Hypergraph models of biological networks to identify genes critical to pathogenic viral response

Song Feng, Emily Heath, Brett Jefferson, Cliff Joslyn, Henry Kvinge, Hugh D. Mitchell, Brenda Praggastis, Amie J. Eisfeld, Amy C. Sims, Larissa B. Thackray, Shufang Fan, Kevin B. Walters, Peter J. Halfmann, Danielle Westhoff-Smith, Qing Tan, Vineet D. Menachery, Timothy P. Sheahan, Adam S. Cockrell, Jacob F. Kocher, Kelly G. Stratton, Natalie C. Heller, Lisa M. Bramer, Michael S. Diamond, Ralph S. Baric, Katrina M. Waters, Yoshihiro Kawaoka, Jason E. McDermott, Emilie Purvine

Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems. Hypergraphs are generalizations of graphs that naturally model multi-way relationships and have shown promise in modeling systems such as protein complexes and metabolic reactions. In this paper we seek to understand how hypergraphs can more faithfully identify, and potentially predict, important genes based on complex relationships inferred from genomic expression data sets. We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges represent significantly perturbed genes, and vertices represent individual biological samples with specific experimental conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. Our results demonstrate the utility of using hypergraphs to represent complex biological systems and highlight central important responses in common to a variety of highly pathogenic viruses.