中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (5): 132-139.

• 论文 • 上一篇    下一篇

改进双钙库模型的分岔分析

牛帅1,孙小强2,祁宏1   

  1. 1. 山西大学复杂系统研究所,山西 太原 030006;
    2. 中山大学中山医学院,广东 广州 510089
  • 收稿日期:2017-12-14 出版日期:2018-09-25 发布日期:2018-09-25
  • 通讯作者: 祁宏(1984年生),男;研究方向:系统生物学;E-mail:hongqi@sxu.edu.cn

Bifurcation analysis of the improved  two-pool calcium model

NIU Shuai1,SUN Xiaoqiang2,QI Hong1   

  1. 1. Complex Systems Research Center, Shanxi University, Taiyuan 030006, China;
    2. Zhongshan School of Medicine, Sun Yatsen University, Guangzhou 510089, China
  • Received:2017-12-14 Online:2018-09-25 Published:2018-09-25

摘要:

钙离子(Ca2+)是细胞内最常用的信号分子,它通过钙振荡的形式调节多种不同的细胞活动。双钙库模型是一个经典的钙振荡模型,它描述了细胞内钙振荡发生的详细机制。但是,该模型中的希尔系数高,不利于数学分析。本文在降低希尔系数的基础上提出了改进模型,并应用定性理论和分岔理论对其进行了数学分析。改进双钙库模型的动力学性质与原始双钙库模型相似,但其钙振荡区间更大,振幅变化更明显,更好地体现了Ca2+编码细胞信号的方式。双参数分岔分析结合参数敏感性分析的结果表明:Ca2+流出细胞的速率常数、钙库上钙释放通道和钙泵的激活常数均可对钙振荡产生明显影响,这些参数的改变可能会引发Ca2+相关的疾病。本研究有助于人们更好地从数学层面研究双钙库模型,对理解钙信号及其相关疾病也有一定帮助。

关键词: 双钙库模型, 钙振荡, 分岔分析, 敏感性分析

Abstract:

Ca2+ is the most commonly used signal that appears as sustained oscillations to regulate many diverse cellular processes. Two-pool model is a classical mathematical model to explain how these Ca2+ oscillations occur. However, the Hill coefficient in this model is too high to do mathematical analysis. In this paper, we improve the original model by lower the Hill coefficient. Based on the qualitative theory and bifurcation theory, we analyze the existence and stability of equilibrium points, and discuss the type of bifurcation points in the improved model. The improved model has similar dynamic properties as the original model, but a wider region for Ca2+ oscillations and a more obvious amplitude change, which better reflects the information encoding role of Ca2+ signaling. The results of two-parameter bifurcation analysis combined with parameter sensitivity analysis indicate that the efflux rate constant of Ca2+ out of the cell, as well as the threshold constants for activation and pumping of Ca2+ store have significant impact on Ca2+  oscillations. The variation of these parameters may contribute to calcium-related disease. This research is not only helpful for studying the two-pool model from the mathematical aspect, but also for understanding the Ca2+ signaling and related diseases.

Key words: two-pool model, calcium oscillation, bifurcation analysis, parameter sensitivity analysis

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