Hunting $\varepsilon$: The Origin and Validity of Quasi-Steady-State Reductions in Enzyme Kinetics
DOI10.1137/20M135073XzbMath1481.92051arXiv2109.03957MaRDI QIDQ5023529
Santiago Schnell, Malgorzata Anna Tyczynska, Justin S. Eilertsen
Publication date: 24 January 2022
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.03957
enzyme kineticsscaling analysisquasi-steady-state approximationtranscritical bifurcationsFenichel theorygeometrical singular perturbation analysis
Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Singular perturbations of ordinary differential equations (34D15)
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Cites Work
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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
- Enzyme kinetics at high enzyme concentration
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- On the validity of the steady state assumption of enzyme kinetics
- Applications of centre manifold theory
- Geometric singular perturbation theory for ordinary differential equations
- Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations
- Classical quasi-steady state reduction -- a mathematical characterization
- Extending the quasi-steady state approximation by changing variables
- On fast-slow consensus networks with a dynamic weight
- On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism
- The quasi-steady-state approximations revisited: timescales, small parameters, singularities, and normal forms in enzyme kinetics
- Kinetic analysis of a general model of activation of aspartic proteinase zymogens
- Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics
- Determining ``small parameters for quasi-steady state
- Multi-timescale systems and fast-slow analysis
- Approaches for the estimation of timescales in nonlinear dynamical systems: timescale separation in enzyme kinetics as a case study
- Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics
- Stochastic approaches for modelling in vivo reactions
- New trends and perspectives in nonlinear intracellular dynamics: one century from Michaelis-Menten paper
- Extending slow manifolds near transcritical and pitchfork singularities
- Multiple Geometric Viewpoints of Mixed Mode Dynamics Associated with Pseudo-plateau Bursting
- Mixed-Mode Oscillations with Multiple Time Scales
- A Geometric Model for Mixed-Mode Oscillations in a Chemical System
- Quasi-Steady State and Nearly Invariant Sets
- The Quasi-Steady-State Assumption: A Case Study in Perturbation
- Big Ducks in the Heart: Canard Analysis Can Explain Large Early Afterdepolarizations in Cardiomyocytes
- Noise-Induced Phenomena in Slow-Fast Dynamical Systems
- Geometric Singular Perturbation Theory Beyond the Standard Form
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