On the pseudo-steady-state approximation and Tikhonov theorem for general enzyme systems
type: Item
instance of: scholarly article
title: On the pseudo-steady-state approximation and Tikhonov theorem for general enzyme systems
zbMATH Open document ID: 0581.92010
DOI: 10.1016/0025-5564(85)90039-2
author: F. Battelli
author: Claudio Lazzari
published in: Mathematical Biosciences
publication date: 1985-01-01T00:00:00Z
review text: The dynamical behaviour of enzymatic networks is given by a set of nonlinear autonomous differential equations. They are usually solved by a pseudo-steady-state approximation (PSSA), corresponding to the adiabatic approximation in physics, such that the slowest reaction determines the overall velocity. The authors consider the mathematical background and establish sufficient conditions applying Tikhonov's theorem to this situation, and propose some statements about uniqueness and stability. The PSSA does not hold in open systems or in closed systems such that the crucial small parameter \(\epsilon =E_ 0/S_ 0\) (total amount of enzym by total amount of ligands) approaches zero by \(1/S_ 0\to O\) instead of \(E_ 0\to O\).
reviewed by: R.Repges
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 3930783
zbMATH Keywords: general closed enzyme systems
zbMATH Keywords: ligand stoichiometry
zbMATH Keywords: open enzyme systems
zbMATH Keywords: steady state solutions
zbMATH Keywords: enzymatic networks
zbMATH Keywords: nonlinear autonomous differential equations
zbMATH Keywords: pseudo-steady-state approximation
zbMATH Keywords: adiabatic approximation
zbMATH Keywords: Tikhonov's theorem
zbMATH Keywords: uniqueness
zbMATH Keywords: stability
zbMATH Keywords: PSSA
MaRDI profile type: Publication
full work available at URL: 0025-5564(85)90039-2
OpenAlex ID: W2074319787
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description: scientific article; zbMATH DE number 3930783