Evolution of Protein-protein Interaction Networks in Duplication-Divergence Model

Abstract

Protein interacts with one another resulting in complex functions in living organisms. Like many other real-world networks, the networks of protein-protein interactions possess a certain degree of ordering, such as the scale-free property. The latter means that the probability $P$ to find a protein that interacts with $k$ other proteins follows a power law, $P(k) \sim k^{-\gamma}$. Protein interaction networks (PINs) have been studied by using a stochastic model, the duplication-divergence model, which is based on mechanisms of gene duplication and divergence during evolution. In this work, we show that this model can be used to fit experimental data on the PIN of yeast Saccharomyces cerevisae at two different time instances simultaneously. Our study shows that the evolution of PIN given by model is consistent with growing experimental data over time, and that the scale-free property of protein interaction network is robust against random deletion of interactions.