Limits...
Taking multiple infections of cells and recombination into account leads to small within-host effective-population-size estimates of HIV-1.

Balagam R, Singh V, Sagi AR, Dixit NM - PLoS ONE (2011)

Bottom Line: Whether HIV-1 evolution in infected individuals is dominated by deterministic or stochastic effects remains unclear because current estimates of the effective population size of HIV-1 in vivo, N(e), are widely varying.From comparisons of our simulations with patient data, we estimate N(e)~10³-10⁴, implying predominantly stochastic evolution.Further, we show that the previous estimate of N(e)>10⁵ reduces as the frequencies of multiple infections of cells and recombination assumed increase.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical Engineering, Indian Institute of Science, Bangalore, India.

ABSTRACT
Whether HIV-1 evolution in infected individuals is dominated by deterministic or stochastic effects remains unclear because current estimates of the effective population size of HIV-1 in vivo, N(e), are widely varying. Models assuming HIV-1 evolution to be neutral estimate N(e)~10²-10⁴, smaller than the inverse mutation rate of HIV-1 (~10⁵), implying the predominance of stochastic forces. In contrast, a model that includes selection estimates N(e)>10⁵, suggesting that deterministic forces would hold sway. The consequent uncertainty in the nature of HIV-1 evolution compromises our ability to describe disease progression and outcomes of therapy. We perform detailed bit-string simulations of viral evolution that consider large genome lengths and incorporate the key evolutionary processes underlying the genomic diversification of HIV-1 in infected individuals, namely, mutation, multiple infections of cells, recombination, selection, and epistatic interactions between multiple loci. Our simulations describe quantitatively the evolution of HIV-1 diversity and divergence in patients. From comparisons of our simulations with patient data, we estimate N(e)~10³-10⁴, implying predominantly stochastic evolution. Interestingly, we find that N(e) and the viral generation time are correlated with the disease progression time, presenting a route to a priori prediction of disease progression in patients. Further, we show that the previous estimate of N(e)>10⁵ reduces as the frequencies of multiple infections of cells and recombination assumed increase. Our simulations with N(e)~10³-10⁴ may be employed to estimate markers of disease progression and outcomes of therapy that depend on the evolution of viral diversity and divergence.

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Estimation of Ne from comparisons with data from patients.Sum of squares of the errors (SSE) between data from patients [36] and our predictions of viral diversity, dG, and divergence, dS, for different values of the population size, C, (Fig. 1) and the viral generation time, τ, shown for each of the nine patients. C and τ that yield the lowest SSE provide the best fit to the data. The best-fit value of C yields Ne (Table 1).
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pone-0014531-g002: Estimation of Ne from comparisons with data from patients.Sum of squares of the errors (SSE) between data from patients [36] and our predictions of viral diversity, dG, and divergence, dS, for different values of the population size, C, (Fig. 1) and the viral generation time, τ, shown for each of the nine patients. C and τ that yield the lowest SSE provide the best fit to the data. The best-fit value of C yields Ne (Table 1).

Mentions: With data from each patient, we compare our predictions of dG and dS for different values of C, viz., 200, 400, 500, 1000, 1500, 5000, 10000, and 20000 cells, and a range of values of the viral generation time, τ, viz., 0.6 to 2.0 days per replication [10], [11], [54], [55] in increments of 0.1 days per replication. τ may vary substantially across patients [10], [11], [14], [54], [55]. For each patient, we find the sum of squares of the errors (SSE) between experimental data and our predictions of dG and dS for different values of C and τ (Fig. 2). The combination of C and τ that results in the lowest SSE for a patient yields the best fit of our predictions to data from that patient. The best-fit predictions are shown in Fig. 3. Our simulations provide good fits to data from each of the nine patients. The best fit values of C yield Ne (Table 1). We thus find that the mean Ne is ∼2400 (range 400–10000) for these patients. The mean τ is 1.1 day (range 0.7–1.7 day).


Taking multiple infections of cells and recombination into account leads to small within-host effective-population-size estimates of HIV-1.

Balagam R, Singh V, Sagi AR, Dixit NM - PLoS ONE (2011)

Estimation of Ne from comparisons with data from patients.Sum of squares of the errors (SSE) between data from patients [36] and our predictions of viral diversity, dG, and divergence, dS, for different values of the population size, C, (Fig. 1) and the viral generation time, τ, shown for each of the nine patients. C and τ that yield the lowest SSE provide the best fit to the data. The best-fit value of C yields Ne (Table 1).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3020941&req=5

pone-0014531-g002: Estimation of Ne from comparisons with data from patients.Sum of squares of the errors (SSE) between data from patients [36] and our predictions of viral diversity, dG, and divergence, dS, for different values of the population size, C, (Fig. 1) and the viral generation time, τ, shown for each of the nine patients. C and τ that yield the lowest SSE provide the best fit to the data. The best-fit value of C yields Ne (Table 1).
Mentions: With data from each patient, we compare our predictions of dG and dS for different values of C, viz., 200, 400, 500, 1000, 1500, 5000, 10000, and 20000 cells, and a range of values of the viral generation time, τ, viz., 0.6 to 2.0 days per replication [10], [11], [54], [55] in increments of 0.1 days per replication. τ may vary substantially across patients [10], [11], [14], [54], [55]. For each patient, we find the sum of squares of the errors (SSE) between experimental data and our predictions of dG and dS for different values of C and τ (Fig. 2). The combination of C and τ that results in the lowest SSE for a patient yields the best fit of our predictions to data from that patient. The best-fit predictions are shown in Fig. 3. Our simulations provide good fits to data from each of the nine patients. The best fit values of C yield Ne (Table 1). We thus find that the mean Ne is ∼2400 (range 400–10000) for these patients. The mean τ is 1.1 day (range 0.7–1.7 day).

Bottom Line: Whether HIV-1 evolution in infected individuals is dominated by deterministic or stochastic effects remains unclear because current estimates of the effective population size of HIV-1 in vivo, N(e), are widely varying.From comparisons of our simulations with patient data, we estimate N(e)~10³-10⁴, implying predominantly stochastic evolution.Further, we show that the previous estimate of N(e)>10⁵ reduces as the frequencies of multiple infections of cells and recombination assumed increase.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical Engineering, Indian Institute of Science, Bangalore, India.

ABSTRACT
Whether HIV-1 evolution in infected individuals is dominated by deterministic or stochastic effects remains unclear because current estimates of the effective population size of HIV-1 in vivo, N(e), are widely varying. Models assuming HIV-1 evolution to be neutral estimate N(e)~10²-10⁴, smaller than the inverse mutation rate of HIV-1 (~10⁵), implying the predominance of stochastic forces. In contrast, a model that includes selection estimates N(e)>10⁵, suggesting that deterministic forces would hold sway. The consequent uncertainty in the nature of HIV-1 evolution compromises our ability to describe disease progression and outcomes of therapy. We perform detailed bit-string simulations of viral evolution that consider large genome lengths and incorporate the key evolutionary processes underlying the genomic diversification of HIV-1 in infected individuals, namely, mutation, multiple infections of cells, recombination, selection, and epistatic interactions between multiple loci. Our simulations describe quantitatively the evolution of HIV-1 diversity and divergence in patients. From comparisons of our simulations with patient data, we estimate N(e)~10³-10⁴, implying predominantly stochastic evolution. Interestingly, we find that N(e) and the viral generation time are correlated with the disease progression time, presenting a route to a priori prediction of disease progression in patients. Further, we show that the previous estimate of N(e)>10⁵ reduces as the frequencies of multiple infections of cells and recombination assumed increase. Our simulations with N(e)~10³-10⁴ may be employed to estimate markers of disease progression and outcomes of therapy that depend on the evolution of viral diversity and divergence.

Show MeSH
Related in: MedlinePlus