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arXiv · 1912.04083

Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation

A. V. Paraskevov·T. S. Zemskova
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Abstract

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.

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BibTeXRIS

A. V. Paraskevov, T. S. Zemskova. 2019-12-09. Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation. https://doi.org/10.1016/j.physleta.2021.127379

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