Exponential function for calculating saturable enzyme kinetics.

Abstract

Enzyme kinetics are usually described by the Michaelis-Menten equation, where the time-dependent decrease of substrate (-dS/dt) is a hyperbolic function of maximal velocity (Vmax), Michaelis constant (Km), and amount of substrate (S). Because the Michaelis-Menten function in its most general meaning requires an assumption of steady-state, it is less curvilinear than true enzyme kinetics. A saturation-type exponential function is more curvilinear than the hyperbolic function and more closely approximates enzyme kinetics: -dS/dt = Vmax [1 - exp(-S/Km)]. The mathematical representation of enzyme kinetics can be further improved by introducing a deceleration term (Vdec), to make the assumption of a steady state unnecessary. For the action of chymotrypsin on N-acetyltyrosylethylester, the Michaelis-Menten equation yields the following: Vmax = 3.74 mumol/min and Km = 833 mumol. According to decelerated enzyme kinetics, the values Vmax = 4.80 mumol/min, Vdec = 0.0118 mumol/min, and the association constant (Ka) = 0.00111/mumol are more nearly accurate for this reaction (where 1/Ka = 901 mumol approximately Km).