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

根据我们的经典霍奇金式类型模型，我们首先开发了一种新型的Sinoatrial节点细胞的热力学模型。为了开发新型模型，由Na^+-K^+泵和Na^+/Ca^<2+>交换器的离子通道的门控动力学和离子传输动力学通过时间均匀的Markovian状态模型来描述，其状态过渡速率常数由单个Expient function faction time-Markone satemant Models基于眼神的绝对反应速率。此外，将抗心律失常药物的结合和解开动力学纳入了基础模型。我们还开发了方法和计算机程序来研究参数变化期间模型系统的分叉结构。基于分叉理论，我们计算了平衡点，它们的稳定性和极限周期的动力学。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，并阐明动态我……更多的是起搏器生成的Chanism。要验证新型模型以及经典模型，我们模拟了支持赞助商的动作电位和离子电位的动力学，并实验了两次can extrimentimenciment <liriciarliarrialriicy> Antiarrialhymicty的影响，以阻止效果^exteriment> neffer> extermiacty> Exents undermic> （i_ <ca，l>）和SA节点起搏器上的延迟晶状体k^+（i_ <kr>）电流。此外，我们通过构造分叉图探索了I_ <CA，L>或I_ <kr>的抑制期间模型细胞的分叉结构。我们的发现总结如下：1）新型模型在模仿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，阻止I_ <Ca，L>或I_ <kr>通过HOPF分叉稳定了EP，这在I_ <CA，L>或I_ <kr>抑制作用过程中均可导致起搏器活性停止，这表明模型系统的分叉结构本质上是相同的。有人建议，经典的霍奇金 - 赫克斯利类型模型仍然可用于探索起搏器生成的机制，可用于构建整个心脏模型。较少的

项目成果

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.

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。