Patterns of interval correlations in neural oscillators with adaptation

TL;DR

This paper analytically investigates how adaptation currents in neural oscillators induce interval correlations, revealing their relation to phase-response curves and voltage dynamics, with implications for spike train variability.

Contribution

It provides a general analytical framework linking interval correlations to phase-response curves and voltage traces in noisy neural oscillators with adaptation.

Findings

Neighboring intervals are anti-correlated in adapting neurons with type I PRC.

Correlation structures are related to voltage trace patterns after spikes.

Long-term spike train variability decreases at high firing rates regardless of model details.

Abstract

Neural firing is often subject to negative feedback by adaptation currents. These currents can induce strong correlations among the time intervals between spikes. Here we study analytically the interval correlations of a broad class of noisy neural oscillators with spike-triggered adaptation of arbitrary strength and time scale. Our weak-noise theory provides a general relation between the correlations and the phase-response curve (PRC) of the oscillator, proves anti-correlations between neighboring intervals for adapting neurons with type I PRC and identifies a single order parameter that determines the qualitative pattern of correlations. Monotonically decaying or oscillating correlation structures can be related to qualitatively different voltage traces after spiking, which can be explained by the phase plane geometry. At high firing rates, the long-term variability of the spike train associated with the cumulative interval correlations becomes small, independent of model details. Our results are verified by comparison with stochastic simulations of the exponential, leaky, and generalized integrate-and-fire models with adaptation.