Abstract
Constraint-based modeling helps researchers to understand metabolic networks. Minimal Cut Sets (MCSs) are minimal knock-out sets that block a target reaction in metabolic networks. Most approaches for finding the MCSs for a target reaction in constrained-based models require the computation of the set of elementary flux modes (EFMs) either as an intermediate step or as a byproduct of the calculation. Recently, Ballerstein et al. [BvKKH11] proposed a method of computing the MCSs directly. We propose an alternate method to compute the MCSs directly, based on linear programming duality. We prove the correctness of our new approach, extending the last author’s doctoral work [Chi10]. The key idea is to find the EFMs of a fully reversible network with stoichiometric matrix equal to the transposed nullspace matrix of the original network’s stoichiometric matrix. We implement our method and show that it succeeds in calculating the set of MCSs in many models where other approaches are not able to finish within a reasonable amount of time. Thus, in addition to its theoretical novelty, our approach provides a practical advantage over existing methods.