A view on the equivalence point in the precipitin test

Abstract

The equivalence point is defined as the mixing ratio of antibody to antigen at which the sum of the number of moles of antigen and that of antibody reaches a minimum in the supernatant. Under this definition, an attempt is made to explain the phenomenon of equivalence in the precipitin test. The main conclusion to be mathematically drawn from the above definition is as follows: At the equivalence point, the sum of antigen and antibody remaining in the supernatant is at a minimum (a definition of equivalence), and the product of them reaches a maximum, and yet these two different values are held constant each. Such a state of things in the supernatant is established when the same number of antigen and antibody molecules inclusive of zero exists in the supernatant. Consequently, for some precipitin systems, the equivalence point precipitation may be complete, and for others, it may be incomplete. In the latter case, however, the incompleteness of the precipitation disappears and the precipitation of antigen and antibody comes to be complete, when sufficient quantities of antigen and antibody are mixed at the equivalence point. From the above considerations, it was inferred that the antigen-antibody complexes with equimolar ratio are in the equivalence point precipitate and they are only slightly soluble in a physiological saline solution, and also that the completeness of the equivalence point precipitation largely depends upon the value of the solubility product constant of this compound and the initial quantities of antigen and antibody which are mixed.