Analytical determination of receptor-ligand dissociation constants of two populations of receptors from displacement curves

The determination of receptor-ligand dissociation constants from displacement data has been restricted until recently to the condition of receptor saturation, in which the concentration of receptor is negligible as compared to the displaced ligand and the displacing ligand used. This restriction has lately been removed since an accurate method has been developed for the determination of the dissociation constants for all experimental conditions for a system that includes a single type of binding site. In many cases, however, there are two types of receptor binding sites that exhibit different affinities toward the ligand. The present study provides an analytic solution for the problem of determination of the two dissociation constants as well as the proportion of the two receptor types. The formal derivation of the equations is described, along with analysis of a displacement simulation. The sensitivity of the method to the ratio between the two dissociation constants is also investigated. The application of the method is demonstrated for the analysis of the binding of β-adrenergic receptors to the agonist isoproterenol as monitored by the displacement of the β-antagonist ¹²⁵I-labeled cyanopindolol.