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Title:Qualitative analysis of the minimal Higgins model of glycolysis
Authors:ID Ferčec, Brigita (Author)
ID Mencinger, Matej (Author)
ID Petek, Tatjana (Author)
ID Aybar, Orhan Ozgur (Author)
ID Aybar, Ilknur Kusbeyzi (Author)
Files:URL URL - Source URL, visit https://match.pmf.kg.ac.rs/issues/m90n3/m90n3_563-580.html
 
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Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:Glycolysis, one of the leading metabolic pathways, involves many different periodic oscillations emerging at positive steady states of the biochemical models describing this essential process. One of the models employing the molecular diffusion of intermediates is the Higgins biochemical model to explain sustained oscillations. In this paper, we investigate the center-focus problem for the minimal Higgins model for general values of the model parameters with the help of computational algebra. We demonstrate that the model always has a stable focus point by finding a general form of the first Lyapunov number. Then, varying two of the model parameters, we obtain the first three coefficients of the period function for the stable focus point of the model and prove that the singular point is actually a bi-weak monodromic equilibrium point of type [1,2]. Additionally, we prove that there are two (small) intervals for a chosen parameter a>0 for which one critical period bifurcates from this singular point after small perturbations.
Keywords:biological processes, biochemical models, glycolysis
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2023
Year of publishing:2023
Number of pages:str. 563-580
Numbering:Vol. 90, no. 3
PID:20.500.12556/DiRROS-18446 New window
UDC:51-7
ISSN on article:0340-6253
DOI:10.46793/match.90-3.563F New window
COBISS.SI-ID:157794563 New window
Note:
Publication date in DiRROS:18.03.2024
Views:603
Downloads:265
Metadata:XML DC-XML DC-RDF
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FERČEC, Brigita, MENCINGER, Matej, PETEK, Tatjana, AYBAR, Orhan Ozgur and AYBAR, Ilknur Kusbeyzi, 2023, Qualitative analysis of the minimal Higgins model of glycolysis. Match : communications in mathematical and in computer chemistry [online]. 2023. Vol. 90, no. 3, p. 563–580. [Accessed 7 April 2025]. DOI 10.46793/match.90-3.563F. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18446
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Record is a part of a journal

Title:Match : communications in mathematical and in computer chemistry
Shortened title:Match
Publisher:University of Kragujevac, Faculty of Science
ISSN:0340-6253
COBISS.SI-ID:2624551 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:P1-0306-2022
Name:Uporabna matematika, teoretična fizika in inteligentni sistemi
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:P1-0288-2022
Name:Algebra in njena uporaba
Funder:ARRS - Slovenian Research Agency
Project number:BI-TR/19- 22-003

Secondary language

Language:Slovenian
Keywords:glikoliza, biokemija


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