Non-Uniform Survival Rate of Heterodimerization Links in the Evolution of the Yeast Protein-Protein Interaction Network

Protein-protein interaction networks (PINs) are scale-free networks with a small-world property. In a small-world network, the average cluster coefficient (<C>) is much higher than in a random network, but the average shortest path length (<L>) is similar between the two networks. To understand the evolutionary mechanisms shaping the structure of PINs, simulation studies using various network growth models have been performed. It has been reported that the heterodimerization (HD) model, in which a new link is added between duplicated nodes with a uniform probability, could reproduce scale-freeness and a high <C>. In this paper, however, we show that the HD model is unsatisfactory, because (i) to reproduce the high <C> in the yeast PIN, a much larger number (n (HI)) of HD links (links between duplicated nodes) are required than the estimated number of n (HI) in the yeast PIN and (ii) the spatial distribution of triangles in the yeast PIN is highly skewed but the HD model cannot reproduce the skewed distribution. To resolve these discrepancies, we here propose a new model named the non-uniform heterodimerization (NHD) model. In this model, an HD link is preferentially attached between duplicated nodes when they share many common neighbors. Simulation studies demonstrated that the NHD model can successfully reproduce the high <C>, the low n (HI), and the skewed distribution of triangles in the yeast PIN. These results suggest that the survival rate of HD links is not uniform in the evolution of PINs, and that an HD link between high-degree nodes tends to be evolutionarily conservative. The non-uniform survival rate of HD links can be explained by assuming a low mutation rate for a high-degree node, and thus this model appears to be biologically plausible.