Quantitative estimation of potentiation and antagonism by dose ratios corrected for slopes of dose-response curves deviating from one.

A shift of dose-response curves of a receptor agonist A by a receptor antagonist B to the right is frequently expressed or quantitated by calculating the dose ratio (DR) from the ED50 values obtained in the absence and presence of B. A comparison of ED50 values or a DR is also used in a more general way to express the effects of other antagonists or of potentiators. For this situation, where B is not competing with A for a binding site, slope-values may often deviate from one. Because the slope of shifted dose-response curves (deviating from one) affects the magnitude of enhancement or diminution at a given DR, we have to take it into account. For example, the same changes in effects are associated with DR = 10 at curves with slope = 1, but with DR = 2.15 in case of slope = 3. Enhancement and diminution expressed by dose ratios is more or less underestimated in case of curves with slope > 1. We therefore propose to quantitate potentiation and antagonism by a corrected DR (DRcorr), which can simply be calculated from the uncorrected DR at a given slope. Consequently, a DRcorr reflects a true measure of enhancement or diminution for curves with slope = 1, equivalent to that which would have been observed for curves with slope = 1. The practical value of this modification is exemplified and illustrated by analysis of experimental data.