Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips

Abstract

Most HIV-infected patients when treated with combination antiretroviral therapy achieve viral loads that are below the current limit of detection of standard assays after a few months. Despite this, virus eradication from the host has not been achieved. Latent, replication-competent HIV-1 can generally be identified in resting memory CD4(+) T cells in patients with "undetectable" viral loads. Turnover of these cells is extremely slow but virus can be released from the latent reservoir quickly upon cessation of therapy. In addition, a number of patients experience transient episodes of viremia, or HIV-1 blips, even with suppression of the viral load to below the limit of detection for many years. The mechanisms underlying the slow decay of the latent reservoir and the occurrence of intermittent viral blips have not been fully elucidated. In this study, we address these two issues by developing a mathematical model that explores a hypothesis about latently infected cell activation. We propose that asymmetric division of latently infected cells upon sporadic antigen encounter may both replenish the latent reservoir and generate intermittent viral blips. Interestingly, we show that occasional replenishment of the latent reservoir induced by reactivation of latently infected cells may reconcile the differences between the divergent estimates of the half-life of the latent reservoir in the literature.

Figure 1

Schematic representation of the viral load before and after HAART. Before treatment, the viral load is at a steady state level. After initiation of HAART, the viral load undergoes multiphasic decay and is suppressed to below the limit of detection (50 RNA copies/mL) of standard assays after several months. A low level of viremia below 50 copies/mL may persist in patients for many years despite apparently effective antiretroviral treatment. Intermittent viral blips with transient HIV-1 RNA above the limit of detection are usually observed in well-suppressed patients.

Figure 2

(a) Infectious and non-infectious viral levels simulated by the basic model (1). (b) The difference between non-infectious and infectious HIV-1 RNA concentrations. Shortly after initiation of potent antiretroviral therapy, the difference between non-infectious and infectious viral levels (base 10 logarithm) approaches a constant (~ 0.27). The parameter values used in the simulation are: λ = 10⁴ ml⁻¹ day⁻¹, d_T = 0.01 day⁻¹, k = 2.4 × 10⁻⁸ ml day⁻¹, α_L = 0.001, ∈_RT = 0, ∈_PI = 0.65, d_L = 0.004 day⁻¹, a = 0.1 day⁻¹, δ = 1 day⁻¹, N = 4000, c = 23 day⁻¹.

Figure 3

Schematic representation of asymmetric division of latently infected cells upon antigenic stimulation. Suppose a daughter cell has probability p_L to stay in the latent state, and probability (1 − p_L) to differentiate into a productively infected cell. (a) The probability that both two daughter cells are in the latent state is $p_L^2$; (b) The probability that one daughter cell is latently infected and the other is activated infected is 2p_L(1 − p_L); (c) The probability that two daughter cells are both activated infected is (1 − p_L)². The expectation of the number of latently infected cells generated every time a parental cell divides is $2·p_L^2+1·2p_L(1-p_L)=2p_L$.

Figure 4

Numerical simulations of model (5) with asymmetric division of latently infected cells stimulated by persistent antigen. The top panels: latently infected cell and HIV-1 RNA levels with p_L = 0.3. The renewal ability of latently infected cells is not good enough to maintain the latent reservoir. The model is sensitive to changes of the drug efficacy. Both activation from latent cells and ongoing viral replication cannot sustain the persistence of a low level of viremia. The bottom panels: the probability p_L is 0.7. Because of the higher potential to replenish the latent cell pool, the size of the latent reservoir increases substantially. Consequently, the viral load cannot be suppressed to below the limit of detection. The other parameter values are chosen as in Table 1. The green line represents the detection limit of conventional assays, i.e., 50 RNA copies/mL.

Figure 5

Simulations of model (5) with persistent antigen. The probability p_L is fixed at 0.51 and hence latent cell activation can hardly influence the decay of the latent reservoir. The time evolution of (a) latent infected cells and (b) the viral load with different drug efficacies: ∈ = 1 (red solid line); ∈ = 0.9 (blue dashed line); ∈ = 0.8 (black dotted line). The half-life of the latent reservoir is determined by the intrinsic turnover of latently infected cells rather than ongoing viral replication. The HAART potency affects the magnitude of the viral load but not the half-life of the viral decay. The green line represents 50 RNA copies/mL, the detection limit of conventional assays.

Figure 6

Model (5) is able to generate viral blips with intermittent antigenic activation (panels (b)(d)). The probability p_L is fixed at 0.58 in the presence of antigen. N = 3000 and ∈ = 0.8. The other parameter values are the same as in Table 1. The top panels: activations occur at 50 and 100 days; The bottom panels: activations occur more frequently at 20, 40, 60, and 80 days. Each activation lasts 5 days. Occasional replenishment from asymmetric division prevents rapid depletion of the latent reservoir (panels (a)(c)). Although asymmetric division of latent cells is able to generate blips, the viral load decreases to an unreasonably low level between two successive activations (panel (b)). This problem can be overcome with more frequent antigenic stimulation (panel (d)). However, the viral load is still sensitive to the drug efficacy in this case.

Figure 7

Asymmetric division of latently infected cells stimulated by intermittent antigen (model (7)) can generate intermittent viral blips. The left column: activations occur at the time of 10, 60, 110 and 160 day, and each lasts 4, 5, 5, and 6 days, respectively. The right column: activations occur at the same time, but the antigen lasts twice as long as the left column. In (b)(c)(e)(f), we performed simulations with different drug efficacies: ∈ = 0.8 (red solid line); ∈ = 0.9 (blue dashed line). For a higher level of drug efficacy, the amplitude of blips is smaller. Viral blips emerge whenever there exists antigenic stimulation. When the antigen is present for a longer time (the right column), the duration of blips is longer. If the probability p_L is small (< 0.5), then the size of latent reservoir decreases; if p_L is big (> 0.5), then the size of latent reservoir increases. This can be used to reconcile the different half-life estimates of the latent reservoir.

Figure 8

Stochastic simulations of asymmetric division of latently infected cells (model (7)). The model can robustly generate intermittent viral blips. Column (a): the interval between adjacent infections, ΔT, ~ N(50, 10); the duration each activation lasts, Δt, ~ U(4, 6); the probability p_L ~ U(0.65, 0.8). Column (b): ΔT ~ N(40, 10), Δt ~ U(4, 6), p_L ~ U(0.6, 0.7). Column (c): ΔT ~ N(50, 10), Δt ~ U(7, 14), p_L ~ U(0.4, 0.55), viral production rate p_υ = 2500 day⁻¹. Three realizations display variable viral decay kinetics of the latent reservoir. (a) The decay rate is not statistically significantly different from zero, suggesting that the latent reservoir may not decay. (b) Although the latently infected cell pool size decreases, the decay rate is very small, corresponding to a very long half-life, for example, 44 months. (c) The latent reservoir shows a quicker decay than the scenario (b), corresponding to a shorter half-life, such as ~ 6 months. The probability that a daughter cell remains in the latent state when cells divide and the duration of each activation are two key factors controlling the decay of the latent reservoir.