Killing of targets by CD8 T cells in the mouse spleen follows the law of mass action

Abstract

It has been difficult to correlate the quality of CD8 T cell responses with protection against viral infections. To investigate the relationship between efficacy and magnitude of T cell responses, we quantify the rate at which individual CD8 effector and memory T cells kill target cells in the mouse spleen. Using mathematical modeling, we analyze recent data on the loss of target cells pulsed with three different peptides from the mouse lymphocytic choriomeningitis virus (LCMV) in mouse spleens with varying numbers of epitope-specific CD8 T cells. We find that the killing of targets follows the law of mass-action, i.e., the death rate of individual target cells remains proportional to the frequency (or the total number) of specific CD8 T cells in the spleen despite the fact that effector cell densities and effector to target ratios vary about a 1000-fold. The killing rate of LCMV-specific CD8 T cells is largely independent of T cell specificity and differentiation stage. Our results thus allow one to calculate the critical T cell concentration at which growth of a virus with a given replication rate can be prevented from the start of infection by memory CD8 T cell response.

Figure 1. Schematic representation of the in vivo cytotoxicity assays undertaken to investigate the quantitative details of CD8 T cell mediated killing of peptide-pulsed targets in the mouse spleen.

In the first set of experiments (“LCMV infection”, panel A), B6 mice were infected with LCMV-Arm and 8 or 37–100 days later, three populations of target cells (pulsed with either NP296 or GP276 peptides of LCMV and unpulsed) were transferred into these mice. In the second set of experiments (“adoptive transfer”, panel B), P14 TCR Tg CD8 T cells, specific to the GP33 epitope of LCMV, were transferred into B6 mice and then infected with LCMV-Arm. Eight or 40 days later, different number of effector (day 8) or memory (day 40) P14 CD8 T cells from these mice were transferred into new naive B6 mice (in panel B, we shown an example where effectors or memory CD8 T cells are transferred). Two hours later, two populations of targets (pulsed with the GP33 peptide of LCMV and unpulsed) were transferred into these mice now harboring GP33-specific CD8 T cells. In both sets of experiments, killing of peptide-pulsed targets was measured in spleens of mice at different times after cell transfer .

Figure 2. Fits of the mathematical model to data involving adoptive transfer of different numbers of GP33-specific effector (panels A&C) or memory (panels B&D) CD8 T cells.

Panels A and B show that the number of unpulsed targets in the spleen at different times after cell transfer remains approximately constant. Panels C and D show the decrease in the ratio of the frequencies of peptide-pulsed and unpulsed targets in the spleen over time. Different symbols denote data from different adoptive transfer experiments with , , , or P14 cells transferred. Filled symbols denote individual mouse measurements with the averages per time point being connected by solid lines. Open symbols are the model predictions with averages being connected by dashed lines. Parameters providing the best fits of the model are shown in Table 1. Note that in panel A, the model can not predict the decline in the number of unpulsed targets with time in experiments with transfer of GP33-specific effectors. Such decline in the number of unpulsed targets in the spleen is unexpected and is most likely due to a measurement error.

Figure 3. The estimated death rate of peptide-pulsed targets due to killing by epitope-specific CD8 T cells is proportional to the average percent (panel A) or average number (panel B) of epitope-specific CD8 T cells in the spleen.

Note that the percent of antigen-specific CD8 T cells is calculated among all cells in the spleen. Estimates are given for targets pulsed with NP396 (), GP276 (▴), or GP33 (▪) peptides from LCMV. Filled symbols are for killing by effector CD8 T cells, and open symbols are for killing by memory CD8 T cells. Lines show the linear regression for the transformed estimates of the death rate and density of CD8 T cells. Slopes for the regressions are not statistically different from one (panel A: slope = 1.13, ; panel B: slope = 0.98, ).

Figure 4. The estimated per capita killing efficacy of CD8 T cells is independent of the average percent (panel A) or average number of epitope-specific CD8 T cells in the spleen.

We estimate the killing efficacy by dividing the death rate of targets by the frequency (panel A) or the number (panel B) of epitope-specific CD8 T cells in the spleen . Notations are the same as in Fig. 3. Lines show linear regression for the estimates of the killing efficacy and transformed frequency (panel A) or number (panel B) of epitope-specific CD8 T cells. Slopes for the regressions are not statistically different from zero (panel A: slope = 0.89, ; panel B: slope = −0.06, ). A large positive slope for the correlation between per capita killing and the frequency of epitope-specific CD8 T cells in panel A is due to an outlier for killing by NP396-specific effector CD8 T cells. Removing this outlier led to the estimated slope = 0.06, . The average killing efficacy of CD8 T cells is (panel A) or (panel B).

Figure 5. Predicted changes in viral load for different initial numbers of virus-specific memory CD8 T cells.

Using the model given in eqns. (3)–(4), we plot the dynamics of the virus () over the course of infection when the initial number of virus-specific memory CD8 T cells () is low (, panel A) or high (, panel B). Viral density declines following infection as memory CD8 T cells reach the threshold level of cells per spleen. Other parameters are , , , , , .