We showthat 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 detailedMorris–Lecar firing statistics reproduces theMorris–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.
Journal of Mathematical Biology, 2013, Vol 67, Issue 2, p. 239-259