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

在经典的Hodgkin-Huxley模型的基础上，我们首次提出了一种新的窦房结细胞热力学模型。在新模型的建立过程中，离子通道的门控动力学和Na^-K泵和Na^/Ca^&lt；2&gt；交换器的离子输运动力学均采用时齐马尔科夫状态模型描述，状态转移速率常数由基于Eyring绝对反应速率理论的单指数函数表示。此外，在基础模型中加入了抗心律失常药物结合和解离的动力学。我们还开发了研究模型系统在参数变化时的分叉结构的方法和计算机程序。基于分支理论，我们计算了平衡点、平衡点的稳定性和极限环的动力学。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，并阐明动力学Me…为了验证新模型和经典模型，我们模拟了自发动作电位和离子电流动力学，并实验检测了抗心律失常药物阻断L型钙离子通道电流和延迟整流性K通道电流对SA结起搏的影响。此外，我们还通过构建分叉图，探索了模型细胞在抑制I_&lt；Ca、L&Gt；或I_&lt；Kr&gt；时的分叉结构。我们的研究结果总结如下：1)新模型在模拟I&lt；Kr&gt；抑制过程中动作电位变化方面优于经典模型。2)在两种模型中，阻断I_lt；Ca、L和Kr&gt；或I_&lt；Kr&gt；或I_&lt；Kr&gt；可通过稳定EP的Hopf分叉引起起搏活动的停止，提示模型系统在I_&lt；Ca、L&gt；或I_&lt；Kr&gt；抑制时的分叉结构基本相同。结果表明，经典的Hodgkin-Huxley模型仍可用于研究起搏器的发生机制，并可用于构建全心模型。较少

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