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An analytic approximation of the feasible space of metabolic networks.

ABSTRACT: Assuming a steady-state condition within a cell, metabolic fluxes satisfy an underdetermined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with linear programming (as flux balance analysis), and their marginal distributions can be approximately computed with Monte Carlo sampling. Here we present an approximate analytic method for the latter task based on expectation propagation equations that does not involve sampling and can achieve much better predictions than other existing analytic methods. The method is iterative, and its computation time is dominated by one matrix inversion per iteration. With respect to sampling, we show through extensive simulation that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.

SUBMITTER: Braunstein A

PROVIDER: S-EPMC5384209 | biostudies-literature | 2017 Apr

REPOSITORIES: biostudies-literature

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An analytic approximation of the feasible space of metabolic networks.

Braunstein Alfredo A Muntoni Anna Paola AP Pagnani Andrea A

Nature communications 20170406

Assuming a steady-state condition within a cell, metabolic fluxes satisfy an underdetermined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with linear programming (as flux balance analysis), and their marginal distributions can be a ...[more]

PMID: 28382977

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Project description:BACKGROUND: Cellular metabolism is one of the most investigated system of biological interactions. While the topological nature of individual reactions and pathways in the network is quite well understood there is still a lack of comprehension regarding the global functional behavior of the system. In the last few years flux-balance analysis (FBA) has been the most successful and widely used technique for studying metabolism at system level. This method strongly relies on the hypothesis that the organism maximizes an objective function. However only under very specific biological conditions (e.g. maximization of biomass for E. coli in reach nutrient medium) the cell seems to obey such optimization law. A more refined analysis not assuming extremization remains an elusive task for large metabolic systems due to algorithmic limitations. RESULTS: In this work we propose a novel algorithmic strategy that provides an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. Using a technique derived from the fields of statistical physics and information theory we designed a message-passing algorithm to estimate the size of the affine space containing all possible steady-state flux distributions of metabolic networks. The algorithm, based on the well known Bethe approximation, can be used to approximately compute the volume of a non full-dimensional convex polytope in high dimensions. We first compare the accuracy of the predictions with an exact algorithm on small random metabolic networks. We also verify that the predictions of the algorithm match closely those of Monte Carlo based methods in the case of the Red Blood Cell metabolic network. Then we test the effect of gene knock-outs on the size of the solution space in the case of E. coli central metabolism. Finally we analyze the statistical properties of the average fluxes of the reactions in the E. coli metabolic network. CONCLUSION: We propose a novel efficient distributed algorithmic strategy to estimate the size and shape of the affine space of a non full-dimensional convex polytope in high dimensions. The method is shown to obtain, quantitatively and qualitatively compatible results with the ones of standard algorithms (where this comparison is possible) being still efficient on the analysis of large biological systems, where exact deterministic methods experience an explosion in algorithmic time. The algorithm we propose can be considered as an alternative to Monte Carlo sampling methods.

Project description:NASA's planned mission to Mars will result in astronauts being exposed to ∼350 mSv/yr of Galactic Cosmic Radiation (GCR). A growing body of data from ground-based experiments indicates that exposure to space radiation doses (approximating those that astronauts will be exposed to on a mission to Mars) impairs a variety of cognitive processes, including cognitive flexibility tasks. Some studies report that 33% of individuals may experience severe cognitive impairment. Translating the results from ground-based rodent studies into tangible risk estimates for astronauts is an enormous challenge, but it would be germane for NASA to use the vast body of data from the rodent studies to start developing appropriate countermeasures, in the expectation that some level of space radiation (SR) -induced cognitive impairment could occur in astronauts. While some targeted studies have reported radiation-induced changes in the neurotransmission properties and/or increased neuroinflammation within space radiation exposed brains, there remains little information that can be used to start the development of a mechanism-based countermeasure strategy. In this study, we have employed a robust label-free mass spectrometry (MS) -based untargeted quantitative proteomic profiling approach to characterize the composition of the medial prefrontal cortex (mPFC) proteome in rats that have been exposed to 15 cGy of 600 MeV/n28Si ions. A variety of analytical techniques were used to mine the generated expression data, which in such studies is typically hampered by low and variable sample size. We have identified several pathways and proteins whose expression alters as a result of space radiation exposure, including decreased mitochondrial function, and a further subset of proteins differs in rats that have a high level of cognitive performance after SR exposure in comparison with those that have low performance levels. While this study has provided further insight into how SR impacts upon neurophysiology, and what adaptive responses can be invoked to prevent the emergence of SR-induced cognitive impairment, the main objective of this paper is to outline strategies that can be used by others to analyze sub-optimal data sets and to identify new information.

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An analytic approximation of the feasible space of metabolic networks.

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An analytic approximation of the feasible space of metabolic networks.

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