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


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.


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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