Morris-Lecar系统中通道噪声诱导的自发性动作电位研究

在生物物理学中,越来越多的现象是由于分段确定性的动力系统与连续时间马氏过程之间的耦合作用而产生的.因为这种耦合性,相关的数学模型更适合取为随机混合系统而不是扩散过程(基于It?o随机微分方程).本文从理论上和数值上研究了在弱噪声条件下无鞍点状态的随机混合Morris-Lecar系统中,由通道噪声诱导的自发性放电现象.一个动作电位的初始阶段可视为噪声诱导的逃逸事件,其最优路径和拟势可由辅助Hamilton系统给出.由于系统不存在鞍点,因此可选择虚拟分界线(ghost separatrix)为阈值,研究噪声诱导的自静息态的逃逸事件.通过计算在阈值处的拟势,便可发现其值有一个明显的最小值,其作用类似于鞍点.通过改进的Monte Carlo模拟方法,计算了历程概率分布,其结果对初始阶段和兴奋阶段的理论解均给出了验证.此外,基于前人将拟势等高线作为阈值的另一种选择,我们对两种阈值取法的优劣性进行了比较.最后,本文研究了钠离子和钾离子通道噪声的不同组合对最优路径和拟势的影响.结果表明:钾离子通道噪声在自发性放电过程中起主导作用,且两种噪声强度存在一个最优比例能使总的噪声强度达到最小.

RESEARCH ON SPONTANEOUS ACTION POTENTIAL INDUCED BY CHANNEL NOISE IN MORRIS-LECAR SYSTEM 1)

There are a growing number of problems in biological physics involving the coupling between a piecewise deterministic dynamical system and a continuous time Markov process, which is more appropriate to be modeled as a stochastic hybrid system than a diffusion process. Specifically, we investigate the spontaneous action potential induced by channel noise in stochastic hybrid Morris-Lecar system without a saddle state both theoretically and numerically in the case of weak noise. The initiation phase of an action potential can be regarded as an event of noise induced escape, for which the optimal paths and then the quasi-potential are computed via an auxiliary Hamiltonian system. Due to the absence of the saddle point, the ghost separatrix is chosen as threshold for studying the transition events from the resting state. Through evaluating the quasi-potential on the threshold, we have found an obvious minimum that acts similarly as a saddle point. Prehistory probability distribution has been performed by improved Monte Carlo simulation, which confirmed the theoretical results for not only the initial phase but also the excitable phase. In addition, the contour line of quasi-potential as another choice of threshold selected by previous researchers has been introduced and their advantages and disadvantages are compared. Finally, the impacts on patterns of optimal paths and quasi-potential about various combinations of Na$^{+}$ and K$^{+}$ channel noise are studied thoroughly. The results shows that it is the fluctuation of K$^{+}$ channel that plays the dominant role in the process of spontaneous excitability and there exists an optimal ratio for the two channel noises which minimizes the fluctuation strength.