A Quantitative Theory of the Precipitin Reaction

Abstract

THE theory which follows is, in the main, based on the same fundamental ideas as have recently been employed by several authors^1,2,3,4. The mathematical treatment, it is believed, is more simple than that of Heidelberger and Kendall, and the results seem to have a more general significance. The principle applied is the same as that governing the dissociation of a weak polybasic acid of the type H⁺_NX-, namely, that of step dissociation. The antibody A (corresponding to the hydrogen, H) is assumed to be uni-valent and combines in steps with the polyvalent antigen G (corresponding to the X ion of the acid with the valency N) to form compounds AG, A₂G ... to A_NG. All these compounds exist simultaneously, their relative quantities being dependent on the total concentration of G, the concentration of free A and the equilibrium constants k₁, k₂ ... to k_N, exactly as the proportions of the various anions of the acid H_NX are governed by its total concentration, the hydrogen ion concentration and the N dissociation constants. The simultaneous equilibria are