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

<p>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 <b>A</b>, 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>B</b>, we use different fractions of new infections that result in latency: (blue solid), (red dashed), and (purple dotted). In column <b>C</b>, 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi-1000533-g007" target="_blank">Figure 7</a>.</p

Multiphasic viral decline after potent treatment.

<p>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.</p

Relative contributions of ongoing viral replication and latent cell activation.

<p><b>A and B:</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 . <b>C and D:</b> relative contributions of ongoing viral replication ( was fixed) and latent cell activation to the latent reservoir and viral persistence. <b>C:</b> the ratio of to , and <b>D:</b> the ratio of to . We chose . The other parameter values used are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi-1000533-t001" target="_blank">Table 1</a>.</p

Schematic representation of the model with latently infected cell activation (Eq. (4)).

<p>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.</p

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

<p>The system is at steady state and at drug is applied. <b>A, D, G</b> and <b>J</b>: the latent reservoir size; <b>B, E, H</b> and <b>K</b>: viral load; <b>C, F, I</b> and <b>L</b>: the ratio of to , i.e., the relative contributions to the latent reservoir persistence from ongoing viral replication and latently infected cell proliferation. <b>A, B</b> and <b>C</b>: 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. <b>D, E</b> and <b>F</b>: is fixed. Different carrying capacities of the total latently infected cells are used: (green dashed), (blue solid), (red dash-dotted). <b>G, H</b> and <b>I</b>: we use different fractions of infections that result in latency: (red dashed), (blue solid), and (black dotted). <b>J, K</b> and <b>L</b>: 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi-1000533-t001" target="_blank">Table 1</a>.</p

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

<p>The model with programmed expansion and contraction of latently infected cells can generate viral blips with reasonable amplitude and duration. , . Column <b>A: </b>. Activated latently infected cells divide about times over an interval <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi.1000533-Perelson1" target="_blank">[4]</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi.1000533-Hammer1" target="_blank">[6]</a> days. No statistically significant decay of the latent reservoir is observed. Column <b>B: </b>. The latent reservoir decays at a very slow rate. This realization shows a half-life of months. Column <b>C: </b>. Activated cells divide about times over the same time interval. The latent reservoir decays more quickly than it does in <b>B</b>, corresponding to a half-life of roughly months. The other parameter values used are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi-1000533-t001" target="_blank">Table 1</a>. The blue horizontal line represents the detection limit of 50 RNA copies/mL.</p

Summary of stochastic simulations of the model, Eq. (4), with programmed expansion and contraction of latently infected cells.

<p>Abbreviations: ave (average), min (minimum), max (maximum). Values above brackets are the average values over 30 simulation runs. Values in brackets are the ranges. There are 5 antigenic activations within 300 days. When or , viral blip emerges each time activation occurs. When , not every activation generates a viral blip. In some simulations with or , the latent reservoir size is predicted to increase and hence has no half-life.</p

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

<p>We fixed the proliferation rate of activated cells to be . Column <b>A: </b>, . No statistically significant decay of the latent reservoir is observed. Column <b>B: </b>, . The latent reservoir decays at a very slow rate. Column <b>C: </b>, . In this realization, there are 8 activations in 300 days. The latent reservoir decays more quickly than in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi-1000533-g003" target="_blank">Figure 3C</a>. The other parameter values used are the same as those in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000533#pcbi-1000533-g003" target="_blank">Figure 3</a>. The blue horizontal line represents the detection limit of 50 RNA copies/mL.</p

Schematic diagram of the one-compartment model.

<p>Inflammatory cytokines released during cell death by pyroptosis attract more CD4+ T cells (<i>T</i>) to be infected. The term <i>γ</i>_<i>i</i><i>C·kVT</i> represents cytokine enhanced viral infection due to increased CD4+ T cell availability.</p

Modeling the Slow CD4+ T Cell Decline in HIV-Infected Individuals

<div><p>The progressive loss of CD4+ T cell population is the hallmark of HIV-1 infection but the mechanism underlying the slow T cell decline remains unclear. Some recent studies suggested that pyroptosis, a form of programmed cell death triggered during abortive HIV infection, is associated with the release of inflammatory cytokines, which can attract more CD4+ T cells to be infected. In this paper, we developed mathematical models to study whether this mechanism can explain the time scale of CD4+ T cell decline during HIV infection. Simulations of the models showed that cytokine induced T cell movement can explain the very slow decline of CD4+ T cells within untreated patients. The long-term CD4+ T cell dynamics predicted by the models were shown to be consistent with available data from patients in Rio de Janeiro, Brazil. Highly active antiretroviral therapy has the potential to restore the CD4+ T cell population but CD4+ response depends on the effectiveness of the therapy, when the therapy is initiated, and whether there are drug sanctuary sites. The model also showed that chronic inflammation induced by pyroptosis may facilitate persistence of the HIV latent reservoir by promoting homeostatic proliferation of memory CD4+ cells. These results improve our understanding of the long-term T cell dynamics in HIV-1 infection, and support that new treatment strategies, such as the use of caspase-1 inhibitors that inhibit pyroptosis, may maintain the CD4+ T cell population and reduce the latent reservoir size.</p></div