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Network Mixture Models: an Introduction and Application to Protein Interactomes

Human Protein Interactomics represents a crucial research area in systems biology, and several new data sources and methods have been recently proposed. In our work, we refer to data integration and network inference domains, and with focus on group selection and modularity refinement. Our reference dataset is Ulitsky, Karp and Shamir (http://acgt.cs.tau.ac.il/clean), which integrates various sources, BIND, HPRD, BioGRID, and includes interactions detected from small-scale experiments, thus listing 7, 385 nodes and 23, 462 links. Concerning network inference, we explore graph mining techniques from both a deterministic and a probabilistic standpoint. It is widely adopted the application of the former methods to protein interactomes, of which we provide two examples, but it is definitely harder to see the application of probabilistic methods. Comparative examples are provided here. We look first at corenessand community-based grouping techniques, but then also at statistical mixture modelling with the goal of detecting human protein sub-interactomes. We suggest a novel way to select and prioritize information otherwise usually extracted under connectivity-based principles. A graph can be represented by an adjacency matrix (AM) embedding the interaction and non-interaction structure of the observed graph. The result for the case of undirected graphs is a binary AM. We show that the AM can be efficiently sampled to deal better with the inherent sparsity property of biological networks, and then proceed by adopting mixture models under flexible statistical assumptions.