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Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation
Physics Letters A ( IF 2.3 ) Pub Date : 2021-04-22 , DOI: 10.1016/j.physleta.2021.127379
A.V. Paraskevov , T.S. Zemskova

The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval, there is four-stage damping of the spike amplitude: 1) minor primary damping, which reflects a typical transient to stationary dynamic state, 2) plateau of nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a constant asymptotic value of the neuron potential. We have shown that in the vicinity of the asymptote the Morris-Lecar equations can be reduced to the standard equation for exponentially damped harmonic oscillations. Importantly, all coefficients of this equation can be explicitly expressed through parameters of the original Morris-Lecar model, enabling direct comparison of the numerical and analytical solutions for the neuron potential dynamics at later stages of the spike amplitude damping.



中文翻译:

大恒定刺激下Morris-Lecar神经元模型线性方程组的解析解

神经元兴奋性的经典生物物理Morris-Lecar模型预测,当用足够大的恒定去极化电流刺激神经元时,电流值存在一定的间隔,在该间隔处会出现周期性的尖峰。在此区间的上限之上,有四个阶段的尖峰幅度阻尼:1)较小的初级阻尼,它反映了典型的从瞬态到平稳的动态状态; 2)几乎没有阻尼的周期性振荡的平稳期; 3)强阻尼;以及4)达到神经元电位的恒定渐近值。我们已经表明,在渐近线附近,Morris-Lecar方程可以简化为指数阻尼谐波振荡的标准方程。重要的,

更新日期:2021-04-22
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