# Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation

## TL;DR

This paper derives a generalized Michaelis-Menten equation for enzyme kinetics in conformational nonequilibrium steady states, incorporating non-equilibrium effects and cyclic conformational currents, thus expanding understanding of enzyme behavior beyond traditional models.

## Contribution

It introduces a generalized MM equation accounting for conformational currents and establishes a link between non-MM terms and cyclic kinetic loops in enzyme kinetics.

## Key findings

- Generalized MM equation includes non-MM corrections from conformational currents.
- When detailed balance holds, the equation reduces to traditional MM form.
- Provides a framework to predict enzyme cooperativity in nonequilibrium conditions.

## Abstract

In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. Based on a discrete kinetic network model, we use the integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its validity for many enzymatic systems. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics has been observed in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.