A quantitative theory of affinity-driven T cell repertoire selection

Binding of the T cell antigen receptor (TCR) to peptides presented on molec ules encoded by major histocompatibility complex (MHC) genes is the key eve nt driving T cell development and activation. Selection of the T cell reper toire in the thymus involves two steps. First, positive selection promotes the survival of cells binding thymic self-MHC-peptide complexes with suffic ient affinity. The resulting repertoire is self-MHC restricted: it recogniz es foreign peptides presented on self, but not foreign MHC. Second, negativ e selection deletes cells which may be potentially harmful because their re ceptors interact with self-MHC-peptide complexes with too high an affinity. The mature repertoire is also highly alloreactive: a large fraction of T c ells respond to tissues harboring foreign MHC. We derive mathematical expre ssions giving the frequency of alloreactivity, the level of self-MHC restri ction, and the fraction of the repertoire activated by a foreign peptide, a s a function of the parameters driving the generation and selection of the repertoire: self-MHC and self-peptide diversity, the stringencies of positi ve and negative selection, and the number of peptide and MHC polymorphic re sidues that contribute to T cell receptor binding. Although the model is ba sed on a simplified digit string representation of receptors, all the param eters 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 bind ing, and find that their relative, rather than absolute value, is important in shaping the mature repertoire. This result makes it possible to adopt d ifferent physical interpretations for the digit string formalism. We also f ind that the alloreactivity level can be inferred directly from data on the stringency of selection, and that, in agreement with recent experiments, i t is not affected by thymic selection. (C) 1999 Academic Press.