Evidence of a universal power law characterizing the evolution of metabolic networks

Abstract

Metabolic networks are known to be scale free but the evolutionary origin of this structural property is not clearly understood. One way of studying the dynamical process is to compare the metabolic networks of species that have arisen at different points in evolution and hence are related to each other to varying extents. We have compared the reaction sets of each metabolite across and within 15 groups of species. For a given pair of species and a given metabolite, the number $Δk$ of reactions of the metabolite that appear in the metabolic network of only one species and not the other is a measure of the distance between the two networks. While $Δk$ is small within groups of related species and large across groups, we find its probability distribution to be $\sim (Δk)^{-γ'}$ where $γ'$ is a universal exponent that is the same within and across groups. This exponent equals, upto statistical uncertainties, the exponent $γ$ in the scale free degree distribution $\sim k^{-γ}$. We argue that this, as well as our finding that $Δk$ is approximately linearly correlated with the degree $k$ of the metabolite, is evidence of a `proportionate change' process in evolution. We also discuss some molecular mechanisms that might be responsible for such an evolutionary process.