The immune checkpoint inhibitors have demonstrated promising clinical efficacy across various tumor types, yet the percentage of patients who benefit from them remains low. The bindings between tumor antigens and HLA-I/TCR molecules determine the antigen presentation and T-cell activation, thereby playing an important role in the immunotherapy response. In this paper, we propose UnifyImmun, a unified cross-attention transformer model designed to simultaneously predict the bindings of peptides to both receptors, providing more comprehensive evaluation of antigen immunogenicity. We devise a two-phase strategy using virtual adversarial training that enables these two tasks to reinforce each other mutually, by compelling the encoders to extract more expressive features. Our method demonstrates superior performance in predicting both pHLA and pTCR binding on multiple independent and external test sets. Notably, on a large-scale COVID-19 pTCR binding test set without any seen peptide in training set, our method outperforms the current state-of-the-art methods by more than 10\%. The predicted binding scores significantly correlate with the immunotherapy response and clinical outcomes on two clinical cohorts. Furthermore, the cross-attention scores and integrated gradients reveal the amino-acid sites critical for peptide binding to receptors. In essence, our approach marks a significant step toward comprehensive evaluation of antigen immunogenicity.

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