A quantitative theory of affinity-driven T cell repertoire selection

Binding of the T cell antigen receptor (TCR) to peptides presented on molecules encoded by major histocompatibility complex (MHC) genes is the key event driving T cell development and activation. Selection of the T cell repertoire in the thymus involves two steps. First, positive selection promotes the survival of cells binding thymic self-MHC-peptide complexes with sufficient affinity. The resulting repertoire is self-MHC restricted: it recognizes foreign peptides presented on self, but not foreign MHC. Second, negative selection deletes cells which may be potentially harmful because their receptors interact with self-MHC-peptide complexes with too high an affinity. The mature repertoire is also highly alloreactive: a large fraction of T cells respond to tissues harboring foreign MHC. We derive mathematical expressions giving the frequency of alloreactivity, the level of self-MHC restriction, and the fraction of the repertoire activated by a foreign peptide, as a function of the parameters driving the generation and selection of the repertoire: self-MHC and self-peptide diversity, the stringencies of positive and negative selection, and the number of peptide and MHC polymorphic residues that contribute to T cell receptor binding. Although the model is based on a simplified digit string representation of receptors, all the parameters but one relate directly to experimentally determined quantities. The only parameter without a biological counterpart has no effect on the model's behavior besides a trivial and easily preventable discretization effect. We further analyse the role of the MHC and peptide contribution to TCR binding, and find that their relative, rather than absolute value, is important in shaping the mature repertoire. This result makes it possible to adopt different physical interpretations for the digit string formalism. We also find that the alloreactivity level can be inferred directly from data on the stringency of selection, and that, in agreement with recent experiments, it is not affected by thymic selection.