Tissue response as a functional discriminator of receptor heterogeneity: effects of mixed receptor populations on Schild regressions.

A model is described that predicts the behavior of competitive antagonists in tissues with more than one receptor mediating response. The receptor stimuli for two receptor types are summed and processed, via a cellular stimulus-response mechanism, into tissue response. The primary receptor is described by a standard Langmurian isotherm, and a secondary receptor input with a variable maximal strength, for which the agonist has variable sensitivity, is added. The prediction of drug effects in this system does not depend on the way in which the two stimuli are combined or on the absolute magnitudes of the parameters used to make the calculations. The model is maximally flexible, in that no pharmacological significance is put on the magnitudes of the inputs from the secondary receptor system (i.e., they can vary with either agonist intrinsic efficacy, receptor number, or efficiency of stimulus-response coupling). The theoretical Schild regressions for selective antagonists in two-receptor systems are calculated for various secondary receptor inputs. These regressions generally are curvilinear whenever the secondary receptor significantly contributes to agonist response. These calculated data also indicate that minor variations in biological input from secondary receptor systems would obscure curvature in the Schild regression and result in a seemingly linear regression with a slope of less than unity. However, further calculations indicate three possible ways to use Schild analysis to detect receptor heterogeneity in tissues. One indicator of receptor heterogeneity is a change in the slope of the dose-response curve for the agonist in the presence of a selective antagonist. A second indicator would be a marked heteroscedasticity of errors in the Schild regression, i.e., the magnitude of the standard errors in the ordinate values would depend upon the concentration of the antagonist. A third, and most experimentally accessible, aspect of heterogeneous receptor systems predicts that changes in the overall sensitivity of organ response mechanisms will differentially alter the relative strength of two receptor inputs. This would be observed as a change in the potency of an antagonist. Under these circumstances, differences in the stimulus-response characteristics of a tissue would result in a change in the Schild regression for a selective antagonist. These concepts are discussed in terms of the use of Schild analysis in functional systems for the detection of physiologically relevant mixtures of receptors and the possible advantages over biochemical binding data.