Interactions between T cell receptors and peptides bound to molecules encoded by the MHC genes underly T cell activation. More than 1% of T cells are activated by foreign (allogenic) MHC molecules, a phenomenon called alloreactivity. Reconciling the high frequency of alloreactivity with the fact that only 1 T cell in 10 4 -10 6 responds to a given foreign antigen presented on self MHC has been a longstanding puzzle. We show, by using a quantitative model, that this difference follows from the affinity model of T cell selection. Further, we demonstrate that highly alloreactive pre-and post-selection repertoires can be obtained without assuming germline bias of T cell receptors toward recognition of allelespecific MHC residues. It has been proposed that alloreactivity occurs because self and foreign MHCs bind different subsets of self peptides or alter their conformation differently. We find that such effects decrease rather than increase alloreactivity. Overall, our results show that the affinity model of T cell selection can quantitatively explain both self MHC restriction and high alloreactivity.Maturation of T cells in the thymus involves a two-step selection process driven by the affinity of their T cell receptors (TCR) for self peptides presented on proteins encoded by MHC genes. The first step, positive selection (1, 2), disgards thymocytes bearing TCRs with low affinity for MHC-peptide complexes expressed in the thymus. This eliminates T cells that cannot recognize MHC molecules. The second step, negative selection (3, 4), deletes cells with high affinity receptors for thymic MHC-peptide complexes. Thus, removing many self reactive cells. Overall, only 3% of the T cells produced in the thymus have TCRs with the intermediate affinity required to reach the periphery (5).Because MHC genes are extremely polymorphic, two individuals are very unlikely to express the same set of MHC molecules. As a result of positive selection, T cells are self MHC restricted: they recognize pathogens presented by self MHC molecules but ignore them if presented by foreign MHC molecules (6-14). MHC polymorphism is also the main obstacle to tissue transplantation (15). Typically, 1-24% of T cells are alloreactive (16, 17), i.e., they respond to foreign (allogenic) MHC molecules. Reconciling this high alloresponse frequency with the fact that among naive T cells only 1 in 10 4 -10 6 recognizes a given pathogen (18, 19) is a long-standing immunological puzzle. In this paper, we examine quantitatively three hypotheses proposed to explain the high frequency of alloreactivity.The first hypothesis, due to Matzinger and Bevan (20), suggests that the 2-4 orders of magnitude difference between antigen and MHC response frequencies results from the difference in the diversity of these two types of molecule on the surface of antigen presenting cells (APCs). Because each individual expresses only a few distinct MHC molecules and eachThe publication costs of this article were defrayed in part by page charge payment. This article must the...