Abstract
THE theory which follows is, in the main, based on the same fundamental ideas as have recently been employed by several authors1,2,3,4. 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 ANG. 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 kN, exactly as the proportions of the various anions of the acid HNX are governed by its total concentration, the hydrogen ion concentration and the N dissociation constants. The simultaneous equilibria are
Published Version
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