Interpreting the effect of vaccination on steady state infection in animals challenged with Simian immunodeficiency virus

Abstract

A representative vaccinated macaque challenged with SIVmac251 establishes a persistent infection with a lower virus load, higher CTL frequencies, and much higher helper cell frequencies, than a representative control animal. The reasons for the difference are not fully understood. Here we interpret this effect using a mathematical model we developed recently to explain results of various experiments on virus and CTL dynamics in SIV-infected macaques and HIV-infected humans. The model includes two types of cytotoxic lymphocytes (CTLs) regulated by antigen-activated helper cells and directly by infected cells, respectively, and predicts the existence of two steady states with different viremia, helper cell and CTL levels. Depending on the initial level of CTL memory cells and helper cells, a representative animal ends up in either the high-virus state or the low-virus state, which accounts for the observed differences between the two animal groups. Viremia in the low-virus state is proportional to the antigen sensitivity threshold of helper cells. Estimating the infectivity ratio of activated and resting CD4 T cells at 200-300, the correct range for the critical memory cell percentage and the viremia peak suppression is predicted. However, the model does not explain why viremia in the "low-virus state" is surprisingly high , relative to vaccinated animals infected with SHIV, and broadly distributed among challenged animals. We conclude that the model needs an update explaining extremely low sensitivity of uninfected helper cells to antigen in vaccinated animals.

Figure 1

Three blocks of a model of interaction between HIV/SIV and the immune system. The detailed structure of each block is shown in Fig. 2. “Direct” and “indirect” CTLs refer to helper-independent and helper cell-dependent CTLs, respectively.

Figure 2. Detailed model diagram

(A) Model block with non-HIV specific CD4 T cells, including infected cells and cells permissive for virus replication. R and A: Resting and activated uninfected CD4 T cells permissive for virus replication, respectively. I_R and I_A: Corresponding infected cells in the eclipse phase of replication cycle. P_R and P_A: Corresponding infected cells in the virus-producing phase. White oval: Linear combination of compartments, P = P_R+P_A, P_V = P_R+xP_A, P_H = P_R+x³P_A. Here x > 1 is the virion productivity ratio for activated versus resting infected cells, P is the total number of virus-producing cells, P_V is the effective number of virus-producing cells for free virus, and P_H is the effective number of virus-producing cells detected by helper cells. Virus load, V = v P_V (not shown). (B) Model block with HIV-specific CD8 T helper cells (CTLs). E and E_D: helper-dependent (“indirect”) and helper-independent (“direct”) effector CD8 T cells. (C) Model block with HIV-specific CD4 T cells. Inset: Control functions for the control of helper cells by antigen (α), direct effector cells by virus (β), and indirect effector cells by helper cells and antigen (σ), derived in Appendix B of Ref. (Sergeev et al., 2009). H = H_E+H_I+H_P is the total number of helper cells secreting cytokines, P₀ and P_H0 are antigen-sensitivity thresholds for direct CTL and helper cells, respectively, and H₀ is the characteristic threshold for indirect CTL in terms of helper cell percentage. (A-C) Colored oval: A cell compartment characterized by the number of cells in it. Arrow: Flux of cells from one compartment to another, or from a source to a compartment, or the proliferation or death of cells. Lower-case Roman letters and notation N_i, H_Ni, P₀, P_H0, and T_i: Model parameters (values in Table 1 and Appendix B). Expression at an arrow: Exponential rate of the process. The total CD4 count, T = A+R+I_A+I_R+P_A+P_R. Long-lived latently infected cells (not shown) are simulated by introducing several infected cells at random times.

Figure 3. Predicted effect of vaccination

(A) Simulated and observed virus dynamics for animal AC-04 used as an unvaccinated control in Ref. (Letvin et al., 2006). Model parameters (Table 1 and Appendix B; p_A/p_R = 2500) are estimated previously (Sergeev et al., 2009). Circles: Data points from Ref. (Letvin et al., 2006). Lines: Simulated cell compartments (Fig. 2) shown as percentage of CD4 T or CD8 T cell count in an average uninfected animal. (B and C) Two outcomes of vaccination depending on the initial level of memory cells. Simulated virus dynamics is shown for a vaccinated animal with the same parameter set as unvaccinated animal AC-04: (B) M(0) = 1% CD8 count (ends in the high-virus state), and (C) M(0) = 2% (ends in the low-virus state). Initial helper cell percentage, H_E(0) = 0.01% CD4 count.

Figure 4. Critical condition of the transition to the low-virus steady state (or the oscillating state) after acute infection

(A) Critical initial level of memory CTLs, M_c(0), required for the switch to the low-virus state or oscillating state, as a function of the initial helper cell level, H_N(0)+H_E(0). Cell levels are shown as percentage of CD4 T or CD8 T cell count in an average uninfected animal. (B) Decrease of the maximum virus load at the critical point, as compared to its value in a non-vaccinated animal. (A and B) The infectivity parameter ratio, p_A/p_R and identifiers of three unvaccinated animals from Ref. (Letvin et al., 2006), M-575 (blue), AC-04 (red), and 44-I (green), whose parameter sets were used for simulation (Table 1 and Appendix B), are shown in the legend. Solid lines with open squares: p_A/p_R=250. Dotted lines with other symbols: Other values of p_A/p_R, as shown.

Figure 5

Sketch of the effect of vaccination on virus dynamics, based on Fig. 2 in Ref. (Letvin et al., 2006).