Qualitative Analysis of the Minimal Higgins Model of Glycolysis

IF 2.9 2区化学 Q2 CHEMISTRY, MULTIDISCIPLINARY

Match-Communications in Mathematical and in Computer Chemistry Pub Date : 2023-07-01 DOI:10.46793/match.90-3.563f

B. Ferčec, M. Mencinger, T. Petek, O. O. Aybar, I. K. Aybar

{"title":"Qualitative Analysis of the Minimal Higgins Model of Glycolysis","authors":"B. Ferčec, M. Mencinger, T. Petek, O. O. Aybar, I. K. Aybar","doi":"10.46793/match.90-3.563f","DOIUrl":null,"url":null,"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","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Match-Communications in Mathematical and in Computer Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.46793/match.90-3.563f","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 1

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

查看原文本刊更多论文

糖酵解最小希金斯模型的定性分析

糖酵解是主要的代谢途径之一，在描述这一基本过程的生化模型的正稳定状态下，涉及许多不同的周期振荡。希金斯生化模型是利用中间产物的分子扩散来解释持续振荡的模型之一。本文利用计算代数的方法，研究了最小希金斯模型参数一般值的中心焦点问题。我们通过寻找第一李雅普诺夫数的一般形式证明了模型总是有一个稳定的焦点。然后，通过改变其中两个模型参数，我们得到了模型稳定焦点的周期函数的前三个系数，并证明了该奇点实际上是一个类型为[1,2]的双弱单平衡点。此外，我们证明了对于所选参数> 0存在两个(小)区间，其中一个临界周期在小扰动后从该奇点分叉

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Match-Communications in Mathematical and in Computer Chemistry 化学-化学综合

CiteScore

4.40

自引率

26.90%

发文量

审稿时长

2 months

期刊介绍： MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.