Decomposition of flux distributions into metabolic pathways

Genome-scale reconstructions are often used for studying relationships between fundamental components of a metabolic system. In this study, we develop a novel computational method for analyzing predicted flux distributions for metabolic reconstructions. Because chemical reactions may have multiple reactants and products, a directed hypergraph where hyperarcs may have multiple tail vertices and head vertices is a more appropriate representation of the metabolic network than a conventional network. We use this view to represent predicted flux distributions by maximum generalized flows on hypergraphs. We then demonstrate that the generalized hyperflow problem may be transformed to an equivalent network flow problem with side constraints. This transformation allows a flux to be decomposed into chains of reactions. Subsequent analysis of these chains helps to characterize active pathways in a flux distribution. Such characterizations facilitate comparisons of flux distributions for different environmental conditions. The proposed method is applied to compare predicted flux distributions for Salmonella typhimurium to study changes in metabolism that cause enhanced virulence during a space flight. The differences between flux distributions corresponding to normal and enhanced virulence states confirm previous observations concerning infection mechanisms and suggest new pathways for exploration.