Patterns of interval correlations in neural oscillators with adaptation

• Published in: Frontiers in computational neuroscience Vol. 7; p. 164
• Main Authors: Schwalger, Tilo, Lindner, Benjamin
• Format: Journal Article
• Language: English
• Published: Switzerland Frontiers Research Foundation 29.11.2013; Frontiers Media S.A
• Subjects: Adaptation; Firing pattern; integrate-and-fire model; long-term variability; Neuroscience; Neurosciences; Noise; non-renewal process; Oscillators; phase-response curve; serial correlation coefficient; Signal processing; spike-frequency adaptation; Theory; Germany; spike-frequency adaptation; phase-response curve; non-renewal process; serial correlation coefficient; integrate-and-fire model; long-term variability
• ISSN: 1662-5188; 1662-5188
• DOI: 10.3389/fncom.2013.00164

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.