When is an Integrate-and-fire Neuron like a Poisson Neuron?

In the Poisson neuron model, the output is a rate-modulated Poisson process (Snyder and Miller, 1991); the time varying rate parameter ret) is an instantaneous function G[.] of the stimulus, ret) G[s(t)]. In a Poisson neuron, then, ret) gives the instantaneous firing rate-the instantaneous probability of firing at any instant t-and the output is a stochastic function of the input. In part because of its great simplicity, this model is widely used (usually with the addition of a refractory period), especially in in vivo single unit electrophysiological studies, where set) is usually taken to be the value of some sensory stimulus. In the integrate-and-fire neuron model, by contrast, the output is a filtered and thresholded function of the input: the input is passed through a low-pass filter (determined by the membrane time constant T) and integrated until the membrane potential vet) reaches threshold 8, at which point vet) is reset to its initial value. By contrast with the Poisson model, in the integrate-and-fire model the ouput is a deterministic function of the input. Although the integrate-and-fire model is a caricature of real neural dynamics, it captures many of the qualitative features, and is often used as a starting point for conceptualizing the biophysical behavior of single neurons.