Antagonist inhibition curves and the measurement of dissociation constants

1. Experiments carried out on guinea-pig isolated ileum with carbachol as agonist and diphenyl-acetoxyethyl-dimethyl-ethyl-ammonium (DADMEA) bromide as antagonist gave results which fit the theoretical relation between fractional inhibition (Q) of the effects of an agonist ([A]) and the concentration of a competitive antagonist ([B]): this also involves the Hill coefficient (logistic slope factor, P) for the agonist concentration-response curve and the degree of agonist stimulation, [A]/[A]50, where [A]50 produces a half-maximum response. 2. Values of IC50 and an exponent, P', can be obtained by fitting Q to [B] using a logistic approximation to the relation. Both P' and IC50 should be greater with higher agonist stimulation but the increase in P' may be masked by errors in extreme values of Q. Estimates of IC50, however, invariably increased with higher agonist stimulation but with a steep concentration-response curve (P > 1) and low agonist stimulation ([A]/[A]50 < 1, IC50 can be less than KD. 3. KD was calculated from the results in three ways; (i) by a least-squares fit of Q to [B] using the values of P and [A]/[A]50 calculated from the control concentration-response curve; (ii) from the value of IC50 for each line and the values of P and [A]/[A]50 and (iii) by using the agonist concentration-response curve to calculate the dose-ratio and estimate of KD for each in the presence of the antagonist. The methods gave similar results (nM: 11 experiments), 12.4 +/- 1.1 (i), 11.7 +/- 0.9 (ii), 14.8 +/- 1.6 (iii) but there are advantages in using methods (i) or (ii) rather than (iii). 4. The method by which KD is calculated is less important than the experimental design: the plan used in this work, with alternative small and large responses from the tissue, is very suitable for estimating KD with low concentrations of antagonists and small dose-ratios. Although it is not a sensitive test for competitive behaviour because only a small range of concentrations of antagonist is tested, the estimate of affinity should be free from complications involved in the use of higher concentrations of antagonist (and agonist) and the nature of the antagonism can always be checked by doing further experiments in the presence of a known competitive antagonist.