Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy

Abstract

Although potent combination therapy is usually able to suppress plasma viral loads in HIV-1 patients to below the detection limit of conventional clinical assays, a low level of viremia frequently can be detected in plasma by more sensitive assays. Additionally, many patients experience transient episodes of viremia above the detection limit, termed viral blips, even after being on highly suppressive therapy for many years. An obstacle to viral eradication is the persistence of a latent reservoir for HIV-1 in resting memory CD4(+) T cells. The mechanisms underlying low viral load persistence, slow decay of the latent reservoir, and intermittent viral blips are not fully characterized. The quantitative contributions of residual viral replication to viral and the latent reservoir persistence remain unclear. In this paper, we probe these issues by developing a mathematical model that considers latently infected cell activation in response to stochastic antigenic stimulation. We demonstrate that programmed expansion and contraction of latently infected cells upon immune activation can generate both low-level persistent viremia and intermittent viral blips. Also, a small fraction of activated T cells revert to latency, providing a potential to replenish the latent reservoir. By this means, occasional activation of latently infected cells can explain the variable decay characteristics of the latent reservoir observed in different clinical studies. Finally, we propose a phenomenological model that includes a logistic term representing homeostatic proliferation of latently infected cells. The model is simple but can robustly generate the multiphasic viral decline seen after initiation of therapy, as well as low-level persistent viremia and intermittent HIV-1 blips. Using these models, we provide a quantitative and integrated prospective into the long-term dynamics of HIV-1 and the latent reservoir in the setting of potent antiretroviral therapy.

Figure 1. Multiphasic viral decline after potent treatment.

After initiation of HAART, the plasma viral load undergoes a multiphasic decay and declines to below the detection limit (e.g., 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. Schematic representation of the model with latently infected cell activation (Eq. (4)).

Following encounter with cell-specific antigens, latently infected cells are activated and undergo programmed clonal expansion and contraction. A number of activated latently infected cells transition to the productive class and produce virions, whereas another small fraction of activated cells revert back to the latent state, providing a mechanism to replenish the latent reservoir.

Figure 3. Stochastic simulations of the model with programmed expansion and contraction (Eq. (4)).

The model with programmed expansion and contraction of latently infected cells can generate viral blips with reasonable amplitude and duration. , . Column A: . Activated latently infected cells divide about times over an interval , days. No statistically significant decay of the latent reservoir is observed. Column B: . The latent reservoir decays at a very slow rate. This realization shows a half-life of months. Column C: . Activated cells divide about times over the same time interval. The latent reservoir decays more quickly than it does in B, corresponding to a half-life of roughly months. The other parameter values used are listed in Table 1. The blue horizontal line represents the detection limit of 50 RNA copies/mL.

Figure 4. Sensitivity tests on the activation rate and the transition rate in Eq. (4).

The proliferation rate of activated cells, , is fixed. Column A: the transition rate is fixed and the activation rate varies: (red solid), (blue dashed) and (black dotted). is fixed. Column B: the activation rate is fixed and the transition rate varies: (red solid), (blue dashed) and (black dotted). is fixed. Column C: and are fixed. The viral production rate varies: (red solid) and (black dotted). The other parameter values used are the same as those in Figure 3. The blue horizontal line represents the detection limit of 50 RNA copies/mL.

Figure 5. Numerical simulations of Eq. (4) with different duration and frequency of activation.

We fixed the proliferation rate of activated cells to be . Column A: , . No statistically significant decay of the latent reservoir is observed. Column B: , . The latent reservoir decays at a very slow rate. Column C: , . In this realization, there are 8 activations in 300 days. The latent reservoir decays more quickly than in Figure 3C. The other parameter values used are the same as those in Figure 3. The blue horizontal line represents the detection limit of 50 RNA copies/mL.

Figure 6. Simulations of the model with a biphasic contraction phase (Eq. (6)).

The model is able to generate viral blips as well as low-level persistent viremia. The low-level viral load is maintained by a low level of activated latently infected cells during the second slower contraction phase in the latent cell response. In the first row, is the expansion function (red) and is the rapid contraction function (blue). Different proliferation rates, i.e., (Column A), (Column B), and (Column C), result in differential decay characteristics of the latent reservoir as in Figure 3. The other parameter values used are listed in Table 1. The blue horizontal line represents the detection limit of 50 RNA copies/mL.

Figure 7. Relative contributions of ongoing viral replication and latent cell activation.

A and B: the effects of ongoing viral replication (influenced by the overall drug efficacy) on the latent reservoir and viral load in the model given by Eq. (6). Different drug efficacies are used: (red dashed line) and (blue solid line). Ongoing viral replication is only a minor contributor to the stability of the latent reservoir and low-level persistent viremia, as indicated by the minor effect of changing drug efficacy from to . C and D: relative contributions of ongoing viral replication ( was fixed) and latent cell activation to the latent reservoir and viral persistence. C: the ratio of to , and D: the ratio of to . We chose . The other parameter values used are listed in Table 1.

Figure 8. Sensitivity tests on several parameters when studying the relative contributions using model (6).

The upper panels: the latent reservoir size; the middle panels: viral load; and the lower panels: the ratio of the relative contributions, i.e., the ratio of to . In column A, we use different activation rates: (blue solid), (red dashed), and (purple dotted). There is no change in the ratio of relative contributions. In column B, we use different fractions of new infections that result in latency: (blue solid), (red dashed), and (purple dotted). In column C, we use different reversion rates to latency: (blue solid), (red dashed), and (purple dotted). The other parameter values used are the same as those in Figure 7.

Figure 9. Numerical simulations of the homeostasis model (Eq. (7)) and sensitivity tests of several parameters.

The system is at steady state and at drug is applied. A, D, G and J: the latent reservoir size; B, E, H and K: viral load; C, F, I and L: the ratio of to , i.e., the relative contributions to the latent reservoir persistence from ongoing viral replication and latently infected cell proliferation. A, B and C: the carrying capacity of total latently infected cells is . We use different proliferation rates: (blue solid), (green dash-dotted), and (red dashed). The black solid line represents the detection limit. D, E and F: is fixed. Different carrying capacities of the total latently infected cells are used: (green dashed), (blue solid), (red dash-dotted). G, H and I: we use different fractions of infections that result in latency: (red dashed), (blue solid), and (black dotted). J, K and L: we use different drug efficacies: (red dashed), (blue solid), (black dotted). and the carrying capacity are fixed for the last two rows. The other parameter values used are listed in Table 1.

Figure 10. Simulations of the homeostasis model (Eq. (7)) with occasional increases of the transition rate .

A Poisson process with an average waiting time of 2 months is used to model the random encounter between latently infected cells and antigens. We assume the total body carrying capacity of latently infected cells is . Column A: ; column B: ; column C: . Different values of represent different potentials of latently infected cells to renew themselves, and thus lead to different decay rates of the latent reservoir. The other parameter values used are listed in Table 1.