On series approximations of Michaelis-Menten kinetics

Abstract

The Michaelis-Menten reaction mechanism yields a system of nonlinear differential equations that have recently been approximated using various series approaches and, in some cases, [ L / L ] Pade approximants. The coefficients of the series obtained from these different techniques are identical, so any differences in perfomance of the approximations are determined by the number of terms or the form of the approximant employed. Furthermore, the approximations successfully represent only the initial phase of the reaction and do not describe the entire timecourse. Some improvement can be obtained using Pade approximants of a different form and, from these, we provide an estimate of the time at which the steady-state occurs.