On the quasi-steady-state assumption in enzyme kinetics: rigorous analysis

TL;DR

This paper rigorously analyzes the quasi-steady-state assumption in enzyme kinetics, providing a clear quantitative framework and challenging some traditional practices in the modeling of enzymatic reactions.

Contribution

It introduces a novel, rigorous approach to defining and scaling the quasi-steady-state assumption, clarifying its components and removing ambiguities.

Findings

Re-establishment of known results with rigorous proof

A new algorithm for proper problem scaling

Clarification on the dispensability of a third assumption

Abstract

We study, from a purely quantitative point of view, the quasi-steady-state assumption for the fundamental mathematical model of the general enzymatic reaction: we re-establish, on a rigorous basis, certain already known results and we propose a novel approach to the subject, that makes waivable an ambiguous, widely used, practice. In particular, we define the two parts of the assumption in a quantitative fashion, we employ a simple algorithm for the proper scaling of the corresponding problem which naturally provides us with the necessary and sufficient information, and we comment, among other issues, on a dispensable third part of the assumption.