Spectra and waiting-time densities in firing resonant and nonresonant neurons

Abstract

The response of a neural cell to an external stimulus can follow one of the two patterns: Nonresonant neurons monotonously relax to the resting state after excitation while resonant ones show subthreshold oscillations. We investigate how do these subthreshold properties of neurons affect their suprathreshold response. Vice versa we ask: Can we distinguish between both types of neuronal dynamics using suprathreshold spike trains? The dynamics of neurons is given by stochastic FitzHugh-Nagumo and Morris-Lecar models with either having a focus or a node as the stable fixpoint. We determine numerically the spectral power density as well as the interspike interval density in response to a random (noise-like) signals. We show that the information about the type of dynamics obtained from power spectra is of limited validity. In contrast, the interspike interval density gives a very sensitive instrument for the diagnostics of whether the dynamics has resonant or nonresonant properties. For the latter value we formulate a fit formula and use it to reconstruct theoretically the spectral power density, which coincides with the numerically obtained spectra. We underline that the renewal theory is applicable to analysis of suprathreshold responses even of resonant neurons.