Critical parameters for singular perturbation reductions of chemical reaction networks

TL;DR

This paper characterizes parameter values that enable singular perturbation reductions in chemical reaction networks, focusing on classes like complex balanced and first order networks, and provides conditions for model simplification.

Contribution

It introduces conditions under which Tikhonov-Fenichel parameter values arise by turning off reactions or removing species in certain classes of reaction networks.

Findings

Conditions for TFPVs in complex balanced networks

Conditions for TFPVs in first order reaction networks

Characterization of reduction methods via parameter tuning

Abstract

We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and may depend on many parameters, it is frequently of interest to obtain a reduction of dimension in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov and Fenichel, provides a path toward such reductions. In the present paper we discuss parameter values that lead to singular perturbation reductions (so-called Tikhonov-Fenichel parameter values, or TFPVs). An algorithmic approach is known, but it is feasible for small dimensions only. Here we characterize conditions for classes of reaction networks for which TFPVs arise by turning off reactions (by setting rate parameters to zero), or by removing certain species (which relates to the classical quasi-steady state approach to model reduction). In particular, we obtain definitive results for the class of complex balanced reaction networks (of deficiency zero) and first order reaction networks.