Enumeration of minimal stoichiometric precursor sets in metabolic networks

Background: What an organism needs at least from its environment to produce a set of metabolites, e.g. target(s) of interest and/or biomass, has been called a minimal precursor set. Early approaches to enumerate all minimal precursor sets took into account only the topology of the metabolic network (topological precursor sets). Due to cycles and the stoichiometric values of the reactions, it is often not possible to produce the target(s) from a topological precursor set in the sense that there is no feasible flux. Although considering the stoichiometry makes the problem harder, it enables to obtain biologically reasonable precursor sets that we call stoichiometric. Recently a method to enumerate all minimal stoichiometric precursor sets was proposed in the literature. The relationship between topological and stoichiometric precursor sets had however not yet been studied. Results: Such relationship between topological and stoichiometric precursor sets is highlighted. We also present two algorithms that enumerate all minimal stoichiometric precursor sets. The first one is of theoretical interest only and is based on the above mentioned relationship. The second approach solves a series of mixed integer linear programming problems. We compared the computed minimal precursor sets to experimentally obtained growth media of several Escherichia coli strains using genome-scale metabolic networks. Conclusions: The results show that the second approach efficiently enumerates minimal precursor sets taking stoichiometry into account, and allows for broad in silico studies of strains or species interactions that may help to understand e.g. pathotype and niche-specific metabolic capabilities. sasita is written in Java, uses cplex as LP solver and can be downloaded together with all networks and input files used in this paper at http://www.sasita.gforge.inria.fr.