On the Computation of Minimal Cut Sets in Genome Scale Metabolic Networks

A cut set for an objective reaction in a metabolic network is a set of reactions whose knockout disables flux through that reaction at steady state. Cut sets represent a particular type of failure mode of a metabolic network and may correspond to novel drug targets. In this paper, we demonstrate how cut sets can be obtained from the computation of sub-elementary modes (sub-EM). The sub-EM's of a metabolic network are the elementary modes (EM) of a submatrix of the stoichiometry matrix formed by taking a subset of its rows. Sub-EM's emerge naturally in the intermediate steps of the standard tableau algorithm for computation of EM, and are thus obtainable for a network of any size. By employing properties of the feasible flux cone, we show how cut sets for a reaction can be constructed by enumerating minimal hitting sets for the sub-EM's containing that reaction. Though the resulting cut sets are not guaranteed to be minimal, they can be reduced to minimality via a second linear programming pruning step. We demonstrate the applicability of this approach to a recent genome scale metabolic model of E.coli.