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A Note on the Calculation of Antibody-Antigen Ratio

Departments of Bacteriology and Ophthalmology, Washington University School of Medicine, St. Louis, Missouri

Abstract

In the past decade a moderately large number of antibody-antigen systems have been examined quantitatively. The published results show that the relative proportion of antibody to antigen in specific precipitates at optimal ratio has varied from 0.68 to 11. The additional information that the proportion is relatively constant for a given system and that ratio of antibody to antigen is apparently related to the molecular weight of the antigen indicates a possibility of the theoretical calculation of these ratios. The solution to this problem offered by Boyd and Hooker (1) fits the experimental findings quite well. The present communication supplements and extends their work through the derivation of a simpler equation and through the incorporation of a correction-factor obtained from the comparison of actual systems of spheres with the theoretical calculations. In general the agreement between sphere-system and immunological experiment is found to be even better than indicated by previous calculations (1, 2).