Understanding the failure of CD8+ T-cell vaccination against simian/human immunodeficiency virus

Abstract

Although CD8+ T cells play an important role in controlling viral infections, boosting specific CD8+ T cells by prophylactic vaccination with simian immunodeficiency virus (SIV) epitopes fails to provide sterilizing immunity. Viral replication rates and viral contraction rates after the peak viremia hardly depend on the presence of memory CD8+ T cells. To study these paradoxical findings, we parameterize novel mathematical models for acute SIV and human immunodeficiency virus infection. These models explain that failure of vaccination is due to the fact that effector/target ratios are too low during the viral expansion phase. Because CD8+ T cells require cell-to-cell contacts, immune protection requires high effector/target ratios at the primary site of infection. Effector/target ratios become favorable for immune control at the time of the peak in the viral load when the virus becomes limited by other factors, such as the availability of uninfected target cells. At the viral set point, effector/target ratios are much higher, and perturbations of the number of CD8+ effector cells have a large impact on the viral load. Such protective effector/target ratios are difficult to achieve with nucleic acid- or protein-based vaccines.

FIG. 1.

Acute infection dynamics in the model described in THEORY. The lines depict the target cells (T) (light solid line), the viral load (V) (heavy solid line), the immune response (E) (dashed line), and the naive T cells (N) (dashed-dotted line). From left to right, the production rate varies from p = 1 to p = 10 to p = 100 virions day⁻¹ (and hence, β = 6.3, 0.63, and 0.063, respectively). From top to bottom, the killing rate varies from k = 1 to k = 10 to k = 100 day⁻¹. Other parameters are as follows: γ = δ = 1 day⁻¹, σ = 10⁸ cells day⁻¹, d_T = 0.01 day⁻¹, d = 0.02 day⁻¹, d_E = 0.5 day⁻¹, m = 1.5 day⁻¹, h_a = h_m = 1,000 cells, h_k = 10⁵ cells, h_β = 10⁸ cells, and a = 0.1 day⁻¹.

FIG. 2.

SIV dynamics in vaccinated monkeys. The lines depict the target cells (T) (light solid line), the viral load (V) (heavy solid line), the immune response (E) (dashed line), and the memory T cells (N) (dashed-dotted line). By increasing the activation rate 10-fold to a = 1 day⁻¹, the naive T cells of equation 4 now represent memory T cells. In panels a to d, simulations start with various levels of memory cells, i.e., N₁ = 10², 10³, 10⁴, and 10⁵ cells, respectively. Other parameters are described in the legend of Fig. 1e, i.e., p = k = 10. Vaccination changes the initial infection dynamics only at high numbers of memory cells; otherwise, the response is too late and too slow and becomes important after the peak. Note that the peak viremia decreases somewhat from panel a to panel c and that the peak has disappeared in panel d. Because the model has only one attractor for these parameter values, the same viral set point is approached in all four panels. In reality, vaccinated animals approach lower set points.

FIG. 3.

Therapeutic vaccination (a) and CD8⁺ T-cell depletion (b). Considering the chronic phase, we ignore the naive T cells. In panel a, P in equation 5 is replaced with P + D, where D is antigen-loaded dendritic cells that are introduced at day zero and that disappear exponentially [D(t) = 10⁵e^−0.02t]. Note that a small increase in the immune response (dashed line) markedly decreases the viral load (solid line). In panel b, the specific CD8⁺ T-cell response is depleted to 10% of its steady-state value at day zero. Parameters are described in the legend of Fig. 1e, i.e., p = k = 10.

FIG. A1.

Cytotoxic immune response to an acute infection. Consider the model with density-dependent pathogen growth: of a pathogen, L, growing exponentially at a rate, r, as long as ɛL ≪ 1 (depicted by the solid line), and an immune response, E, growing exponentially at a rate of dE/dt = mE (depicted by the dashed line). For ɛ = c_L = c_E = 0, one obtains the mass-action model dL/dt = (r − k′E)L, where k′ = k/h. The heavy solid line in panel a shows that the pathogen growth drops to zero at the critical immune response E = r/k′. We take expansion rates that are realistic for SIV infection of macaques, i.e., r = 1.5 > m = 1 day⁻¹ (21), and set k equal to 2 and h equal to 10³ cells. The light solid line in panel a depicts uncontrolled pathogen growth that is obtained for the same parameters when we allow for saturation in the number of targets by setting c_L equal to 1 (16, 26, 76). In panel b, the replication rate of the pathogen is reduced at high pathogen densities (by setting ɛ equal to 10⁻⁷ cells). The saturated immune response (with c_L = 1) can eradicate the pathogen after its growth has slowed down. This model accounts for the observed limited effects of prophylactic vaccination, because the initial replication rate of the pathogen remained unaffected by vaccination, and similar peak values were observed; see panel c, where we start with E = 0.01, 0.1, 1, or 10 effector cells at time point zero. After the peak dL/dt ≈ rL − kE, and because the effector population is very large, the rate at which the pathogen is cleared is unrealistically fast. This is unrealistic because there are many effector cells per target cell, each killing target cells at rate k. We solve this problem by setting c_E equal to 1, which makes the killing also limited by the target cells (d). By setting the killing rate, k, equal to 2 day⁻¹, the down slope in panel d approaches the observed invariant, r − k = −0.5 day⁻¹.

FIG. A2.

Acute infection dynamics without an eclipse phase. The effect of the eclipse phase on the down slope after the peak in viral load can be seen by comparing this figure with Fig. 1. The eclipse phase is eliminated from the model by increasing the maturation parameter, γ, by 100-fold and decreasing the death rate, δ, of virus-producing cells to keep the same expected life span of 2 days for productively infected cells. For low killing rates, k = 1 day⁻¹, the immune response hardly affects the viral load, and there is hardly any down slope. For intermediate killing rates, k = 10 day⁻¹, the down slope is much steeper than in the model with an eclipse phase, and the virus is eliminated after 3 weeks. Such a steep down slope and the clearance of the virus are unrealistic. The lines depict the target cells (T) (light solid line), the viral load (V) (heavy solid line), the immune response (E) (dashed line), and naive T cells (N) (dash-dotted line). Parameters are described in the legend of Fig. 1 but with γ = 100 day⁻¹ and δ = 0.5 day⁻¹.