Antiretroviral dynamics determines HIV evolution and predicts therapy outcome

Abstract

Despite the high inhibition of viral replication achieved by current anti-HIV drugs, many patients fail treatment, often with emergence of drug-resistant virus. Clinical observations show that the relationship between adherence and likelihood of resistance differs dramatically among drug classes. We developed a mathematical model that explains these observations and predicts treatment outcomes. Our model incorporates drug properties, fitness differences between susceptible and resistant strains, mutations and adherence. We show that antiviral activity falls quickly for drugs with sharp dose-response curves and short half-lives, such as boosted protease inhibitors, limiting the time during which resistance can be selected for. We find that poor adherence to such drugs causes treatment failure via growth of susceptible virus, explaining puzzling clinical observations. Furthermore, our model predicts that certain single-pill combination therapies can prevent resistance regardless of patient adherence. Our approach represents a first step for simulating clinical trials of untested anti-HIV regimens and may help in the selection of new drug regimens for investigation.

Figures

Figure 1

Drug concentrations determine the relative fitness of the wild-type virus and a resistant mutant. (a) The fitness of the wild-type virus (R0, blue line) decreases with increasing drug concentration, following Equation (1). A drug-resistant strain (R′0, red line) is less fit than the wild type at low concentrations, but more fit at higher concentrations due to an increased IC50 or a reduced slope. The mutant selection window (MSW) is the range of concentrations where a resistant mutant, if present, will grow faster than the wild type and still has R′0> 1. The wild-type growth window (WGW) is the range of low concentrations where the wild type has R0> 1, leading to treatment failure without the need for resistance. For drug concentrations in the overlapping range of these windows, virologic failure (VF) can occur even without resistance, but will be hastened by the appearance of a faster-growing mutant. (b) As drug concentrations decay after the last dose is taken, the viral fitness passes through the four different selection ranges. Depending on the drug, dose level, and mutation, not all of these ranges may exist. The time spent in each selection window is also determined by the drug half-life.

Figure 2

Selection windows can be calculated for particular drug-mutation pairs. (a) The distance to the right along each horizontal bar is the time since the last dose, and the color corresponds to the selection window during that time interval (described in Fig. 1b) (b)–(e) Examples of dose-response curves for drug-mutation combinations indicated in (a). Shading indicates the MSW. If the cost of a mutation is too high or its benefit (ρ or σ) too low, it is possible that the MSW does not exist. (f) Rank of each drug for relative risk of wild-type versus mutant virus growth, independent of the overall risk of therapy failure. For each drug, we show a “synthetic,” worst-case, single-nucleotide mutation (Supplementary Methods, Supplementary Fig. 1). NRTI & NNRTI, (non)-nucleoside/nucleotide reverse transcriptase inhibitors; PI, protease inhibitors; FI, fusion inhibitors; II, integrase inhibitors; 3TC, lamivudine; ABC, abacavir; AZT, zidovudine; d4T, stavudine; ddI, didanosine, FTC, emtricitabine; TDF, tenofovir disoproxil fu-marate; EFV, efavirenz; ETV, etravirine; NVP, nevirapine; ATV, atazanavir; DRV, darunavir; IDV, indinavir; LPV, lopinavir; NFV, nelfinavir; SQV, saquinavir; TPV, tipranavir; EVG, elvitegravir; RAL, raltegravir; ENF, enfuvirtide. PIs are often “boosted” (co-formulated) with ritonovir (/r), which interferes with break-down in the liver and increases half-life.

Figure 3

Schematic of algorithm for simulating viral dynamics in a patient undergoing treatment. (a) A single simulated patient takes a particular drug (or drug combination) with a designated adherence level, starting with a chosen initial viral load. Over a 48-week clinical trial, drug levels fluctuate and viral load levels are simulated according to a viral dynamics model. (b) Drug levels fluctuate according to patient’s dosing pattern and pharmacokinetics (dose size, half-life, bioavailability); gaps show missed doses (figure shows single drug). (c) Wild-type viral fitness (R0) fluctuates in response to drug concentration depending on the dose-response curve. (d) Fitness of drug-resistant strain (R′0) depends on an altered dose-response curve; at high drug concentrations, mutant fitness exceeds that of the wild type. (e) Wild-type viral load depends on viral dynamics equations, which account for active replication, exit from the latent reservoir, and competition between strains. (f) A mutant virus may appear (red star) but be below the threshold for detection (dotted red line) before eventually leading to virologic failure.

Figure 4

Outcomes for simulated patients in a clinical trial. The height of the area shaded indicates probability of the corresponding outcome at a given adherence level (a) or time-point (b and c). (a) Adherence (x-axis) is defined as the fraction of scheduled doses taken. These are maintenance trials (see Methods). (b–c) Time is on the x-axis; measurements are taken every 2 weeks for simulated patients with a distribution of adherence levels (Supplementary Methods, Supplementary Fig. 2b). (b) Suppression trials (see Methods). (c) Maintenance trials. (I) 3TC therapy (pattern includes AZT, ABC, d4T, ENF, EVG, FTC, NVP, RAL, TDF). (II) EFV and ETV therapy. (III) NFV therapy (pattern includes ddI). (IV) DRV/r and ATV/r therapy (pattern includes ATV, TPV/r; variation on this pattern described in text includes LPV/r, SQV, SQV/r IDV, IDV/r).

Figure 5

Our calculated adherence-resistance relations are in agreement with those observed in clinical trials. (a) Adherence versus simulated probability of resistance in a 48-week suppression trial for a PI, a boosted PI and an NNRTI. The inset shows a qualitative summary of results from a meta-analysis of clinical trials, which agrees with our simulations. (b) Adherence versus fraction of time spent in the MSW for the same drugs. Adherence-resistance trends demonstrate that “time in MSW” is a good proxy for the risk of mutant-based virologic failure (VF). For both plots, curves were generated by averaging over all boosted PIs, all unboosted PIs, and the NNRTIs EFV and ETV. PI curves in (a) were fitted to skewed-T distributions to smooth step-like behavior. NVP, which was excluded from this figure, displays a different pattern from the other two NNRTIs; specifically, mutant VF can occur even for perfect adherence (Supplementary Figs. 3, 4).

Figure 6

Outcomes of DRV/r + RAL dual suppression therapy simulations, considering resistant mutants for both drugs. (a) Each drug is taken independently and adherence may differ between them. The brightness of each color at a particular point indicates the probability of the corresponding outcome, with the black contours showing where each outcome occurs 95% of the time. Success depends largely on adherence to DRV/r (almost certain if > 50%), while the type of failure is determined by adherence to RAL (resistance almost certain if > 30%). All failure via resistance is due to RAL mutant-based VF. DRV mutant-based virologic failure (VF) never occurs in the simulations. (b)–(c) Drugs are taken with equal average adherence. The height of the area shaded indicates probability of the corresponding outcome at that adherence level. (b) Drugs are taken as separate pills. Average adherence is the same but pills are taken independently. (c) Drugs are packaged as a combination pill and are always taken together. Mutant VF occurs only when the two drugs are given in separate pills; combination pills eliminate mutant VF but increase the adherence required for near-certain success.