Preferential duplication in the sparse part of yeast protein interaction network

Gene duplication is an important mechanism driving the evolution of biomolecular network. Thus, it is expected that there should be a strong relationship between a gene's duplicability and the interactions of its protein product with other proteins in the network. We studied this question in the context of the protein interaction network (PIN) of Saccharomyces cerevisiae. We found that duplicates have, on average, significantly lower clustering coefficient (CC) than singletons, and the proportion of duplicates (PD) decreases steadily with CC. Furthermore, using functional annotation data, we observed a strong negative correlation between PD and the mean CC for functional categories. By partitioning the network into modules and assigning each protein a modularity measure Q(n), we found that CC of a protein is a reflection of its modularity. Moreover, the core components of complexes identified in a recent high-throughput experiment, characterized by high CC, have lower PD than that of the attachments. Subsequently, 2 types of hub were identified by their degree, CC and Q(n). Although PD of intramodular hubs is much less than the network average, PD of intermodular hubs is comparable to, or even higher than, the network average. Our results suggest that high CC, and thus high modularity, pose strong evolutionary constraints on gene duplicability, and gene duplication prefers to happen in the sparse part of PINs.