Z-analysis: a new approach to analyze stimulation curves with intrinsic basal stimulation

In the study of receptor biology it is of considerable importance to describe the stimulatory properties of an agonist according to mathematically defined models. However, the presently used models are insufficient if the experimental preparation contains an intrinsic basal stimulation. We have developed a novel approach, tentatively named Z-analysis. In this approach, the concentration of endogenous agonist is calculated by extending the stimulation curve to zero effect. The concentration of endogenous agonist is then combined with the concentration of added agonist to estimate the true EC(50) value. We developed a new model, the Z-model, specifically for this purpose, but in addition, we describe how Z-analysis can be applied to the traditional E(0)-model. Models were applied to computer-generated curves with different Hill coefficients, using iterative curve fitting procedures. In addition to applying the models to ideal cases, we also used Monte Carlo-simulated data. Specific transformations were used to enable comparisons between parameters determined from these models. Both models were able to provide estimates of all eight parameters analyzed, both using ideal data and on Monte Carlo-simulated data. The Z-model was found to provide better estimates of the concentration of endogenous agonist, the EC(50) values, and the Hill value, in curves with Hill coefficient deviating from one. In conclusion, Z-analysis was suitable both to determine the concentration of endogenous agonists and to determine true EC(50) values. We found several advantages with the Z-model compared to traditional E(0)-model for analysis of stimulation curves that contain basic intrinsic stimulation.