Precipitation at equivalence and equilibrium: a method for the determination of equilibrium constants of reaction between multideterminant antigen and specific polyclonal antibodies.
A theoretical approach for the determination of the equilibrium constant, Ka, of the reaction between a multideterminant antigen (Ag) and specific polyclonal antibodies (Ab) forming the insoluble Ab/Ag immune complex, is derived. The constant can be expressed as a function of the two accessible experimental parameters, the precipitating concentration of the antigen and the Ab/Ag molar ratio. For this purpose Ab/Ag immune complex must be prepared at equivalence, and equilibrium between precipitated and soluble species must be reached. The proposed method is experimentally tested on the system human serum albumin (HSA) and polyclonal rabbit antibodies. The Ab/Ag precipitates are prepared by the direct mixing of biological fluids in which immunoreacting components naturally occur. Previous separation, purification, or labeling of immunoreacting components are not required. The conditions for the precipitation of Ab/Ag complexes at equivalence, the stoichiometric composition or the average number of Ab molecules bound to one Ag molecule, and the solubility of the immunoprecipitating components are determined by a rectangular two-dimensional double immunodiffusion. Since the solubility determined under the conditions of a double immunodiffusion is a result of the interaction of the global diffusion of the precipitating components and particle growth kinetics, it mostly refers to the dynamic conditions. To find the solubility under equilibrium conditions, it is sufficient to determine the minimal factor by which the solutions of both immunoprecipitating components should be diluted so that no precipitate is formed upon their mixing at equivalence. The dilution factor is determined by a measurement of the laser light scattering of the immunoprecipitating systems prepared with serially diluted Ag and Ab solutions.