  T lymphocytes (T cells) orchestrate adaptive immune responses upon
activation. T cell activation requires sufficiently strong binding of T cell
receptors (TCRs) on their surface to short peptides (p) derived from foreign
proteins, which are bound to major histocompatibility (MHC) gene products
(displayed on antigen presenting cells). A diverse and self-tolerant T cell
repertoire is selected in the thymus. We map thymic selection processes to an
extreme value problem and provide an analytic expression for the amino acid
compositions of selected TCRs (which enable its recognition functions).
