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Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks.

ABSTRACT: The metabolism of organisms can be studied with comprehensive stoichiometric models of their metabolic networks. Flux balance analysis (FBA) calculates optimal metabolic performance of stoichiometric models. However, detailed biological interpretation of FBA is limited because, in general, a huge number of flux patterns give rise to the same optimal performance. The complete description of the resulting optimal solution spaces was thus far a computationally intractable problem. Here we present CoPE-FBA: Comprehensive Polyhedra Enumeration Flux Balance Analysis, a computational method that solves this problem. CoPE-FBA indicates that the thousands to millions of optimal flux patterns result from a combinatorial explosion of flux patterns in just a few metabolic sub-networks. The entire optimal solution space can now be compactly described in terms of the topology of these sub-networks. CoPE-FBA simplifies the biological interpretation of stoichiometric models of metabolism, and provides a profound understanding of metabolic flexibility in optimal states.

SUBMITTER: Kelk SM

PROVIDER: S-EPMC3419370 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks.

Kelk Steven M SM Olivier Brett G BG Stougie Leen L Bruggeman Frank J FJ

Scientific reports 20120815

The metabolism of organisms can be studied with comprehensive stoichiometric models of their metabolic networks. Flux balance analysis (FBA) calculates optimal metabolic performance of stoichiometric models. However, detailed biological interpretation of FBA is limited because, in general, a huge number of flux patterns give rise to the same optimal performance. The complete description of the resulting optimal solution spaces was thus far a computationally intractable problem. Here we present C ...[more]

PMID: 22896812

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Project description:BackgroundGenome-scale metabolic models are important tools in systems biology. They permit the in-silico prediction of cellular phenotypes via mathematical optimisation procedures, most importantly flux balance analysis. Current studies on metabolic models mostly consider reaction fluxes in isolation. Based on a recently proposed metabolite-centric approach, we here describe a set of methods that enable the analysis and interpretation of flux distributions in an integrated metabolite-centric view. We demonstrate how this framework can be used for the refinement of genome-scale metabolic models.ResultsWe applied the metabolite-centric view developed here to the most recent metabolic reconstruction of Escherichia coli. By compiling the balance sheets of a small number of currency metabolites, we were able to fully characterise the energy metabolism as predicted by the model and to identify a possibility for model refinement in NADPH metabolism. Selected branch points were examined in detail in order to demonstrate how a metabolite-centric view allows identifying functional roles of metabolites. Fructose 6-phosphate aldolase and the sedoheptulose bisphosphate bypass were identified as enzymatic reactions that can carry high fluxes in the model but are unlikely to exhibit significant activity in vivo. Performing a metabolite essentiality analysis, unconstrained import and export of iron ions could be identified as potentially problematic for the quality of model predictions.ConclusionsThe system-wide analysis of split ratios and branch points allows a much deeper insight into the metabolic network than reaction-centric analyses. Extending an earlier metabolite-centric approach, the methods introduced here establish an integrated metabolite-centric framework for the interpretation of flux distributions in genome-scale metabolic networks that can complement the classical reaction-centric framework. Analysing fluxes and their metabolic context simultaneously opens the door to systems biological interpretations that are not apparent from isolated reaction fluxes. Particularly powerful demonstrations of this are the analyses of the complete metabolic contexts of energy metabolism and the folate-dependent one-carbon pool presented in this work. Finally, a metabolite-centric view on flux distributions can guide the refinement of metabolic reconstructions for specific growth scenarios.

Project description:A regulated genome-scale model for Clostridium acetobutylicum ATCC 824 was developed based on its metabolic network reconstruction. To aid model convergence and limit the number of flux-vector possible solutions (the size of the phenotypic solution space), modeling strategies were developed to impose a new type of constraint at the endo-exo-metabolome interface. This constraint is termed the specific proton flux state, and its use enabled accurate prediction of the extracellular medium pH during vegetative growth of batch cultures. The specific proton flux refers to the influx or efflux of free protons (per unit biomass) across the cell membrane. A specific proton flux state encompasses a defined range of specific proton fluxes and includes all metabolic flux distributions resulting in a specific proton flux within this range. Effective simulation of time-course batch fermentation required the use of independent flux balance solutions from an optimum set of specific proton flux states. Using a real-coded genetic algorithm to optimize temporal bounds of specific proton flux states, we show that six separate specific proton flux states are required to model vegetative-growth metabolism and accurately predict the extracellular medium pH. Further, we define the apparent proton flux stoichiometry per weak acids efflux and show that this value decreases from approximately 3.5 mol of protons secreted per mole of weak acids at the start of the culture to approximately 0 at the end of vegetative growth. Calculations revealed that when specific weak acids production is maximized in vegetative growth, the net proton exchange between the cell and environment occurs primarily through weak acids efflux (apparent proton flux stoichiometry is 1). However, proton efflux through cation channels during the early stages of acidogenesis was found to be significant. We have also developed the concept of numerically determined sub-systems of genome-scale metabolic networks here as a sub-network with a one-dimensional null space basis set. A numerically determined sub-system was constructed in the genome-scale metabolic network to study the flux magnitudes and directions of acetylornithine transaminase, alanine racemase, and D-alanine transaminase. These results were then used to establish additional constraints for the genome-scale model.

Project description:Determination of internal metabolic fluxes is crucial for fundamental and applied biology because they map how carbon and electrons flow through metabolism to enable cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) and Two-Scale 13 C Metabolic Flux Analysis (2S- 13 C MFA) are two techniques used to determine such fluxes. Both operate on the simplifying approximation that metabolic flux from peripheral metabolism into central "core" carbon metabolism is minimal, and can be omitted when modeling isotopic labeling in core metabolism. The validity of this "two-scale" or "bow tie" approximation is supported both by the ability to accurately model experimental isotopic labeling data, and by experimentally verified metabolic engineering predictions using these methods. However, the boundaries of core metabolism that satisfy this approximation can vary across species, and across cell culture conditions. Here, we present a set of algorithms that (1) systematically calculate flux bounds for any specified "core" of a genome-scale model so as to satisfy the bow tie approximation and (2) automatically identify an updated set of core reactions that can satisfy this approximation more efficiently. First, we leverage linear programming to simultaneously identify the lowest fluxes from peripheral metabolism into core metabolism compatible with the observed growth rate and extracellular metabolite exchange fluxes. Second, we use Simulated Annealing to identify an updated set of core reactions that allow for a minimum of fluxes into core metabolism to satisfy these experimental constraints. Together, these methods accelerate and automate the identification of a biologically reasonable set of core reactions for use with 13 C MFA or 2S- 13 C MFA, as well as provide for a substantially lower set of flux bounds for fluxes into the core as compared with previous methods. We provide an open source Python implementation of these algorithms at https://github.com/JBEI/limitfluxtocore.

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Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks.

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Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks.

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