Estimation of competitive antagonist affinity from functional inhibition curves using the Gaddum, Schild and Cheng‐Prusoíf equations

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Abstract
The estimation of antagonist affinity from functional experiments in which the effect of a fixed agonist concentration is reduced by a range of antagonist concentrations (‘functional inhibition curves’) has been considered from both a theoretical and experimental viewpoint. Theoretical predictions are compared with results obtained from the stimulation of [35S]‐GTPγS binding by acetylcholine to membranes of Chinese hamster ovary (CHO) cells stably transfected with human m1–m4 muscarinic receptors, and inhibition of the stimulated binding by pirenzepine and AQ‐RA 741. The usual procedure of applying the Cheng‐Prusoff correction is shown to be theoretically invalid, and predictions are made of the size and distribution of errors associated with this procedure. A different procedure for estimating antagonist affinity, using the principles of dose‐ratio analysis and analogous to use of the Gaddum equation, is found to be accurate and theoretically valid. A novel method of analysis allows accurate estimation of both antagonist affinity and Schild slope, by fitting the combined data from an antagonist inhibition curve and an agonist activation curve directly to a form of the Schild equation (derived by Waud) using non‐linear regression analysis. It is shown that the conventional Schild analysis can be enhanced by treating part of the data as a family of inhibition curves and including in the Schild plot dose‐ratios estimated from the inhibition curves.