The firing statistics of Poisson neuron models driven by slow stimuli

TL;DR

This paper derives analytical expressions for firing statistics of Poisson neuron models with different receptive fields driven by slow stimuli, elucidating how intrinsic properties and input signals influence spike train variability.

Contribution

It provides new analytical formulas linking stimulus characteristics and receptive field types to neuron firing statistics, enhancing understanding of neural coding.

Findings

Derived expressions for peri-stimulus time histogram and inter-spike interval distribution.

Showed how stimulus dynamics and receptive field types shape spike train variability.

Clarified the roles of intrinsic neural properties and input signals in spike train regulation.

Abstract

The coding properties of cells with different types of receptive fields have been studied for decades. ON-type neurons fire in response to positive fluctuations of the time-dependent stimulus, whereas OFF cells are driven by negative stimulus segments. Biphasic cells, in turn, are selective to up/down or down/up stimulus upstrokes. In this paper, we explore the way in which different receptive fields affect the firing statistics of Poisson neuron models, when driven with slow stimuli. We find analytical expressions for the time-dependent peri-stimulus time histogram and the inter-spike interval distribution in terms of the incoming signal. Our results enable us to understand the interplay between the intrinsic and extrinsic factors that regulate the statistics of spike trains. The former depend on biophysical neural properties, whereas the latter hinge on the temporal characteristics of the input signal.