Parallel versus off-pathway Michaelis-Menten mechanism for single-enzyme kinetics of a fluctuating enzyme

TL;DR

This paper models single-enzyme kinetics considering parallel and off-pathway mechanisms, revealing how enzyme fluctuations influence turnover times and explaining experimental deviations from classic Michaelis-Menten behavior.

Contribution

It provides an exact analytical framework for distinguishing between parallel and off-pathway enzyme mechanisms using turnover time distributions.

Findings

Parallel and off-pathway mechanisms show different substrate concentration dependencies.

Off-pathway mechanism with enzyme-substrate fluctuations explains experimental data.

Distinct fluctuation signatures help identify the operative mechanism.

Abstract

Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of $\beta$-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 $\beta$-galactosidase.