title: Identifying all moiety conservation laws in genome-scale metabolic networks.
abstract: The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.
authors.affiliation: CNR-IPCF, Unità di Roma-Sapienza, Roma, Italy; Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy; Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, Roma, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: De Martino
authors.affiliation: Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, Roma, Italy.
authors.forename: Daniele
authors.initials: D
authors.lastname: De Martino
authors.affiliation: Henri-Poincaré-Group of Complex Systems and Department of Theoretical Physics, Physics Faculty, University of Havana, La Habana, Cuba.
authors.forename: Roberto
authors.initials: R
authors.lastname: Mulet
authors.affiliation: DISAT and Centre for Computational Sciences, Politecnico di Torino, Torino, Italy; Human Genetics Foundation, Torino, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Pagnani
mesh_terms: D000818:Animals; D004926:Escherichia coli / Q000502:physiology*; D053263:Gene Regulatory Networks / Q000502:physiology*; D016680:Genome, Bacterial / Q000502:physiology*; D015894:Genome, Human / Q000502:physiology*; D006801:Humans; D055442:Metabolome / Q000502:physiology*; D008954:Models, Biological