The Morris–Lecar neuron model embeds a leaky integrate-and-fire model
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.
KeywordsStochastic dynamics Diffusions Interspike intervals Conditional firing probability
Mathematics Subject Classification60G17 92Bxx 37N25 92C20
S. Ditlevsen was supported by the Danish Council for Independent Research|Natural Sciences. P. Greenwood was supported by the Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, N.C., and the Mathematical, Computational and Modeling Sciences Center at Arizona State University. The Villum Kann Rasmussen foundation supported a 4 months visiting professorship for P. Greenwood at University of Copenhagen.
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