An approximate solution of the Michaelis-Menten mechanism for quasi-steady and state quasi-equilibrium

Abstract

The Michaelis-Menten mechanism S+E ⇌ k −1 k 1 X → k 2 P+E leads for quasi-equilibrium ( k -1⪢ k 2) as well as for quasi-steady state (small values of total enzyme concentration) to a singularly perturbed differential equation system. An unified treatment of both cases produces an approximate solution which corresponds to the improved Michaelis-Menten equation reported by Otten and Duysens [6]. The convergence of this approximate solution to the exact solution for k 2⧸ k −1→0 or e tot⧸ K M →0 is proved. An error estimation for the Michaelis-Menten approximate solution leads to a smaller error bound than that reported by Wong [3]. The time course of several approximate solutions in relation to that of the exact solution has also been estimated.