Simulating Weak Attacks in a New Duplication-Divergence Model with Node Loss

A better understanding of protein-protein interaction (PPI) networks representing physical interactions between proteins could be beneficial for evolutionary insights as well as for practical applications such as drug development. As a statistical model for PPI networks, duplication-divergence models have been proposed, but they suffer from resulting in either very sparse networks in which most of the proteins are isolated, or in networks which are much denser than what is usually observed, having almost no isolated proteins. Moreover, in real networks, where a gene codes a protein, gene loss may occur. The loss of nodes has not been captured in duplication-divergence models to date. Here, we introduce a new duplication-divergence model which includes node loss. This mechanism results in networks in which the proportion of isolated proteins can take on values which are strictly between 0 and 1. To understand this new model, we apply strong and weak attacks to networks from duplication-divergence models with and without node loss, and compare the results to those obtained when carrying out similar attacks on two real PPI networks of E. coli and of S. cerevisiae. We find that the new model more closely reflects the damage caused by strong and weak attacks found in the PPI networks.