Spontaneous activity from stochastic ion channels in the Morris-Lecar model of a neuron

Jay Newby
Mathematical Biosciences Institute, The Ohio State University

(January 24, 2013 10:20 AM - 11:15 AM)

Spontaneous activity from stochastic ion channels in the Morris-Lecar model of a neuron

Abstract

A stochastic interpretation of spontaneous action potential initiation is developed for the Morris-Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method.  Using the fact that the activating ionic channel's random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current.  Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used.  We also explore why different diffusion approximation techniques fail to estimate the MFT.