Natural parameter conditions for singular perturbations of chemical and biochemical reaction networks

DOI10.1007/s11538-023-01150-7zbMath1519.92362arXiv2211.10836MaRDI QIDQ6044243

Sebastian Walcher, Justin S. Eilertsen, Santiago Schnell

Publication date: 17 May 2023

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.10836

zbMATH Keywords

Lyapunov function eigenvalue singular perturbation dimension reduction perturbation parameter symmetric polynomial quasi-steady-state approximation reaction network timescale

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biochemistry, molecular biology (92C40) Singular perturbations of ordinary differential equations (34D15) Systems biology, networks (92C42)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Michaelis-Menten kinetics at high enzyme concentrations
A constructive approach to quasi-steady state reductions
Phase-plane geometries in coupled enzyme assays
Tikhonov's theorem and quasi-steady state
Enzyme kinetics at high enzyme concentration
On the validity of the steady state assumption of enzyme kinetics
Geometric singular perturbation theory for ordinary differential equations
A kinetic analysis of coupled (or auxiliary) enzyme reactions
Classical quasi-steady state reduction -- a mathematical characterization
Analysis of the computational singular perturbation reduction method for chemical kinetics
On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism
Coordinate-independent singular perturbation reduction for systems with three time scales
On the anti-quasi-steady-state conditions of enzyme kinetics
The quasi-steady-state approximations revisited: timescales, small parameters, singularities, and normal forms in enzyme kinetics
A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails
Determining ``small parameters for quasi-steady state
Quasi-steady state in the Michaelis-Menten system
Mathematical physiology. I: Cellular physiology
Extending slow manifolds near transcritical and pitchfork singularities
The Quasi-Steady-State Assumption: A Case Study in Perturbation
Hunting $\varepsilon$: The Origin and Validity of Quasi-Steady-State Reductions in Enzyme Kinetics
Noise-Induced Phenomena in Slow-Fast Dynamical Systems
Quasi-Steady State: Searching for and Utilizing Small Parameters
Fenichel Theory for Multiple Time Scale Singular Perturbation Problems

This page was built for publication: Natural parameter conditions for singular perturbations of chemical and biochemical reaction networks