Nonlinear kinetics and the 1-exp function in nephropharmacology

Abstract

The basic law in nephropharmacology states that pharmacokinetic parameters depend linearly on renal function. Few exceptions to linear dependence have been reported, e.g. substances with saturable tubular reabsorption or secretion. A further example is cyclosporin, which was found to be eliminated according to log-concave nonlinear kinetics in 3 patients with hepatotoxicity after kidney transplantation. The nonlinear cyclosporin kinetics were computer-fitted to the integrated forms of the 1-exp function and the Michaelis-Menten equation by nonlinear regression analysis. The same maximal velocity (Vmax = 23 ng ml-1 h-1) and Michaelis constant (Km = 686 ng ml-1) were calculated for cyclosporin when applying either the 1-exp function or the Michaelis-Menten equation. The nonlinear elimination of cyclosporin, however, was described even more closely by the 1-exp function than by the Michaelis-Menten equation.

The 1-exp Function as an Alternative Model of Non-Linear Saturable Kinetics

“…With the Michaelis-Menten equation, conversion velocity is (v = 0.5 max) for the condition ([S] = AT m );iwith a l-exp function, the velocity is greater and (v = 0.63 F max ) applies under the same condition. This suggests that the more inflected l-exp function should be -used for true enzyme reaction kinetics (11,12).…”

“…Thus, it ought to be used more often, as it might enable a more accurate calculation of saturation kinetics in general (12,14).…”