Study of Linearization of Hill Dose-Effect Curve with Metabolic Velocity Instead of Drug Concentration

ObjectiveTo explore the velocity-effect relationship in order to the establish linearization of effect on an equation with regard to the consistency of the Hill dose-effect expression with the metabolic kinetics of receptors.

MethodsThe linear velocity-effect expression was obtained by solving multivariant differential equation groups, which were established to compare the coincidences and basic relations between the Hill dose-effect and metabolic kinetic Michaelis-Menten equation for receptors. The validation test was conducted with acetylcholine, adrenaline, and their mixture as model drugs.

ResultsThe linear velocity-effect modelling was represented in vivo or in vitro, for single and multidrug systems. Pharmacodynamic parameters, especially suitable for multicomponent CMM formulas, could be determined and calculated for single or multicomponent formulas at high saturating or low linear concentration for receptors. The validation test showed that the pharmacodynamic parameters of acetylcholine were: k, 2.675×10^-3 s^-1; k_a, 5.786×10^-9 s^-1; k_m, 2.500×10^-7 s^-1; α, 4.619×10⁹张 s·m g^-1; E₀, 13张(P < 0.01) and those of adrenaline were: k, 1.415×10^-3 s^-1; k_a, 5.846×10^-9 s^-1; k_m, 2.300×10^-7 s^-1; α, -1.627×10⁹张 s·m g^-1; E₀, 9.2张(P < 0.01). For the mixture of the two components, the values were: α, 1.375×10¹⁰张 s·m g^-1; -6.150×10⁹张 s m g^-1 for acetylcholine and adrenaline, respectively, and E₀ was 7.08张in both, with the other parameters unchanged (P < 0.01).

ConclusionThe velocity-effect equation can linearize the Hill dose-effect relationship, which can be applied to study the pharmacodynamics and availability of CMM formulations in vivo and in vitro.