On inner and outer descriptions of the steady-state flux cone of a metabolic network

Constraint-based approaches have proved successful in analyzing complex metabolic networks. They restrict the range of all possible behaviors that a metabolic system can display under governing constraints. The set of all possible flux distributions over a metabolic network at steady state defines a polyhedral cone, the steady-state flux cone. This cone can be analyzed using an inner description based on sets of generating vectors such as elementary flux modes or extreme pathways. Another possibility is the use of an outer description based on sets of non-negativity constraints. In this paper, we study the relationship between inner and outer descriptions of the cone. We give a generic procedure to show how inner descriptions can be computed from the outer one. Then we use this procedure to explain why, for large-scale metabolic networks, the size of the inner descriptions may be several orders of magnitude larger than that of the outer description. © 2008 Springer Berlin Heidelberg.