replaced by a set of target compounds in a straight-forward manner. In order to solve these problems, three mathematical models have been utilized: flux balance analysis (FBA) model, elementary mode (EM) model, and Boolean model. In this mini-review, we explain these three models in the context of MRC, and briefly review MRI.Although there may exist various modification problems, we focus on the following two major problems in this mini-review: (i) c1,…,c13} is a set of compounds, and {r1,…,r5} is a set of reactions. For example, reaction r1 has the substrates (reactants) {c1, c2}, and products {c6, c7}. If either indegree (the number of input nodes) or outdegree (the number of output nodes) of a compound node is 0, it is called an external node. {c1, c2, c3, c4, c5, c6, c9, c10, c13} is a set of external nodes in source nodes and sink nodes. Compound nodes with indegree 0 are called source nodes and are assumed to be supplied by the external environment. {c1, c2, c3, c4, c5} are source nodes. On the other hand, compound nodes with outdegree 0 are called sink nodes. {c6, c9, c10, c13} are sink nodes. Target nodes are chosen from sink nodes. In c9} is chosen as a target node.Before explaining details of each model, we briefly explain MRC. Suppose that a metabolic network of r2, r3} because c9 is produced only from r2 or r2. However, in the EM and FBA models, if there is a chemical reaction “A + B → C + D”, C and D should also exist for the reaction to take place, in addition to A and B, because steady states are assumed (see latter sections for details of EM and FBA models). Therefore, deletion of any single reaction is the solution of MRC in the FBA and EM models since all reactions must take place at a time if some reaction takes place.For example, in MRC, the solution in the Boolean model is deleting {2Flux balance analysis (FBA) is a constraint-based mathematical framework using the stoichiometry of a given metabolic network. In many cases, FBA is used to optimize a biologically relevant objective function to identify optimal flux distributions For MRC and MRI in the FBA model, in addition to the objective function in the standard FBA, the number of added or deleted reactions should also be taken into account. Furthermore, we may need to consider two objectives: cellular objective and bioengineering objective.In order to identify gene knockout strategies for microbial strain optimization under such a complex situation, a bilevel programming framework was introduced in targetv denote the flux of the reaction that produces the target compound. Our purpose is to find the minimum number of reactions deletion of which always makes targetv = 0. Then, MRC in the FBA model can be formalized as follows by starting with K = 0, and increment K by 1 until targetv = 0 is obtained, where K is the upper limit of the number of deleted reactions.js is a 0–1 variable, ijs is a stoichiometry matrix for the ith compound and jth reaction, jv  is a flux vector, I is a set of compounds, J is a set of reactions, and jLB and jUB are the lower and upper bounds of jv , respectively. js represents whether jth reaction is knocked-out, where js = 0 indicates that jth reaction is knocked-out since jv is forced to be 0.Here, we consider MRC under the bilevel programming framework. Let In the above, we used the same function (but with different signs) as the objective functions in outer and inner optimization problems. However, there are various versions of the problem setting based on objective functions for the inner problem and the outer problem.For example, the minimization of metabolic adjustment method (MOMA) minimizes the difference between the wild and the knocked-out flows 3Aex, Bex, Cex, Dex} is a set of external compounds. In this network, there are 5 EMs, which are shown in An elementary mode (EM) represents a feasible and balanced (steady-state) flux distribution of the network The most standard version of MRC in the EM model is formalized as a minimal cut set (MCS) problem by exE in the metabolic network of b4, which can be represented as:x ∧ y denotes the logical “AND” of x and y . The Boolean constraints in the above are converted into the following linear inequalities.Once EMs are given, MRC in the EM model (MCS) can be formalized by Integer Linear Programming (ILP) 4In the Boolean model, all reaction and compound nodes are assigned either 0 or 1. If 1 is assigned, it means that the compound is producible, or the reaction can take place. On the other hand, if 0 is assigned, it means that the compound is not producible or the reaction cannot take place.r1 represents a chemical reaction “c1 + c2 → c6 + c7”. In the Boolean model, for r1 to take place, both c1 and c2 are necessary. Therefore, the condition of r1 is represented by r1 = c1 ∧ c2. Similarly, c9 is producible if either r2 or r3 takes place. Therefore, the condition of c9 is represented by c9 = r2 ∨ r3.Moreover, reaction and compound nodes are represented by logical “AND” and “OR” functions, respectively. For example, in For MRC in the Boolean model, the Boolean reaction cut (BRC) problem has one of the most standard problem settings. In BRC, the number of deleted reactions is minimized to make the target compounds non-producible, and an ILP-based method for solving it was developed in Another standard problem setting is to minimize the side effect instead of the number of deleted reactions. The Optimal enzyme drug target identification algorithm based on metabolic networks (OPMET) was developed in As MRC in the FBA model can be formalized by the bilevel programming with the inner and outer problems, MRC in the Boolean model also has such two layers of problems. Because each set of deleted reactions can have multiple 0/1 assignments which satisfies all Boolean constrains, some objective function should be optimized in the inner problem even in the Boolean model. This is necessary especially for properly accounting for the effect of directed cycles in metabolic networks. For this purpose, N1, but are producible in N2.In the above problem settings, the main desired effects and side non-desired effects are considered in a single metabolic network. A reasonable extension is to consider them in multiple networks. In ILP, every constraint must be represented by linear equations or inequalities. Boolean constraints can be transformed into linear equations or inequalities as follows.y = x1 ∧ x2 ∧ ⋯ ∧ xk can be converted into LP1 y = x1 ∨ x2 ∨ ⋯ ∨ xk can be converted into Similarly, as the Boolean “OR” relation LP2 Similarly, the Boolean “OR” can be represented by the following linear inequalities:O((m + n)2), where m and n are the numbers of compounds and reactions, respectively. Because, the computational time for solving ILP is often exponential for the number of variables, the naive method cannot be applied for large scale networks.To calculate the MaxVA, using the notion of time is convenient in the ILP formalization O(f(m + n + f)), where f is the size of the FVS.To handle this problem, The problems formalized by ILP can also be solved by SAT-based methods since both are NP-complete problems, where SAT denotes the Boolean satisfiability problem. MRC may also be represented as an abduction problem if it is formalized by a logic programming-based method. Meta-level abduction is a method of abducting missing rules to account for observations. 5MRC problems are for finding reaction deletion strategies to satisfy given constrains. Different from MRC, the minimum reaction insertion (MRI) problems are for finding reaction addition strategies to satisfy constraints.r1} belongs to the host network, whereas none of {r2, r3,r4,r5} belongs to the host network. Suppose that {c1, c2, c3, c4, c5} is a set of source nodes, {c6, c9, c10, c13} is a set of sink nodes, and c10 is a target node. In the Boolean model, adding {r2, r4} is the solution, whereas adding {r2, r3,r4,r5} is the solution in the FBA model.In the given network of MRI, reactions are classified into the currently available part and the currently non-available part. We call the former and latter a host network and a reference network, respectively. In When a metabolic network is newly reconstructed from a DNA sequence, a host network is often constructed according to the ortholog information of DNAs. However, this network often has gaps, and some of necessary compounds are not producible in this initial model. In such a case, gaps are often found and filled by FBA-based simulations. GapFind identifies non-producible metabolites based on the initial FBA model, and GapFill fills these gaps by the minimum set of additional reactions Cell growth rate and gene essentiality are also utilized for the modification of metabolic networks. GrowMatch identifies the gaps based on the inconsistencies of cell growth rates between the simulation results on the model and the biological experiment results 66.1In this article, we have briefly reviewed studies on MRC and MRI problems in the FBA, EM and Boolean-based models. The FBA and EM models can be classified into flow-based models. The flow-based models can realize more detailed simulation, because they account for the chemical reaction coefficients, the upper and lower bounds of each flux, and the steady state. Therefore, if the purpose of the research is to construct an exact model which meets the data obtained in biological experiments, the flow-based models are better than the Boolean model.However, at the same time, this high performance of the flow models includes the risk of the overfitting. Because knowledge and data about metabolic networks are not yet perfect, an exact model may be useful only for the data used to reconstruct the model. Although the Boolean model is less detailed than the flow-based models, it is considered to be more robust from this point of view.r5 is one of the optimal solution of the flow models. However, if there is an unknown reaction r6 whose substrates are c8 and c12 and products are c10 and c13, then c9 is still producible even if r5 is deleted. This shows that the flow-based models are less robust for the lack of information in the downstream of a flux. On the other hand, the optimal solution of the Boolean model is to delete {r2, r3}. Even if there is the hidden reaction r6, deleting {r2, r3} is still the optimal solution in the Boolean model. Thus, the Boolean model is more robust for the lack of information in the downstream of a flux, and there is a tradeoff between the accuracy of the model and the risk of the overfitting.For example, in MRC of In the flow models, if free variables are introduced or inequalities for the stoichiometric constraint are allowed for internal nodes, the flow model may become more robust for the incorrectness of the distant nodes. However, in such a case, there may be a risk that constraints are not appropriately propagated.The main difference between the FBA model and EM model is as follows. The basic version of the FBA model requires an objective function, and is formalized as a linear program. On the other hand, in the EM model, all EMs are often enumerated and then are utilized in some optimization problem. These suggest that the FBA model needs an objective function on some target flow(s), whereas the EM model  does not. Therefore, it is suggested that the FBA model is suitable if the objective function is well-defined, otherwise the EM model and/or the Boolean model might be more suitable.The basic version of the FBA model is efficiently solvable since the linear programming problem is solvable in polynomial time. However, most optimization problems including MCS are NP-hard. For the EM-based model, since the number of EMs may be exponential to the size of the network, the EM-based methods are not feasible for many optimization problems with large-scale networks. The EM-based methods are useful for analyzing details of the flow-based models. Although the MRC of the Boolean model is also NP-hard, improvements of ILP solvers such as CPLEX lead to the speedup for solving the Boolean MRC.Here, we briefly discuss the scalability of each method based on several reports on computational experiments using real metabolic network data. Related to the FBA-based MRI, the gap-filler method was applied to completion of the metabolic network in the EcoCyc database (version 15.5), which contained 1888 reactions 6.2Many of the constraint-based methods are realized in a software package called COBRA Toolbox, which works on MATLAB Although we separately discussed MRC and MRI in this article, adding and deleting reactions at the same time is a reasonable approach in the metabolic network modification. OptReg identifies reaction activations or inhibitions to suggest up-regulation or down-regulation of genes to overproduce biochemicals Escherichia coli, and can be used for the simulation of cell growth rate for gene knockouts The FBA-based methods are often used in the process of reconstructing genome-scale metabolic networks, and industrial metabolic engineering. For example, iJO1366 is an FBA-based genome-scale metabolic network of For the Boolean model, measures of the impact of knockouts were studied for finding novel drug targets and/or crucial genes for diseases. For example,