Thermodynamics for Reduced Models of Chemical Reactions by PEA and QSSA

TL;DR

This paper investigates how classical chemical reaction reduction methods, PEA and QSSA, affect the thermodynamic properties of the original models, revealing potential loss of thermodynamic structure during reduction.

Contribution

It establishes a quantitative thermodynamic connection between original and reduced models, highlighting issues in preserving thermodynamic properties during reduction.

Findings

PEA and QSSA may not preserve thermodynamic structures

Loss of non-negativity of free energy dissipation rate observed

Validated through analytical and numerical analysis of Michaelis-Menten reactions

Abstract

Partial equilibrium approximation (PEA) and quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies mainly focus on the accuracy of solutions before and after applying model reduction. While, in this paper we start from a thermodynamic view, and try to establish a quantitative connection on the essential thermodynamic quantities, like entropy production rate, free energy dissipation rate and entropy flow rate, between the original reversible chemical mass-action equations and the reduced models by either PEA or QSSA. Our results reveal that the PEA and QSSA do not necessarily preserve the nice thermodynamic structure of the original full model during the reduction procedure (e.g. the loss of non-negativity of free energy dissipation rate), especially when adopting the algebraic relations in replace of differential equations. These results are further validated though the application to Michaelis-Menten reactions analytically and numerically as a prototype. We expect our study would motivate a re-examination on the effectiveness of various model reduction or approximation methods from a new perspective of non-equilibrium thermodynamics.