An accurate method for determination of receptor-ligand and enzyme-inhibitor dissociation constants from displacement curves.

Receptor-ligand dissociation constants are usually calculated from the displacement curve of a radioactively labeled ligand bound to the receptor. The formula used is restricted to cases in which the concentration of receptor is negligible compared to the concentration of both the displacing ligand and the radioactive ligand used. In this study, we rigorously derive a simple equation that can be used for calculating receptor-ligand dissociation constants for any set of experimental conditions. A linearized form of this equation provides a convenient plot from which the dissociation constant of the displacing ligand can be directly obtained. The plot is also a test for the competitive mode of binding. This exact equation now allows us to estimate the error incurred by the conventionally used equations. Similarly, we show that for competitive inhibition in enzymology, one can derive the analogous formula. Our new formula is free of the usual restrictions--namely, that the enzyme concentration is very small compared to the concentration of both the substrate and the inhibitor. It may therefore be applied to any set of experimental conditions.