If viral strains are sufficiently similar in their immunodominant epitopes, then populations of cross-reactive T cells may be boosted by exposure to one strain and provide protection against infection by another at a later date. This type of pre-existing immunity may be important in the adaptive immune response to influenza and to coronaviruses. Patterns of recognition of epitopes by T cell clonotypes (a set of cells sharing the same T cell receptor) are represented as edges on a bipartite network. We describe different methods of constructing bipartite networks that exhibit cross-reactivity, and the dynamics of the T cell repertoire in conditions of homeostasis, infection and re-infection. Cross-reactivity may arise simply by chance, or because immunodominant epitopes of different strains are structurally similar. We introduce a circular space of epitopes, so that T cell cross-reactivity is a quantitative measure of the overlap between clonotypes that recognize similar (that is, close in epitope space) epitopes.
Keywords: bipartite network; competition process; cross-reactivity; heterologous infection; mathematical modeling; pre-existing immunity.