  The classic Michaelis-Menten equation describes the catalytic activities for
ensembles of enzyme molecules very well. But recent single-molecule experiment
showed that the waiting time distribution and other properties of single enzyme
molecule are not consistent with the prediction based on the viewpoint of
ensemble. It has been contributed to the slow inner conformational changes of
single enzyme in the catalytic processes. In this work we study the general
dynamics of single enzyme in the presence of dynamic disorder. We find that at
two limiting cases, the slow reaction and nondiffusion limits, Michaelis-Menten
equation exactly holds although the waiting time distribution has a
multiexponential decay behaviors in the nondiffusion limit.Particularly, the
classic Michaelis-Menten equation still is an excellent approximation other
than the two limits.
