Asymptotic analysis of a TMDD model: when a reaction contributes to the destruction of its product

DOI10.1007/s00285-018-1234-xzbMath1417.34104OpenAlexW2802846012WikidataQ52314632 ScholiaQ52314632MaRDI QIDQ667708

Lida I. Michalaki, Dimitrios A. Goussis

Publication date: 1 March 2019

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

Full work available at URL: https://doi.org/10.1007/s00285-018-1234-x

zbMATH Keywords

perturbation analysiscomputational singular perturbation (CSP)partial equilibrium approximation (PEA)quasi-steady-state approximation (QSSA)target-mediated drug disposition (TMDD)

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Invariant manifolds for ordinary differential equations (34C45) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items

Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism, A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails

Cites Work

• Asymptotic analysis of a target-mediated drug disposition model: algorithmic and traditional approaches
• Topics in mathematical pharmacology
• Multiple time scale dynamics
• Dynamics of target-mediated drug disposition: how a drug reaches its target
• Geometric singular perturbation theory for ordinary differential equations
• Computational singular perturbation analysis of stochastic chemical systems with stiffness
• Analysis of the computational singular perturbation reduction method for chemical kinetics
• The role of slow system dynamics in predicting the degeneracy of slow invariant manifolds: the case of vdP relaxation-oscillations
• Physical understanding of complex multiscale biochemical models via algorithmic simplification: glycolysis in saccharomyces cerevisiae
• Geometric singular perturbation theory in biological practice
• The ``hidden dynamics of the Rössler attractor
• Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
• Algorithmic asymptotic analysis of the NF-\(\kappa\mathrm B\) signaling system
• Glycolysis in saccharomyces cerevisiae: algorithmic exploration of robustness and origin of oscillations
• Analysis of Kinetic Reaction Mechanisms
• Geometry of the Computational Singular Perturbation Method
• 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
• Quasi steady state and partial equilibrium approximations: their relation and their validity
• H₂/air autoignition: The nature and interaction of the developing explosive modes
• Model Reduction and Physical Understanding of Slowly Oscillating Processes: The Circadian Cycle