The time evolution of sequential enzyme reactions: A singular perturbation approach

A perturbative procedure is developed to describe the entire time course of a sequential enzyme reaction occurring in a closed system. The perturbation parameter is the ratio of the enzyme concentration to a reference concentration defined in analogy with the Michaelis-Menten constant. It is shown that damped oscillations may occur about the quasi-steady state for certain realistic values of the parameters. Even under the most favourable circumstances, the damping is exceptionally heavy. In contrast, the evolution to the equilibrium is always monotonic.