Unbounded solutions of models for glycolysis

Publication type:
Journal article
Metadata:
Abstract
<jats:title>Abstract</jats:title><jats:p>The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of a Poincaré compactification of the system and a shooting argument. This system was originally derived from another system with Michaelis–Menten kinetics. A Poincaré compactification of the latter system is carried out and this is used to show that the Michaelis–Menten system, like that with mass action, has solutions which diverge to infinity in a monotone manner. It is also shown to admit subcritical Hopf bifurcations and thus unstable periodic solutions. We discuss to what extent the unbounded solutions cast doubt on the biological relevance of the Selkov oscillator and compare it with other models for the same biological system in the literature. </jats:p>
Autoren
DOI
10.1007/s00285-021-01560-y
eISSN
1432-1416
ISSN
0303-6812
Ausgabe der Veröffentlichung
1-2
Zeitschrift
Journal of Mathematical Biology
Sprache
en
Artikelnummer
1
Online publication date
2021
Datum der Veröffentlichung
2021
Status
Published
Herausgeber
Springer Science and Business Media LLC
Herausgeber URL
http://dx.doi.org/10.1007/s00285-021-01560-y
Datum der Datenerfassung
2021
Titel
Unbounded solutions of models for glycolysis
Ausgabe der Zeitschrift
82

Data source: Crossref

Other metadata sources:
Abstract
The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of a Poincaré compactification of the system and a shooting argument. This system was originally derived from another system with Michaelis-Menten kinetics. A Poincaré compactification of the latter system is carried out and this is used to show that the Michaelis-Menten system, like that with mass action, has solutions which diverge to infinity in a monotone manner. It is also shown to admit subcritical Hopf bifurcations and thus unstable periodic solutions. We discuss to what extent the unbounded solutions cast doubt on the biological relevance of the Selkov oscillator and compare it with other models for the same biological system in the literature.
Addresses
  • Institut für Mathematik Johannes Gutenberg-Universität, Staudingerweg 9, 55099, Mainz, Germany.
Autoren
DOI
10.1007/s00285-021-01560-y
eISSN
1432-1416
Externe Identifier
  • PubMed Identifier: 33475794
  • PubMed Central ID: PMC7819955
Funding acknowledgements
  • Projekt DEAL:
Open access
true
ISSN
0303-6812
Ausgabe der Veröffentlichung
1-2
Zeitschrift
Journal of mathematical biology
Schlüsselwörter
  • Glycolysis
  • Kinetics
  • Models, Biological
Sprache
eng
Medium
Electronic
Online publication date
2021
Open access status
Open Access
Paginierung
1
Datum der Veröffentlichung
2021
Status
Published
Publisher licence
CC BY
Datum der Datenerfassung
2021
Titel
Unbounded solutions of models for glycolysis.
Sub types
  • Research Support, Non-U.S. Gov't
  • research-article
  • Journal Article
Ausgabe der Zeitschrift
82

Files

https://link.springer.com/content/pdf/10.1007/s00285-021-01560-y.pdf https://europepmc.org/articles/PMC7819955?pdf=render

Data source: Europe PubMed Central

Abstract
The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of a Poincaré compactification of the system and a shooting argument. This system was originally derived from another system with Michaelis-Menten kinetics. A Poincaré compactification of the latter system is carried out and this is used to show that the Michaelis-Menten system, like that with mass action, has solutions which diverge to infinity in a monotone manner. It is also shown to admit subcritical Hopf bifurcations and thus unstable periodic solutions. We discuss to what extent the unbounded solutions cast doubt on the biological relevance of the Selkov oscillator and compare it with other models for the same biological system in the literature.
Date of acceptance
2020
Autoren
Autoren-URL
https://www.ncbi.nlm.nih.gov/pubmed/33475794
DOI
10.1007/s00285-021-01560-y
eISSN
1432-1416
Externe Identifier
  • PubMed Central ID: PMC7819955
Ausgabe der Veröffentlichung
1-2
Zeitschrift
J Math Biol
Schlüsselwörter
  • Dynamical system
  • Glycolysis
  • Oscillations
  • Glycolysis
  • Kinetics
  • Models, Biological
Sprache
eng
Country
Germany
Paginierung
1
PII
10.1007/s00285-021-01560-y
Datum der Veröffentlichung
2021
Status
Published online
Datum, an dem der Datensatz öffentlich gemacht wurde
2021
Titel
Unbounded solutions of models for glycolysis.
Sub types
  • Journal Article
  • Research Support, Non-U.S. Gov't
Ausgabe der Zeitschrift
82

Data source: PubMed

Author's licence
CC-BY
Autoren
Hosting institution
Universitätsbibliothek Mainz
Sammlungen
  • JGU-Publikationen
Resource version
Published version
DOI
10.1007/s00285-021-01560-y
File(s) embargoed
false
Open access
true
ISSN
1432-1416
Zeitschrift
Journal of mathematical biology
Schlüsselwörter
  • 510 Mathematik
  • 510 Mathematics
Sprache
eng
Open access status
Open Access
Paginierung
1
Datum der Veröffentlichung
2021
Public URL
https://openscience.ub.uni-mainz.de/handle/20.500.12030/7253
Herausgeber
Springer
Datum der Datenerfassung
2022
Datum, an dem der Datensatz öffentlich gemacht wurde
2022
Zugang
Public
Titel
Unbounded solutions of models for glycolysis
Ausgabe der Zeitschrift
82

Files

unbounded_solutions_of_models-20220627115629724.pdf

Data source: OPENSCIENCE.UB

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