A universal power law and proportionate change process characterize the evolution of metabolic networks

Abstract

Biological and social systems have been found to possess a non-trivial underlying network structure of interacting components. An important current question concerns the nature of the evolutionary processes that have led to the observed structural patterns dynamically. By comparing the metabolic networks of evolutionarily closeby as well distant species, we present results on the evolution of these networks over short as well as long time scales. We observe that the amount of change in the reaction set of a metabolite across different species is proportional to the degree of the metabolite, thus providing empirical evidence for a `proportionate change' mechanism. We find that this evolutionary process is characterized by a power law with a universal exponent that is independent of the pair of species compared.