Effects of thymic selection on T cell recognition of foreign and tumor antigenic peptides

Abstract

The advent of cancer immunotherapy has generated renewed hope for the treatment of many malignancies by introducing a number of novel strategies that exploit various properties of the immune system. These therapies are based on the idea that cytotoxic T lymphocytes (CTLs) directly recognize and respond to tumor-associated neoantigens (TANs) in much the same way as they would to foreign peptides presented on cell surfaces. To date, however, nearly all attempts to optimize immunotherapeutic strategies have been empirical. Here, we develop a model of T cell selection based on the assumption of random interaction strengths between a self-peptide and the various T cell receptors. The model enables the analytical study of the effects of selection on the CTL recognition of TANs and completely foreign peptides and can estimate the number of CTLs that can detect donor-matched transplants. We show that negative selection thresholds chosen to reflect experimentally observed thymic survival rates result in near-optimal production of T cells that are capable of surviving selection and recognizing foreign antigen. These analytical results are confirmed by simulation.

Keywords: T cell; applied probability; immunotherapy; neoantigen.

Fig. 1.

Alternative TCR–MHC interactions formulations. (A) S-MJ. Each TCR is represented by a string of amino acids, and the binding energy with a self-peptide is the sum of pairwise binding energies between the TCR amino acids and those in corresponding positions along the peptides. (B) PIRA. TCR regions (shaded dark blue in the cartoon) that bind peptide are characterized by TCR-specific binding energies for each given amino acid type, all drawn from a standard Gaussian distribution. These binding energies are assumed to be position-independent. (C) RICE. The behavior of TCR contact regions is now position-dependent (hence represented by different colors in the cartoon). A TCR is represented by a 20 $\times$ 10 array of IID standard Gaussian random variables, indicating the binding energy contribution for each amino acid/contact position pair along the peptide.

Fig. 2.

TCR recognition probability for each model. Recognition occurs whenever the interaction energy is greater than an upper threshold, $E_n$. Recognition rates as a function of threshold for (A) S-MJ as well as (B) PIRA and RICE. General recognition behavior is similar among all three formulations. In each case, ${10}^5$ thymocytes are simulated to undergo selection.

Fig. 3.

Peptide potency for each model. The ${10}^4$ self-peptides were ordered by “potency” or the fraction of (the ${10}^5$) thymocytes recognizing them during selection simulations. Potent self-peptides were those that were recognized most often by the TCRs. The cumulative contributions of each self-peptide to negative selection were plotted in decreasing order of self-peptide potency for the S-MJ, PIRA, and RICE models. In all cases, the selection thresholds are chosen to give $50\%$ survival. We see that, for the S-MJ model, the most potent self-peptide is responsible for roughly $90\%$ of the selection behavior, whereas for the PIRA (RICE) model, 200 (7,100) of ${10}^4$ self-peptides generate this level of selection.

Fig. 4.

RICE recognition behavior. (A and B) Probabilities for a single selected TCR to recognize (A) random peptides and (B) point mutants of self-peptides for the analytically tractable limits and for higher values of $N_n$. In both cases, the effect of increasing the number of negatively selecting self-peptides to $N_n={\mathrm{\hspace{0.17em}10}}^4$ has a relatively small effect on recognition rates in the range of relevant values ($11$–$13$) of $E_n$. The simulation averaged over all of the surviving TCRs from the initial cohort of ${10}^5$, a lower estimate of the mouse T cell diversity for a single MHC (36); ${10}^4$ random and point-mutant variants were tested. (C) The total recognition probability for the surviving ($5\times {\mathrm{\hspace{0.17em}10}}^4$) TCR cohort to recognize: a random peptide (black curve) and a single-site mutant of a native peptide (red). (D) The ratio of the two recognition probabilities in C; ${10}^4$ peptides of each class were tested. Included in D is the theoretical estimate of the ratio $(1-{(1-{\stackrel{\sim }{p}}_1)}^{N_s})/(1-{(1-{\widehat{p}}_0)}^{N_s})$, where $N_s(E_n)$ is the number of TCRs that survived selection.

Fig. 5.

The effects of increasing differences in host and donor thymic self-peptides on alloreactivity percentages in the RICE model. The simulation was performed with an original cohort of ${10}^5$ TCRs, of which $50\%$ survived selection under ${10}^4$ self-peptides ($E_n=11.52$). Increasing numbers of nonnative peptides [either random (black curves) or single-difference mutants (red curves)] were introduced, and the numbers of TCRs reacting to these were recorded. The theoretical estimate is from Eq. 16, with single-TCR recognition probabilities for random and single-mutant peptide taken from Fig. 4 A and B.