Maximum likelihood inference of the evolutionary history of a PPI network from the duplication history of its proteins.

Evolutionary history of protein-protein interaction (PPI) networks provides valuable insight into molecular mechanisms of network growth. In this paper, we study how to infer the evolutionary history of a PPI network from its protein duplication relationship. We show that for a plausible evolutionary history of a PPI network, its relative quality, measured by the so-called loss number, is independent of the growth parameters of the network and can be computed efficiently. This finding leads us to propose two fast maximum likelihood algorithms to infer the evolutionary history of a PPI network given the duplication history of its proteins. Simulation studies demonstrated that our approach, which takes advantage of protein duplication information, outperforms NetArch, the first maximum likelihood algorithm for PPI network history reconstruction. Using the proposed method, we studied the topological change of the PPI networks of the yeast, fruitfly, and worm.