Host-pathogen co-evolution and the emergence of broadly neutralizing antibodies in chronic infections
Armita Nourmohammad, Jakub Otwinowski, Joshua B. Plotkin

The vertebrate adaptive immune system provides a flexible and diverse set of molecules to neutralize pathogens. Yet, viruses that cause chronic infections, such as HIV, can survive by evolving as quickly as the adaptive immune system, forming an evolutionary arms race within a host. Here we introduce a mathematical framework to study the co-evolutionary dynamics of antibodies with antigens within a patient. We focus on changes in the binding interactions between the antibody and antigen populations, which result from the underlying stochastic evolution of genotype frequencies driven by mutation, selection, and drift. We identify the critical viral and immune parameters that determine the distribution of antibody-antigen binding affinities. We also identify definitive signatures of co-evolution that measure the reciprocal response between the antibody and viruses, and we introduce experimentally measurable quantities that quantify the extent of adaptation during continual co-evolution of the two opposing populations. Finally, we analyze competition between clonal lineages of antibodies and characterize the fate of a given lineage dependent on the state of the antibody and viral populations. In particular, we derive the conditions that favor the emergence of broadly neutralizing antibodies, which may be used in designing a vaccine against HIV.