Immunodiffusion in gels containing erythrocyte antigen. I. Theory for diffusion of antiserum from a circular well.

A theory for the diffusion of antibodies in a gel containing erythrocyte antigen is presented. We show that when t ⪢ (k2−1 (K2 is the reverse rate constant for the binding of an antibody to an erythrocyte binding site) the free antibody concentration appears to diffuse with a reduced diffusion coefficient D∗ = D2/(1 + Kϱ0). D2 is the antibody diffusion coefficient in the gel, ϱ0 is the density of binding sites, and K the equilibrium constant for binding of an antibody to an erythrocyte binding site. The theory is developed for experiments in which a circular well is cut from the gel and antiserum placed within the well. Expression for the free and bound antibody concentrations as a function of position and time are derived. We show how these expressions can be used to (1) determine diffusion coefficients and (2) gain information about the distribution of equilibrium constants which characterize the antiserum.