To identify the edited neoantigens, we extended our previous neoantigen quality model4,5 that quantifies the immunogenic features of a neoantigen to propose that two competing outcomes determine whether a neoantigen is high-quality—whether the immune system recognizes or tolerates a neoantigenic mutation (Fig. 3a). To estimate the likelihood the immune system recognizes a neoantigen, we measure the sequence similarity of the mutant neopeptide (pMT) to known immunogenic antigens. This infers the ‘non-self’ recognition potential R of pMT, a proxy for peptides within the recognition space of the T cell receptor (TCR) repertoire.

Fig. 3: High-quality neoantigens are immunoedited in LTS  PDACs.
figure 3

a, Neoantigen quality model. b, The model and experimental approach to estimate cross-reactivity distance C. c, d, Measured (top) and fitted (bottom) pMT–TCR activation curves (c, amino acid (AA) position 4), and activation heat maps (d, all amino acid positions) for stronger and weaker pWT–TCR pairs. e, Composite pMT–TCR EC50 values of all stronger and weaker pWT–TCR pairs. f, pMT–TCR activation heat map and observed versus modelled C(pWT, pMT) for the HLA-B*27:05-restricted pWT–TCR pair. n indicates the number of single-amino-acid-substituted pWT, pMT and pMT, pMT pairs. g, Cross-reactivity distance model C and dendrogram of agglomerative clustering of substitution matrix M. h, Observed amino acid substitution frequency versus matrix M-defined substitution distance in primary and recurrent STS and LTS PDACs. M distance is the matrix M-defined amino acid distance from g. Circles indicate substituted residues. n indicates the number of substitutions. i, Cumulative probability distributions of log(C) and D. n indicates the number of neoantigens. The red rectangles in the heat maps indicate amino acids in pWT. The green line is a linear regression fit. Heat maps are ordered according to the amino acid order in the dendogram in g. P values were determined using two-tailed Pearson correlation (f and h) and two-sided Kolmogorov–Smirnov tests (i).

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By contrast, we posit that the immune system can also fail to discriminate pMT from its wild-type (WT) peptide (pWT), and therefore tolerate it as ‘self’. The immune system must therefore exert greater self discrimination D (Fig. 3a) in tumours to overcome the principles of negative T cell selection, the adaptation that limits autoreactivity to host tissues. We approximate the D between pWT and pMT by two features—differential MHC presentation and differential T cell reactivity. Differential MHC presentation of pWT and pMT (({K}_{{rm{d}}}^{text{WT}}/{K}_{{rm{d}}}^{text{MT}})), previously introduced as the MHC amplitude A (refs. 4,5), estimates the availability of T cells to recognize pMT. If pWT is not presented to T cells in the thymus or the periphery (as with a high ({K}_{{rm{d}}}^{text{WT}}), which implies poor pWT–MHC binding), pWT-specific T cells escape negative selection to expand the peripheral T cell precursor pool available to recognize a pMT presented on MHC (low ({K}_{{rm{d}}}^{text{MT}}))20. Here we extend this concept and introduce cross-reactivity distance C, a new model term that estimates the antigenic distance required for T cells to discriminate between pMT and pWT. Thus, self discrimination D = log(A) + log(C) is a proxy for peptides outside the toleration space of the TCR repertoire. In summary, we define neoantigen quality as Q = R × D (Fig. 3a), now with components that estimate whether a neoantigen can be recognized as non-self and discriminated from self.

To model C, we leveraged recent findings that conserved structural features underlie TCR–peptide recognition. Specifically, the binding domains of peptide-degenerate TCRs21,22 and TCR-degenerate peptides23 share common amino acid motifs, suggesting that T cell cross-reactivity between pMT and pWT could estimate the relative C of different neoantigenic substitutions (Fig. 3b). We selected an HLA-A*02:01-restricted strong epitope (NLVPMVATV (NLV)) from human cytomegalovirus24 that was previously used to model TCR–peptide degeneracy21,22 as a model pWT, and three NLV-specific TCRs (Extended Data Fig. 4a–c). We then varied the NLV peptide by every amino acid at each position to model pMT substitutions, and compared how TCRs cross-react between each pMT and its pWT across a 10,000-fold concentration range where pWT changes maximally altered T cell activation (Fig. 3b). We observed that substitutions were either highly, moderately or poorly cross-reactive (Fig. 3c, d), and the cross-reactivity pattern depended on the substituted position and residue (Extended Data Fig. 5a). Interestingly, we found similar patterns of cross-reactivity between a model HLA-A*02:01-restricted weaker pWT epitope in the melanoma self-antigen gp10025,26 (Extended Data Figs. 4d and 5b), three pWT-specific TCRs and single-amino-acid-substituted pMTs, suggesting that conserved substitution patterns define C (Fig. 3e and Extended Data Fig. 5b). Thus, we quantified the cross-reactivity distance C between a pWT and its corresponding pMT as (,Cleft({{bf{p}}}^{{rm{WT}}},{{bf{p}}}^{{rm{MT}}}right)={{rm{EC}}}_{50}^{{rm{MT}}}/{{rm{EC}}}_{50}^{{rm{WT}}}). We chose the half maximal effective concentration (EC50) to model C, as T cell activation to pWT was consistently a sigmoidal function (Extended Data Figs. 4c, d and 6a, b) described by a Hill equation, where EC50 determines how a ligand activates a receptor. We next estimated the EC50 of all 1,026 TCR–pMT pairs to infer a model for C that estimates whether a neoantigenic substitution is cross-reactive (and therefore tolerated) based on the substituted amino acid position and residue (Extended Data Figs. 6a, b and 7a, b). We then tested whether C predicted cross-reactive substitutions in an HLA-B*27:05-restricted neopeptide–TCR pair from an LTS (Extended Data Fig. 4e). Notably, C predicted cross-reactive pWT, pMT and pMT, pMT substitutions in this neopeptide–TCR pair (Fig. 3f and Extended Data Fig. 5c, 6c). Thus, we combined all 1,197 TCR–pMT pairs to derive a composite C—the antigenic distance for a TCR to cross-react between amino-acid-substitution pairs (Fig. 3g and Extended Data Fig. 7c). Broadly, two factors promote cross-reactivity: substitutions at peptide termini27 and within amino acid biochemical families (driven by amino acids of similar size and hydrophobicity; Fig. 3g). With this composite C, we now define self-discrimination D between a pWT and its corresponding pMT (Fig. 3a) as

$$D({{bf{p}}}^{{rm{W}}{rm{T}}}to {{bf{p}}}^{{rm{M}}{rm{T}}})=(1-w)log ,left(frac{{K}_{{rm{d}}}^{{rm{W}}{rm{T}}}}{{K}_{{rm{d}}}^{{rm{M}}{rm{T}}}}right)+w,log ,left(frac{{{rm{E}}{rm{C}}}_{50}^{{rm{M}}{rm{T}}}}{{{rm{E}}{rm{C}}}_{50}^{{rm{W}}{rm{T}}}}right),$$

(1)

where (w) sets the relative weight between the two terms. We chose the parameters of the neoantigen quality model to maximize the log-rank test score of survival analysis on an independent cohort of 58 patients with PDAC5 (Supplementary Methods and Extended Data Table 1a).



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