Prediction of Rate‐Limiting Reactions for Growth‐Associated Production Using a Constraint‐Based Approach

Identification of a rate‐limiting step in pathways is a key challenge in metabolic engineering. Although the prediction of rate‐limiting steps using a kinetic model is a powerful approach, there are several technical hurdles for developing a kinetic model. In this study, an in silico screening algorithm of key enzyme for metabolic engineering is developed to identify the possible rate‐limiting reactions for the growth‐coupled target production using a stoichiometric model without any experimental data and kinetic parameters. In this method, for each reaction, an upper‐bound flux constraint is imposed and the target production is predicted by linear programming. When the constraint decreases the target production at the optimal growth state, the reaction is thought to be a possible rate‐limiting step. For validation, this method is applied to the production of succinate or 1,4‐butanediol (1,4‐BDO) in Escherichia coli, in which the experimental engineering for eliminating rate‐limiting steps has been previously reported. In succinate production from glycerol, nine reactions including phosphoenolpyruvate carboxylase are predicted as the rate‐limiting steps. In 1,4‐BDO production from glucose, eight reactions including pyruvate dehydrogenase are predicted as the rate‐limiting steps. These predictions include experimentally identified rate‐limiting steps, which would contribute to metabolic engineering as a practical tool for screening candidates of rate‐limiting reactions.     

Construction of a Genome-Scale Metabolic Model of Arthrospira platensis NIES-39 and Metabolic Design for Cyanobacterial Bioproduction

Arthrospira (Spirulina) platensis is a promising feedstock and host strain for bioproduction because of its high accumulation of glycogen and superior characteristics for industrial production. Metabolic simulation using a genome-scale metabolic model and flux balance analysis is a powerful method that can be used to design metabolic engineering strategies for the improvement of target molecule production. In this study, we constructed a genome-scale metabolic model of A. platensis NIES-39 including 746 metabolic reactions and 673 metabolites, and developed novel strategies to improve the production of valuable metabolites, such as glycogen and ethanol. The simulation results obtained using the metabolic model showed high consistency with experimental results for growth rates under several trophic conditions and growth capabilities on various organic substrates. The metabolic model was further applied to design a metabolic network to improve the autotrophic production of glycogen and ethanol. Decreased flux of reactions related to the TCA cycle and phosphoenolpyruvate reaction were found to improve glycogen production. Furthermore, in silico knockout simulation indicated that deletion of genes related to the respiratory chain, such as NAD(P)H dehydrogenase and cytochrome-c oxidase, could enhance ethanol production by using ammonium as a nitrogen source.     

Identification of genome-scale metabolic network models using experimentally measured flux profiles

Genome-scale metabolic network models can be reconstructed for well-characterized organisms using genomic annotation and literature information. However, there are many instances in which model predictions of metabolic fluxes are not entirely consistent with experimental data, indicating that the reactions in the model do not match the active reactions in the in vivo system. We introduce a method for determining the active reactions in a genome-scale metabolic network based on a limited number of experimentally measured fluxes. This method, called optimal metabolic network identification (OMNI), allows efficient identification of the set of reactions that results in the best agreement between in silico predicted and experimentally measured flux distributions. We applied the method to intracellular flux data for evolved Escherichia coli mutant strains with lower than predicted growth rates in order to identify reactions that act as flux bottlenecks in these strains. The expression of the genes corresponding to these bottleneck reactions was often found to be downregulated in the evolved strains relative to the wild-type strain. We also demonstrate the ability of the OMNI method to diagnose problems in E. coli strains engineered for metabolite overproduction that have not reached their predicted production potential. The OMNI method applied to flux data for evolved strains can be used to provide insights into mechanisms that limit the ability of microbial strains to evolve towards their predicted optimal growth phenotypes. When applied to industrial production strains, the OMNI method can also be used to suggest metabolic engineering strategies to improve byproduct secretion. In addition to these applications, the method should prove to be useful in general for reconstructing metabolic networks of ill-characterized microbial organisms based on limited amounts of experimental data.     

Enhancing sesquiterpene production in Saccharomyces cerevisiae through in silico driven metabolic engineering

A genome-scale metabolic model was used to identify new target genes for enhanced biosynthesis of sesquiterpenes in the yeast Saccharomyces cerevisiae. The effect of gene deletions on the flux distributions in the metabolic model of S. cerevisiae was assessed using OptGene as the modeling framework and minimization of metabolic adjustments (MOMA) as objective function.Deletion of NADPH-dependent glutamate dehydrogenase encoded by GDH1 was identified as the best target gene for the improvement of sesquiterpene biosynthesis in yeast. Deletion of this gene enhances the available NADPH in the cytosol for other NADPH requiring enzymes, including HMG-CoA reductase. However, since disruption of GDH1 impairs the ammonia utilization, simultaneous over-expression of the NADH-dependent glutamate dehydrogenase encoded by GDH2 was also considered in this study.Deletion of GDH1 led to an approximately 85% increase in the final cubebol titer. However, deletion of this gene also caused a significant decrease in the maximum specific growth rate. Over-expression of GDH2 did not show a further effect on the final cubebol titer but this alteration significantly improved the growth rate compared to the GDH1 deleted strain.     

Interpreting Expression Data with Metabolic Flux Models: Predicting Mycobacterium tuberculosis Mycolic Acid Production

Metabolism is central to cell physiology, and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. We present a novel method for modeling metabolic states using whole cell measurements of gene expression. Our method, which we call E-Flux (as a combination of flux and expression), extends the technique of Flux Balance Analysis by modeling maximum flux constraints as a function of measured gene expression. In contrast to previous methods for metabolically interpreting gene expression data, E-Flux utilizes a model of the underlying metabolic network to directly predict changes in metabolic flux capacity. We applied E-Flux to Mycobacterium tuberculosis, the bacterium that causes tuberculosis (TB). Key components of mycobacterial cell walls are mycolic acids which are targets for several first-line TB drugs. We used E-Flux to predict the impact of 75 different drugs, drug combinations, and nutrient conditions on mycolic acid biosynthesis capacity in M. tuberculosis, using a public compendium of over 400 expression arrays. We tested our method using a model of mycolic acid biosynthesis as well as on a genome-scale model of M. tuberculosis metabolism. Our method correctly predicts seven of the eight known fatty acid inhibitors in this compendium and makes accurate predictions regarding the specificity of these compounds for fatty acid biosynthesis. Our method also predicts a number of additional potential modulators of TB mycolic acid biosynthesis. E-Flux thus provides a promising new approach for algorithmically predicting metabolic state from gene expression data.     

Combinatorial network of transcriptional regulation and microRNA regulation in human cancer

Background

In order to reduce time and efforts to develop microbial strains with better capability of producing desired bioproducts, genome-scale metabolic simulations have proven useful in identifying gene knockout and amplification targets. Constraints-based flux analysis has successfully been employed for such simulation, but is limited in its ability to properly describe the complex nature of biological systems. Gene knockout simulations are relatively straightforward to implement, simply by constraining the flux values of the target reaction to zero, but the identification of reliable gene amplification targets is rather difficult. Here, we report a new algorithm which incorporates physiological data into a model to improve the model??s prediction capabilities and to capitalize on the relationships between genes and metabolic fluxes.

Results

We developed an algorithm, flux variability scanning based on enforced objective flux (FVSEOF) with grouping reaction (GR) constraints, in an effort to identify gene amplification targets by considering reactions that co-carry flux values based on physiological omics data via ??GR constraints??. This method scans changes in the variabilities of metabolic fluxes in response to an artificially enforced objective flux of product formation. The gene amplification targets predicted using this method were validated by comparing the predicted effects with the previous experimental results obtained for the production of shikimic acid and putrescine in Escherichia coli. Moreover, new gene amplification targets for further enhancing putrescine production were validated through experiments involving the overexpression of each identified targeted gene under condition-controlled batch cultivation.

Conclusions

FVSEOF with GR constraints allows identification of gene amplification targets for metabolic engineering of microbial strains in order to enhance the production of desired bioproducts. The algorithm was validated through the experiments on the enhanced production of putrescine in E. coli, in addition to the comparison with the previously reported experimental data. The FVSEOF strategy with GR constraints will be generally useful for developing industrially important microbial strains having enhanced capabilities of producing chemicals of interest.     

Metabolic modeling for multi-objective optimization of ethanol production in a Synechocystis mutant

Cyanobacteria have potential to produce drop-in bio-fuels such as ethanol via photoautotrophic metabolism. Although model cyanobacterial strains have been engineered to produce such products, systematic metabolic engineering studies to identify optimal strains for the same have not been performed. In this work, we identify optimal ethanol producing mutants corresponding to appropriate gene deletions that result in a suitable redirection in the carbon flux. In particular, we systematically simulate exhaustive single and double gene deletions considering a genome scale metabolic model of a mutant strain of the unicellular cyanobacterium Synechocystis species strain PCC 6803. Various optimization based metabolic modeling techniques, such as flux balance analysis (FBA), method of minimization of metabolic adjustment (MOMA) and regulatory on/off minimization (ROOM) were used for this analysis. For single gene deletion MOMA simulations, the Pareto front with biomass and ethanol fluxes as the two objectives to be maximized was obtained and analyzed. Points on the Pareto front represent maximal utilization of resources constrained by substrate uptake thereby representing an optimal trade-off between the two fluxes. Pareto analysis was also performed for double gene deletion MOMA and single and double gene deletion ROOM simulations. Based on these analyses, two mutants, with combined gene deletions in ethanol and purine metabolism pathways, were identified as promising candidates for ethanol production. The relevant genes were adk, pta and ackA. An ethanol productivity of approximately 0.15 mmol/(gDW h) was predicted for these mutants which appears to be reasonable based on experimentally reported values in literature for other strains.     

Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism

Elementary modes (EMs) are steady-state metabolic flux vectors with minimal set of active reactions. Each EM corresponds to a metabolic pathway. Therefore, studying EMs is helpful for analyzing the production of biotechnologically important metabolites. However, memory requirements for computing EMs may hamper their applicability as, in most genome-scale metabolic models, no EM can be computed due to running out of memory. In this study, we present a method for computing randomly sampled EMs. In this approach, a network reduction algorithm is used for EM computation, which is based on flux balance-based methods. We show that this approach can be used to recover the EMs in the medium- and genome-scale metabolic network models, while the EMs are sampled in an unbiased way. The applicability of such results is shown by computing “estimated” control-effective flux values in Escherichia coli metabolic network.     

Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

Overexpression of isocitrate lyase—glyoxylate bypass influence on metabolism in Aspergillus niger

In order to improve the production of succinate and malate by the filamentous fungus Aspergillus niger the activity of the glyoxylate bypass pathway was increased by over-expression of the isocitrate lyase (icl) gene. The hypothesis was that when isocitrate lyase was up-regulated the flux towards glyoxylate would increase, leading to excess formation of malate and succinate compared to the wild-type. However, metabolic network analysis showed that an increased icl expression did not result in an increased glyoxylate bypass flux. The analysis did show a global response with respect to gene expression, leading to an increased flux through the oxidative part of the TCA cycle. Instead of an increased production of succinate and malate, a major increase in fumarate production was observed.The effect of malonate, a competitive inhibitor of succinate dehydrogenase (SDH), on the physiological behaviour of the cells was investigated. Inhibition of SDH was expected to lead to succinate production, but this was not observed. There was an increase in citrate and oxalate production in the wild-type strain. Furthermore, in the strain with over-expression of icl the organic acid production shifted from fumarate towards malate production when malonate was added to the cultivation medium.Overall, the icl over-expression and malonate addition had a significant impact on metabolism and on organic acid production profiles. Although the expected succinate and malate formation was not observed, a distinct and interesting production of fumarate and malate was found.     

Increasing the flux in metabolic pathways: A metabolic control analysis perspective

The problems of engineering increased flux in metabolic pathways are analyzed in terms of the understanding provided by metabolic control analysis. Over-expression of a single enzyme is unlikely to be effective unless it is known to have a high flux control coefficient, which can be used as an approximate predictive tool. This is likely to rule out enzymes subject to feedback inhibition, because it transfers control downstream from the inhibited enzyme to the enzymes utilizing the feedback metabolite. Although abolishing feedback inhibition can restore flux control to an enzyme, it is also likely to cause large increases in the concentrations of metabolic intermediates. Simultaneous and coordinated over-expression of most of the enzymes in a pathway can, in principle, produce substantial flux increases without changes in metabolite levels, though technically it may be difficult to achieve. It is, however, closer to the method used by cells to change flux levels, where coordinated changes in the level of activity of pathway enzymes are the norm. Another option is to increase the demand for the pathway product, perhaps by increasing its rate of excretion or removal. Copyright 1998 John Wiley & Sons, Inc.     

Differential Bees Flux Balance Analysis with OptKnock for In Silico Microbial Strains Optimization

Microbial strains optimization for the overproduction of desired phenotype has been a popular topic in recent years. The strains can be optimized through several techniques in the field of genetic engineering. Gene knockout is a genetic engineering technique that can engineer the metabolism of microbial cells with the objective to obtain desirable phenotypes. However, the complexities of the metabolic networks have made the process to identify the effects of genetic modification on the desirable phenotypes challenging. Furthermore, a vast number of reactions in cellular metabolism often lead to the combinatorial problem in obtaining optimal gene deletion strategy. Basically, the size of a genome-scale metabolic model is usually large. As the size of the problem increases, the computation time increases exponentially. In this paper, we propose Differential Bees Flux Balance Analysis (DBFBA) with OptKnock to identify optimal gene knockout strategies for maximizing the production yield of desired phenotypes while sustaining the growth rate. This proposed method functions by improving the performance of a hybrid of Bees Algorithm and Flux Balance Analysis (BAFBA) by hybridizing Differential Evolution (DE) algorithm into neighborhood searching strategy of BAFBA. In addition, DBFBA is integrated with OptKnock to validate the results for improving the reliability the work. Through several experiments conducted on Escherichia coli, Bacillus subtilis, and Clostridium thermocellum as the model organisms, DBFBA has shown a better performance in terms of computational time, stability, growth rate, and production yield of desired phenotypes compared to the methods used in previous works.     

Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm

MotivationGenome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.ResultsHere, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.AvailabilityMMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.     

Genome-scale modeling using flux ratio constraints to enable metabolic engineering of clostridial metabolism in silico

ABSTRACT: BACKGROUND: Genome-scale metabolic networks and flux models are an effective platform for linking an organism genotype to its phenotype. However, few modeling approaches offer predictive capabilities to evaluate potential metabolic engineering strategies in silico. METHODS: A new method called "flux balance analysis with flux ratios (FBrAtio)" was developed in this research and applied to a new genome-scale model of Clostridium acetobutylicum ATCC 824 (iCAC794) that contains 707 metabolites and 794 reactions. FBrAtio was used to model wild-type metabolism and metabolically engineered strains of C. acetobutylicum where only flux ratio constraints and thermodynamic reversibility of reactions were required. The FBrAtio approach allows solutions to be found through standard linear programming. RESULTS: Five flux ratio constraints were required to achieve a qualitative picture of wild-type metabolism for C. acetobutylicum for the production of: (i) acetate, (ii) lactate, (iii) butyrate, (iv) acetone, (v) butanol, (vi) ethanol, (vii) CO2 and (viii) H2. Results of this simulation study coincide with published experimental results and show the knockdown of the acetylacetyl-CoA transferase increases butanol to acetone selectivity, while the simultaneous over-expression of the aldehyde/alcohol dehydrogenase greatly increases ethanol production. CONCLUSIONS: FBrAtio is a promising new method for constraining genome-scale models using internal flux ratios. The method was effective for modeling wild-type and engineered strains of C. acetobutylicum.     

OptForce: An Optimization Procedure for Identifying All Genetic Manipulations Leading to Targeted Overproductions

Computational procedures for predicting metabolic interventions leading to the overproduction of biochemicals in microbial strains are widely in use. However, these methods rely on surrogate biological objectives (e.g., maximize growth rate or minimize metabolic adjustments) and do not make use of flux measurements often available for the wild-type strain. In this work, we introduce the OptForce procedure that identifies all possible engineering interventions by classifying reactions in the metabolic model depending upon whether their flux values must increase, decrease or become equal to zero to meet a pre-specified overproduction target. We hierarchically apply this classification rule for pairs, triples, quadruples, etc. of reactions. This leads to the identification of a sufficient and non-redundant set of fluxes that must change (i.e., MUST set) to meet a pre-specified overproduction target. Starting with this set we subsequently extract a minimal set of fluxes that must actively be forced through genetic manipulations (i.e., FORCE set) to ensure that all fluxes in the network are consistent with the overproduction objective. We demonstrate our OptForce framework for succinate production in Escherichia coli using the most recent in silico E. coli model, iAF1260. The method not only recapitulates existing engineering strategies but also reveals non-intuitive ones that boost succinate production by performing coordinated changes on pathways distant from the last steps of succinate synthesis.     

Physiologically Shrinking the Solution Space of a Saccharomyces cerevisiae Genome-Scale Model Suggests the Role of the Metabolic Network in Shaping Gene Expression Noise

Sampling the solution space of genome-scale models is generally conducted to determine the feasible region for metabolic flux distribution. Because the region for actual metabolic states resides only in a small fraction of the entire space, it is necessary to shrink the solution space to improve the predictive power of a model. A common strategy is to constrain models by integrating extra datasets such as high-throughput datasets and C¹³-labeled flux datasets. However, studies refining these approaches by performing a meta-analysis of massive experimental metabolic flux measurements, which are closely linked to cellular phenotypes, are limited. In the present study, experimentally identified metabolic flux data from 96 published reports were systematically reviewed. Several strong associations among metabolic flux phenotypes were observed. These phenotype-phenotype associations at the flux level were quantified and integrated into a Saccharomyces cerevisiae genome-scale model as extra physiological constraints. By sampling the shrunken solution space of the model, the metabolic flux fluctuation level, which is an intrinsic trait of metabolic reactions determined by the network, was estimated and utilized to explore its relationship to gene expression noise. Although no correlation was observed in all enzyme-coding genes, a relationship between metabolic flux fluctuation and expression noise of genes associated with enzyme-dosage sensitive reactions was detected, suggesting that the metabolic network plays a role in shaping gene expression noise. Such correlation was mainly attributed to the genes corresponding to non-essential reactions, rather than essential ones. This was at least partially, due to regulations underlying the flux phenotype-phenotype associations. Altogether, this study proposes a new approach in shrinking the solution space of a genome-scale model, of which sampling provides new insights into gene expression noise.     

Active transport: Definitions and criteria

The thermodynamic definition of active transport is restated in terms of the rate of entropy production. A substance is said to be transported actively when the product of its flux by the force acting upon it across the membrane is negative. A general expression for the rate of entropy production in a complex membrane is which chemical reactions may occur is given, and this expression is developed for a somewhat simplified case. The resulting relation is used as a basis for defining and establishing experimental criteria for types of active transport. Two basic types are distinguished and are designatedcoupled transport andforced transport, respectively. Only the latter type is dependent upon energyielding chemical reactions.     

Conservation of high-flux backbone in alternate optimal and near-optimal flux distributions of metabolic networks

Constraint-based flux balance analysis (FBA) has proven successful in predicting the flux distribution of metabolic networks in diverse environmental conditions. FBA finds one of the alternate optimal solutions that maximizes the biomass production rate. Almaas et al. have shown that the flux distribution follows a power law, and it is possible to associate with most metabolites two reactions which maximally produce and consume a given metabolite, respectively. This observation led to the concept of high-flux backbone (HFB) in metabolic networks. In previous work, the HFB has been computed using a particular optima obtained using FBA. In this paper, we investigate the conservation of HFB of a particular solution for a given medium across different alternate optima and near-optima in metabolic networks of E. coli and S. cerevisiae. Using flux variability analysis (FVA), we propose a method to determine reactions that are guaranteed to be in HFB regardless of alternate solutions. We find that the HFB of a particular optima is largely conserved across alternate optima in E. coli, while it is only moderately conserved in S. cerevisiae. However, the HFB of a particular near-optima shows a large variation across alternate near-optima in both organisms. We show that the conserved set of reactions in HFB across alternate near-optima has a large overlap with essential reactions and reactions which are both uniquely consuming (UC) and uniquely producing (UP). Our findings suggest that the structure of the metabolic network admits a high degree of redundancy and plasticity in near-optimal flow patterns enhancing system robustness for a given environmental condition.     

Inferring Metabolic States in Uncharacterized Environments Using Gene-Expression Measurements

The large size of metabolic networks entails an overwhelming multiplicity in the possible steady-state flux distributions that are compatible with stoichiometric constraints. This space of possibilities is largest in the frequent situation where the nutrients available to the cells are unknown. These two factors: network size and lack of knowledge of nutrient availability, challenge the identification of the actual metabolic state of living cells among the myriad possibilities. Here we address this challenge by developing a method that integrates gene-expression measurements with genome-scale models of metabolism as a means of inferring metabolic states. Our method explores the space of alternative flux distributions that maximize the agreement between gene expression and metabolic fluxes, and thereby identifies reactions that are likely to be active in the culture from which the gene-expression measurements were taken. These active reactions are used to build environment-specific metabolic models and to predict actual metabolic states. We applied our method to model the metabolic states of Saccharomyces cerevisiae growing in rich media supplemented with either glucose or ethanol as the main energy source. The resulting models comprise about 50% of the reactions in the original model, and predict environment-specific essential genes with high sensitivity. By minimizing the sum of fluxes while forcing our predicted active reactions to carry flux, we predicted the metabolic states of these yeast cultures that are in large agreement with what is known about yeast physiology. Most notably, our method predicts the Crabtree effect in yeast cells growing in excess glucose, a long-known phenomenon that could not have been predicted by traditional constraint-based modeling approaches. Our method is of immediate practical relevance for medical and industrial applications, such as the identification of novel drug targets, and the development of biotechnological processes that use complex, largely uncharacterized media, such as biofuel production.