Consequences of avidity in lymphocyte receptor-multivalent antigen binding in affinity maturation

A mathematical model proposed by Crothers & Metzger (Immunochemistry9, 341-357, 1972), describing the influence of multiple site interactions on the effective antigen binding property of anti-bodies was used to assess the possible role of lymphocyte receptor affinity in antibody affinity maturation. The model proposed that observed association constants (K_OBSs) were primarily dependent on the number of allowed active site antigen interactions (n), the density and orientation of antigenic sites and the intrinsic association constant (K₁) of an univalent antibody active site interacting with an univalent antigen. Because of the inherent uncertainty involved in the estimation of lymphocyte membrane structure and molecular parameters necessary to utilize other mathematical models, the Crothers and Metzger model was applied to the case of surface membrane bound immunoglobulin (sm1g) on B-lymphocytes interacting with polyvalent antigens as a simple and direct concept. Consideration of red blood cells, dinitrophenyl₁₆ guinea-pig albumin, and fluorescyl₂₂₀ keyhole limpet hemocyanin as model antigens revealed that K_OBS was many orders of magnitude higher than K₁ when only a few interactions were allowed. A dissociation rate of several hours for release of polyvalent antigen from cooperating sm1g was calculated for receptors with a K₁ as low as 10³M^-1. Assuming prolonged antigen contact as necessary to activate lymphocytes, cells bearing low-affinity receptors are functionally indistinguishable from those carrying higher-affinity smIg in their ability to retain antigen. The presumed role for antigen-driven selection of lymphocytes bearing increasingly higher-affinity smlg, which results in antibody affinity maturation, must be reexamined if the K₁ of smIg does not confer a selective advantage to lymphocytes for retaining antigen.