Investigating the role of hemagglutinin protein stability in influenza A evolutionary dynamics*

Influenza A viruses (IAVs) cause a significant burden to human populations. They are notable for their rapid evolution arising from error-prone RNA polymerases in conjunction with selective pressures from hosts. Most host immune responses target the surface protein hemagglutinin (HA) and typically generate lifelong antibodies to seen strains. Thus to survive, IAVs must undergo mutations in HA that allow immune escape, while the HA protein must also satisfy functional constraints. We formulate a mathematical model of IAV evolution and transmission that spans scales from molecular to population processes. We couple models for HA protein thermal stability, mutation, and cross-immunity with a population-level model for the spread of infection, and characterize the effects of stability. Certain residues buried in the core of the HA protein may affect stability but not immunogenicity. We adapt our model to include these “buried” residues, and evaluate their influence on viral diversity, transmission, and evolutionary dynamics.