Correlation transfer in stochastically driven oscillators over long and short time scales

TL;DR

This paper analytically investigates how neural oscillators transfer input correlations to output spike correlations over different time scales, revealing the influence of phase resetting curves and oscillator types.

Contribution

It derives new analytical expressions linking phase resetting curve properties to correlation transfer over long and short time scales in neural oscillators.

Findings

Output correlation scales with phase resetting curve autocorrelation over long time scales.

Shape of phase resetting curve affects initial slope of correlation over short time scales.

Type I oscillators transfer correlations more faithfully over long time scales than Type II.

Abstract

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics, but also depends on the length of the observation window over which the correlation is calculated. In this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales, a quantity which provides a convenient proxy for the spike count correlation. Over short time scales, we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference. Our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales. We also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales. These analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type I oscillators transfer correlations more faithfully than do type II over long time scales, while the reverse holds true for the better understood case of short time scales.