Extreme pathway lengths and reaction participation in genome-scale metabolic networks.

Extreme pathways are a unique and minimal set of vectors that completely characterize the steady-state capabilities of genome-scale metabolic networks. A framework is provided to mathematically characterize extreme pathway length and to study how individual reactions participate in the extreme pathway structure of a network. The length of an extreme pathway is the number of reactions that comprise it. Reaction participation is the percentage of extreme pathways that utilize a given reaction. These properties were computed for the production of individual amino acids and protein production in Helicobacter pylori and individual amino acid production in Haemophilus influenzae. Reaction participation classifies the reactions into groups that are always, sometimes, or never utilized for the production of a target product. The utilized reactions can be further grouped into correlated subsets of reactions, some of which are non-obvious, and which may, in turn, suggest regulatory structure. The length of the extreme pathways did not correlate with product yield or chemical complexity. The distributions of extreme pathway lengths in H. pylori were also very different from those in H. influenzae, showing a distinct systemic difference between the two organisms, despite overall similar metabolic networks. Reaction participation and extreme pathway lengths thus serve to elucidate systemic biological features.