Parallel versus Off-Pathway Michaelis-Menten Mechanism for Single-Enzyme Kinetics of a Fluctuating Enzyme

Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase.