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 (V(max)), Michaelis constant (K(m)), 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 = V(max)[1 - exp(-S/K(m))]. The mathematical representation of enzyme kinetics can be further improved by introducing a deceleration term (V(dec)), to make the assumption of a steady state unnecessary. For the action of chymotrypsin on N-acetyltyrosylethylester, the Michaelis-Menten equation yields the following: V(max) = 3.74 μmol/min and K(m) = 833 μmol. According to decelerated enzyme kinetics, the values V(max) = 4.80 μmol/min, V(dec) = 0.0118 μmol/min, and the association constant (K(a)) = 0.00111/μmol are more nearly accurate for this reaction (where 1/K(a) = 901 μmol ~ K(m)).