Contribution of the main and epistatic effects to the recombination effect on adaptation on the HIV-1 fitness landscape.

<p>The x and y axes show the values of the constants by which the elements of the main and epistatic effects, respectively, are multiplied in the hierarchical fitness landscape. The plot shows the logarithm (base 10) of the ratio of mean fitness of the recombining to that of the non-recombining populations at generation 100, averaged across 100 simulations. Parameters take values: and .</p

A) Population fitness and B) fitness variance in the recombining and non-recombining populations over time.

<p>Red and blue curves correspond to the mean value across 100 simulations in the recombining and non-recombining settings, respectively. Fitness and fitness variance values are normalized with the fitness of the reference sequence. The shaded regions show 95% confidence intervals. Parameters take values: and .</p

The impact of the correlation structure of epistasis on the fitness landscape.

<p>Distribution of ruggedness (A), correlation length (B), and neutrality (C), for different randomizations of the reference landscape. The following randomization schemes are used: In scheme 1 we draw main effects randomly with replacement from the distribution of main effects underlying the RL, whereas epistatic effects are kept as they are in the RL. This destroys any correlation between epistasis and main effects. In scheme 2 we additionally shuffle the non-zero epistasis values. This retains the information of which loci interact epistatically, but shuffles the value of any such interaction. Finally, in scheme 3, we fully shuffle all epistasis and main effect values, and thus destroy all correlations between effects. Each measure is inferred for 100 randomizations of each randomization type and the interpolation of the resulting distribution is plotted. : No randomization (i.e. the 100 realizations are done on the same landscape; black), scheme 1 (red), scheme 2 (blue), scheme 3 (green). For the latter two cases it should be noted that main effects and epistatic effects are shuffled separately, i.e. main effects remain main effects and epistatic effects remain epistatic effects.</p

Properties of the reference landscape.

<p>(A) Number of different optima attained from steepest-ascent hill-climbing walks starting from random genotypes plotted as a function of the number of starting genotypes. (B) Distribution of attraction domains of steepest-ascent hill-climbing walks: Starting genotypes are chosen in the neighborhoods of 500 randomly chosen reference genotypes. Of each reference genotype, 100 random single, double, triple, fourfold, and fivefold mutants are considered as starting genotypes. Each dot corresponds to a local optimum. Coordinates indicate from how many unique neighborhoods (y-axis) and from what fraction of starting-genotypes in these neighborhoods the optimum is reached (x axis). Thus the y- and x-axis correspond to the global and local density of the attraction domain respectively. (C) Autocorrelation of log-fitness along random walks as a function of the number of steps. The red line corresponds to the linear least square fit of the autocorrelation and the correlation length is given by −1/(slope of the line). (D) Range explored by quasi-neutral walks for different discrete values of the maximal fitness-effect <i>ε</i> which quasi-neutral mutations are allowed to have. Points correspond to the mean over 10⁵ walks of length 1000. 95%-confidence-intervals of the mean (inferred through 1000 bootstrap samples) are smaller than point size.</p

The impact of epistasis on the structure of fitness landscapes.

<p>Ruggedness (A), correlation length (B), and neutrality (C) as a function of the magnitude of epistasis in HL_ε. For all panels, the 95% confidence interval of the mean (inferred through 1000 bootstrap samples) is smaller than the size of the data point symbol.</p

Fitness landscapes across different environments characterized by the absence of drugs or by the presence of a single antiretroviral.

<p>(A) Ruggedness (i.e. number of different optima reached from 1000 steepest-ascent hill-climbing walks) for the no-drug and 15 single-drug environments. X-axis labels indicate the antiretroviral drug characterizing each environment (see <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002551#s3" target="_blank">Materials and Methods</a>) and color indicates drug-class (red: no drug; cyan: non-nucleoside reverse transcriptase inhibitor; blue: nucleoside analog reverse transcriptase inhibitor; green: protease inhibitor). Each point corresponds to the mean over 100 such measures of ruggedness. 95%-confidence-intervals of the mean (inferred through 1000 bootstrap samples) are smaller than point size. (B) Correlation-length of log-fitness on random walks. Correlation-length is inferred from 10⁴ random walks of length 50 starting from random initial conditions. Points correspond to the mean over 100 such measurements of correlation length. 95%-confidence-intervals of the mean (inferred through 1000 bootstrap samples) are smaller than point size. (C) Range explored by quasi-neutral walks (threshold ε = 0.001) for different environments. Points correspond to the mean over 10⁵ walks of length 1000. Error-bars correspond to the 95% confidence-interval of the mean, inferred through 1000 bootstrap samples.</p

Population effect in the observed cost of escape from HLA presentation.

<p>The distribution of replicative fitness effects (DFE) of random mutations in HIV-1 (green) will differ from the corresponding distribution of mutations derived from the patient population (blue/orange) as the latter will feature only mutations which have undergone selection. Mutations with a particularly high replicative cost (i.e., low replicative capacity) will have a low probability of being present in the patient-derived data because they will persist at very low frequencies in the virus population. However, escape mutations carry an additional benefit of avoiding being killed by the immune system and therefore are expected to have a higher <i>in vivo</i> fitness, which allows for persistence in spite of a lower replicative capacity. For this reason, even if the DFE of escape and non-escape mutations are identical, the escape mutations derived from the patient population (blue) may appear to have on average a lower replicative capacity than the non-escape mutations derived from the patient population (orange).</p

Cost of escape from the protective and the non-protective HLA alleles.

<p>(<b>Top row</b>) Effect of mutations on binding affinity to 10 most protective HLA molecules according to two alternative epitope definitions (absolute criterion: , relative criterion: ). Protectiveness of alleles was characterized based on the relative hazard for AIDS progression (see Materials & Methods). A significant correlation between the fitness of single mutants and the impairment of binding to the most protective HLA molecules was observed (absolute criterion: , ; relative criterion: , ). (<b>Bottom row</b>) Effect of mutations on binding affinity to 10 most non-protective HLA molecules according to two alternative epitope definitions (absolute criterion: , relative criterion: ). In this case, no significant correlation between the fitness of single mutants and the impairment of binding to the most non-protective HLA molecules was found (absolute criterion: ; relative criterion: ). For the sake of illustration, the blue line shows the best fit of a linear regression and the 95% confidence interval.</p

Cost of escape from rare HLA-A alleles.

<p>Correlation between fitness of single mutations and impairment of binding to rare (lower than 0.5%, see Materials & Methods) HLA-A molecules (absolute criterion: , relative criterion: ). We observed a significant correlation for both epitope definitions (absolute criterion: , ; relative criterion: , ). For the sake of illustration, the blue line shows the best fit of a linear regression and the 95% confidence interval.</p

Cost of mutations which impair the HLA-binding.

<p>(<b>Top row</b>) Effect of mutations on binding affinity to HLA-A molecules according to two alternative epitope definitions (absolute criterion: , relative criterion: ). In both cases we observed a significant correlation between the fitness of single mutants and the impairment of binding to HLA-A (absolute criterion: , ; relative criterion: , ). Each datapoint corresponds to a single amino acid substitution in the genetic region restricted by HLA alleles of the corresponding locus, A or B. Note, that if multiple HLA molecules were affected by a single mutation at a given locus, the strongest impairment was plotted here. (<b>Bottom row</b>) Effect of mutations on binding affinity to HLA-B molecules for the two alternative epitope definitions (absolute criterion: , relative criterion: ). Here, no significant correlation between the quantities in question was found (absolute criterion: ; relative criterion: ). For the sake of illustration, the blue line shows the best fit of a linear regression and the 95% confidence interval.</p