The Topology of Evasion: Persistent Homology of Gene Repertoires of Immunity

Families of genes that are important in adaptive immunity are often large in number and evolve through both mutations and recombination. Extensive recombination produces complex reticulate relationships between genes that require additional analytic tools beyond phylogenetics. We consider several families of genes involved in defense and immune systems from plants, antibiotic resistant bacteria, and trypanosomatid parasites, using the framework of persistent homology from topological data analysis. Some of the gene families considered possess extensive higher-dimensional persistent homological representatives, which may be typical of other gene families participating in adaptive immunity.