Abstract

In this report, the equilibrium composition of a multicomponent crossreactive ligand-binding system is characterized by solving the mass action equations. Several results in simulation and parameter fitting for radioimmunoassay, ion-protein reactions, etc., are derived from these equations: (1) The Scatchard binding curve bound-to-free ratio for ligand (vs bound ligand concentration) is shown to be a hyperbola, and is expressed in the explicit form y = f(x), for the case of two ligands and one binding group, or one ligand and two binding groups. (2) Graphic methods are presented for estimation of binding parameters (affinity constants and total concentrations of reactant) by measuring the Scatchard curve in the abovementioned cases. (3) Computational methods are presented for fitting parameters to data in the case of arbitrarily many ligands and arbitrarily many binding groups. (4) Formulae are derived for the partial derivatives of the bound-to-free ligand ratio with respect to all binding parameters. (5) An illustrative application is made to data from the literature on thyroid hormone binding.