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The stoichiometry of metabolic networks usually gives rise to a family ofconservation laws for the aggregate concentration of specific pools ofmetabolites, which not only constrain the dynamics of the network, but alsoprovide key insight into a cell's production capabilities. When the conservedquantity identifies with a chemical moiety, extracting all such conservationlaws from the stoichiometry amounts to finding all integer solutions to anNP-hard programming problem. Here we propose a novel and efficientcomputational strategy that combines Monte Carlo, message passing, andrelaxation algorithms to compute the complete set of irreducible integerconservation laws of a given stoichiometric matrix, also providing acertificate for correctness and maximality of the solution. The method isdeployed for the analysis of the complete set of irreducible integer pools oftwo large-scale reconstructions of the metabolism of the bacterium Escherichiacoli in different growth media. In addition, we uncover a scaling relation thatlinks the size of the irreducible pool basis to the number of metabolites, forwhich we present an analytical explanation.

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