Organising metabolic networks: Cycles in flux distributions.

Metabolic networks are among the most widely studied biological systems. The topology and interconnections of metabolic reactions have been well described for many species. This is, however, not sufficient to understand how their activity is regulated in living organisms. These descriptions depict a static set of possible chains of reactions, with no information about the dynamic activity of reaction fluxes. Cyclic structures are thought to play a central role in the homeostasis of biological systems and in their resilience to a changing environment. In this work, we present a methodology to help investigating dynamic fluxes associated to biochemical reactions in metabolic networks. We introduce an algorithm for partitioning fluxes between cyclic and acyclic sub-networks, adapted from an algorithm initially developed to study fluxes in trophic networks. Using this algorithm, we analyse three metabolic systems: the central metabolism of wild type and a deletion mutant of Escherichia coli, erythrocyte metabolism and the central metabolism of the bacterium Methylobacterium extorquens. This methodology unveils the role of cycles in driving and maintaining metabolic fluxes under perturbations in these examples, and may be used to further investigate and understand the organisational invariance of biological systems.