title: Analysis of asymmetry of agonist concentration-effect curves.
abstract: 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.
authors.affiliation: Leiden/Amsterdam Center for Drug Research, Division of Pharmacology, The Netherlands. piet_van_der_graaf@sandwich.pfizer.com
authors.forename: P H
authors.initials: PH
authors.lastname: Van der Graaf
authors.forename: R C
authors.initials: RC
authors.lastname: Schoemaker
mesh_terms: D000316:Adrenergic alpha-Agonists / Q000494:pharmacology*; D000317:Adrenergic alpha-Antagonists / Q000494:pharmacology*; D000818:Animals; D001011:Aorta / Q000187:drug effects; D004305:Dose-Response Relationship, Drug; D004347:Drug Interactions; D066298:In Vitro Techniques; D008297:Male; D015233:Models, Statistical; D009119:Muscle Contraction / Q000187:drug effects; D009131:Muscle, Smooth, Vascular / Q000187:drug effects; D009638:Norepinephrine / Q000494:pharmacology*; D011224:Prazosin / Q000494:pharmacology*; D051381:Rats; D017208:Rats, Wistar
chemical_list: D000316:Adrenergic alpha-Agonists; D000317:Adrenergic alpha-Antagonists; D009638:Norepinephrine; D011224:Prazosin