  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.
