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Timing the emergence of resistance to anti-HIV drugs with large genetic barriers.

Arora P, Dixit NM - PLoS Comput. Biol. (2009)

Bottom Line: We apply our model to describe the development of resistance to tipranavir in in vitro serial passage experiments.Model predictions of the times of emergence of different mutant genomes with increasing resistance to tipranavir are in quantitative agreement with experiments, indicating that our model captures the dynamics of the development of resistance to antiretroviral drugs accurately.Further, model predictions provide insights into the influence of underlying evolutionary processes such as recombination on the development of resistance, and suggest guidelines for drug design: drugs that offer large genetic barriers to resistance with resistance sites tightly localized on the viral genome and exhibiting positive epistatic interactions maximally inhibit the emergence of resistant genomes.

View Article: PubMed Central - PubMed

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

ABSTRACT
New antiretroviral drugs that offer large genetic barriers to resistance, such as the recently approved inhibitors of HIV-1 protease, tipranavir and darunavir, present promising weapons to avert the failure of current therapies for HIV infection. Optimal treatment strategies with the new drugs, however, are yet to be established. A key limitation is the poor understanding of the process by which HIV surmounts large genetic barriers to resistance. Extant models of HIV dynamics are predicated on the predominance of deterministic forces underlying the emergence of resistant genomes. In contrast, stochastic forces may dominate, especially when the genetic barrier is large, and delay the emergence of resistant genomes. We develop a mathematical model of HIV dynamics under the influence of an antiretroviral drug to predict the waiting time for the emergence of genomes that carry the requisite mutations to overcome the genetic barrier of the drug. We apply our model to describe the development of resistance to tipranavir in in vitro serial passage experiments. Model predictions of the times of emergence of different mutant genomes with increasing resistance to tipranavir are in quantitative agreement with experiments, indicating that our model captures the dynamics of the development of resistance to antiretroviral drugs accurately. Further, model predictions provide insights into the influence of underlying evolutionary processes such as recombination on the development of resistance, and suggest guidelines for drug design: drugs that offer large genetic barriers to resistance with resistance sites tightly localized on the viral genome and exhibiting positive epistatic interactions maximally inhibit the emergence of resistant genomes.

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Model predictions of emergence and fixation times.The expected waiting time for the emergence of (A) genomes with different numbers of resistance mutations for different n when E = 0, (B) the corresponding nth mutants as a function of E, (C) quintuple mutants when n = 5 as a function of the crossover frequency (ρl), for E = 0.005 (green), 0 (red), −0.005 (blue). The inset in (C) shows the corresponding reduction in the time of emergence, 1−W(ρl)/W(ρl = 0). (D) Model predictions of emergence (filled symbols) and fixation (open symbols) times of double mutants when n = 2 and E = 0.05 (green), 0 (red), −0.05 (blue). In (A) to (C), we let ε0 = 0.85 and εn = 0.25, whereas in (D) ε0 = 0.1 and εn = 0. All the other parameters are identical to those in Figure 4.
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pcbi-1000305-g005: Model predictions of emergence and fixation times.The expected waiting time for the emergence of (A) genomes with different numbers of resistance mutations for different n when E = 0, (B) the corresponding nth mutants as a function of E, (C) quintuple mutants when n = 5 as a function of the crossover frequency (ρl), for E = 0.005 (green), 0 (red), −0.005 (blue). The inset in (C) shows the corresponding reduction in the time of emergence, 1−W(ρl)/W(ρl = 0). (D) Model predictions of emergence (filled symbols) and fixation (open symbols) times of double mutants when n = 2 and E = 0.05 (green), 0 (red), −0.05 (blue). In (A) to (C), we let ε0 = 0.85 and εn = 0.25, whereas in (D) ε0 = 0.1 and εn = 0. All the other parameters are identical to those in Figure 4.

Mentions: To examine the influence of the genetic barrier, we vary n for fixed values of ε0, εn, and E, and predict W. We find that W increases dramatically with n. For instance, W increases from ∼12 days when n = 2 to ∼100 days when n = 5 (Figure 5A), underscoring the advantage of a drug with a large n. As n increases, the number of mutations necessary for resistance increases. The number of replication cycles required to accumulate the necessary mutations increases correspondingly and delays the emergence of resistant genomes. The development of resistance is inhibited further by the delayed emergence of intermediate mutants. For the same ε0 and εn, the incremental fitness advantage with each mutation decreases as n increases. The smaller this advantage, the longer it takes for the resolution of the competition between different mutants. Thus, following their emergence, double mutants take longer to outgrow single mutants when n = 4 than when n = 3. When the influence of recombination is weak, triple mutants emerge predominantly by mutation of double mutants. Consequently, the waiting time for the emergence of triple mutants is larger when n = 4 than when n = 3. Indeed, triple mutants emerge in ∼40 days when n = 3 and ∼55 days when n = 4 (Figure 5A). Thus, the increasing number of replication cycles required and the slower emergence of intermediate mutants together result in the dramatic increase of W with n.


Timing the emergence of resistance to anti-HIV drugs with large genetic barriers.

Arora P, Dixit NM - PLoS Comput. Biol. (2009)

Model predictions of emergence and fixation times.The expected waiting time for the emergence of (A) genomes with different numbers of resistance mutations for different n when E = 0, (B) the corresponding nth mutants as a function of E, (C) quintuple mutants when n = 5 as a function of the crossover frequency (ρl), for E = 0.005 (green), 0 (red), −0.005 (blue). The inset in (C) shows the corresponding reduction in the time of emergence, 1−W(ρl)/W(ρl = 0). (D) Model predictions of emergence (filled symbols) and fixation (open symbols) times of double mutants when n = 2 and E = 0.05 (green), 0 (red), −0.05 (blue). In (A) to (C), we let ε0 = 0.85 and εn = 0.25, whereas in (D) ε0 = 0.1 and εn = 0. All the other parameters are identical to those in Figure 4.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2643484&req=5

pcbi-1000305-g005: Model predictions of emergence and fixation times.The expected waiting time for the emergence of (A) genomes with different numbers of resistance mutations for different n when E = 0, (B) the corresponding nth mutants as a function of E, (C) quintuple mutants when n = 5 as a function of the crossover frequency (ρl), for E = 0.005 (green), 0 (red), −0.005 (blue). The inset in (C) shows the corresponding reduction in the time of emergence, 1−W(ρl)/W(ρl = 0). (D) Model predictions of emergence (filled symbols) and fixation (open symbols) times of double mutants when n = 2 and E = 0.05 (green), 0 (red), −0.05 (blue). In (A) to (C), we let ε0 = 0.85 and εn = 0.25, whereas in (D) ε0 = 0.1 and εn = 0. All the other parameters are identical to those in Figure 4.
Mentions: To examine the influence of the genetic barrier, we vary n for fixed values of ε0, εn, and E, and predict W. We find that W increases dramatically with n. For instance, W increases from ∼12 days when n = 2 to ∼100 days when n = 5 (Figure 5A), underscoring the advantage of a drug with a large n. As n increases, the number of mutations necessary for resistance increases. The number of replication cycles required to accumulate the necessary mutations increases correspondingly and delays the emergence of resistant genomes. The development of resistance is inhibited further by the delayed emergence of intermediate mutants. For the same ε0 and εn, the incremental fitness advantage with each mutation decreases as n increases. The smaller this advantage, the longer it takes for the resolution of the competition between different mutants. Thus, following their emergence, double mutants take longer to outgrow single mutants when n = 4 than when n = 3. When the influence of recombination is weak, triple mutants emerge predominantly by mutation of double mutants. Consequently, the waiting time for the emergence of triple mutants is larger when n = 4 than when n = 3. Indeed, triple mutants emerge in ∼40 days when n = 3 and ∼55 days when n = 4 (Figure 5A). Thus, the increasing number of replication cycles required and the slower emergence of intermediate mutants together result in the dramatic increase of W with n.

Bottom Line: We apply our model to describe the development of resistance to tipranavir in in vitro serial passage experiments.Model predictions of the times of emergence of different mutant genomes with increasing resistance to tipranavir are in quantitative agreement with experiments, indicating that our model captures the dynamics of the development of resistance to antiretroviral drugs accurately.Further, model predictions provide insights into the influence of underlying evolutionary processes such as recombination on the development of resistance, and suggest guidelines for drug design: drugs that offer large genetic barriers to resistance with resistance sites tightly localized on the viral genome and exhibiting positive epistatic interactions maximally inhibit the emergence of resistant genomes.

View Article: PubMed Central - PubMed

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

ABSTRACT
New antiretroviral drugs that offer large genetic barriers to resistance, such as the recently approved inhibitors of HIV-1 protease, tipranavir and darunavir, present promising weapons to avert the failure of current therapies for HIV infection. Optimal treatment strategies with the new drugs, however, are yet to be established. A key limitation is the poor understanding of the process by which HIV surmounts large genetic barriers to resistance. Extant models of HIV dynamics are predicated on the predominance of deterministic forces underlying the emergence of resistant genomes. In contrast, stochastic forces may dominate, especially when the genetic barrier is large, and delay the emergence of resistant genomes. We develop a mathematical model of HIV dynamics under the influence of an antiretroviral drug to predict the waiting time for the emergence of genomes that carry the requisite mutations to overcome the genetic barrier of the drug. We apply our model to describe the development of resistance to tipranavir in in vitro serial passage experiments. Model predictions of the times of emergence of different mutant genomes with increasing resistance to tipranavir are in quantitative agreement with experiments, indicating that our model captures the dynamics of the development of resistance to antiretroviral drugs accurately. Further, model predictions provide insights into the influence of underlying evolutionary processes such as recombination on the development of resistance, and suggest guidelines for drug design: drugs that offer large genetic barriers to resistance with resistance sites tightly localized on the viral genome and exhibiting positive epistatic interactions maximally inhibit the emergence of resistant genomes.

Show MeSH
Related in: MedlinePlus