Contact map dependence of a T-cell receptor binding repertoire

The T-cell arm of the adaptive immune system provides the host protection against unknown pathogens by discriminating between host and foreign material. This discriminatory capability is achieved by the creation of a repertoire of cells each carrying a T-cell receptor (TCR) specific to non-self-antigens displayed as peptides bound to the major histocompatibility complex (pMHC). The understanding of the dynamics of the adaptive immune system at a repertoire level is complex, due to both the nuanced interaction of a TCR-pMHC pair and to the number of different possible TCR-pMHC pairings, making computationally exact solutions currently unfeasible. To gain some insight into this problem, we study an affinity-based model for TCR-pMHC binding in which a crystal structure is used to generate a distance-based contact map that weights the pairwise amino acid interactions. We find that the TCR-pMHC binding energy distribution strongly depends both on the number of contacts and the repeat structure allowed by the topology of the contact map of choice; this in turn influences T-cell recognition probability during negative selection, with higher variances leading to higher survival probabilities. In addition, we quantify the degree to which neoantigens with mutations in sites with higher contacts are recognized at a higher rate.

Figure 1

The TCR-pMHC interface and contact maps. (a) The CDR3-pMHC interface in the crystal structure of the 2B4 TCR binding to the MCC/I-E^k complex (PDB ID 3QIB); with the antigen MCC highlighted in green, the $\mathrm{CDR}3\alpha$ loop in purple, and the $\mathrm{CDR}3\beta$ loop in orange. (b) Eight contact maps estimated from four crystal structures, contact maps of the $\mathrm{CDR}3\alpha$-pMHC ($\mathrm{CDR3}\beta$-pMHC) interfaces in the top (bottom) row; 3QIB, 3QIU, and 3QIW are MHC class-II restricted, whereas 5C0A is MHC class-I restricted.

Figure 2

The variance of the TCR-pMHC binding energy distribution depends on the total number of contacts and on the repeat structure allowed by the topology in the contact map. (a) Binding energy $U(t,q)$ variance scaling with the number of contacts, $|N_C|$; calculated variances with their variance (vertical error bars) were plotted as a function of total contacts $|N_C|$ in the contact map. Horizontal error bars represent the range of threshold used for determining each contact map (lower estimates corresponding to counting contacts $>0.9$, and upper estimates corresponding to including contacts $>0.1$). (b) The binding energy PDFs and corresponding simulated standard deviations (${\sigma }_r$, ${\sigma }_1$, etc.) for pMHC repertoires of randomly chosen AA sequences (blue) and with all TCRs constrained to the same repeated AAs motif; repertoires constrained to each of the four most likely pMHC repeat motifs are shown with different colors and are labeled in decreasing order of likelihood. In the simulations, ${\sigma }^2=1$.

Figure 3

Negative-selection recognition probability as a function of the survival energy threshold for T cells auditioning for negative selection. All curves involving the use of contact maps are generated from simulations sharing the same parameters apart from the contact maps. The prediction of the RICE model (brown), the identity matrix giving a diagonal contact map case (black), and the limiting case where all AAs in the CDR3 loop interact with all AAs in the pMHC (yellow) are included for comparison. Plots are averaged over the different random energy matrices in use, and shaded areas indicate the corresponding standard error of the mean.

Figure 4

Recognition probability of point-mutated peptides by T cells that have undergone negative selection. (a) The point-mutant recognition probability from simulations plotted for T cells that have received negative selection against self-peptide repertoires of three different sizes, $N_q=\{{10}^2,{10}^3,{10}^4\}$. (b) The point-mutant recognition probability from simulations that changed the site of the mutated AA; for the $\mathrm{CDR}3\alpha$-pMHC interface of 3QIB [top left panel of Fig. 1] in use, pMHC-AAs in high-contact sites are in contact with 5 TCR-AAs, whereas pMHC-AAs in sparse-contact sites are in contact with only 1 TCR-AA; and when picking random sites to mutate, the number of peptide-AAs that a given TCR-AA can contact ranges from 1 to 5.