Coevolution of Quasispecies: B-Cell Mutation Rates Maximize Viral Error Catastrophes

Coevolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this coadaptive model, besides the classical error catastrophe for high virus mutation rates, a second "adaptation" catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement, one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.