Analysis of asymmetry of agonist concentration-effect curves.

We have developed a fitting procedure, based on nonlinear mixed effect modelling and original work by Richards (1959, J Exp Botany 10, 290-300), to describe the degree of asymmetry of concentration-effect E/[A] curves and analysed the shape of E/[A] curves obtained with alpha1-adrenoceptor agonists in rat aorta. The four-parameter Richards model provided a significantly better fit of the data than the standard logistic/Hill model for all ligands investigated, which implies that E/[A] curves were asymmetrical. With the exception of ST 587, the asymmetry parameter (delta) tended toward zero and the Richards model could be replaced without significant loss of goodness-of-fit by the three-parameter, asymmetrical Gompertz model. The alpha1-adrenoceptor antagonist, prazosin (10 nM), had no effect on the asymmetry of the noradrenaline E/[A] curve but significantly increased the slope at the point of inflection. In contrast, pretreatment with the irreversible antagonist, phenoxybenzamine (60 nM), produced a shift of the delta estimate for noradrenaline from zero to unity, indicating a change from an asymmetrical to a symmetrical curve. Therefore, detailed statistical analysis of E/[A] curve asymmetry demonstrates that alpha1-adrenoceptors in rat aorta do not operate as a homogenous one-receptor-one-transducer system. This conclusion could not have been reached by either an analysis with the standard logistic/Hill model or visual inspection of experimental data. Overall, the curve-fitting analysis developed in this study provides a quantitative and sensitive measure of asymmetry and a novel method for the objective discrimination of agonist action on the basis of curve shape. The method is generally applicable to other pharmacological assays and provides a new tool in receptor classification studies.