Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism
DOI10.1007/s00285-023-01962-0zbMath1521.34060MaRDI QIDQ6116338
Dimitris G. Patsatzis, Dimitrios A. Goussis
Publication date: 18 July 2023
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
reduced modelspartial equilibrium approximationcomputational singular perturbationMichaelis-Menten reaction mechanismquasi steady-state approximation
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13) Computational methods for invariant manifolds of dynamical systems (37M21)
Cites Work
- Unnamed Item
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- Michaelis-Menten kinetics at high enzyme concentrations
- Computing quasi-steady state reductions
- Multiple time scale dynamics
- A constructive approach to quasi-steady state reductions
- Quasi steady-state approximations in complex intracellular signal transduction networks - a word of caution
- Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
- Asymptotic analysis of a TMDD model: when a reaction contributes to the destruction of its product
- A perturbation solution of Michaelis-Menten kinetics in a ``total framework
- On the validity of the quasi-steady state approximation of bimolecular reactions in solution
- Enzyme kinetics at high enzyme concentration
- The total quasi-steady-state approximation for complex enzyme reactions
- Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks
- On the validity of the steady state assumption of enzyme kinetics
- Geometric singular perturbation theory for ordinary differential equations
- Singular perturbation methods for ordinary differential equations
- Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations
- Theory on the rate equation of Michaelis-Menten type single-substrate enzyme catalyzed reactions
- Invariant manifolds for physical and chemical kinetics
- Analysis of the computational singular perturbation reduction method for chemical kinetics
- Extending the quasi-steady state approximation by changing variables
- The role of slow system dynamics in predicting the degeneracy of slow invariant manifolds: the case of vdP relaxation-oscillations
- The total quasi-steady-state approximation is valid for reversible enzyme kinetics
- A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails
- Geometric singular perturbation theory in biological practice
- A multi-time-scale analysis of chemical reaction networks. I: Deterministic systems
- The ``hidden dynamics of the Rössler attractor
- The total quasi-steady-state approximation for fully competitive enzyme reactions
- Methods of small parameter in mathematical biology
- A simplified perturbation solution of Michaelis-Menten kinetics equations in a ``total framework
- Quasi-steady state in the Michaelis-Menten system
- Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
- An efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems
- New trends and perspectives in nonlinear intracellular dynamics: one century from Michaelis-Menten paper
- Algorithmic asymptotic analysis of the NF-\(\kappa\mathrm B\) signaling system
- Small periodic perturbations of an autonomous system with a stable orbit
- Analysis of Kinetic Reaction Mechanisms
- Geometry of the Computational Singular Perturbation Method
- Consequences of the partial-equilibrium approximation for chemical reaction and transport
- The partial-equilibrium approximation in reacting flows
- Asymptotic Solution of Stiff PDEs with the CSP Method: The Reaction Diffusion Equation
- Model Reduction for Combustion Chemistry
- Fast and Slow Dynamics for the Computational Singular Perturbation Method
- The Quasi-Steady-State Assumption: A Case Study in Perturbation
- Quasi steady state and partial equilibrium approximations: their relation and their validity
- Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems
- Two perspectives on reduction of ordinary differential equations
- Surprises in a Classic Boundary-Layer Problem
- Explicit time-scale splitting algorithm for stiff problems: Auto-ignition of gaseous mixtures behind a steady shock
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