Fitness valleys constrain HIV-1's adaptation to its secondary chemokine coreceptor

Fitness valleys, in which mutations at different loci are singly deleterious but jointly beneficial, arise because of reciprocal sign epistasis. Recent theoretical work provides analytical approximations of times to cross fitness valleys via three mechanisms: sequential fixation, stochastic tunnelling and recombination. These times depend critically on the effective population size (N(e)). Human immunodeficiency virus type 1 (HIV-1) encounters fitness valleys in adapting to its secondary cell-surface chemokine coreceptor, CXCR4. Adaptation to CXCR4 tends to occur late in infection and only in about 50% of patients and is associated with disease progression. It has been hypothesized that the need to cross fitness valleys may explain the delayed and inconsistent adaptation to CXCR4. We have identified four fitness valleys from a previous study of fitness epistasis in adaptation to CXCR4 and use estimates of the within-patient variance N(e) for different patient treatment statuses and infection stages (conditions) to estimate times to cross the valleys. These valleys may be crossed predominantly by stochastic tunnelling, although mean crossing times are consistently longer than the durations of the conditions for which they are calculated. These results were confirmed with stochastic simulation. Simulations show that crossing times for a given condition are highly variable and that for each condition there is a low probability of crossing each valley. These findings support the hypothesis that fitness valleys constrain the adaptation of HIV-1 to CXCR4. This study provides the first detailed analysis of the evolutionary dynamics associated with empirical fitness valleys.