Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1

Abstract

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.

FIG. 1.

Schematic illustration of a viral replication cycle in the computer model. A number of N cells are either singly or doubly infected. They contain one or two proviruses inserted in their nucleus. For simplicity, only two viral types are shown, either as light or dark gray. Infected cells produce virions according to the fitness of the inserted proviruses. From the total virus population, (1 + f)N virions are selected that will infect N new target cells. The infecting virions are distributed randomly to the cells. A heterozygous virion can produce a recombinant provirus during reverse transcription, here shown in black.

FIG. 2.

Evolution of drug resistance. The homogenous wild-type population is replaced by the resistant double mutant. (A) In a small population of infected cells (N_e = 10³), the first single mutation typically rises to fixation before the population acquires the second mutation. (B) In simulations with a larger population of infected cells (N_e = 10⁴), the single mutations are typically both present at the same time. Therefore, recombination can combine the two single mutations and accelerate the evolution of the double mutant.

FIG. 3.

Reduction in time to fixation of a double mutant through recombination as a function of different population sizes and selection strengths. (A) Recombination has a significant effect for a population size of 10⁴ and intermediate selection strengths. However, at smaller population sizes, the effect is dramatically reduced. The following parameters were used: f = 0.75 and r = 0.5. (B) Using smaller parameters (f = 0.25 and r = 0.1) results in an overall decrease of the beneficial effect of recombination. In all simulations, the mutation rate was μ = 3 × 10⁻⁵ per base pair.

FIG. 4.

Reduction in time to fixation of the double mutant through recombination as a function of the effective population size when there is positive or negative epistasis between resistance mutations. Drift effects dominate in populations smaller than 10⁵, and in these populations, recombination reduces the time to fixation. For larger populations, genetic drift is smaller and epistatic interactions determine the population structure. In these populations, recombination only reduces the time to fixation for negative epistasis. For positive epistasis, recombination increases the time to fixation. The following parameters were used: μ = 3 × 10⁻⁵,r = 0.5,f = 0.75. The fitness levels of the wild type and double mutant were set to 1 and 1.2, respectively. The fitness levels of both single mutants were 1.05 for positive epistasis and 1.15 for negative epistasis.