Development of a novel thermodynamical model for sinoatrial node pacemaker cells and bifurcation analysis of the model systems in terms of nonlinear dynamics.

开发窦房结起搏器细胞的新型热力学模型，并根据非线性动力学对模型系统进行分叉分析。

• 批准号: 15590195
• 负责人: KURATA Yasutaka
• 金额: $ 1.47万
• 依托单位: KANAZAWA MEDICAL UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15590195/
• 关键词: sinoatrial node; ionic channels; ion transporters; nonlinear dynamical systems; Markovian state models; rate theory; computer simulations; bifurcation analysis

On the basis of our classical Hodgkin-Huxley type model, we have first developed a novel thermodynamical model for sinoatrial node cells. For the development of the novel model, gating kinetics of ionic channels and dynamics of ion transports by Na^+-K^+ pump and Na^+/Ca^<2+> exchangers were described by time-homogeneous Markovian state models with state transition rate constants being formulated with single exponential functions based on Eyring's absolute reaction rate theory. Furthermore, the dynamics of binding and unbinding of antiarrhythmic drugs were incorporated to the base model. We have also developed the methods and computer programs to investigate bifurcation structures of model systems during changes in parameters. Based on bifurcation theory, we calculated equilibrium points, their stability, and dynamics of limit cycles. Exploring bifurcation structures of model systems allowed us to validate the mathematical models more accurately as well as to elucidate the dynamical me … More chanisms of pacemaker generation.To validate the novel model as well as the classical model, we simulated spontaneous action potentials and ionic current dynamics, and also experimentally examined the effects of antiarrhythmic agents to block L-type Ca^<2+> (I_<Ca,L>) and delayed-rectifier K^+ (I_<Kr>) currents on SA node pacemaking. Moreover, we explored bifurcation structures of model cells during inhibitions of I_<Ca,L> or I_<Kr> by constructing bifurcation diagrams. Our findings are summarized as follows : 1)The novel model is superior to the classical model in mimicking the action potential change during I_<Kr> inhibition. 2)In both the models, blocking I_<Ca,L> or I_<Kr> caused cessation of pacemaker activity via a Hopf bifurcation where an EP was stabilized, suggesting that bifurcation structures of the model systems during I_<Ca,L> or I_<Kr> inhibitions are essentially the same. It was suggested that a classical Hodgkin-Huxley type model is still useful in exploring the mechanisms of pacemaker generation, and can be used for constructing whole heart models. Less

在我们经典的Hodgkin-Huxley型模型的基础上，我们首先开发了一种新颖的窦房结细胞热力学模型。为了开发新模型，离子通道的门控动力学以及Na^+-K^+泵和Na^+/Ca^<2+>交换器的离子传输动力学通过时间齐次马尔可夫状态模型来描述，状态转换速率常数由基于艾林绝对反应速率理论的单指数函数表示。此外，抗心律失常药物的结合和解离动力学也被纳入基础模型中。我们还开发了方法和计算机程序来研究模型系统在参数变化期间的分叉结构。基于分岔理论，我们计算了平衡点、它们的稳定性以及极限环的动力学。探索模型系统的分叉结构使我们能够更准确地验证数学模型，并阐明起搏器产生的动力学机制。为了验证新颖模型和经典模型，我们模拟了自发动作电位和离子电流动力学，并通过实验检查了抗心律失常药物阻断 L 型 Ca^<2+> 的效果。 SA 节点起搏的 (I_<Ca,L>) 和延迟整流器 K^+ (I_<Kr>) 电流。此外，我们通过构建分叉图探索了 I_<Ca,L> 或 I_<Kr> 抑制过程中模型细胞的分叉结构。我们的研究结果总结如下： 1）新模型在模拟 I_<Kr> 抑制期间的动作电位变化方面优于经典模型。 2) 在这两个模型中，阻断 I_<Ca,L> 或 I_<Kr> 会通过 Hopf 分叉导致起搏器活动停止，其中 EP 稳定，这表明在 I_<Ca,L> 或 I_<Kr> 抑制期间模型系统的分叉结构本质上是相同的。有人认为经典的Hodgkin-Huxley型模型对于探索起搏器产生机制仍然有用，并且可以用于构建全心脏模型。较少的

项目成果

Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking:: insights from stability and bifurcation analyses of a mathematical model

• DOI: 10.1152/ajpheart.01050.2002
• 发表时间: 2003-12-01
• 期刊: AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY
• 影响因子: 4.8
• 作者: Kurata, Y;Hisatome, I;Shibamoto, T
• 通讯作者: Shibamoto, T

Dynamical mechanisms of pacemaker generation in I_<KI>-downregulated human ventricular myocytes : insights from bifurcation analyses of a mathematical model

I_<KI> 下调的人心室肌细胞中起搏器生成的动力学机制：数学模型分叉分析的见解

• 发表时间: 2005
• 期刊: Biophys J 89・4
• 作者: Kurata Y;et al.
• 通讯作者: et al.

Dynamical mechanisms of pacemaker generation in IK1-downregulated human ventricular myocytes: Insights from bifurcation analyses of a mathematical model

• DOI: 10.1529/biophysj.105.060830
• 发表时间: 2005-10-01
• 期刊: BIOPHYSICAL JOURNAL
• 影响因子: 3.4
• 作者: Kurata, Y;Hisatome, I;Shibamoto, T
• 通讯作者: Shibamoto, T

Kurata Y, et al.: "Roles of L-type Ca^<2+> delayed-rectifier K^+ currents in sinoatrial node pacemaking : insights from stability and bifurcation analyses of a mathematical model"Am J Physiol Heart Circ Physiol. 285. H2804-H2819 (2003)

Kurata Y 等人：“L 型 Ca^<2> 延迟整流 K^ 电流在窦房结起搏中的作用：数学模型稳定性和分叉分析的见解”Am J Physiol Heart Circ Physiol。