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型细胞模型的基础上，我们首次建立了一种新的窦房结细胞模型。为了建立新的模型，离子通道的门控动力学以及Na ^+-K ^+泵和Na ^+/Ca ^2+交换剂的离子输运动力学均采用基于Eyring绝对反应速率理论的时间均匀马尔可夫状态模型，状态转移速率常数采用单指数函数表示。此外，结合和解结合的抗肿瘤药物的动力学被纳入基础模型。我们还开发了研究参数变化时模型系统分岔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，它们的稳定性和极限环的动力学。探讨模型系统的分岔结构，可以更准确地验证数学模型，阐明系统的动力学机制， 关于我们 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，并实验研究了阻断L型Ca ^&lt;2 +&gt;（I_&lt;Ca，L&gt;）和延迟整流K ^+（I_）电流的抗心律失常药物对SA结起搏的影响。<Kr>此外，我们还通过构造分岔图，探讨了I_&lt;Ca，L&gt;或I_2抑制时模型细胞的分岔结构。<Kr>我们的研究结果总结如下：1）新模型在模拟I_2抑制过程中动作电位变化方面优于经典模型上级。<Kr>（2）在两个模型中，阻断I_&lt;Ca，L&gt;或I_2均通过一个稳定EP的Hopf分岔引起起搏活动的停止，表明I_&lt;Ca，L&gt;或I_2抑制时模型系统的分岔结构基本相同。<Kr><Kr>这表明经典的Hodgkin-Huxley型模型在研究起搏器产生机制方面仍然是有用的，并可用于构建全心脏模型。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