Quasi-steady state in the Michaelis–Menten system

We discuss the differential equations derived from the Michaelis–Menten model of an enzyme-catalyzed reaction, with no a priori conditions on parameters or initial concentrations. Using an elementary approach, we derive and investigate inequalities and conditions for the validity of the quasi-stationary approximation, confirming results by Segel and Slemrod, and determine new estimates for the pre-steady state period.