  Many of the chemical reactions that take place within a living cell are
irreversible. Due to evolutionary pressures, the number of allowable reactions
within these systems are highly constrained and thus the resulting metabolic
networks display considerable asymmetry. In this paper, we explore possible
evolutionary factors pertaining to the reduced symmetry observed in these
networks, and demonstrate the important role environmental variability plays in
shaping their structural organization. Interpreting the returnability index as
an equilibrium constant for a reaction network in equilibrium with a
hypothetical reference system, enables us to quantify the extent to which a
metabolic network is in disequilibrium. Further, by introducing a new directed
centrality measure via an extension of the subgraph centrality metric to
directed networks, we are able to characterise individual metabolites by their
participation within metabolic pathways. To demonstrate these ideas, we study
116 metabolic networks of bacteria. In particular, we find that the equilibrium
constant for the metabolic networks decreases significantly in-line with
variability in bacterial habitats, supporting the view that environmental
variability promotes disequilibrium within these biochemical reaction systems.

Molecular Networks;Statistical Mechanics;Biological Physics