Identifying all irreducible conserved metabolite pools in genome-scale metabolic networks: a general method and the case of Escherichia coli

TL;DR

This paper introduces a novel computational method combining Monte Carlo, message passing, and relaxation algorithms to identify all irreducible conserved metabolite pools in large-scale metabolic networks, exemplified on E. coli.

Contribution

It presents an efficient, general approach to find all integer conservation laws in metabolic networks, addressing an NP-hard problem with a new algorithmic strategy.

Findings

Successfully analyzed E. coli metabolic reconstructions in different media.

Discovered a scaling relation linking pool size to metabolite number.

Provided a certificate for the correctness and maximality of solutions.

Abstract

The stoichiometry of metabolic networks usually gives rise to a family of conservation laws for the aggregate concentration of specific pools of metabolites, which not only constrain the dynamics of the network, but also provide key insight into a cell's production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all integer solutions to an NP-hard programming problem. Here we propose a novel and efficient computational strategy that combines Monte Carlo, message passing, and relaxation algorithms to compute the complete set of irreducible integer conservation laws of a given stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. The method is deployed for the analysis of the complete set of irreducible integer pools of two large-scale reconstructions of the metabolism of the bacterium Escherichia coli in different growth media. In addition, we uncover a scaling relation that links the size of the irreducible pool basis to the number of metabolites, for which we present an analytical explanation.