Comparisons of our simulations with the quasispecies theory.

<p>Structure of the quasispecies for different values of (substitutions/site/replication) indicated determined by our simulations (circles connected by lines) and by the quasispecies theory (pluses) for (A) isolated peak fitness landscape, (B) exponential landscape with <i>s</i> = 0.01, and (C) the experimental landscape with <i>d₅₀</i> = 3.</p

Viral genomic diversification in one realization of our simulations.

<p>(A) The frequencies of proviral genomes in different Hamming classes at various times (generations) indicated in one realization of our simulations with nucleotides, cells, substitutions/site/replication and infections/cell. Other parameters are mentioned in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#s4" target="_blank">Methods</a>. The quasispecies (thick black line) is the average frequency distribution over the last 1500 generations. (B) The corresponding evolution of the Shannon entropy (purple) and its mean over the last 1500 generations (black).</p

Dependence of the error threshold on the recombination rate.

<p>The mean steady state Shannon entropy, , as a function of the mutation rate, , for different recombination rates, , indicated (crossovers/site/replication) with (A) infections/cell and (B) determined from a distribution with few multiple infections (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#s4" target="_blank">Methods</a>). Here, nucleotides, cells, and the other parameters are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi-1002684-g001" target="_blank">Fig. 1</a>. The corresponding structures of the quasispecies are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi.1002684.s004" target="_blank">Fig. S4</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi.1002684.s005" target="_blank">Fig. S5</a>, respectively. (C) and (D) The resulting dependence of the error threshold, , on in (A) and (B), respectively. <i>Inset</i> in (C) shows the quasispecies for different (crossovers/site/replication) indicated with substitutions/site/replication and infections/cell.</p

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

<div><p>The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.</p> </div

Dependence of the error threshold on the population size.

<p>(A) The mean steady state Shannon entropy, , as a function of the mutation rate, , for different population sizes, <i>C</i> (cells), indicated. Other parameters are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi-1002684-g001" target="_blank">Fig. 1</a>. The corresponding structures of the quasispecies are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi.1002684.s003" target="_blank">Fig. S3</a>. (B) The resulting dependence of the error threshold, , on <i>C</i>. <i>Inset</i> in (B) shows a linear fit (line) to the data (symbols) yielding .</p

Dependence of the error threshold on the genome length.

<p>(A) The mean steady state Shannon entropy, , as a function of the mutation rate, , for different genome lengths, <i>L</i> (nucleotides), indicated. Other parameters are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi-1002684-g001" target="_blank">Fig. 1</a>. The corresponding structures of the quasispecies are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi.1002684.s002" target="_blank">Fig. S2</a>. (B) The resulting dependence of the error threshold, , on <i>L</i>. <i>Inset</i> in (B) shows a linear fit (line) to the data (symbols) yielding .</p

Structure of the quasispecies and the error threshold.

<p>The structure of the quasispecies at different values of indicated (substitutions/site/replication) with (A) and (B) nucleotides. <i>Inset</i> in (B) compares the quasispecies structure predicted by our simulations for substitutions/site/replication (line) with that expected when all genomes occur with equal likelihood (i.e., ; see text) (symbols). (C) The mean Shannon entropy, , corresponding to the quasispecies in (A) and (B). Other parameters are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi-1002684-g001" target="_blank">Fig. 1</a>.</p

Stochastic evolution near the error threshold.

<p>Time-evolution of the Shannon entropy, , in several independent realizations of our simulations at three values of , namely, (A) , (B) and (C) substitutions/site/replication. The other parameters are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002684#pcbi-1002684-g002" target="_blank">Fig. 2B</a>. The different realizations in (A) and (C) nearly overlap and are indistinguishable.</p