Despite the close association between gene expression and metabolism, experimental evidence shows that gene expression levels alone cannot predict metabolic phenotypes, indicating a knowledge gap in our understanding of how these processes are connected. Here, we present a method that integrates transcriptome, fluxome, and metabolome data using kinetic models to create a mechanistic link between gene expression and metabolism.Saccharomyces cerevisiae treated with weak organic acids  and the histidine synthesis inhibitor 3-aminotriazole under steady-state conditions. We found that the transcriptional response led to alterations in yeast metabolism that mimicked measured metabolic fluxes and concentration changes. Further analyses generated mechanistic insights of how S. cerevisiae responds to these stresses. In particular, these results suggest that S. cerevisiae uses different regulation strategies for responding to these insults: regulation of two reactions accounted for most of the tolerance to the four weak organic acids, whereas the response to 3-aminotriazole was distributed among multiple reactions. Moreover, we observed that the magnitude of the gene expression changes was not directly correlated with their effect on the ability of S. cerevisiae to grow under these treatments. In addition, we identified another potential mechanism of action of 3-aminotriazole associated with the depletion of tetrahydrofolate.We developed a modeling framework to construct kinetic models that connect the transcriptional and metabolic responses of a cell to exogenous perturbations. The framework allowed us to avoid extensive experimental characterization, literature mining, and optimization problems by estimating most model parameters directly from fluxome and transcriptome data. We applied the framework to investigate how gene expression changes led to observed phenotypic alterations of Our simulation results show that the modeling framework provided an accurate mechanistic link between gene expression and cellular metabolism. The proposed method allowed us to integrate transcriptome, fluxome, and metabolome data to determine and interpret important features of the physiological response of yeast to stresses. Importantly, given its flexibility and robustness, our approach can be applied to investigate the transcriptional-metabolic response in other cellular systems of medical and industrial relevance. It is well known that cells regulate gene expression to carry out different functions depending on their physiological state and environment. However, it is less well understood how this regulation is orchestrated and how gene expression changes drive cells to adapt particular phenotypes. Developments in high-throughput technologies have contributed to answer these questions by generating a wealth of data on different cellular components and processes . Hence, one of the challenges in systems biology is how to integrate and analyze such data to elucidate the underlying cellular physiology. In particular, the development of genome-scale computational models and analysis tools can help expand our understanding of how gene transcription alters cellular metabolism.Mycobacterium tuberculosis to hypoxia and identify metabolic alterations required for adaptation to a lifestyle of low metabolic activity [Different approaches have already made considerable headway in integrating gene expression and metabolism -6. Perhaactivity . Alternaactivity , which iactivity -15.Combining stoichiometric models of metabolic networks and gene expression data has proven useful in analyzing transcriptome, proteome, and fluxome data but presents limitations in analyzing metabolome data. These limitations can be overcome using kinetic models, in which metabolite concentrations are the primary variables as opposed to fluxes in constraint-based methods. However, the use of large-scale kinetic models  has been daunted by the general belief that the chances of obtaining a useful model, given the lack of accurate reaction rate expressions and kinetic parameters, are low. This paradigm has begun to change due, in part, to the high-throughput techniques that have increased the abundance, quality, and scope of the data needed for model construction.In addition to data availability, there are two other factors, arising from the biology of the systems, that ease the construction of large-scale kinetic models . The firIn this work, our objective was to investigate how the response of a cell to a perturbation (in terms of transcriptome or proteome data) induces changes in its phenotype (in terms of fluxome and metabolome data). For this purpose, we developed a computational approach based on kinetic models that provides a mechanistic link between transcriptional regulation and metabolism. Our proposed modeling framework overcomes the major obstacles in the construction of large-scale kinetic models of metabolism, namely, the detailed definition of appropriate reaction rate expressions and the determination of model parameters. As in previous approaches -22, we aS. cerevisiae based on two independent studies in which the transcriptional and metabolic responses to treatment were measured in chemostat cultures with weak organic acids (WOAs) [S. cerevisiae that would not have been possible by the independent analyses of the gene expression data or the metabolic network alone.Here, we constructed kinetic models to analyze the steady-state metabolism of s (WOAs)  and undes (WOAs) . The simFigure we used the expression form:ai and bj denote the stoichiometric coefficients of species Ai and Bj in the reaction, respectively, r represents the reaction rate, the parameter v denotes the value of the reaction rate or flux through the reaction at a reference condition, g represents the overall gene expression ratio (between a condition of interest and a reference condition) of the genes associated with the reaction, and the square brackets denote normalized metabolite concentrations. The constants mi (mj) are set to 2.0 if ai (bj) is 2.0, or to 1.0 otherwise. This choice of the constants mi (mj) is arbitrary, however, as shown in the Results Section, it has a minor effect on the simulation results. For lumped reactions , γ denotes the number of irreversible steps and γ=1 for individual reactions. A lumped reaction is irreversible if at least one of its steps is irreversible. Note that the actual reaction rates depend linearly on the protein levels. However, in this work, we have substituted protein levels with the more readily available gene expression data. This approximation is supported by experimental evidence that shows a moderate correlation between protein and mRNA expression ratios for S. cerevisiae[where erevisiae,27. As sSimilarly, for a general reversible reaction, we used the expression form:vf and vb were determined as follows:where β is a parameter that relates the rate of the forward and backward reactions to the overall flux at the reference condition. The value of β depends on the equilibrium constant and on the reactants concentration at the reference condition. If these data are not available, as in the experiments analyzed here, β could be estimated by a fitting procedure using other available data. However, to avoid over fitting and assuming that the model behavior has low sensitivity to individual βs we started by approximating all βs with the same value  and the subscript j comprises all the amino acids. The second factor, representing the lowest concentration of any amino acid, was included based on the assumption that a low concentration of any amino acid would slow down protein synthesis and therefore the drain fluxes of the other amino acids. The reaction rate for the other drain fluxes was defined as follows:where the value of y et al. . The subi comprises the metabolites consumed in each drain flux.where the subscript The end product of Step 1 is a kinetic model describing the mass balances of the metabolites in the metabolic network and it is derived directly from the network reconstruction, which provides the stoichiometry of each reaction, and the rate expressions obtained from Eqs. 2, 3, 6, 7, and 8. The kinetic model can be represented as:C is a diagonal matrix with elements equal to the absolute metabolite concentrations used for normalization, c represents the vector of normalized metabolite concentrations and ċ denotes its time derivative, S denotes the stoichiometric matrix of the metabolic network reconstruction, r represents the vector of reaction rates, v denotes the flux distribution, g represents the vector of gene expression ratios, and p denotes a vector of the other model parameters . Under steady-state conditions, C is not required and, thus, for steady-state analysis, the only parameters to be estimated are v, g, and p.where c and g become equal to 1.0, and r=vref, where vref is the flux distribution at the reference condition. Therefore, for steady-state analysis, the model for the reference condition was parameterized with vref. A flux distribution determined using 13C-labeling experiments provides a good estimate of vref. If such flux distribution is not available, a reasonable estimate can be obtained using exchange fluxes, as described in Additional file In Step 2, we parameterized the model for the reference condition. Using the reference condition for normalizing the metabolite concentrations and gene expression levels, both Another notable feature of the method is that the model can be parameterized to simulate other conditions using the gene expression ratio between the condition of interest and the reference condition (Step 3). We assumed that relative changes in gene expression led to similar relative changes in protein abundance and we neglected post-translational and other regulatory mechanisms of enzymatic activity. Note that, if available, proteome data can be used instead of gene expression data. For reactions associated with multiple genes, we computed an overall gene expression change as described in Additional file In Step 4, we tuned the constructed models by comparing model predictions  with experimental measurements. We resolved detected inconsistencies until the model gave satisfactory performance. Finally, once its performance is satisfactory, the model can be used to carry out different model-based analyses, such as predicting non-measured variables, determining the effect of a particular expression level on a given metabolic function, or to identify important reactions in the network (Step 5).S. cerevisiae to treatment with a WOA  were obtained from Abbott et al. [2 were reported, as well as the biomass yield and concentration, and the extracellular glucose concentration for each treatment condition.The experimental data for the analysis of the response of t et al. . To compt et al.  and the 13C-labeling experiments, and the concentration changes of 17 free amino acids for chemostat culture of wild-type and gcn4-knockout mutant strains of S. cerevisiae.For the analysis of the metabolic response induced by the Gcn4 regulator, the experimental data were taken from Moxley et al. . They reModel construction, data processing, and simulations were carried out in MATLAB . The kinetic model (MATLAB scripts and in SBML format) and parameter sets for simulating both experiments are provided in Additional file S. cerevisiae. We constructed the metabolic network based on the network presented by Moxley et al. [v and g directly from experimental data [p were estimated as described in Additional file c were computed by solving the model (Eq. 9) assuming steady state conditions in all simulations. We used the constructed models to analyze the transcriptional and metabolic responses of S. cerevisiae under histidine starvation conditions and to treatment with WOAs. The details of the metabolic network are given in Additional file We applied the method to construct condition-specific kinetic models of the metabolic network of y et al. . Figure tal data ,25 and tS. cerevisiae regulates the expression of nearly all genes encoding enzymes involved in amino acid synthesis under starvation conditions [gcn4-knockout mutant (Δgcn4) strains of S. cerevisiae in aerobic chemostats treated with 3-aminotriazole (3-AT), an inhibitor of imidazoleglycerol-phosphate dehydratase, the sixth step of the histidine synthesis pathway. The concentration of 3-AT was adjusted such that the Δgcn4 and wild-type cultures produced similar biomass levels and uptake and production rates of extracellular metabolites. They measured gene expression levels , and the intracellular concentration of free amino acids for each culture. We used the measured metabolic fluxes of the Δgcn4 culture as the reference condition vref and the gene expression ratios between the two cultures g to parameterize the model for simulating the wild-type cultures. The parameters in p used in these simulations are given in Table The activator protein Gcn4 of nditions . Moxley nditions  studied ρ between the predicted and measured metabolic fluxes was 0.99 and the slope of the best linear fit was 0.91. This high accuracy was due to the similarity between the experimental flux distributions of the reference  and the wild-type conditions  has only five fitting parameters  for the amino acid concentration changes. Briefly, we simulated the perturbation of each intracellular reaction  by multiplying its rate by a constant between 0.1 and 10.0 that minimized the SSE. Table S. cerevisiae to grow at the dilution rate of the chemostat in the presence of 3-AT. Briefly, for each reaction, we predicted the maximum inhibition level tolerated by the Δgcn4 and the wild-type cultures by adding or removing the gene expression changes of every reaction (one reaction at a time) and computed a normalized tolerance change (NTC) as illustrated in Figure We used the model to determine the effect of gene expression changes of individual reactions on the ability of ρ = 0.06). Moreover, nine of the top ten reactions in Figure Another interesting result was that the magnitude of the individual effects was not correlated with the magnitude of the gene expression changes  in anaerobic chemostat cultures. For comparison purposes, cultures were treated with one WOA at a concentration that reduced the biomass yield to 50% of the biomass yield of untreated cultures. Metabolic and gene expression profiles were obtained for these cultures and for an untreated culture, which was used as the reference condition  because all model parameters were fixed at the same values. The effect on the metabolic fluxes was less noticeable. Figure Given their satisfactory performance, we used the models to investigate the effect of the transcriptional response on the predicted metabolic response. Thus, we compared the predicted metabolic responses to WOA treatment of cultures with and without considering the transcriptional response captured by the gene expression data . The results showed that gene expression changes affected metabolite concentrations and metabolic fluxes differently. Gene expression changes had a marked effect on the predicted biomass and extracellular glucose concentrations Table . For allS. cerevisiae. Figure S. cerevisiae to the WOA treatments. Taken together, these results suggest that while the network structure had a predominant role on the metabolic flux distribution, gene expression changes contributed to flux regulation and had a major effect on metabolite concentration changes.We further investigated the effect of the transcriptional response by comparing the predicted metabolic response of untreated cultures while considering the gene expression levels of the untreated or the treated cultures . Under the reference condition, the WOA uptake rate is the corresponding diffusive uptake flux of the acetic acid produced by S. cerevisiae to WOA treatment . In principle, S. cerevisiae should adjust its gene expression levels to better cope with these stress conditions. To probe if model predictions were in line with this premise, we predicted the biomass level as a function of the WOA uptake rate in treated cultures with and without gene expression changes. In addition, hypothesizing that the transcriptional response was graded depending on the stress intensity, we tested if, at higher WOA uptake rates, amplified gene expression changes would result in higher biomass growth than the measured gene expression changes. Thus, we also predicted the biomass levels assuming gene expression changes extrapolated from the experimental data . Figure S. cerevisiae to different WOA uptake rates by interpolating or extrapolating measured gene expression data. In agreement with the above premise, these simulation results suggest that the measured gene expression changes allowed S. cerevisiae to tolerate higher WOA uptake rates.We also used the constructed models to investigate the role of the transcriptional response on the tolerance of S. cerevisiae to grow at the dilution rate under WOA treatment. Here, we used the predicted WOA uptake rate that decreases the biomass concentration to 5.0% of the biomass of the untreated culture as a measure of tolerance as illustrated in Figure As in the simulations under histidine starvation, we used the models to determine the effect of gene expression changes associated with individual reactions on the ability of α, β, and γ. We investigated the effect of these fitting parameters on model predictions by simulating the model for different values of these parameters. For the WOA treatment experiments, we determined the normalized SSE between the predicted and experimental values of the exchange fluxes and biomass yield as a function of each parameter. The analysis showed that the predicted fluxes were robust with respect to changes in these parameters  for which a metabolic network reconstruction, metabolic flux measurements, and gene expression data are available for the conditions of interest.Long-standing barriers impeding the construction of large-scale kinetic models of metabolism are being overcome with the help of developments in high-throughput technologies and computational analyses. Modelers are now faced with the challenge of integrating the increasingly available building blocks to create coherent mathematical representations of biological systems. Here, we presented our efforts to develop a modeling framework for constructing large-scale kinetic models that mechanistically link transcriptional regulation and metabolism. This allowed us to gain understanding of complex physiological relations from fluxome, metabolome, and gene expression data. We demonstrated the ability of our method to capture these relations, its flexibility to simulate different experiments, and its robustness with respect to modeling approximations and data uncertainty by analyzing the response of One of the major challenges in constructing large-scale kinetic models is the definition of appropriate reaction rate expressions. Instead of defining mechanistic reaction rate expressions on a case-by-case basis, some approaches streamline this process by relying on generic expressions to translate a metabolic network into a kinetic model in an automated or semi-automated fashion. Different general forms have been proposed, such as log-linear kinetics , Michaelβ) for relating the forward and backward reaction rates to the overall rate for all reversible reactions. This crude approximation, inspired in part by the “sloppiness” property of biological systems, worked surprisingly well for the examples studied here. Our method performed well even if the uptake and production rates of extracellular metabolites were the only metabolic data available, as demonstrated in the analysis of S. cerevisiae tolerance to WOAs  could be impractical for large-scale models. Approaches using GMA kinetics partially avoid literature mining. In these approaches, such as MASS modeling , thermodS. cerevisiae glycolysis based on a mechanistic model developed by Teusink et al. [An additional attribute of our method is the use of gene expression data to parameterize the model to simulate different conditions, an element that has been used in constraint-based approaches to create context-specific models -10, but k et al. . Howeverk et al.  estimateS. cerevisiae response to WOAs, Abbott et al. [S. cerevisiae tightly regulates the expression levels of two reactions  to increase the tolerance under all treatment conditions. Firstly, this generic response was not identified in the Abbott et al. [S. cerevisiae has a generic response to WOAs that is critical for the adaptation to these stressors.We demonstrated that the constructed models were able to integrate transcriptional and metabolic responses to produce insights that would have been difficult to grasp from the analysis of the individual responses. For example, in their analysis of t et al.  identifit et al.  analysisS. cerevisiae. Similar to these efforts, our method was able to identify important regulated reactions under specific conditions. However, our method also provided mechanistic insights into how the cell regulates such reactions through transcriptional regulation and how this response is reflected in its phenotype.Identification of important reactions in a metabolic network has been one of the major goals of several model-based approaches. For example, Kummel et al.  developeρ = 0.80) with the experimentally estimated flux changes for a subset of reactions. For the same subset, our model predictions showed a considerably higher correlation (ρ = 0.96). Moreover, our method required less information because knowledge of the metabolite-enzyme interaction network is not needed. Interestingly, their predictions, using only the metabolic network model (without considering metabolite-enzyme interactions), had a similar ρ of approximately 0.75, reflecting the major contribution of the network structure to its function. In terms of biological insights, they observed a redistribution of the glycine synthesis fluxes. They proposed that the increase in glycine production from threonine is mediated by the increased expression of the associated genes, but they do not fully explain why the flux from serine to glycine decreased. Our analysis led to the plausible explanation that the decrease in the flux from serine to glycine could have been caused by the decrease of tetrahydrofolate, which, in turn, could have been caused by off-target inhibitions of 3-AT. In addition, and in contrast with their approach, our method also predicted concentration changes. In fact, we are unaware of other modeling efforts with similar scope that produce similar levels of accuracy, using condition-specific data directly as model parameters and using only five fitting parameters.In another effort to link the regulatory and metabolic responses, Moxley et al.  proposedAn additional conjecture about the use of gene expression changes to parameterize protein activity changes can be derived from our simulation results. We omitted post-translational and other regulatory mechanisms and yet the model predictions were consistent with experimental data. This suggests that, for the metabolic network and the experiments considered here, transcriptional regulation was the main mechanism that regulated the response at the system level. Moreover, the accuracy of the model predictions suggests that gene expression changes were a good approximation for protein level changes, in agreement with experimental observations ,39.The proposed method does not need knowledge of the absolute values of metabolite concentrations for steady-state simulations, but these are required for analysis of transient behavior. Developments in analytical techniques have increased the accuracy and scope of metabolite concentration measurements. However, such data are still generally incomplete and, thus, missing data must be estimated or assumed. Note that the requirement of metabolite concentrations to describe dynamic behavior is common to similar modeling approaches. Thus, it remains to be investigated how the proposed modeling framework performs in describing dynamic and transient properties associated with metabolic processes.mi and β. This may not be always the case and estimating more accurate parameters values may be necessary. As for any method, identifying and correcting modeling errors is a painstaking task. This could be especially true for automated model generation. Procedures to address this problem in a systematic way need to be developed. Furthermore, our method needs to be tested to determine whether it can be applied to genome-scale metabolic networks. Such application could be problematic because of the higher uncertainty of lowly expressed genes and small metabolic fluxes, the buildup of approximation errors, and numerical challenges to solve the model. Regarding its scope, the proposed method is limited to gene expression and metabolism. Although it enables a deeper, mechanistic analysis of these processes, further developments to include other cellular processes  would greatly enhance the modeling framework.The models constructed with the proposed method present some limitations. For example, the generic rate expressions may be poor approximations for some reactions or may miss important allosteric regulations  and other factors that have an effect on protein activity and abundance . Lumping sequential reactions reduced the size of the model. However, in our approach, the rate expressions for lumped reactions are only an approximation to the sequence of individual reactions. In the experiments we analyzed, the final results were not sensitive to our somewhat arbitrary parameter choice S. cerevisiae to treatment with WOA and under histidine starvation generated several insights and testable hypotheses: 1) 3-AT also inhibits the synthesis of tetrahydrofolate; 2) S. cerevisiae has an important generic response to WOA, involving glucose uptake and decarboxylation of pyruvate to acetaldehyde; 3) the contribution to tolerance to 3-AT is distributed among several reactions while the contribution to tolerance to WOA is mainly concentrated in two reactions; 4) the magnitude of gene expression changes was not correlated with the magnitude of their effect on the overall response. Taken together, these results suggest that the proposed framework is able to dissect different “omics” data to determine important features of the transcriptional-metabolic response of S. cerevisiae.In summary, we investigated how gene expression changes induce metabolic responses when cells adapt to a stressful condition. For this purpose, we developed a modeling framework for constructing and simulating large-scale kinetic models that provided a mechanistic link between transcriptional regulation and cellular metabolism. Analysis of the response of The authors declare that they have no competing interests.All authors contributed to the design of the research. FGV performed the computational implementations. FGV and AW wrote the article, which was edited by JR. All authors read and approved the final manuscript.Supplementary materials (pdf file): detailed information about the method for constructing large-scale kinetic models, fitting parameters, off-targets of 3-AT, and expression profiles of important genes under weak organic acid treatment.Click here for fileKinetic model (Zip file): MATLAB scripts for simulating the kinetic model and a XML file with the model in SBML format).Click here for fileMetabolic network (Excel file): detailed description of the reactions in the metabolic network and lists of the ranked reactions according to its effect on reducing inconsistencies and on tolerance to 3-AT.Click here for file


E. coli. The resulting mutant strain was able to grow on a medium containing glycerol and lactate, which served as an exogenous pyruvate source. Heterologous expression of a pyruvate carboxylase gene from Corynebacterium glutamicum was used for anaplerosis of the TCA cycle. Selective conditions were controlled in a continuous culture with limited lactate feed and an excess of glycerol feed. After 200–300 generations pyruvate-prototrophic mutants were isolated. The genomic analysis of an evolved strain revealed that the genotypic basis for the regained pyruvate-prototrophy was not obvious. A constraint-based model of the metabolism was employed to compute all possible detours around the given metabolic block by solving a hierarchy of linear programming problems. The regulatory network was expected to be responsible for the adaptation process. Hence, a Boolean model of the transcription factor network was connected to the metabolic model. Our model analysis only showed a marginal impact of transcriptional control on the biomass yield on substrate which is a key variable in the selection process. In our experiment, microarray analysis confirmed that transcriptional control probably played a minor role in the deregulation of the alternative pathways for the circumvention of the block.Bacterial strains that were genetically blocked in important metabolic pathways and grown under selective conditions underwent a process of adaptive evolution: certain pathways may have been deregulated and therefore allowed for the circumvention of the given block. A block of endogenous pyruvate synthesis from glycerol was realized by a knockout of pyruvate kinase and phosphoenolpyruvate carboxylase in  E. coli to ethanol. Models for evolving regulatory networks were developed by Crombach et al. [Since the long term evolution experiment of Lenski et al. , laborat et al.  and Xie  et al. . Constra et al. .Here, we present the concept of an adaptive evolution experiment in a bioreactor. In such a process, the evolutive pressure on the microorganisms for either fast growth or optimal biomass yield on a limiting substrate can be used to attain or improve the production of a desired compound. Motivated to know possible endpoints of the evolution experiment, we developed an algorithm for computing the endpoints of such an experiment. These endpoints are alternative flux distributions for the circumvention of a metabolic block. We further examined the role of a regulatory network in the usage of the alternative flux distribution and we validated the model by microarray analysis.Escherichia coli which lacks both the pyruvate kinases PykA/PykF and the phosphoenolpyruvate carboxylase (Ppc). The pyruvate kinases are expected to be the main source of pyruvate on a glycerol minimal medium [pyc) of Corynebacterium glutamicum was inserted into the chromosomal malEG locus under control of the tac-promotor. The Pyc enzyme catalyzes the carboxylation of pyruvate to form oxaloacetate [The experiment utilized a mutant of the intestinal bacterium  medium . The Ppc medium . As replacetate .malE::pyc is pyruvate-auxotrophic . The stoichiometric information for balanced compounds was described by the matrix n0 and ne as the number of balanced and unbalanced compounds, respectively. To denote the external substrate availability, the vector bglyc was negative and if lactate was not available blac=0). Furthermore, the growth rate was fixed to the dilution rate Jμ = D due to chemostat conditions. Since thermodynamic constraints on reactions exist, some reactions are irreversible and the direction of the flux is fixed. The following equality and inequality constraints were collected in the constraint set The metabolic compounds which can be further analyzed by using objective functions for optimization.f = cτJ. Minimizing f  results in an optimal value fopt and a particular solution Jopt. Applying objective functions will often result in non-unique optima. Consequently, the set of optimal solutions has to be further analyzed. By extending the constraints in Equation (1) with the equation fopt = cτJ enforcing the optimal objective function value, a new constraint set Properties of the constraint set Yield: The yield is defined as growth per substrate uptake μ is determined by the dilution rate D. For optimization purposes, the yield can be maximized by minimizing the substrate uptake JSup,→ min.Turnover rate: With a balanced metabolite the consumption and production rate are equal, which is a measure for the turnover. We define the turnover rate as the production rate of a compound. The objective function Ci with νi,jas a stoichiometric coefficient. A yield optimal minimal turnover rate (YMTR) was computed by extending the constraints with the fixed minimal substrate uptake rate results in a minimal turnover rate (MTR) of a balanced compound Ciwas developed   whether 2. Construct a constraint set l be the number of constraints in 3. Starting with k = 1, compute the optimal yields of k reactions. All 4. If there is a feasible solution for the set restricting all previously found solutions k and repeat step 3.Ci were obtained. To reconstruct the alternative pathways from a substrate to the MOI, this algorithm had to be used recursively. At first it was applied to the MOI, then to the reactants of the last reactions to the MOI and then to the reactants of those reactions and so on.In this manner, all minimal combinations of alternative reactions to produce The computational effort is high due to the recursive usage of the algorithm. Because the point of interest was the buildup of a metabolite’s carbon core, it was only necessary to track the reactants that carry parts of the carbon core for the metabolite. To decide whether or not a reactant contributes to the carbon core, we used the following equivalence relation:Given a set of cofactorsCo, two metabolitesCi and Cjare equivalent up toCo, the regulatory network is not necessarily optimal any more. Consequently, random mutations leading to an altered regulatory network were expected by Crombach et al.  as a driWe intended to study how transcriptional regulation affects the availability of enzymes that are essential for the predicted alternative pathways Table . Therefoσand anti-σfactor knockouts. Only 41 of the evaluated factors are included in the iMC1010v2 model. The environmental conditions of the experiments were expressed in a constraint set such as σ factors changed the TFN and resulted in a changed constraint set k denoted the factor which was deleted. The objective function of minimal substrate uptake was evaluated on the constraint sets malE::pyc.We used data of the transcription factor knockout study of Haverkorn et al.  in ordermalE::pyc and the evolved strains showed different growth features. In fact eight alternative metabolic pathways exist to circumvent the metabolic block of regular pyruvate formation. This raised the question why F41malE::pyc was not able to use these eight alternative metabolic pathways on minimal media (MM) with glycerol. After a cultivation phase of F41malE::pyc in MM with glycerol, growth could be obtained by adding lactate. This indicated that F41malE::pyc was not poisoned by toxic metabolites. The useability of some of the eight alternative pathways was proven by the sheer existence of the evolved pyruvate prototrophic strains. Therefore, we examined the hypothesis if transcriptional regulation prevents the transcription of genes which are essential for the usage of the alternative pathways. We checked how the transcriptional network impacts the eight alternative pathways  , the strThe results indicated that estimating from the microarray data, the enzymatic capability of using the alternative pathways was available in all three compared strains. The TFN did not predict a transcriptional downregulation of the pathways in most cases, which was in accordance with the microarray data, except for the Entner-Doudoroff-path and alternative acetyl-CoA synthesis path. This means that the hypothesis of restricting the alternative pathways by transcriptional regulation did not hold.malE::pyc on glycerol with an additional pyruvate source. The introduced algorithm for the computation of alternative pathways was employed to predict pathways from glycerol to pyruvate as possible endpoints of evolution for the strain F41malE::pyc. The evolution experiment with F41malE::pyc resulted in five evolved strains. This proved that the usage of alternative pathways was possible after adaptive evolution. However, F41malE::pyc was unable to grow without a pyruvate source. We assumed that transcriptional restriction of the predicted pathways hindered the growth. Therefore, a Boolean transcription factor network (TFN) was employed to further restrict the solutions of the metabolic network (MN). The prediction of the TFN together with microarray analysis revealed that in this case it is improbable that transcriptional regulation was exclusively responsible for the activation of the proposed alternative pathways during adaptation. It was shown that mRNA of genes which are important for the functionality of the predicted pathways were present in all compared strains.We have illustrated the idea of an adaptive evolution experiment in a chemostat bioreactor, where mutation and selection led to circumvention of a metabolic block. Constraint-based methods were utilized to identify targets for blocks and to predict alternative pathways for this circumvention. We performed the experiment with a pyruvate-auxotrophic strain F41However, a clear elucidation of the course of genetic events during adaptation was not yet possible. Metabolic feedbacks and non-regulatory effects may play an important role. We believe that the TFN will help to support further analysis by giving the possibility to determine the regulatory effects of metabolic and environmental signals and to distinguish between cause and effect of the up/down regulation of a gene. This will warrant further study in the field of transcription factor networks and their input in order to understand the whole sequence of events during adaptive evolution.2PO4·2 H2O, 11.5 g K2PO4, 2.64 g (NH4)2SO4, 0.74 g MgSO4·7H2O, 14.7 mg CaCl2·2H2O, 13.5 mg ZnCl2, 2.8 mg FeSO4·7H2O, 10μl 1N HCl, 20 mg Thiamine, 0.2 mM IPTG per liter. In shaking flask experiments 0.5% (w/v) glycerol was used as carbon source. When a mixture of glycerol and D,L-lactate was used the concentrations were 0.4% glycerol and 0.1% DL-lactate in order to have constant carbon availability in all experiments. Cells were cultivated in 250 ml shaking flasks filled with 25 ml growth medium. Prior to use, the cells were streaked onto LB-agar plates freshly from −80°C frozen stocks and incubated overnight at 37°C. Single colonies from LB-agarplates were then adapted to growth on minimal medium on MM agar plates for three days. Cultures were initiated directly from MM agar plates at OD600 = 0.1. After overnight incubation at 37°C without shaking the cells were grown at 37°C and 70 rpm.The strains used in the experiments are listed in Table 2 was kept above 50%. The feeding contained MM with 5 g/L glycerol and lactate concentrations in the range from 0.125 g/L down to 0 g/L of 95% L-lactate. The last 100 fermentation hours the feeding contained no lactate. The glycerol concentration measured in the fermentation broth was close to zero.Chemostat fermentations were performed in a Bioengineering fermentor KLF at 37°C, with stirring rate of 500–1000 rpm, an input air of 1 L/min, controlled pH at 7 and pOFor genome resequencing the cells were grown to stationary phase. Chromosomal DNA was isolated via Phenol/Chloroform precipitation . The resmalE::pyc were compared after growth on minimal medium containing glycerol and D,L-lactate as carbon source. Cells were harvested after reaching OD600 = 0.8. The DNA chips were custom-synthesized by Agilent company and processed according to the manufacture’s instruction. A complete description of transcript data will be published elsewhere, but can be obtained from the authors directly.For transcriptome analysis strains K98-62 and LJ110 were compared after growth on minimal medium containing glycerol as carbon source and K98-62 and F412 spot intensities over all biological replicates and colors. If the average expression value of a mRNA was measured below 6 units, it is uncertain that the mRNA was present in the probe. If the fold change value was not significantly different from zero and the average expression value was above 7.0, we assumed that mRNA of a gene was present in both compared strains. Observing significant fold change values, we studied the strain specific average expression to assess whether mRNA was present or not. The mean average expression value over all spots was 6.93 in the comparison K98-62 versus wild type and 7.37 for K98-62 versus F41malE::pyc. Data to estimate the enzymatic capability of the predicted pathways was included in Additional file The average expression is the mean value of all normalized LogJATPm in JATPm = 8.39[mmolh−1gDCW−1 from Feist et al. [In Equation (1), we regarded also ATP requirements for the maintenance metabolism  et al. , which iCombination of iAF1260 and iMC1010v2: The computation of a regulatory model combined with metabolic model was outlined by Covert et al. . The netaccoa: Acetyl-CoA; prpp: 5-Phospho-α-D-ribose-1-diphosphate; acgam6p: N-Acetyl-Dglucosamine6phosphate; pser: Phospho-L-serine; akg: Oxoglutarate; pyr: Pyruvate; anth: Anthranilate; r5p: α-D-Ribose-5-phosphate; aspsa: L-Aspartate-4-semialdehyde; ser-D/L: D/L-Serine; chor: Chorismate; skm: Shikimate; cys-L: L-Cysteine; succ: Succinate; dha: Dihydroxyacetone; thf: Tetrahydrofolate; dhap: Dihydroxyacetone-phosphate; thr-L: L-Threonine; e4p: D-Erythrose-4-phosphate; trp-L: L-Tryptophan; fdp: D-Fructose-1-6-bisphosphate; uacgam: UDP-N-Acetyl-D-glucosamine; for: Formate; 10fthf: 10-Formyltetrahydrofolate; fum: Fumarate; 13dpg: 3-Phospho-D-glyceroyl-phosphate; f6p: D-Fructose-6-phosphate; 2ddg6p: 2-Dehydro3deoxy-D-gluconate6phosphate; glyc: Glycerol; 2dr1p: 2-Deoxy-D-ribose-1-phosphate; glyc-R: R-Glycerate; 2mcit: 2-Methylcitrate; glyc3p: Glycerol-3-phosphate; 2obut: 2-Oxobutanoate; g3p: Glyceraldehyde-3-phosphate; 2pg: D-Glycerate-2-phosphate; ichor: Isochorismate; 23ddhb: 2-3-Dihydro-2-3-dihydroxybenzoate; lac-D/L: D/L-Lactate; 3pg: 3-Phospho-D-glycerate; malACP: Malonyl-acyl-carrier-protein; 3php: 3-Phosphohydroxypyruvate; malcoa: Malonyl-CoA; 4abz: 4-Aminobenzoate; mlthf: 5-10-Methylenetetrahydrofolate; 4adcho: 4-Amino-4-deoxychorismate; mthgxl: Methylglyoxal; 4hbz: 4-Hydroxybenzoate; oaa: Oxaloacetate; 4pasp: 4-Phospho-L-aspartate; 6pgc: 6-Phospho-D-gluconate.The authors declare that they have no competing interests.RF has written the manuscript, has done modeling and experimental study and did conceptual study. KG has done experimental study including transcript analysis. GV has done the computations for the model analysis of transcription factor knockout study. JK and SS have supervised the study of GV and did theoretical studies with the transcriptional network. MB and OS contributed to the design of the project. GS contributed to the design of the project and to the interpretation of data. ME contributed to the design of the project, has developed a preliminary version of the computational algorithm, has done conceptual study on the article and helped to interpret the data. All authors read and approved the final manuscript.Alternative pathway classes. Additional file 1 contains detailed information about the alternative pathway classes from Section “Abbreviations”.click here for fileModifications of iMC1010v2, input signals and predicted inactive genes. Additional file 2 describes how iMC1010v2 can be adapted to the metabolic model iAF1260. It contains input signals for three environmental conditions and the according outputs.click here for file


Predicting cellular responses to perturbations is an important task in systems biology. We report a new approach, RELATCH, which uses flux and gene expression data from a reference state to predict metabolic responses in a genetically or environmentally perturbed state. Using the concept of relative optimality, which considers relative flux changes from a reference state, we hypothesize a relative metabolic flux pattern is maintained from one state to another, and that cells adapt to perturbations using metabolic and regulatory reprogramming to preserve this relative flux pattern. This constraint-based approach will have broad utility where predictions of metabolic responses are needed. Escherichia coli that have undergone adaptive evolution [E. coli strains in different environmental conditions [Computational modeling of metabolic networks has been useful in studying microbial metabolism and developing tools for many applications. Among different computational approaches, constraint-based models utilize genome-scale metabolic networks to predict metabolic flux distributions in microbial cells, and they have been used to guide metabolic engineering , drug divolution ,7. Recenvolution ,9. Incornditions . Genomicnditions  have alsSeveral constraint-based approaches for integrating omics data  with metabolic models have been developed to predict metabolic flux distributions in different environmental or genetic conditions -16. For Since FBA assumes that cells grow optimally, other approaches are used to predict the behavior of perturbed strains that exhibit suboptimal growth  due to regulatory restrictions or other metabolic limitations, without requiring any data from the perturbed state. One such approach is minimization of metabolic adjustment (MOMA), which predicts the behaviors of unevolved mutants by minimizing the sum of squared differences in flux distributions between mutant and parent strains . MOMA ha13C metabolic flux analysis (MFA) results, physiological measurements, and gene expression data to approximate the genome-scale flux distribution and corresponding enzyme contribution in a reference state . Here, enzyme contribution refers to the flux a particular enzyme contributes towards the total flux through a reaction when contributions from all isozymes are considered. The gene expression data allow higher enzyme contributions for more highly expressed genes. Next, the flux distribution for a perturbed strain  is predicted by minimizing relative flux changes and latent pathway activation  from the reference state, without requiring any data from the perturbed state. We have applied RELATCH to predict flux distributions in genetically or environmentally perturbed Escherichia coli, Saccharomyces cerevisiae, and Bacillus subtilis strains, and compared the model predictions to experimental data regarding fluxes, enzyme activity, gene expression, and genetic mutations. RELATCH predicts the metabolic behaviors of both unevolved and evolved knockout mutants and environmentally perturbed strains with significantly greater accuracy than existing approaches (with up to 100-fold decrease in the sum of squared errors between predicted and observed fluxes). Moreover, important metabolic and regulatory changes predicted by RELATCH are highly consistent with experimental observations, including gene expression, enzyme activity, and whole-genome resequencing. As a highly accurate tool for predicting metabolic flux responses to perturbations, we believe RELATCH can improve our understanding of changes that occur over adaptive evolution and how metabolism responds to perturbations.In this work, we report a new approach, RELATCH for RELATive CHange Figure , which eE. coli strains before and after adaptive laboratory evolution described in the next section  for latent pathway activation and a limit on enzyme contribution increases (γ) for active enzymes . The underlying rationale for the RELATCH parameters is that strains would initially adjust to new perturbations with limited metabolic and regulatory adjustments, whereas over time they could adapt to these conditions by increasing the capacity of previously active and latent pathways. Here, we considered the recent loss of metabolic enzymes  or a change in growth conditions that cells are less accustomed to  as conditions the cells are not adapted to. For these non-adapted conditions, we used tight parameter values, including a high penalty for latent pathway activation α = 10) and restricted enzyme contribution increases in active enzymes from the parental state (γ = 1.1). We considered cells to be adapted to a condition if knockout strains were adaptively evolved, if parental strains were grown in conditions cells were accustomed to , or if strains were grown in a chemostat . For th0 and resE. coli K-12 MG1655  before and after adaptive laboratory evolution. MFA flux values for the parental strain were taken from an existing study [E. coli strain grown aerobically in glucose minimal medium from an earlier study [We first used RELATCH to predict flux distributions in knockout mutants of ng study  and mappng study . Gene exer study  and MFA er study .Δpgi, Δppc, and Δtpi), as well as slight increase in glucose uptake rate for the Δpta mutant , and unaltered flux through pentose phosphate and Entner-Doudoroff pathways were successfully predicted by RELATCH. Activation of the glyoxylate shunt was also accurately predicted for the Δppc mutant, enabling an alternative mechanism for synthesizing citric acid cycle intermediates. The most notable initial response in the Δpta mutant was secretion of pyruvate instead of acetate, which was only predicted by RELATCH . RELATCH's pyruvate secretion prediction in the Δpta mutant is due to the minimization of relative flux changes, since lowering the penalty for latent pathway activation and/or removing enzyme contribution constraints still led to pyruvate secretion predictions. In agreement with the MFA measurements and in vitro enzyme assays [Δtpi mutant. Interestingly, RELATCH predicted no growth for the Δppc and Δtpi mutants when a very high penalty for latent pathway activation was used  often over-predicted the flux values Figure . RELATCHe assays , RELATCHΔpgi mutant, RELATCH predicted further increase in fluxes through the NADPH-producing pentose phosphate pathway and subsequent conversion of excess NADPH to NADH via NAD(P)H transhydrogenase , as compared to the unevolved mutant. This suggests that redox balancing is a bottleneck in the unevolved Δpgi mutant, which is consistent with a previous study [Δpgi strains found frequent mutations in the SthA (converting NADPH to NADH) and PntAB (converting NADH to NADPH) transhydrogenases. RELATCH also predicted a decrease in pyruvate kinase flux, which is consistent with gene expression data [Δpgi strains (E1) had slower growth and considerably higher acetate secretion compared to the other evolved Δpgi strain (E2)  than the flux values in the Δpgi E1 strain (SSE = 1.59). For the evolved Δppc and Δpta mutants, all methods predicted the flux patterns well . The prE. coli mutant strains, but we did not find any instances where the alternative reference states affected prediction errors . We also investigated the existence of alternative optimal solutions in perturbed states using the four E. coli mutant strains. We solved the flux prediction problem , while FBA and ROOM generally predicted higher growth rates as noted in a previous study [Δppc mutant differed significantly among the four methods where FBA, MOMA, and ROOM predicted higher growth rates and RELATCH predicted no growth (note the RELATCH growth predictions differ from earlier Δppc predictions because the reference states differ). The growth of a Δppc mutant requires suppressor mutations in the glyoxylate shunt [-1).To further evaluate the accuracy of the different methods for predicting growth rates, we subsequently grew 22 single knockout mutants of te shunt  and RELAE. coli single gene knockout strains. We compared the growth phenotype predictions by FBA, MOMA, and RELATCH to the list of experimentally essential genes from the iAF1260 study [We also performed growth phenotype predictions for 1,260 60 study . For RELE. coli, S. cerevisiae, and B. subtilis were taken from previous studies [Next, we used RELATCH to predict the effects of gene knockouts, resulting in the total or partial loss of reaction activities, in three different organisms. Existing methods like FBA, MOMA, and ROOM cannot predict the effects of isozyme deletions since they are based on reaction deletions; however, RELATCH can estimate the flux each isozyme contributes towards the total flux through a reaction and predict the consequences of removing individual isozymes. Large-scale MFA datasets for parental and knockout strains of  studies ,32,33, a studies  or relat studies ,35.E. coli mutants grown in chemostat cultures [ΔtktA and ΔrpiB mutants had decreased biomass yields , which was not predicted by RELATCH. In E. coli, transketolase and ribose-5-phosphate isomerase are essential for growth on glucose [E. coli has two isozymes for each . Since TktA is known to be responsible for the major transketolase activity [ΔtktA mutant is not sufficient for efficient growth (the ΔtktB mutant had a similar behavior to the wild type's). However, the behavior of the ΔrpiB mutant was unexpected since RpiB is thought to be the minor isozyme under this growth condition [We first tested the capability of RELATCH to predict fluxes in cultures . The res glucose ,37, and activity , it seemE. coli, we subsequently used RELATCH to predict metabolic flux distributions in 35 knockout S. cerevisiae mutants of central metabolic genes grown in batch cultures [zwf1Δ, ald6Δ, pda1Δ, and oac1Δ) whose fluxes deviated significantly from the parental strain  was done to identify potential model improvements. The rpe1Δ mutant had the lowest measured glucose uptake rate among all 35 mutants , but RELATCH predicted a larger glucose uptake rate  and reversal of the second transketolase reaction . However, reversal of TKT2 was not experimentally observed at a statistically significant flux level in any of the 35 mutants. When the TKT2 reaction was constrained to be irreversible in the forward direction consuming erythrose 4-phosphate, the RELATCH prediction improved significantly for the rpe1Δ mutant (SSE decreased from 22.3 to 0.9), suggesting that the TKT2 reaction may proceed only in the forward direction in this condition, which is supported by a recent thermodynamic analysis study [fum1Δ and mdh1Δ, experimentally had very similar flux distributions and impaired growth, but RELATCH predicted higher growth rates for these two mutants by using alternative routes involving the glyoxylate shunt and malic enzyme. Mdh1 is a component of malate-oxaloacetate and malate-aspartate shuttles, which regulate the NADH/NAD ratio in mitochondria and cytosol [mdh1Δ mutant, as well as the fum1Δ mutant, which would result in limited availability of mitochondrial malate. Interestingly, the oac1Δ mutant, which lacks the mitochondrial oxaloacetate transporter, also had a very similar flux distribution to the mdh1Δ and fum1Δ mutants experimentally, which supports the hypotheses that deletion of mdh1Δ and fum1Δ alters oxaloacetate transport activity. Overall, RELATCH predicted the metabolic responses to a number of genetic perturbations in yeast, as well as led to potential model improvements based on discrepancies , which could affect our metabolic flux distribution and enzyme contribution estimates for the reference state. Among the 137 viable mutants in the dataset, 63 of the deleted genes were in the iYO844 metabolic model [B. subtilis mutants involving different metabolic pathways, except for the Δpgi, Δzwf, ΔtreA, and ΔacoA mutants , which is very similar to the behavior of the evolved E. coli Δpgi mutant [Δzwf mutant also exhibited a flexible response by increasing glycolytic flux and acetate production. The flux distributions for both of these two mutants were more accurately predicted if the relaxed RELATCH parameter values were used instead of the tight parameter values to account for the mutant's robust responses (SSE decreased from 5.57 to 1.28 for the Δpgi mutant and from 6.54 to 1.81 for the Δzwf mutant). The ΔtreA and ΔacoA mutants lack enzymes involved in trehalose and acetoin catabolism, respectively, which were both absent from the medium. RELATCH predicts these genes would be dispensable under the condition tested and it is unclear why these mutants exhibit a significant growth defect (reduced glucose uptake rate and growth rate).We also analyzed a large-scale MFA dataset for parental and mutant strains of cultures . In compic model  and the s Figure . The B. i mutant . The ΔzwE. coli is not well adapted to and grows slowly on galactose, but can improve growth after undergoing adaptive laboratory evolution [E. coli strain grown aerobically in glucose minimal medium [We further tested the ability of RELATCH, FBA, and MOMA to predict shifts in metabolic fluxes due to environmental perturbations, where cells are grown in different media or reactor conditions. First, we analyzed the metabolic flux distributions when cells move from glucose to galactose minimal medium in aerobic batch cultures . In contvolution . We usedl medium  to predil medium   and pyruvate formate lyase (producing formate) fluxes to the measured flux from pyruvate to acetyl-CoA and production of C1 compounds. Surprisingly, RELATCH was able to predict an almost two-fold increase in glycolytic fluxes, as well as significant ethanol production in anaerobic conditions, in agreement with experimental data  and rapidly adapts from growth on glucose to acetate [E. coli BW25113 grown on glucose in chemostat with a dilution rate of 0.2 h-1 were used to first estimate a glucose reference state. Since there are two acetate utilization pathways in E. coli (via Ack-Pta and Acs) and MFA cannot distinguish between them, we used the sum of the predicted fluxes through both pathways in our comparison  in chemostat cultures. Aerobically,  acetate . The met acetate  and expr acetate  for E. cn Figure . The preut study , while Fut study .E. coli BW25113 at D = 0.2 h-1 [-1 [-1), the model predictions were in good agreement with the data . The MFA and expression measurements for  0.2 h-1  were use h-1 [-1  were coma Figure . HoweverE. coli or against environmental perturbations.Genome-scale metabolic models are being rapidly developed for many organisms, and their applications in biological discovery, metabolic engineering, evolution, and drug discovery continue to expand . ConstraE. coli strains were significantly more accurate compared to other methods, especially for strains grown in batch cultures (approximately 5- to 50-fold lower SSE) where substrate uptake and growth rates are difficult to predict. It was previously suggested that B. subtilis maintains suboptimal metabolism for the sake of robustness, which led to flexible responses by maintaining the relative metabolic flux distributions [In this work, we presented a new approach, RELATCH, to predict the quantitative metabolic behaviors of genetically or environmentally perturbed microbial systems. RELATCH utilizes available information to estimate the metabolic state before perturbations  and predict the effects of perturbations using two parameters whose values are chosen according to the nature of the perturbations. We demonstrated RELATCH's prediction capability using large-scale datasets from different perturbation experiments for three model organisms, including unevolved/evolved mutants, batch/chemostat cultures, and genetic/environmental perturbations. Our results show that RELATCH dramatically outperforms existing methods with regard to predicting intracellular flux distributions in gene knockout strains. In addition, RELATCH predictions for environmentally perturbed ibutions . This isΔppc mutants), enzyme assay , and whole-genome resequencing . Using RELATCH, the metabolic changes arising from adaptation to perturbations were postulated by probing the flux space using these two parameters. This allows for the generation of hypotheses regarding the importance of metabolic changes, which is useful for metabolic engineering or drug targeting.While the constraint-based metabolic models may not provide a detailed description of the dynamic metabolic and regulatory mechanisms in response to perturbations, they can still provide accurate snapshots of metabolic states during adaptation at a genome-scale level without the need for detailed kinetic parameters. The underlying metabolic and regulatory responses can be inferred from further analyses of the changes in metabolic flux distributions. We showed here that RELATCH can accurately describe such changes using two simple parameters - a penalty for latent pathway activation and a limit on enzyme contribution increases in active pathways. In addition to consistency with MFA datasets, RELATCH predictions were also consistent with previous experimental data, including transcriptomics -enzyme (n) pairs using gene-to-protein-to-reaction (GPR) associations. To estimate the flux distribution (w) and enzyme contributions (enzW) in a reference state, we utilized MFA measurements and gene expression data. The sum of squared differences between flux variables and MFA estimates (expw) weighted by the reciprocal of confidence intervals (confw), and the sum of squared enzyme contributions weighted by the reciprocal of enzyme expression values (nE) were minimized to calculate the flux distribution and corresponding enzyme contribution (Equation 1). Using Equation 1, isozymes with higher expression will have higher enzyme contributions unless the associated flux is zero. If a reaction j has known GPR (N(j), the flux value through the reaction is constrained by the sum of enzyme contributions for all the associated isozymes (Equation 2). If multiple reactions are associated with a multi-functional enzyme, different enz Wvariables are assigned to each enzyme-reaction pair. External flux values  were constrained using the physiological measurements from the reference state  and enzyme contribution (enzW) in a reference state, the metabolic flux distribution (v) and enzyme contribution (enzV) in a perturbed microbial system was predicted by minimizing the relative flux changes from a reference state for reactions active in the reference state (actJ) and the enzyme contribution increases for enzymes inactive in the reference state (actN\N) with a penalty α (Equation 3). In addition to enzyme contribution constraints on fluxes (Equation 4), we imposed a limit (γ) on contribution increases for active enzymes (actN) (Equation 5). We used two different sets of values for these parameters  when predicting metabolic behaviors to different perturbations  used by RELATCH was also used for MOMA and ROOM calculations. For RELATCH, MOMA, and ROOM calculations, none of the exchange fluxes (except for growth rates in the chemostat cases since these are known a priori) were constrained to the measured values in the perturbed states, but they were instead predicted by the methods. To evaluate the differences between model predictions (v) and experimental MFA results (expv) we calculated the sum of squared errors per flux (SSE) using the following equation:The estimated flux distribution  before and after adaptive evolution.Click here for fileSupplementary Table S1. Comparison of predicted and experimentally measured values of growth, substrate uptake, and product secretion rates for four E. coli mutants before adaptive evolution.Click here for fileSupplementary Table S2. Comparison of predicted and experimentally measured values of growth, substrate uptake, and product secretion rates for four E. coli mutants after adaptive evolution.Click here for fileSupplementary Figure S2. Sensitivity analysis of data used to generate reference flux distributions.Click here for fileSupplementary Figure S3. Sensitivity analysis of metabolic network models.Click here for fileSupplementary Table S3. Growth rate predictions for 22 single knockout E. coli mutants.Click here for fileSupplementary Table S4. Growth phenotype predictions for 1,260 single knockout E. coli mutants.Click here for fileSupplementary Table S5. RELATCH prediction errors (SSE) for E. coli, S. cerevisiae, and B. subtilis knockout mutants shown in Figure Click here for fileSupplementary Figure S4. Comparison of metabolic flux predictions using RELATCH and MOMA for knockout mutants of S. cerevisiae and B. subtilis.Click here for fileSupplementary Figure S5. Comparison of MFA estimated fluxes and predictions by RELATCH for E. coli strains grown on galactose.Click here for fileImplementation of RELATCH. RELATCH is implemented using the COBRA Toolbox for MATLAB.Click here for file


Changes in environmental conditions require temporal effectuation of different metabolic pathways in order to maintain the organisms’ viability but also to enable the settling into newly arising conditions. While analyses of robustness in biological systems have resulted in the characterization of reactions that facilitate homeostasis, temporal adaptation-related processes and the role of cellular pathways in the metabolic response to changing conditions remain elusive.Escherichia coli in conjunction with time-series gene expression data from cold and heat stress results in two distinct time-resolved modes for reaction utilization—constantly active and temporally (de)activated reactions. These patterns contrast the processes for the maintenance of basic cellular functioning and those required for adaptation. They also allow the prediction of reactions involved in time- and stress-specific metabolic response and are verified with respect to existing experimental studies.Here we develop a flux-based approach that allows the integration of time-resolved transcriptomics data with genome-scale metabolic networks. Our framework uses bilevel optimization to extract temporal minimal operating networks from a given large-scale metabolic model. The minimality of the extracted networks enables the computation of elementary flux modes for each time point, which are in turn used to characterize the transitional behavior of the network as well as of individual reactions. Application of the approach to the metabolic network of Altogether, our findings pinpoint the inherent relation between the systemic properties of robustness and adaptability arising from the interplay of metabolic network structure and changing environment. The two properties—robustness and adaptability—do not exclude each other since both arise from the necessity of an organism to cope with its environment.The steady-state metabolism of microorganisms has evolved to optimize growth under ambient conditions. HoweverWhile robustness has been widely studied,7,  capture the whole spectrum of metabolic steady states of a given network. An EFM is defined as a minimal set of reactions that can operate at steady state. EFM-basi.e., constraint- and EFM-based, approaches have proven useful in characterizing stationary metabolic states of an organism. However, the adaptation of metabolism to changing conditions is a temporal process, and the state of the organism strongly depends on the time scale after the perturbation. Therefore, in order to capture adaptation-related processes, it is necessary to develop and apply a computational method which allows the integration of time-series data, uses the advantages of flux-based methods, and overcomes some of the shortcomings of the briefly reviewed approaches.Flux-based, E. coli[Here we present a novel method, which we term Adaptation of Metabolism (AdaM), to identify reactions and pathways that enable system adaptation upon external perturbation. AdaM integrates time-series transcriptomics data with flux-based bilevel optimization to extract minimal operating networks from a given large-scale metabolic model. The minimality of the extracted networks enables the computation of EFMs for each time point. These sets of EFMs are in turn used to characterize the transitional behavior of the network as well as of individual reactions activation upon perturbation, genes often show a bimodal distribution in expression values[cf. Additional filew of a gene as follows: Transcriptomics data are used to weight reactions that are catalyzed by the enzymes encoded in the respective genes. To determine pathways that contribute to the metabolic state of the organism, we consider reactions, that are not only temporally activated upon the changed environmental condition, but also reactions that are constantly active. Therefore, we combine information obtained from the analysis of differential expression as well as the gene expression levels themselves. The significance of differential behavior, is captured by the n values, indicatz denotes the z-score, ξ is the expression value, and ϑ is the determined threshold value. The trivalued indicator I takes values of 1, -1, or 0 if the gene is differentially up- or down-regulated, or shows no differential behavior, respectively. The first term in Equation (1) refers to the differential expression, while the second one combines the normalized difference between the expression value and the gene-specific threshold.where E. coli K-12[cf. Additional fileWe determine weights for transcriptomics data from the cold and heat stress and the control conditions spanning seven time points (0 - 90 min) and map them onto the genome-scale metabolic network reconstruction of oli K-12. If a reoli K-12. With thwj and vj are the weight and the flux of reaction j, respectively. The problem can be cast as a bilevel mixed-integer linear program (MILP), Equations (2)-(8), where each reaction j is assigned a Boolean variable yj ∈ {0,1}. If yj = 0, reaction j does not carry any flux and is not included in the network; if yj = 1, the reaction carries flux in the range determined by the flux boundaries (Equation (6)). The outer optimization level seeks to minimize the number of reactions in the network (Equation (2)), while fulfilling the inner constraints. The inner problem definition is a modification of the standard flux balance analysis (FBA)[cf. Equation (4) and Additional fileIn the following, we develop a formulation of the problem whose solution yields the minimal network of largest weight, quantifying the compliance with the data. More formally, we determine the minimal number of reactions that maximizeis (FBA) formulatfmin of the maximum biomass production fmax of the complete network is achieved (Equation (5) and[cf. Additional fileA further constraint on the fluxes is imposed by demanding that a fraction  (5) and). This rindispensable reactions, which make up most of the biomass production and dispensable reactions, which have a negligible contributions to growth. To define these two groups, we delete, one by one, every reaction and performed FBA on the perturbed network. If the resulting biomass production remains above a defined threshold (99%), we consider the reaction dispensable for the organism’s viability under ambient conditions . Reactions that are considered indispensable are not assigned a Boolean variable. Altogether, we obtain the following formulation To reduce the computational complexity, we seek to reduce the number of integer variables. To this end, we distinguish between Sij is the stoichiometric coefficient of metabolite i in reaction j, cj is the contribution of vj to the objective function andvj, whilewhere Although we investigate time-series data, the program formulation employs a the quasi-steady-state assumption (Equation (4)). We assume a separation of the time-constants at which transcriptional and metabolic regulations take place. This is justified by the evidence that changes taking place on the metabolic level are generally much faster (seconds) compared to those taking place on the transcriptional level (minutes). In othecf. Additional fileTo solve the min-max MILP, it is transformed from a bi-level to a single-level MILP. This procedure employs two steps: 1) finding the dual for the inner linear program and (2)  finding Xij of a reaction i at time j as the ratio between the number of elementary modes involving reaction i and the total number of elementary modes at time j:The reduced size of the networks allows the computation of sets of EFMs for the time- and condition specific minimal networks. It has already been shown that the importance of a reaction for network functionality can be characterized by the number of EFMs in which it is involved. Extendi.98·10−5 andFor both, cold and heat stress, the minimal networks include 416 to 427 metabolites interconnected by 480 to 486 reactions. The biomass production, as a result of the constraint from the minimization approach, ranges between 0i.e., the network extracted by AdaM). In addition, we determine the expected value of the overlap between the networks extracted by MADE and a random set of reactions of the same size as the networks extracted from our approach. By considering 1000 repetitions, we find this value to be 52.3%, thus confirming the similarity between the two approaches. The results are summarized in TablesWe compare the sets of reactions included in the time- and condition-specific networks extracted by both AdaM and MADE. We find that on average 66.6% of reactions are shared between the extracted networks over all time points and conditions, with larger average overlap for the heat condition of 67.2% . To compare the results, we use the intersection of reactions in the minimal networks for each time point. The average overlap of reactions is 94.4% for cold and 94.3% for heat  when comparing all possible parameter sets. When comparing the average overlap of networks for different time-points, we find it to be 94.1% for both cold and heat shock, indicating bigger similarity for networks extracted with different thresholds than for different time points.We investigate the robustness of the approach with respect to: (1) threshold variations for the optimization approach and (2) slightly suboptimal networks. To address the first aspect, we repeat the network minimization for three different thresholds to distinguish between dispensable and indispensable reactions. In addition, we examine three different values of minimal biomass production  compared to those from the heat stress networks (0.012-0.271). These changes in the usage of EFMs, resulting from data-driven network extraction, can be regarded as changes in the distribution of fluxes through the networks. Moreover, the values for the Jaccard index for dispensable reactions remaining in the minimal networks are similar for cold (0.697-0.759) and heat stress (0.618-0.771), suggesting similar changes in activation patterns of reactions.Considering the patterns of change, for cold shock we observe the first strong dissimilarity between sets of EFMs between 0 and 20 min after stress application, indicating that the main metabolic response takes place in this time range. For heat shock, the onset of the response is slightly shifted in time. These findings suggest that the stress response for the two conditions takes place on two slightly different time regimes. Such tendency can also be observed when comparing the time course of the similarities for the sets of dispensable reactions. In addition, for both conditions, the peak in dissimilarity between sets of EFMs occurs between 30 and 50 minutes. Between 50 and 90 minutes, both condition-specific networks exhibit similarity with respect to their sets of EFMs and sets of dispensable reactions, demonstrating that the system has started settling in the new condition.For ease of interpretation, we focus our analysis on the 50 reactions of highest fractional appearance for each time-point. The union of these selected reactions over all time points contains 71 and 76 reactions for the cold and heat shock, respectively. Out of these, 43 are conserved between the two stresses.τ. Furthermore, groups of reactions exhibiting mostly negative correlation towards other reactions indicate different patterns of usage over time and are probably stress induced.The working hypothesis is twofold: Reactions that are grouped together are expected to belong to the same pathways, or are regulated in a similar manner . The results of the clustering are shown in FigureTo further investigate this hypothesis we cluster the fractional appearance profiles of the previously selected reactions  biosynthesis, nucleotide, nucleoside and nucleobase interconversions, amine biosynthesis, coenzyme and carboxylic acid metabolic processes as well as tricarboxylic acid (TCA) cycle. The reactions can further be grouped according to specific pathways.In total, these clusters consist of 36 and 47 reactions for cold and heat stress, respectively, of which 19 of these reactions are conserved between the two stresses. These reactions appear in 5 to 40% of all EFMs, which indicates a major role for network functionality. To gain a general overview of the higher biological processes of this set of reactions, we perform GO term over-representation analysis on their annotated genes  and enolase, which belong to the central carbon metabolism. The constant utilization of glucose uptake system (PTS) is not surprising, since it is crucial for culture grown on this nutrient, as well as for the formation of G6P and flux from PEP to pyruvate. Furthermore, this reaction has also been shown to be constitutively active under different nutritional perturbations in E. coli.The second group contains reactions involved in amino acid metabolism, a process crucial for protein synthesis. Those reactions include acetylornithine transaminase, adenylsuccinate lyase, aspartate kinase, and L-serine transport. Another group contains reactions involved in nucleotides biosynthesis and degradation, processes essential for transcription and replication, including: purine-nucleoside phosphorylase (guanosine), pyrimidine-nucleoside phosphorylase (uracil), and thymidine phosphorylase, as well as thymidine kinase (ATP:thymidine). This group extends to three reactions involved in amino- and nucleotide-sugar metabolism, namely, UDP-N-acetylglucosamine 2-epimerase, UTP-glucose-1-phosphate uridylyltransferase, and UDP-glucose-hexose-1-phosphate uridylyltransferase.E. coli is kept on a high ratio, ensuring proper maintenance of reduced thiol groups, protection against oxidative damage, and formation of deoxyribonucleotide precursors for DNA synthesis[Finally, we observe constant utilization of glutathione reductase and trimethylamine N-oxide reductase. The first can be understood by the fact that the ratio of reduced to oxidized glutathione in ynthesis. The secThe results of the functional enrichment analysis and biological interpretation of the metabolic role of indispensable reactions, showing flat profiles of fractional appearance, supports our assumption that these reactions constitute the most crucial part of the metabolic network.Next we investigate reactions whose temporal appearance in EFMs changes as a result of the applied stress. The number of reactions showing such behavior is smaller compared to that of reactions which are constantly used. There are 35 reactions for cold stress and 29 for heat stress.Over-representation analysis of biological processes reveals that under cold stress cluster 2 is enriched for catabolic processes, in particular, of amino acids, organic acids, and coenzymes, followed by acetyl-CoA biosynthetic process from pyruvate, and glycolysis. The reactions in this cluster are excluded from the networks at 10 min and peak with respect to their fractional appearances at 30 min. A prominent representative in this group of reactions is the glycine cleavage system, which has been found to be slightly affected by cold stress[i.e., homoserine and threonine), carbohydrate (glucose) catabolic process, and pentose-phosphate shunt, among other more general GO terms. The fractional appearance profiles for the included reactions remain unchanged up to 30 min, after which the reactions are excluded from the time-specific networks to be reintroduced 50 min after application of the stress. This cluster includes the reactions: L-threonine dehydrogenase, threonine synthase, and aspartate-semialdehyde dehydrogenase. This suggest that even some prominent pathways, such as amino acid synthesis, are not constantly kept at high level throughout adaptation to the stress. Moreover, transaldolase appears to undergo the same transition in fractional appearance, which is due to the observation that, unlike in exponential growth, cells facing cold stress transiently use this reaction to convert two molecules of fructose-6-phosphate and one molecule of 3PGA[Cluster 3 is enriched for biosynthesis of the aspartate family of amino acids activation may slightly differ. The activation pattern of these processes may further amplify the effect of genes specific to cold/heat stress.Here we proposed a novel approach to investigate adaptation of metabolism upon external perturbation. Based on experimental data we determine time- and condition-specific minimal networks for which sets of EFMs can be calculated. These sets are used to determine the fractional appearance profiles of reactions. This integrative profile combines information from transcriptomics data, the underlying network structure, and biologically meaningful flux distributions in a quasi steady-state; thus it includes information which transcriptomics data would never be able to reveal on their own.The fractional appearance of reactions has already been investigated with respect to the concept of robustness. Here weIt must be noted that our proposed approach extracts network for individual time points, without accounting for their dependency in the time domain. However, since the weighting of the reactions is conducted by using data which already embed the temporal dependency, this also extends to the extracted networks.e.g., biomass yield. Thus, it overcomes one of the drawbacks of FBA, associated with the selection of a suitable objective function, not only for different but also varying conditions. Finally, comparative analysis with MADE, a state-of-the-art method, demonstrates high overlap between the extracted networks. However, in comparison to MADE, our approach results in consistently smaller networks amenable to EFM analysis.Since transcriptomics data do not necessarily reflect enzyme activities , we use the results from the analysis of the expression data only as indicator for the activity of the respective reaction rather that definite values. Furthermore, the approach does not rely on a condition-specific objective function, E. coli. The predictions from the integration of the large-scale metabolic networks with time-series data are in line with observations and conclusions from existing experimental studies. Moreover, analysis of the fractional appearance profiles for heat and cold stress adaptation in E. coli have generated interesting hypothesis to be validated in future experiments. Finally, the proposed method and the presence of the two types of profiles, resulting from its application on a well-investigated model organism, indicate the “tug-of-war” between the systemic properties of robustness and adaptability necessary for maintenance of major processes while settling in a new metabolic state.We applied our approach to time-resolved transcriptomics data from heat and cold shock experiments in The authors declare that they have no competing interests.NT and ZN designed the study and wrote the manuscript. NT performed the study. SJ, NT and ZN interpreted the results. All authors read and approved the final manuscript.Supplementary Information.Click here for file