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

在经典霍奇金-赫胥黎模型的基础上，我们首次建立了一种新的窦房结细胞热力学模型。为了建立新模型，采用时间齐次的马尔可夫状态模型描述了离子通道的门控动力学和Na^+-K^+泵和Na^+/Ca^<2+>交换器的离子输运动力学，并基于Eyring绝对反应速率理论用单指数函数表示了状态转移速率常数。此外，将抗心律失常药物的结合和解结合动力学纳入基础模型。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过程中的分岔结构。基于分岔理论，我们计算了极限环的平衡点、稳定性和动力学。对模型系统分岔结构的探索，使我们能够更准确地验证数学模型，并阐明起搏器产生的更多动力学机制。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，并实验研究了抗心律失常药物阻断L型Ca^<2+> （I_<Ca，L>）和延迟整流K^+ (I_<Kr>)电流对SA节点起搏的影响。此外，我们通过构建分岔图来探索I_<Ca，L>或I_<Kr>抑制时模型细胞的分岔结构。结果表明：1)新模型在模拟I_<Kr>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_<Ca，L>或I_<Kr>通过Hopf分岔导致起搏器活动停止，其中EP稳定，这表明I_<Ca，L>或I_<Kr>抑制期间模型系统的分岔结构基本相同。这表明经典的霍奇金-赫胥黎模型仍然有助于探索起搏器产生的机制，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