Predicting the size of the T-cell receptor and antibody combining region from consideration of efficient self-nonself discrimination

The binding of antibody to antigen or T-cell receptor to major histocompatibility complex-peptide complex requires that portions of the two structures have complementary shapes that can closely approach each other. The question that we address here is how large should the complementary regions on the two structures be. The interacting regions are by necessity roughly the same size. To estimate the size (number of contact residues) of an optimal receptor combining region, we assume that the immune system over evolutionary tune has been presented with a large random set of foreign molecules that occur on common pathogens, which it must recognize, and a smaller random set of self-antigens to which it must fail to respond. Evolutionary, the receptors and the molecular groups that the immune system recognizes as epitopes are imagined to have coevolved to maximize the probability that this task is performed. The probability of a receptor matching a random antigen is estimated from this condition. Using a simple model for receptor-ligand interaction, we estimate that the optimal size binding region on immunoglobulin or T-cell receptors will contain about 15 contact residues, in agreement with experimental observation.