Viral evolution under the pressure of an adaptive immune system - optimal mutation rates for viral escape

Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is limited from above due to genomic information deterioration, and from below by insufficient sequence diversity, which leads to a quick eradication of the virus by the immune system. The mutation rate that optimally balances these two requirements depends to first order on the ratio of the inverse of the virus’ growth rate and the time the immune system needs to develop a specific answer to an antigen. We find that a virus is most viable if it generates exactly one mutation within the time it takes for the immune system to adapt to a new viral epitope. Experimental viral mutation rates, in particular for HIV (human immunodeficiency virus), seem to suggest that many viruses have achieved their optimal mutation rate.