Analytical solutions of a simple enzyme kinetic problem by a perturbative procedure

A systematic perturbative procedure (the method of singular perturbation) is developed to follow the time evolution of an enzyme catalyzed reaction with one intermediate product over the entire time domain of interest. The perturbation parameter is the ratio of the enzyme concentration to the Michaelis-Menten constant. The treatment leads to a meaningful definition of the so-called quasi-steady state often invoked in the description of enzyme catalyzed reactions. The legitimacy and the domain of validity of this assumption are examined in the context of both the reversible and irreversible Michaelis-Menten kinetics.