Damage, connectivity and essentiality in protein-protein interaction networks

The proteome, a set of proteins expressed in an organism, is organized in an intricate web called the protein-protein interaction (PPI) network. In this article we propose a topological parameter called damage, that measures the consequences of the deletion of a protein from the network. We investigate different PPI data sets using this parameter and also traditional ones: the connectivity and the clusterization coefficient. We show that damage histogram obeys a power law in all data sets, and that proteins that cause a large damage are, with high probability, essential. For data sets that consider physical interactions the PPI network is a hierarchical scale-free network, while for data sets that consider functional interactions the PPI network is a scale-free graph.