Estimation of partial agonist affinity by interaction with a full agonist: a direct operational model-fitting approach.

1. The operational model of agonism (Black & Leff, 1983) has been extended to describe the interaction between a partial agonist and a full agonist at the same receptor. The derived equation explicitly describes the interaction and allows the affinity (and efficacy) of the partial agonist to be estimated by direct fitting of raw experimental agonist concentration-effect (E/[A]) curve data. 2. The model was used to analyse experimental E/[A] curve data generated for the interaction between pilocarpine (partial agonist) and carbachol (full agonist) at the M3-muscarinic receptor mediating contraction of the guinea-pig isolated trachea. Pilocarpine affinity estimates obtained by operational model-fitting were compared with those obtained by use of the null method (Stephenson, 1956). These analyses demonstrated that the two methods gave comparable results (mean pKB estimates were 5.79 and 5.86 for the operational model and null method respectively). 3. When multiple concentrations of partial agonist are used, simultaneous operational model-fitting of all the E/[A] curve data allows the competitive nature of the interaction to be studied. 4. We conclude that operational model-fitting is a valid and analytically simple alternative to the conventional null method of analysing full/partial agonist interactions.