The slope parameter of concentration-response curves used as a touchstone for the existence of spare receptors

The present work was stimulated by findings of a large reserve of presynaptic alpha2-autoreceptors in rat neocortex by different investigators and our own group, using classical models of receptor agonism. The mathematical background of these classical models seems erroneous since the asymmetry that spare receptors introduce into concentration-response curves is not considered appropriately. This asymmetry leads to a steepening of curve fits based on the logistic function. Therefore, the slope parameter c of a logistically fitted concentration-response curve can be used as a touchstone for the existence of spare receptors. Spare receptors induce a c > 1. Concentration-response data of the alpha2-autoreceptor-mediated inhibition of evoked [3H]-noradrenaline release in rat neocortex slices were re-analysed. The estimates of the slope parameter c of logistically fitted concentration-response curves obtained after treatment of rats with either vehicle or N-ethoxycarbonyl-2-ethoxy-1,2-dihydroquinoline (EEDQ) to achieve an irreversible inactivation of alpha2-autoreceptors, were not compatible with the existence of a large receptor reserve. A model for nonlinear regression analysis developed under the a priori assumption of spare receptors confirmed the absence of spare receptors. Evaluation methods which neglect the alteration of the geometrical form of concentration-response curves due to non-proportionality between receptor occupation and relative response do not seem appropriate to quantify spare receptors. These methods may detect spare receptors where they do not exist.