# Comments on Nonrenewal Statistics in the Catalytic Activity of Enzyme Molecules at Mesoscopic Concentrations

## TL;DR

This paper clarifies that the Michaelis-Menten equation applies only in the steady state for enzyme kinetics, correcting previous claims that it was invalid at mesoscopic concentrations due to non-stationary considerations.

## Contribution

It demonstrates that the substrate dependence of mean turnover time aligns with MM in steady state, refuting prior inconsistent results at mesoscopic enzyme concentrations.

## Key findings

- MM equation valid in steady state regardless of enzyme number
- Previous non-stationary analysis led to inconsistent conclusions
- Clarifies conditions under which MM applies at mesoscopic scales

## Abstract

It is well known in enzyme kinetics that the Michaelis-Menten (MM) equation is applicable only to enzymes in the steady state. We show that the result obtained in the previous work [Phys. Rev. Lett. 107, 218301 (2011)] is inconsistent with the MM equation, not because the authors considered the enzyme system at mesoscopic concentrations but because they considered the enzyme system in the non-stationary state. The substrate concentration dependence of the mean turnover time is, in fact, consistent with the MM equation in the steady state, regardless of the number of enzymes in the system.

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Source: https://tomesphere.com/paper/1703.04710