ABSTRACT
Hyperbolic and allosteric mathematical equations are used extensively to describe cumulative dose-response curves in pharmacology. In 1954, using an axiom described by Clark, Ariëns suggested the following equation for cumulative dose-response curves: Em/E-1 = Kd/[D], where Em = maximum effect, E = effect, Kd = dissociation constant of the drug-receptor complex and [D] = drug concentration. To evaluate the validity of the modified Ariëns equation on the dose-response curves with a Hill coefficient statistically different from one, we used sodium intestinal cotransport (SIC) with glutamine (Gln) and glucose (Glu). Increasing doses (10 microM to 0.1 M) of Gln and Glu were added to the mucosal side of the isolated rabbit ileum mucosal membrane mounted on Ussing chambers. Sodium cotransport was recorded by measuring short-circuit current (Isc), potential difference (PD) and tissue resistance (TR) at 20-min intervals for 2 h. The Em and ED50 for SIC with glucose were 25% and 150 microM, respectively, using the method proposed by Lineweaver-Burk. The same method could not be used to estimate the Em and ED50 in SIC with glutamine, suggesting a specific limitation of the Gln cotransport kinetic curve in the equation. Therefore, we modified the Ariëns equation to Em/E-1 = (Kd/[D])p. With p = Log (S), Log (Kd) = -pD2 and Log[D] = -pDx, we obtain E = Em/(1 + S(pD x -pD2)), where S is a hyperbolic constant.(ABSTRACT TRUNCATED AT 250 WORDS)