Structural considerations in the fitness landscape of a virus.

Viral fitness is determined by replication within hosts and transmission between them. We examine how pleiotropic mutations that have antagonistic effects (i.e., antibody evasion vs. receptor binding) on viral replication within hosts can impact viral immune escape in the host population. When the host population is vaccinated, the virus escapes from passive immunity by mutations in the antibody-binding region on the surface of the target protein. However, the reduced ability of the antibody to bind the virus is often accompanied by a reduced ability of the virus to bind the cell receptor because the antibody-binding region overlaps with the receptor-binding domain (RBD). The types of permitted mutations are limited. To investigate the causal relation between a mutation in a viral genome and adaptive evolution of a viral population, we developed a mathematical model that describes the population dynamics of viruses, antibodies, and normal/infected cells within a host. The coefficients describe the binding affinity between the virus and the induced antibody and that between the virus and its receptor. Our knowledge-based index enables us to estimate the effect of a mutation in a binding region on the binding affinity. Using population genetic theory, we evaluated the probability that a mutant is fixed in a host population. The mutations that can be fixed with high probabilities may determine how long a vaccine remains effective. We simulate the adaptive evolution of coronavirus, the etiological agent of severe acute respiratory syndrome, and show that some of mutations in the RBD may have high fixation probabilities in the vaccinated host population.