Estimating the size of the solution space of metabolic networks

TL;DR

This paper introduces a new algorithm based on the Bethe approximation to efficiently estimate the volume of the solution space of metabolic networks, enabling faster analysis compared to Monte Carlo methods.

Contribution

The authors develop a polynomial-time algorithm for characterizing the entire set of stable fluxes in metabolic networks, improving computational efficiency over existing methods.

Findings

Algorithm closely matches Monte Carlo estimations

Efficient computation of flux distribution volumes

Analysis of gene knock-outs impacts on solution space

Abstract

In this work we propose a novel algorithmic strategy that allows for an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. The algorithm, based on the well-known Bethe approximation, allows the computation in polynomial time of the volume of a non full-dimensional convex polytope in high dimensions. The result of our algorithm match closely the prediction of Monte Carlo based estimations of the flux distributions of the Red Blood Cell metabolic network but in incomparably shorter time. We also analyze the statistical properties of the average fluxes of the reactions in the E-Coli metabolic network and finally to test the effect of gene knock-outs on the size of the solution space of the E-Coli central metabolism.