Title: Functional geometry of protein-protein interaction networks,
Abstract: 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.