title: Patterns of interval correlations in neural oscillators with adaptation.
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.
authors.affiliation: Bernstein Center for Computational Neuroscience Berlin, Germany ; Department of Physics, Humboldt Universität zu Berlin Berlin, Germany.
authors.forename: Tilo
authors.initials: T
authors.lastname: Schwalger
authors.affiliation: Bernstein Center for Computational Neuroscience Berlin, Germany ; Department of Physics, Humboldt Universität zu Berlin Berlin, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Lindner
keywords: integrate-and-fire model; long-term variability; non-renewal process; phase-response curve; serial correlation coefficient; spike-frequency adaptation