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.

Fano Factor: A Potentially Useful Information.

The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently.

The Jacobi diffusion process as a neuronal model.

The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined.

Statistics of inverse interspike intervals: The instantaneous firing rate revisited.

The rate coding hypothesis is the oldest and still one of the most accepted and investigated scenarios in neuronal activity analyses. However, the actual neuronal firing rate, while informally understood, can be mathematically defined in several different ways. These definitions yield distinct results; even their average values may differ dramatically for the simplest neuronal models.

On two diffusion neuronal models with multiplicative noise: The mean first-passage time properties.

Two diffusion processes with multiplicative noise, able to model the changes in the neuronal membrane depolarization between two consecutive spikes of a single neuron, are considered and compared. The processes have the same deterministic part but different stochastic components. The differences in the state-dependent variabilities, their asymptotic distributions, and the properties of the first-passage time across a constant threshold are investigated.