Figure 1.

Relations between sigmoid reference (red, dashed line), perturbed sigmoid (blue, solid line), and hormetic (orange, dash-dotted line) dose-response curves and hypothetical experimental data (circles) and fitted empirical models (lines). When perturbations preserve the shape of the dose-response curve (blue, solid line versus red, dashed line), the effect of a perturbation can be quantified by the shifts in baseline response and maximal response, and by the difference in the dose required for half-maximal response, as indicated by blue arrows. Analogously, we quantify the differential in the dose (${\pi }_d$, green) and the response $\left({\pi }_{\mathcal{R}}\right)$ components via the distance between points on a reference curve and points on a perturbed curve that have the same proportion of response between the minimum $\left(h=1\right)$ and maximum ($h=0$; correspondence indicated by blue arrows). As indicated by the question mark, such a quantification is not straightforward for dose-response curves with different shapes. To see this figure in color, go online.