A study in Alzheimer’s disease model for pathological effect of oligomers on the interplay between [formula omitted]-amyloid and Ca2＋

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-11-30 DOI:10.1016/j.aml.2024.109407

Mingyan Dong, Yongxin Zhang, Gui-Quan Sun, Zun-Guang Guo, Jiao Zhang

{"title":"A study in Alzheimer’s disease model for pathological effect of oligomers on the interplay between [formula omitted]-amyloid and Ca2＋","authors":"Mingyan Dong, Yongxin Zhang, Gui-Quan Sun, Zun-Guang Guo, Jiao Zhang","doi":"10.1016/j.aml.2024.109407","DOIUrl":null,"url":null,"abstract":"Alzheimer’s disease (AD) is characterized by the progressive deposition of <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>-amyloid (A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>) plaques in the brain, where the A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math> oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math> oligomers on the interplay between A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math> and Ca<ce:sup loc=\"post\">2＋</ce:sup>. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"54 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.aml.2024.109407","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

Alzheimer’s disease (AD) is characterized by the progressive deposition of β-amyloid (Aβ) plaques in the brain, where the Aβ oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of Aβ oligomers on the interplay between Aβ and Ca2＋. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number R0 is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.

查看原文本刊更多论文

阿尔茨海默病模型中低聚物对[公式省略]-淀粉样蛋白和Ca2+相互作用的病理影响的研究

阿尔茨海默病（AD）的特征是大脑中β-淀粉样蛋白（Aβ）斑块的进行性沉积，其中Aβ低聚物已被证实在疾病过程中产生关键的细胞毒性。在本研究中，我们建立了一个模型来描述a β低聚物对a β和Ca2+相互作用的影响。数学分析证明了平衡点的存在性和稳定性，并给出了发生后向分岔和鞍节点分岔的条件。此外，引入总繁殖数R0来表征AD的进展。这些结果可能为研究ad相关的医疗策略提供有价值的见解。

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

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.