心肌细胞钾通道调控早期后除极的动力学机制

Dynamic Mechanisms of Afterdepolarization in the Early Regulation of Cardiac Potassium Channel

针对心肌细胞动作电位复极期振荡的早期后除极(EAD)现象,研究了细胞模型Hopf分岔和EADs的关系以及钾离子通道的作用。在LR91模型中剔除快钠离子电流并引入控制钙和钾离子通道时常数的控制因子形成子系统模型,分离出模型中不同时间尺度的变量,将跨膜电势、钙离子通道激活及失活门控变量视为快变量构成三变量快子系统,慢变量钾离子通道门控参数视为其分岔参数分析膜电位与快子系统稳定性的关系。计算机仿真结果表明,随着钾离子通道门控变量时常数的增大,膜电位越来越接近快子系统的吸引域和Hopf分岔点。当时常数增大到6倍时动作电位时程延长至1 060ms并开始出现膜电位的振荡,时常数增大到15倍时电位振荡个数增加至15,说明快子系统的Hopf分岔导致了钾通道门控作用下EAD的诱发。

The relationships between the Hopf bifurcation in the cellular model and the Early Afterdepolarization （EAD） and the function of potassium channel are investigated for the EAD phenomenon of the voltage oscillation during the repolarizing phase of the cardiac action potential. A subsystem model is developed by removing the fast activated sodium current in the LR91 model and introducing control factors for time constants of calcium and potassium channels. Variables with different time scales are separated. A fast subsystem with 3 variables is formed and the variables are voltage, activation and inactivation gating variables of calcium channel. The relationship between the voltage and the steady state of the fast subsystem is analyzed by regarding the gating variable of the potassium channel as a bifurcation parameter. Simulation results show that the voltage approaches the attraction and Hopf bifurcation point more and more as the time constant of potassium channel gating variable increases. The action potential duration （APD） is prolonged to 1 060 ms and the voltage oscillation appears when the time constant is 6 times of its control value. The number of the oscillation waves increases to 15, when the time constant approaches 15 times. The results show that the Hopf bifurcation of the fast subsystem results in induction of EAD under the control of the potassium channel.