Understanding the slow depletion of memory CD4+ T cells in HIV infection

Abstract

Background: The asymptomatic phase of HIV infection is characterised by a slow decline of peripheral blood CD4(+) T cells. Why this decline is slow is not understood. One potential explanation is that the low average rate of homeostatic proliferation or immune activation dictates the pace of a "runaway" decline of memory CD4(+) T cells, in which activation drives infection, higher viral loads, more recruitment of cells into an activated state, and further infection events. We explore this hypothesis using mathematical models.

Methods and findings: Using simple mathematical models of the dynamics of T cell homeostasis and proliferation, we find that this mechanism fails to explain the time scale of CD4(+) memory T cell loss. Instead it predicts the rapid attainment of a stable set point, so other mechanisms must be invoked to explain the slow decline in CD4(+) cells.

Conclusions: A runaway cycle in which elevated CD4(+) T cell activation and proliferation drive HIV production and vice versa cannot explain the pace of depletion during chronic HIV infection. We summarize some alternative mechanisms by which the CD4(+) memory T cell homeostatic set point might slowly diminish. While none are mutually exclusive, the phenomenon of viral rebound, in which interruption of antiretroviral therapy causes a rapid return to pretreatment viral load and T cell counts, supports the model of virus adaptation as a major force driving depletion.

Figure 1. A Simple Model of Self-Renewing Memory CD4⁺ T Cell Homeostasis in the Absence of HIV Infection, with Density-Dependent Rates of Division and Death of Resting Cells

Figure 2. Extending the Previous Model of Memory CD4⁺ Homeostasis to Include HIV Infection

We now assume that activated cells are infected at a rate proportional to the virus load (which in turn is assumed to be proportional to the productively infected cell count z) and an infectivity parameter p that models the efficiency of the infection process.

Figure 3. Steady-State Pool Size as a Function of Virus Infectivity p

We choose units of peripheral blood cell counts such that healthy memory CD4⁺ T cell numbers are unity. Below a threshold value of p the infection fails to take hold. We expect HIV infections to correspond to the area right of this threshold.

Figure 4. The Predicted Time for Memory CD4⁺ T Cell Numbers to Decline from 100% to 50% of Healthy Numbers, as a Function of Virus Infectivity p

Parameter values (see model equations in caption to Figure 2): a(x) = a ₀(1 − x/κ), where a ₀ = 1/30 d⁻¹, giving a(x*) ≈ 1/60 (here x* refers to the steady state numbers of resting memory CD4⁺ T cells in an uninfected individual); κ = 1; δ(x) = δ ₀ x/κ, where δ ₀ = 1/200, giving δ(x*) ≈ 1/400; μ = 1.06; v = 0.5; and r = 1 (all rates in units of d⁻¹).

Figure 5. Extending the Model of Memory CD4⁺ T Cell Dynamics in HIV Infection to Include Both Homeostatically Activated (y) and Antigen- or Bystander-Activated Cells (w)

Resting memory cells can undergo homeostatic proliferation at rate a, as before; they can also be antigen- or bystander-activated at rate a* and undergo a fold expansion f in the process. These cells are infected at rate pz, die at rate γ ₁, or return to a resting memory state at rate γ₂. The results we present here are insensitive to the values of γ ₁, γ ₂, and f, which we take to be 0.2 d⁻¹, 0.02 d⁻¹, and 100, respectively.

Figure 6. The Predicted Steady-State Pool Size as a Function of Virus Infectivity p, in the Presence of Different Levels of Immune Activation a*

Figure 7. The Predicted Time Course of CD4⁺ Memory T Cell Numbers as They Decline to Their Steady State Level for Different Levels of Immune Activation a* in the Presence of HIV

Steady state levels are indicated by dashed lines. The infectivity parameter p = 200; other parameters are as in previous figures.