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

TL;DR

This paper demonstrates that the stochastic Morris-Lecar neuron model can be approximated by a leaky integrate-and-fire model using a radial Ornstein-Uhlenbeck process, simplifying analysis while preserving firing statistics.

Contribution

The authors introduce a new LIF-based model derived from the Morris-Lecar neuron, capturing its firing behavior with computational efficiency.

Findings

The Morris-Lecar neuron near its stable point can be approximated by a radial OU process.

The new model reproduces the Morris-Lecar ISI distribution accurately.

The model offers computational advantages similar to traditional LIF models.

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.