Topological transitions on protein-protein interaction networks

Abstract

In this work, we utilized concepts of applied algebraic topology to explore the very recent ideas of topological phase transitions in complex networks to the context of the Duplication Divergence model for protein-protein interaction Network. To do so, we used methods of topological data analysis to compute the Euler characteristic analytically, and the Betti numbers numerically for two variants of the Duplication Divergence model, namely the totally asymmetric model and the heterodimerization model. We contrast our theoretical results with experimental data freely available at online repositories of gene coexpression networks of Saccharomyces cerevisiae, also known as baker’s yeast, as well as of the nematode Caenorhabditis elegans. We detected one topological phase transition in Yeast networks obtained according to different similarity measures, corresponding to phase transitions at close critical thresholds. Our results give evidence that the Euler characteristic can be interpreted as an intrinsic bio-marker for Yeast networks and reinforces the hypothesis of the possibility of using topological phase transitions to build topological and geometrical biomarkers for networks more generally.