Onset of negative interspike interval correlations in adapting neurons

TL;DR

This paper analytically investigates how adaptation currents in neurons induce negative interspike interval correlations, reducing spike train variability, using a hidden Markov model and statistical analysis.

Contribution

It provides an analytical derivation of serial correlation coefficients in adapting neuron models, revealing universal behavior under small adaptation conditions.

Findings

Negative serial correlations reduce spike count variability.

Correlations depend on the first-order statistics of the process.

Analytical expressions are derived for arbitrary lag correlations.

Abstract

Negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts. One of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents. In this work, based on a hidden Markov model and a proper statistical description of conditional responses, we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation. We derive the serial correlation coefficients for arbitrary lags, under a small adaptation scenario. In this case, the behavior of correlations is universal and depends on the first-order statistical description of an exponentially driven time-inhomogeneous stochastic process.