Broad cross-reactivity of the T-cell repertoire achieves specific and sufficiently rapid target searching

The molecular recognition of T-cell receptors is the hallmark of the adaptive immunity. Given the finiteness of the T-cell repertoire, individual T-cell receptors are necessary to be cross-reactive to multiple antigenic peptides. In this study, we quantify the variability of the cross-reactivity by using a string model that estimates the binding affinity between two sequences of amino acids. We examine sequences of 10,000 human T-cell receptors and 10,000 antigenic peptides, and obtain a full spectrum of cross-reactivity of the receptor-peptide binding. Then, we find that the cross-reactivity spectrum is broad. Some T-cells are reactive to 1000 peptides, but some T-cells are reactive to only one or two peptides. Since the degree of cross-reactivity has a correlation with the (un)binding affinity of receptors, we further investigate how the broad cross-reactivity affects the target searching of T-cells. High cross-reactive T-cells may not require many trials for searching correct targets, but they may spend long time to unbind from incorrect targets. In contrast, low cross-reactive T-cells may not spend long time to ignore incorrect targets, but they require many trials for screening correct targets. We evaluate this hypothesis, and show that the broad cross-reactivity of the natural T-cell repertoire can balance the trade-off between the rapid screening and unbinding penalty.