Mathematical theory of competitive binding assays: an exact and practical model

In the usual formulation of the equations for competitive binding assays, the free concentrations of the various unlabeled ligands are approximated by the known values of their total concentrations, since the free concentrations are not easily determined. Although equations have been derived previously that give the exact solution with the free concentrations of unlabeled ligands treated as variables, these have not been useful in practice. We have devised a mathematical model for the competitive binding that which is both exact and practical for the general case of one labeled ligand, any number of unlabeled ligands, and any number of classes of binding sites. In this model, the total concentrations of unlabeled ligands are the explicit variables, instead of their free concentrations. The free concentrations of unlabeled ligands can be estimated from the model. The model is based on the law of mass action and the dilution principle, as well as a new concept, called the equivalent competitive binding principle.