Estimate of effective recombination rate and average selection coefficient for HIV in chronic infection

Abstract

HIV adaptation to a host in chronic infection is simulated by means of a Monte-Carlo algorithm that includes the evolutionary factors of mutation, positive selection with varying strength among sites, random genetic drift, linkage, and recombination. By comparing two sensitive measures of linkage disequilibrium (LD) and the number of diverse sites measured in simulation to patient data from one-time samples of pol gene obtained by single-genome sequencing from representative untreated patients, we estimate the effective recombination rate and the average selection coefficient to be on the order of 1% per genome per generation (10(-5) per base per generation) and 0.5%, respectively. The adaptation rate is twofold higher and fourfold lower than predicted in the absence of recombination and in the limit of very frequent recombination, respectively. The level of LD and the number of diverse sites observed in data also range between the values predicted in simulation for these two limiting cases. These results demonstrate the critical importance of finite population size, linkage, and recombination in HIV evolution.

Fig. 1.

Simulation of viral adaptation during chronic HIV infection. Results are shown for the first 1,500 d of infection using parameters estimated from pol in a representative patient: r = 0.01, s₀ = 0.005, M = 10, L = 2000, n = 10⁵, and μ = 3·10⁻⁵. (A) Population distribution in fitness moves as a wave. Distribution is shown at 300-d intervals: day 1 (red), day 300 (green), day 600 (blue), day 900 (yellow), day 1,200 (magenta), and day 1,500 (cyan). (B) Dynamics of beneficial alleles at high frequencies. Trajectories are shown for eight randomly selected sites with the frequency of beneficial alleles per site, f > 0.1, at day 750: in simulation (solid), one-site model prediction (dashed). The values of s at the sites shown are as follows: 0.02 (cyan), 0.004 (black), 0.004 (red), 4.5·10⁻⁴ (green), 0.01 (yellow), 3.1·10⁻⁴ (blue, upper line at t = 750 d), 0.01 (blue, lower line), and 0.01 (magenta). (C) Quantities characterizing average diversity of the population. Shown are the fraction of observably diverse sites, defined as having more than 0.04 of minority allele (magenta); fraction of very diverse sites, defined as having more than 0.25 of minority allele (black); average frequency of beneficial alleles per site <f> (blue); and genetic diversity <2f(1 − f)> averaged over observably diverse sites only (green). (D) Average diversity of observably diverse sites classified according to their selection coefficient, s, for 10 equidistant time points at 300-d intervals, as in A.

Fig. 2.

Estimation of model parameters for chronic HIV infection. The recombination rate, r, and average selection coefficient, s₀, are estimated by comparing four observable quantities in data with their predicted values in simulation. Gray regions indicate the mean ± 1 SD of quantities calculated from data from the pol gene in four patients (Table 1). In simulation, each quantity is calculated at day 1,500 for 11% of the genome. An average over 16 random runs is shown, with error bars showing the SD over runs. Results are shown for a single population size, N = 10⁵, and for three values of the crossover number, M: 3 (red), 10 (black), and 30 (blue). Results for different M values are shifted slightly horizontally for clarity. (A) LD of very diverse pairs for s₀ = 0.005. LD is defined as 1 − <f_AB^LRH/f_Af_B>, where f_AB^LRH is the frequency of the least-represented haplotype for a pair of sites A and B and f_Af_B is the product of one-site frequencies or the value of f_AB^LRH is in the absence of linkage for s₀ = 0.005. (B) Another measure of LD is the fraction of very diverse pairs with the frequency of the least-represented haplotype below 0.04 for s₀ = 0.005. (C) Fraction of sites that are observably diverse (solid) and very diverse (dashed) for r = 0.01. (D) Population average fitness for r = 0.01. Other fixed parameters are shown in the legend for Fig. 1.