Heineken, Tsuchiya and Aris on the mathematical status of the pseudo-steady state hypothesis: a classic from volume 1 of Mathematical Biosciences
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Date
2019
Authors
Roussel, Marc R.
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Volume 1, Issue 1 of Mathematical Biosciences was the venue for a now-classic paper on the application of singular perturbation theory in enzyme kinetics, “On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics” by F. G. Heineken, H. M. Tsuchiya and R. Aris. More than 50 years have passed, and yet this paper continues to be studied and mined for insights. This perspective discusses both the strengths and weaknesses of the work presented in this paper. For many, the justification of the pseudo-steady-state approximation using singular perturbation theory is the main achievement of this paper. However, there is so much more material here, which laid the foundation for a great deal of research in mathematical biochemistry in the intervening decades. The parameterization of the equations, construction of the first-order uniform singular-perturbation solution, and an attempt to apply similar principles to the pseudo-equilibrium approximation are discussed in particular detail.
Description
Sherpa Romeo green journal. Permission to archive author manuscript
Keywords
Singular perturbation theory , Michaelis-Menten mechanism , Pseudo-steady-state approximation , Pseudo-equilibrium approximation
Citation
Roussel, M. R. (2019). Heineken, Tsuchiya and Aris on the mathematical status of the pseudo-steady state hypothesis: A classic from volume 1 of Mathematical Biosciences. Mathematical Biosciences, 318, 108274. https://doi.org/10.1016/j.mbs.2019.108274