Exploring metabolic pathways in genome-scale networks via generating flux modes.

MOTIVATION: The reconstruction of metabolic networks at the genome scale has allowed the analysis of metabolic pathways at an unprecedented level of complexity. Elementary flux modes (EFMs) are an appropriate concept for such analysis. However, their number grows in a combinatorial fashion as the size of the metabolic network increases, which renders the application of EFMs approach to large metabolic networks difficult. Novel methods are expected to deal with such complexity. RESULTS: In this article, we present a novel optimization-based method for determining a minimal generating set of EFMs, i.e. a convex basis. We show that a subset of elements of this convex basis can be effectively computed even in large metabolic networks. Our method was applied to examine the structure of pathways producing lysine in Escherichia coli. We obtained a more varied and informative set of pathways in comparison with existing methods. In addition, an alternative pathway to produce lysine was identified using a detour via propionyl-CoA, which shows the predictive power of our novel approach. AVAILABILITY: The source code in C++ is available upon request.

An optimization model for metabolic pathways.

MOTIVATION: Different mathematical methods have emerged in the post-genomic era to determine metabolic pathways. These methods can be divided into stoichiometric methods and path finding methods. In this paper we detail a novel optimization model, based upon integer linear programming, to determine metabolic pathways. Our model links reaction stoichiometry with path finding in a single approach. We test the ability of our model to determine 40 annotated Escherichia coli metabolic pathways. We show that our model is able to determine 36 of these 40 pathways in a computationally effective manner.