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Heineken, Tsuchiya and Aris on the mathematical status of the pseudo-steady state hypothesis: A classic from volume 1 of Mathematical Biosciences
- Source :
- Mathematical Biosciences. 318:108274
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
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.
- Subjects :
- Statistics and Probability
0303 health sciences
Singular perturbation
010304 chemical physics
General Immunology and Microbiology
Applied Mathematics
Volume (computing)
Computational Biology
General Medicine
History, 20th Century
Models, Theoretical
Biochemistry
01 natural sciences
General Biochemistry, Genetics and Molecular Biology
Biochemical kinetics
03 medical and health sciences
Modeling and Simulation
0103 physical sciences
Periodicals as Topic
General Agricultural and Biological Sciences
Mathematical economics
Pseudo steady state
Strengths and weaknesses
030304 developmental biology
Mathematics
Subjects
Details
- ISSN :
- 00255564
- Volume :
- 318
- Database :
- OpenAIRE
- Journal :
- Mathematical Biosciences
- Accession number :
- edsair.doi.dedup.....87eba0331e90ec07fbf74070be4d5586