Coordinate-independent model reductions of chemical reaction networks based on geometric singular perturbation theory

TL;DR

This paper introduces a coordinate-independent reduction method for chemical reaction networks using geometric singular perturbation theory, enabling systematic and robust model simplification across various parameter regimes without relying on timescale separation.

Contribution

The authors develop a novel reduction framework based on geometric singular perturbation theory that is independent of coordinate choices and applicable even without clear timescale separation.

Findings

Systematic reduction of Michaelis-Menten reaction across multiple parameter regimes

Successful reduction of complex Kim-Forger model without coordinate transformation

Comparison with traditional QSSA methods highlights advantages of the new approach

Abstract

The quasi-steady-state approximation (QSSA) is a standard technique for reducing the complexity of chemical reaction networks (CRNs). The validity of any QSSA-based model is restricted to specific parameter regimes. Selecting the appropriate reduction is not always straightforward. At times, QSSAs are misused outside of their validity regions and, even when a particular QSSA is considered valid in a given parameter regime, other QSSAs may be simultaneously valid, creating ambiguity. Here, we employ a more powerful alternative: a constructive model reduction framework based on coordinate-independent geometric singular perturbation theory (ci-GSPT) and the parametrization method. A key advantage of this approach is its ability to derive reduced models independent of a clear timescale separation in the variables for a specific parameter configuration. We demonstrate our approach on two benchmark systems. For the Michaelis-Menten (MM) reaction, we show that the framework provides a systematic approach by exploring parameter configurations across three orders of magnitude: asymptotically large, small, and `order one'. A consequence of this systematic analysis is a geometric classification that categorizes the resulting model reductions and provides a point of comparison between our approach and common QSSA variants in the literature. For the more complex Kim-Forger model, we show that this approach successfully produces a reduction without the need for a coordinate transformation, showcasing its applicability to larger systems.