Two types of cytotoxic lymphocyte regulation explain kinetics of immune response to human immunodeficiency virus

Abstract

The organization of the cytotoxic T lymphocyte (CTL) response at organismal level is poorly understood. We propose a mathematical model describing the interaction between HIV and its host that explains 20 quantitative observations made in HIV-infected individuals and simian immunodeficiency virus-infected monkeys, including acute infection and response to various antiretroviral therapy regimens. The model is built on two modes of CTL activation: direct activation by infected cells and indirect activation by CD4 helper cells activated by small amounts of virus. Effective infection of helper cells by virus leads to a stable chronic infection at high virus load. We assume that CTLs control virus by killing infected cells. We explain the lack of correlation between the CTL number and the virus decay rate in therapy and predict that individuals with a high virus load can be switched to a low-viremia state that will maintain stability after therapy, but the switch requires fine adjustment of therapy regimen based on the model and individual parameters.

Fig. 1.

Partial model describing dynamics of cells infected with HIV/SIV and permissive for its replication. Ovals, cell compartments; uppercase letters, cell numbers in compartments (dynamic variables); thick arrows, flow of cells from one compartment to another because of change of phenotype or death; thin arrows, control (linear by default) of cell flow between two compartments by a third compartment; lowercase letters and R_i, constant proportionality coefficients (model parameters). Compartment V represents infected cells producing virus. Short-lived virus is cleared, if V and I are below 1 i.d. = 1 productively infected cell per animal = 10^–2 copies of RNA per ml (monkey) = 3.4 × 10^–10 p27 ng/ml.

Fig. 2.

Virus production and two steady states (sketch). (a) Time dependence of virus production by an infected cell (sketch). (b) Net expansion and infection rates of activated helper cells, H_A, and the net expansion rate of direct effector cells, E_D, as functions of the virus load. Small circles, two stable steady states. Values at x-axis: V_high = d_D/a, V_low ≈ V_om_H/(c – d_H), V* = (c – d_H)/p. The helper cell number in the low-virus steady state: H₂ = H₀[(c – d_H)/m_H]ln[(c – d + r)/(c – d)].

Fig. 3.

Partial model of CTL dynamics. Loops with arrows, cell division. Dashed line, a variant model where direct effector cells are produced from naïve cells, not memory cells. The rest of the notation is as in Fig. 1. (Inset) σ(Hg(V)) = 1 – exp[–Hg(V)/H₀], nonlinear control of CTL by helper cells and virus.

Fig. 4.

Partial model of dynamics of virus-specific CD4 T helper cells. (Inset) Nonlinear control of helper cells by virus, g(V) = 1 – exp(–V/V₀). The remaining notation is as in Figs. 1 and 3.

Fig. 5.

Full model of HIV/SIV infection. Ovals in yellow, red, and cyan represent parts of the model from Figs. 1 (nonspecific CD4 T cells), 3 (virus-specific CD8 T cells), and 4 (virus-specific helper CD4 T cells), respectively. Colored thin arrows, respective control. Nonlinear control function: σ(Hg(V)) = 1 – exp[–Hg(V)/H₀], where H = H_A + H_I + H_V. The rest of the notation is as in Figs. 1, 3, and 4.

Fig. 6.

Fitting of three experiments consecutive in time, acute infection (10), onset of ART (25), long-term and interrupted ART (28), based on the model (Fig. 5, without the dashed arrow). (a and b) Acute infection with 20 infectious doses (0.2 RNA copy per ml) of virus. (a) Circle, data for animal p88 infected with SIVmac251 (10). Solid lines, best-fit predicted dependencies. (b) Predicted cell numbers in six important cell compartments (on the curves). The values of V and R are shown in virus units on the right y-axis. Arrows show the values of V_low, V_high, and V* (Fig. 2 and legend) and H₀.(c and d) First weeks of 100% efficacious ART (p = p_R = 0) simulating experiment in ref. . Predicted cell compartments are shown in linear (c) and logarithmic (d) scale. (e and f) Simulated kinetics of interrupted ART similar to experiment in ref. . Drug efficacy: 100% (e) and 94% (f): p(126 < t < 236) = 0.06p(t < 126). One-day pulses of 5 i.d. of virus (V) each 10th day simulate bursts from latent reservoirs. (a–f) Fitting parameters (Fig. 5): p = 100 per day per virus unit (vu); R_i = 3.8vu; d_A = 0.94/day; d_I = 1.26/day; H_Ni = 10^–5; N_i = 2.2 × 10^–3 % CD8 cells; f = 0.14; c = 3.41/day; d = 2.42/day; k = 1.06/day per cell; r = 6.5/day; V₀ = 4.3 × 10^–6vu; H₀ = 4 × 10^–4; a = 1.4/day per vu; d_D = 0.13/day; m = 1.18/day; d_H = 0.085/day; p_R = 1.98/day per vu; s_A = 0.44vu/day. Here, vu = 1 p27 ng/ml = 3 × 10⁷ RNA copies per ml. Fixed parameters: d_N = 10^–3 per day; m_H = 0.1/day; E_m = 100%.