Functional geometry of protein-protein interaction networks

Motivation: Protein-protein interactions (PPIs) are usually modelled as networks. These networks have extensively been studied using graphlets, small induced subgraphs capturing the local wiring patterns around nodes in networks. They revealed that proteins involved in similar functions tend to be similarly wired. However, such simple models can only represent pairwise relationships and cannot fully capture the higher-order organization of protein interactions, including protein complexes. Results: To model the multi-sale organization of these complex biological systems, we utilize simplicial complexes from computational geometry. The question is how to mine these new representations of PPI networks to reveal additional biological information. To address this, we define simplets, a generalization of graphlets to simplicial complexes. By using simplets, we define a sensitive measure of similarity between simplicial complex network representations that allows for clustering them according to their data types better than clustering them by using other state-of-the-art measures, e.g., spectral distance, or facet distribution distance. We model human and baker's yeast PPI networks as simplicial complexes that capture PPIs and protein complexes as simplices. On these models, we show that our newly introduced simplet-based methods cluster proteins by function better than the clustering methods that use the standard PPI networks, uncovering the new underlying functional organization of the cell. We demonstrate the existence of the functional geometry in the PPI data and the superiority of our simplet-based methods to effectively mine for new biological information hidden in the complexity of the higher order organization of PPI networks.