The antigen-antibody reaction. V. A quantitative theory of antigen-antibody reactions which allows for heterogeneity of antibodies

A quantitative theory to describe the reactions between multivalent antigen and bivalent antibody is developed. Unlike the previous theory (Palmiter &; Aladjem, 1963) the present theory allows for heterogeneity of antibodies. Heterogeneity is described in terms of a multivariate probability density function (PDF). A method for finding the PDF from experimental measurements of the amount of antigen-antibody precipitate and of soluble complexes is given; briefly, the method consists of (a) making an initial estimate of the PDF and computing by means of the theory the distribution of complexes, (b) comparing the computed distribution of complexes with the experimental data, and (c) using the criterion of least squares and iterative procedures for consecutively better approximations, finding that distribution of complexes and hence that PDF which best fits the experimental data.The theory suggests experiments and a new method of interpretation of the results.