# Dynamical aspects of the total QSSA in Enzyme Kinetics

## TL;DR

This paper provides a mathematical foundation for the quasi-steady state approximation in enzyme kinetics by linking it to the center manifold theory, enhancing understanding of enzyme reaction dynamics.

## Contribution

It proves the asymptotic equivalence between QSSA and the center manifold in enzyme kinetics, offering a rigorous basis for mechanistic analysis.

## Key findings

- QSSA is asymptotically equivalent to the center manifold.
- Provides a mathematical foundation for enzyme reaction analysis.
- Links Tihonov theory with enzyme kinetics approximations.

## Abstract

In this paper we prove that the well-known quasi-steady state approximations, commonly used in enzyme kinetics, which can be interpreted as the reduced system of a differential system depending on a perturbative parameter, according to Tihonov theory, are asymptotically equivalent to the center manifold of the system. This allows to give a mathematical foundation for the application of a mechanistic method to determine the center manifold of (at this moment, still simple) enzyme reactions.