Single Molecule Michaelis-Menten Equation beyond Quasi-Static Disorder

TL;DR

This paper extends the classic Michaelis-Menten equation to single enzyme molecules considering dynamic disorder, showing it remains valid under various conditions despite complex waiting time behaviors.

Contribution

It provides a generalized Michaelis-Menten framework for single enzymes accounting for dynamic disorder, beyond the quasi-static assumptions.

Findings

Exact validity of Michaelis-Menten in slow reaction and nondiffusion limits.

Michaelis-Menten remains a good approximation outside these limits.

Waiting time distribution exhibits multiexponential decay in nondiffusion limit.

Abstract

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.