Journal of Mathematical Biology

, Volume 67, Issue 2, pp 239–259

The Morris–Lecar neuron model embeds a leaky integrate-and-fire model

Open Access
Article

Abstract

We show that the stochastic Morris–Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein–Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a leaky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris–Lecar firing statistics reproduces the Morris–Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of attention paid to the LIF models.

Keywords

Stochastic dynamics Diffusions Interspike intervals Conditional firing probability 

Mathematics Subject Classification

60G17 92Bxx 37N25 92C20 

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark
  2. 2.Mathematics Annex 1208VancouverCanada

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