Quantitative aspects of antigen-antibody reactions. I. A theory and its corollaries

Abstract

1. A quantitative theory has been developed for the reactions between antigens and antibodies, applicable in particular to the precipitin reaction. The theory is equally applicable to unspecific precipitations, for instance the reaction between proteins and protein precipitating agents such as nucleic acids, etc.2. The theory is based on the concept that the antigen-antibody interaction is governed by the same principles as the dissociation of a polybasic acid, HNT, where the antibody corresponds to the hydrogen ion H, and the antigen to the anion T. In their mutual reactions the antigen G is supposed to be polyvalent and the antibody A monovalent: hence the result of the interaction is a mixture of compounds ANG, AN-1G, …, AG.3. A mathematical deduction is performed starting from the law of mass action, which leads to expressions for the amounts of total precipitate and its constituents in terms of the quantities of antigen and antibody which were mixed and the known equilibria constants.4. A numerical example is given for a tetravalent antigen. Three cases are represented in graphical forms: the ‘X case’ without inhibition zones, the ‘Y case’ with one and the ‘Z case’ with two inhibition zones. Certain characteristics are described and the significance of the ‘equivalence point’ is analysed.5. A discussion deals with the irreversibility in relation to the Danysz phenomenon and the dilution effect, and finally the parameters of the theory are more closely considered.