Recruitment times, proliferation, and apoptosis rates during the CD8(+) T-cell response to lymphocytic choriomeningitis virus

Abstract

The specific CD8(+) T-cell response during acute lymphocytic choriomeningitis virus (LCMV) infection of mice is characterized by a rapid proliferation phase, followed by a rapid death phase and long-term memory. In BALB/c mice the immunodominant and subdominant CD8(+) responses are directed against the NP118 and GP283 epitopes. These responses differ mainly in the magnitude of the epitope-specific CD8(+) T-cell expansion. Using mathematical models together with a nonlinear parameter estimation procedure, we estimate the parameters describing the rates of change during the three phases and thereby establish the differences between the responses to the two epitopes. We find that CD8(+) cell proliferation begins 1 to 2 days after infection and occurs at an average rate of 3 day(-1), reaching the maximum population size between days 5 and 6 after immunization. The 10-fold difference in expansion to the NP118 and GP283 epitopes can be accounted for in our model by a 3.5-fold difference in the antigen concentration of these epitopes at which T-cell stimulation is half-maximal. As a consequence of this 3.5-fold difference in the epitope concentration needed for T-cell stimulation, the rates of activation and proliferation of T cells specific for the two epitopes differ during the response and in combination can account for the large difference in the magnitude of the response. After the peak, during the death phase, the population declines at a rate of 0.5 day(-1), i.e., cells have an average life time of 2 days. The model accounts for a memory cell population of 5% of the peak population size by a reversal to memory of 1 to 2% of the activated cells per day during the death phase.

FIG. 1

Scheme of the basic model depicting the step function f(t). In this model we assume that naive T cells are all activated when proliferation starts at T_on. In the second model the step function f(t) is replaced by a continuous function, 0 < f(t) < 1, that smoothly follows the changes in the viral load. Solid lines indicate processes that are positively influenced by the activation function. Dashed lines are processes inhibited by antigen.

FIG. 2

Fitting the on-off model to the data on the CD8⁺ T-cell response to the NP118 epitope (A) and to the GP283 epitope (B). For each epitope, the dashed lines depict the total population size in the spleen, solid lines show activated cells, and long-dashed lines show memory cells. The circle symbols represent the experimental data.

FIG. 3

Dynamics of the NP118- and GP283-specific cell populations in the continuous model. (A) Broken line gives the viral load in PFU per spleen (14), the heavy line gives the total population size of the NP118 response, and the light line gives that of the GP283 response. (B) Subpopulations within each clone. Solid lines depict activated cells, long-dashed lines show memory cells, and short-dashed lines show naive cells (14).

FIG. 4

Actual activation rates F(V)a (solid lines), proliferation rates F(V)ρ (long-dashed lines), and apoptosis rates F(V)α (short-dashed lines). Heavy lines give the NP118 response, and light lines give the GP283 response.