Self-linking duplication-divergence model for protein interaction networks*

Models of protein-protein interaction networks provide insights into the structure and evolutionary origin of these networks as well as how they behave. The standard duplication-divergence model simulates the degree distribution of real protein-protein interaction data accurately (1). However, this model does not include self-interactions, although the corresponding homodimers play a key role in biology. Here, we extend and analyze the duplication-divergence model with self-linking nodes. Copying a self-linking node leads to a self-linking child with probability σ that connects back to the parent node. This addition gives rise to higher average degree for self-linking nodes than non-self-linking nodes, as is seen in real protein-protein interaction data. Also, in real data the clustering coefficient generally increases as the fraction of self-linking neighbors on a node increases, another pattern captured by our model. Overall, due to the model’s sensitivity to initial conditions, self-links have a major impact on the network topology at all scales.

1. 1. I. Ispolatov, P. L. Krapivsky, and A. Yuryev. Duplication-divergence model of protein interaction network. Phys. Rev E. 71, 061911 (2005).