Estimating the In Vivo Killing Efficacy of Cytotoxic T Lymphocytes across Different Peptide-MHC Complex Densities

Abstract

Cytotoxic T lymphocytes (CTLs) are important agents in the control of intracellular pathogens, which specifically recognize and kill infected cells. Recently developed experimental methods allow the estimation of the CTL's efficacy in detecting and clearing infected host cells. One method, the in vivo killing assay, utilizes the adoptive transfer of antigen displaying target cells into the bloodstream of mice. Surprisingly, killing efficacies measured by this method are often much higher than estimates obtained by other methods based on, for instance, the dynamics of escape mutations. In this study, we investigated what fraction of this variation can be explained by differences in peptide loads employed in in vivo killing assays. We addressed this question in mice immunized with lymphocytic choriomeningitis virus (LCMV). We conducted in vivo killing assays varying the loads of the immunodominant epitope GP33 on target cells. Using a mathematical model, we determined the efficacy of effector and memory CTL, as well as CTL in chronically infected mice. We found that the killing efficacy is substantially reduced at lower peptide loads. For physiological peptide loads, our analysis predicts more than a factor 10 lower CTL efficacies than at maximum peptide loads. Assuming that the efficacy scales linearly with the frequency of CTL, a clear hierarchy emerges among the groups across all peptide antigen concentrations. The group of mice with chronic LCMV infections shows a consistently higher killing efficacy per CTL than the acutely infected mouse group, which in turn has a consistently larger efficacy than the memory mouse group. We conclude that CTL killing efficacy dependence on surface epitope frequencies can only partially explain the variation in in vivo killing efficacy estimates across experimental methods and viral systems, which vary about four orders of magnitude. In contrast, peptide load differences can explain at most two orders of magnitude.

Fig 1. Experimental design of the in vivo killing assay performed on four treatment groups of four mice.

Mice in the control group (a) were not challenged with LCMV, and stayed naïve. Mice in the acute (b) and memory (d) groups were infected with 200 pfu, while the chronic group (c) received 1 × 10⁶ pfu of LCMV Docile. After a delay of eight (acute group) and 42 days (chronic and memory groups) respectively, labelled target cells were injected intravenously into all mice including the naïve group. The transferred cells consisted of subpopulations of cells pulsed with different peptide loads, including a subpopulation of unpulsed cells. The subpopulations were pulsed with the indicated concentrations of GP33-epitope (5 × 10⁶ cells each). At the indicated time points, blood samples were taken and analysed for the proportions of the labelled cells by flow cytometry. Splenectomy was conducted on each mouse 4 hours after cell transfer and the splenocytes analysed for specific lysis of target cells and the proportions of epitope-specific CTLs. Note that in contrast to [15], this design uses an additional treatment group—the memory group, a larger number of target cells is transferred, and the time between infection and cell transfer is tuned to observe the desired effector, chronic and memory CTLs.

Fig 2. FACS analysis of target cells before transfer can reliably differentiate target cell subpopulations.

To assess the reliability of our experimental design, we tested whether the six target cell subpopulations pulsed at different peptide concentrations could be distinguished by their markers alone. Before FACS analysis, equal numbers of the different target cell populations were mixed. The six target cell subpopulations –no peptide in A), and pulsed with increasing GP33 peptide concentrations of ${10}^{-4}\frac{\mu \mathrm{\text{g}}}{\mathrm{\text{ml}}}$ in B) to $1\frac{\mu \mathrm{\text{g}}}{\mathrm{\text{ml}}}$ in F)– employed in our study could reliably be differentiated according to their Ly5.1/Ly5.2 expression and CFSE staining intensity. The percentages of detected target cells are given above the panels A) to F).

Fig 3. Frequency of CD8⁺ T cells in the spleen 4 hours after transfer of the target cells.

Following the experimental design, splenectomies were conducted on the mice of all treatment groups. Panel A) shows the total frequencies of CD8⁺ T cells and B) the frequencies of the GP33-specific CD8⁺ T cells among splenocytes in naïve (unfilled), acute (light grey), chronic (dark grey) and memory (black) treatment groups found in the spleen 4 hours after the transfer of target cells. The black connecting lines show significant deviations in the CD8⁺ T cell frequencies between groups, and are given with the associated p-values.

Fig 4. Relative frequency of target cells in the blood over time for the different mouse groups.

The frequencies are given relative to the total target cell pool measured at 30, 60, 120 and 240 minutes after transfer. A) The frequencies of the target cells in the naive, B) acute, C) chronic and D) memory groups are shown for each individual mouse. The group means for each measurement are connected by lines specific to the pulsing concentration. The frequencies of the target cells found in the spleen after 4h are shown separately next to the dashed black line.

Fig 5. Curves of the killing efficacy model for different values of parameter pairs.

The killing efficacy model $k(k_{\mathrm{\text{max}}},{\lambda }_{\frac{1}{2}},\lambda )$ accounts for the varying efficacy of individual CD8⁺ T cells at killing target cells (k) at different peptide pulsing concentrations λ. The parameter k _max is the maximal killing rate of CD8⁺ T cells, where higher peptide concentrations λ do not increase CD8⁺ T cell killing. The parameter ${\lambda }_{\frac{1}{2}}$ describes at which peptide load killing is half-maximal. The lower this value, the more sensitive the CD8⁺ T cell is to peptide: a less sensitive CD8⁺ T cell would kill at lower rates at the same peptide concentrations. With this model, the comparison of two CTL types determined by distinct parameter pairs can lead to counter-intuitive results. For example, CD8⁺ T cells with low sensitivity but high maximal killing efficacy (blue line: k _max = 1.9, ${\lambda }_{\frac{1}{2}}=-1$) will be less efficient than more sensitive CD8⁺ T cells (red line: k _max = 1 and ${\lambda }_{\frac{1}{2}}=-3$ and green line: k _max = 1.5 and ${\lambda }_{\frac{1}{2}}=-1.8$) over a wide range of pulsed tetramer concentrations.

Fig 6. Likelihood landscapes from independent bootstrap procedures on the acute, chronic and memory treatment groups.

Per group, 1000 bootstrap runs were repeated. A correlation between the estimates for k _max and ${\lambda }_{\frac{1}{2}}$ is visible for all three groups.

Fig 7. Fitted curves of Eq (3) assuming mass-action kinetics on estimated fractions of killed target cells in all mouse groups.

The curves depend on the killing efficacy model $k(k_{\mathrm{\text{max}}},{\lambda }_{\frac{1}{2}},\lambda )$ for distinct estimated group-specific values of parameter pairs (k _max, ${\lambda }_{\frac{1}{2}}$) for A) the acute, B) the chronic and C) the memory groups. The dots are the averages of the fraction of killed target cells of all mice in a treatment group. The estimated values are given in Table 1. The five different lines for each group were calculated with Eq (3) using the group specific parameter pairs, as well as the pulsed peptide concentrations λ.

Fig 8. Estimated dependence of killing efficacies on pulsed peptide concentrations λ with 95% confidence intervals from bootstrap replicates.

The values for the chronic treatment group (green) are clearly larger than values for the acute (red) and memory (blue) groups. The confidence intervals were calculated by determining the 2.5% and 97.5% percentiles of the distribution of $k(k_{\mathrm{\text{max}}},{\lambda }_{\frac{1}{2}},\lambda )$ values for all bootstrapped parameter pairs $(k_{\mathrm{\text{max}}},{\lambda }_{\frac{1}{2}})$ (where 1000 parameter pairs were evaluated) at each concentration λ.