Enzyme Kinetics: A critique of the quasi-steady-state approximation

TL;DR

This paper critically examines the validity of the quasi-steady-state approximation in enzyme kinetics by solving nonlinear equations with new methods, analyzing temporal profiles, and revisiting recent concepts to clarify conditions for Michaelis-Menten kinetics.

Contribution

It introduces a novel approach using dimensionless variables and power-series with Pade approximants to analyze enzyme kinetics beyond steady-state assumptions.

Findings

The scheme accurately captures initial dynamics of enzyme reactions.

Conditions for the validity of the quasi-steady-state approximation are identified.

Reaction constants can be determined without assuming a steady state.

Abstract

The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and hence emergence of the Michaelis-Menten kinetics, with various substrate-enzyme ratios. But, conclusions vary. We solve here the desired set of coupled nonlinear differential equations by invoking a new set of dimensionless variables. Approximate solutions are obtained via the power-series method aided by Pade approximants. The scheme works very successfully in furnishing the initial dynamics at least up to the region where existence of any steady state can be checked. A few conditions for its validity are put forward and tested against the findings. Temporal profiles of the substrate and the product are analyzed in addition to that of the complex to gain further insights into legitimacy of the above approximation. Some recent observations like the reactant stationary approximation and the notions of different timescales are revisited. Signatures of the quasi-steady-state approximation are also nicely detected by following the various reduced concentration profiles in triangular plots. Conditions for the emergence of Michaelis-Menten kinetics are scrutinized and it is stressed how one can get the reaction constants even in the absence of any steady state.