Regulation of T cell expansion by antigen presentation dynamics

Abstract

An essential feature of the adaptive immune system is the proliferation of antigen-specific lymphocytes during an immune reaction to form a large pool of effector cells. This proliferation must be regulated to ensure an effective response to infection while avoiding immunopathology. Recent experiments in mice have demonstrated that the expansion of a specific clone of T cells in response to cognate antigen obeys a striking inverse power law with respect to the initial number of T cells. Here, we show that such a relationship arises naturally from a model in which T cell expansion is limited by decaying levels of presented antigen. The same model also accounts for the observed dependence of T cell expansion on affinity for antigen and on the kinetics of antigen administration. Extending the model to address expansion of multiple T cell clones competing for antigen, we find that higher-affinity clones can suppress the proliferation of lower-affinity clones, thereby promoting the specificity of the response. Using the model to derive optimal vaccination protocols, we find that exponentially increasing antigen doses can achieve a nearly optimized response. We thus conclude that the dynamics of presented antigen is a key regulator of both the size and specificity of the adaptive immune response.

Keywords: T cells; clonal expansion; power law; precursor frequency; vaccination.

Fig. 1.

Limitation of T cell expansion by antigen decay can explain the power law dependence of fold expansion on the initial number of cognate T cells. (A) Transfer of transgenic T cell clones into recipient mice allows for monitoring of T cell proliferation in vivo in response to cognate antigen stimulation (3, 6). (B and C) Comparison of experimental data from ref. with model predictions. (B) Factor of expansion at day 7 as a function of the number of precursor T cells (crosses, geometric mean; error bars, $\pm$SE). (C) T cell and pMHC number vs. time for 300 and 30,000 initial transgenic T cells (crosses, geometric mean; dots, individual mice). (D) Schematic of the model. Dendritic cells take up antigens, process them into short peptides, and present these on MHCs on their surfaces. T cells bind to pMHCs via TCRs. Recognition of cognate pMHC stimulates T cells to proliferate, and continual antigen stimulation is needed to maintain proliferation. Turnover of pMHCs leads to decay of presented peptides over time. Fitted model parameters and asymptotic SEs: $\alpha =1.5\pm 0.3$/d, $\mu =1.2\pm 0.5$/d, $\delta =0.22\pm 0.21$/d, and $C\left(0\right)=10^{6.7\pm 1.1}$. We fixed $K=0.0$ (upper bound from fit $\simeq 700$).

Fig. 2.

Limitation of T cell expansion by antigen decay can account for the power law dependence of fold expansion on affinity. (A and B) Comparison of data from an experiment with L. monocytogenes strains expressing different antigens (see legend for their amino acid sequence) (6) with model predictions. (A) Factor of expansion of the transgenic T cells at day 7 relative to day 4 vs. the relative concentration of different pMHCs needed to elicit half-maximal IFN-$\gamma$ response from the T cells (${\mathrm{E}\mathrm{C}}_{50}$ relative to antigen SIINFEKL’s $\sim 8\hspace{0.17em}\mathrm{p}M$). (B) T cell number vs. time for the different strains. Fitted model parameters and asymptotic SE: $\alpha =2.47\pm 0.13$/d, $\mu =3.1\pm 0.3$/d, $\delta =0.23\pm 0.06$/d, $C\left(4\right)=10^{3.22\pm 0.17}$, and $T\left(4\right)=0.92\pm 0.10$. The number of transgenic T cells is calculated from their fraction $f$ of total T cells as $f/\left(1-f\right)$, with the number at day 4 set to 1. $K$ was set equal to the relative ${\mathrm{E}\mathrm{C}}_{50}$ values of the different ligands.

Fig. 3.

High-affinity T cells can outcompete low-affinity T cells for access to pMHCs, even when pMHC concentrations exceed all T cell affinities. (A–D) Comparisons of the time courses of expansion of mixtures of two types of T cells with high, $K_1=1$, and low, $K_2=10$, affinities (solid curves) with the expansion of the T cells on their own (dashed curves). (A and B) Proliferation driven by a large but exponentially decreasing number of pMHCs ($\mu =1.1$) starting from equal (A) and unequal (B) initial T cell numbers. (C and D) Proliferation driven by a small but exponentially increasing number of pMHCs mimicking antigen dynamics early in an infection [$C\left(t\right)\propto e^{\gamma t}$]. Competition outcome depends strongly on whether pMHC levels increase faster ($\gamma =3$; C) or slower $\gamma$ = (0.5; D) than T cells proliferate. Parameters: $\alpha =1.2$ and $\delta =0$.

Fig. 4.

Impact of antigen kinetics on T cell proliferation. (A) Antigen input schedules: single pulse, constant input, and exponentially increasing input (increase each day by fivefold as in ref. 7). (B) Dynamics of pMHCs. (C) Dynamics of T cells. (D) The optimal schedule is close to the experimentally used exponential schedule. The antigen input schedule over 4 d that optimizes fold expansion at day 6 was computed numerically using a projected gradient algorithm (16). (E) Fold expansion for exponential schedules as a function of the fold increase per day, with the experimental schedule indicated by the dot. Parameters: $\alpha$, $\mu$, and $\delta$ as in Fig. 2; $K=10$; $C\left(0\right)=0,T\left(0\right)=100$; and total administered antigen is $2\cdot 10^6$.