Antigen-antibody reactions in agar. II. Elementary theory and determination of diffusion coefficients of antigen.

Summary 1.A simplified description is given of the manner in which the precipitate in the Oudin tube is formed and moves. 2.On the basis of this simplified picture and with the aid of certain stated assumptions the following limiting equation has been derived: (2) R′AB = AG 0 (1=2/πe y 0 e -y 2 dy) This equation relates R′ , the ratio of antigen to antibody at the equivalence point, Ab , the antibody concentration, Ag 0 , the antigen concentration in the overlaying solution, x , the distance moved in time, t , and D , the diffusion coefficient of the antigen. 3.The above question is a limiting equation applying only to high concentrations of antigen and low concentrations of antibody. 4.From (2) another expression was obtained: which can be applied to the determination of the diffusion coefficient of an antigen present in a mixture. 5.From (2) a third relationship was obtained: where D A is an apparent diffusion coefficient. This equation is of the same form as that which Oudin obtained empirically. 6.Diffusion coefficients were calculated from data obtained for three different antigens using equations 2 and 3. Reasonably good agreement was obtained with the generally accepted values. 7.The various assumptions used in the derivation of equation 2 were critically discussed. 8.The possible uses and limitations of the three equations were briefly indicated.