A simple neuronal model with intrinsic saturation of the firing frequency

We present a comparison of the intrinsic saturation of firing frequency in four simple neural models: leaky integrate-and-fire model, leaky integrate-and-fire model with reversal potentials, two-point leaky integrate-and-fire model, and a two-point leaky integrate-and-fire model with reversal potentials. "Two-point" means that the equivalent circuit has two nodes (dendritic and somatic) instead of one (somatic only). The results suggest that the reversal potential increases the slope of the "firing rate vs input" curve due to a smaller effective membrane time constant, but does not necessarily induce saturation of the firing rate. The two-point model without the reversal potential does not limit the voltage or the firing rate. In contrast to the previous models, the two-point model with the reversal potential limits the asymptotic voltage and the firing rate, which is the main result of this paper. The case of excitatory inputs is considered first and followed by the case of both excitatory and inhibitory inputs.