Effect of the Latent Reservoir on the Evolution of HIV at the Within- and Between-Host Levels

Abstract

The existence of long-lived reservoirs of latently infected CD4+ T cells is the major barrier to curing HIV, and has been extensively studied in this light. However, the effect of these reservoirs on the evolutionary dynamics of the virus has received little attention. Here, we present a within-host quasispecies model that incorporates a long-lived reservoir, which we then nest into an epidemiological model of HIV dynamics. For biologically plausible parameter values, we find that the presence of a latent reservoir can severely delay evolutionary dynamics within a single host, with longer delays associated with larger relative reservoir sizes and/or homeostatic proliferation of cells within the reservoir. These delays can fundamentally change the dynamics of the virus at the epidemiological scale. In particular, the delay in within-host evolutionary dynamics can be sufficient for the virus to evolve intermediate viral loads consistent with maximising transmission, as is observed, and not the very high viral loads that previous models have predicted, an effect that can be further enhanced if viruses similar to those that initiate infection are preferentially transmitted. These results depend strongly on within-host characteristics such as the relative reservoir size, with the evolution of intermediate viral loads observed only when the within-host dynamics are sufficiently delayed. In conclusion, we argue that the latent reservoir has important, and hitherto under-appreciated, roles in both within- and between-host viral evolution.

Fig 1. Schematic overview of the within-host model.

The frequency of n different strains in the active compartment and latent reservoir (x_j and y_j respectively; j = 1, …, n) are tracked. In the active compartment, strain-j virus replicates with strain-specific replication rate γ_j and can mutate into other strains i with probability m_ij. A small fraction, k, of newly infected cells become resting cells and move into the latent reservoir. Latent cells are reactivated at rate a per day. The effect of cells moving between the two compartments on the strain frequencies in these compartments depends on the relative size of the reservoir compared to the active compartment, r_L. The relative reservoir size is assumed to be constant throughout infection, maintained by a balance between inflow and outflow of cells, or by proliferation of latently infected cells if the outflow rate from the reservoir exceeds the entry rate. Specifically, the homeostatic proliferation rate is given by $\rho =a-\frac{k}{r_L}$ (see Methods for derivation). See Table 1for model parameter values.

Fig 2. Estimated relative reservoir size r_L during chronic infection.

Estimates were made using either a direct method based on the number of active and latent infected CD4+ T cells (data from Chun et al. [1]), or an indirect method using HIV DNA levels pre and post-treatment (data from [–26]). For the left four studies, triangles represent single patients and the bar indicates the median. Two studies did not report data on individual patients, but on patient groups only. In these cases, the group mean [23] or median [24] was used to estimate r_L for each group.

Fig 3

Within-host dynamics for the within-host selection model (panels a-c) and the within-host neutral model (panels d-f), (a,d) in the absence of a reservoir (k = a = 0), (b,e) in the presence of a reservoir, but without homeostatic proliferation in the reservoir (r_L = 0.5, k = 5 x 10⁻³, a = 0.01 per day, ρ = 0 per day), and (c,f) in the presence of a reservoir, with a low level of homeostatic proliferation (r_L = 0.5, k = 5 x 10⁻⁴, a = 0.01 per day, ρ = 9 x 10⁻³ per day). The black line indicates the time at which the frequency of the initial strain has declined to 10%. The presence of a latent reservoir delays the within-host dynamics, and this delay becomes even more profound if there is a low level of homeostatic proliferation in the reservoir. The number of strains is n = 16. In the within-host selection model, strains have linearly increasing replication rates between γ₁ = 1.0 and γ₁₆ = 1.05 and the infection is initiated with strain 9. In the within-host neutral model, all strains have equal within-host fitness and strains are characterised by the number of neutral mutations they carry compared to the founder strain. In this case the last strain (carrying ≥15 mutations) is absorbing, i.e. there are no mutations out of this bin. All other parameter values are as stated in Table 1.

Fig 4. Delay in decline of the founder strain for varying reservoir parameter values in the within-host selection model.

Persistence of the founder strain is defined as the time it takes for the founder strain to decline to a frequency <10% in the within-host population, and the delay in decline was calculated as the difference in persistence between the settings of interest and a control case in which the reservoir was absent. (a) Varying the activation rate a and the relative reservoir size r_L in the absence of homeostatic proliferation (ρ = 0, k = r_L ∙ a), and (b) varying the homeostatic proliferation rate ρ and the relative reservoir size r_L for fixed activation rate (a = 0.01 per day). The homeostatic proliferation rate was varied by tuning the proportion of newly infected cells that enter the reservoir, k. The delay of the within-host dynamics increases with the relative size of the reservoir, and with the activation and homeostatic proliferation rate of latently infected cells. Note that the scales in panel (a) and (b) are different: the delays found in the presence homeostatic proliferation can be much larger than if latently infected cells do not proliferate. Results are shown for strains with increasing replication rates (γ₁ = 1.0 - γ₁₆ = 1.05), with the infection founded by strain 9. Similar results were found for the within-host neutral case (S1 Fig).

Fig 5. Dynamics of the between-host model.

The relative prevalence of infections initiated by different viral strains, I_j(t), is shown. The insets show the basic reproduction number R₀ and average set-point viral load (spVL) at the end of the numerical integration. Panels (a) and (b) show baseline expectations for the case without a latent reservoir, comparing a scenario in which within-host evolution is neutral to the within-host selection model. Panel (c) illustrates the effect of adding a latent reservoir. (a) No selection within-host with no reservoir. All strains have equal within-host fitness (γ₁ = γ₁₆ = 1.0), but do differ in spVL and associated virulence and duration of the infection. Moderately virulent strains are selected, which have optimal transmission potential. (b) Within-host selection model with no reservoir; strains have linearly increasing within-host replication rates (between γ₁ = 1.0 and γ₁₆ = 1.05) and increasing virulence. We clearly see the effects of short-sighted evolution: more virulent strains dominate the population, even though this reduces the population level fitness (R₀) of the infection. (c) Within-host selection model with a reservoir; strains have increasing fitness and there is a relatively large reservoir (r_L = 0.5) with a low level of homeostatic proliferation (a = 0.01 per day, k = 5 x 10⁻⁴, ρ = 9 x 10⁻³ per day, settings as in Fig 3C). The presence of a latent reservoir delays within-host dynamics, resulting in the dominance of less virulent strains at the population level, and hence reduces the effects of short-sighted within-host evolution.