Patterns of interval correlations in neural oscillators with adaptation

Frontiers in Computational Neuroscience
Tilo Schwalger, Benjamin Lindner

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.

Citations

May 6, 2015·Journal of Computational Neuroscience·Tilo SchwalgerBenjamin Lindner
Dec 23, 2014·Current Opinion in Neurobiology·Carmen C Canavier
Sep 16, 2014·Frontiers in Computational Neuroscience·Robert RosenbaumRubén Moreno-Bote
Dec 3, 2016·Journal of Computational Neuroscience·Stephen R MeierJoseph M Starobin
Apr 20, 2017·PLoS Computational Biology·Tilo SchwalgerWulfram Gerstner
Jun 23, 2018·PLoS Computational Biology·Alex D Bird, Magnus J E Richardson
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tilo Schwalger, Benjamin Lindner
Jun 18, 2017·Physical Review. E·Wilhelm BraunAndré Longtin
Apr 20, 2019·Physical Review. E·Wilhelm Braun, André Longtin
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Moritz DegerWulfram Gerstner
Sep 19, 2020·Physical Review. E·Bastian PietrasTilo Schwalger
Dec 1, 2020·Neural Computation·William H NesseAndré Longtin
Apr 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Justus A KromerLutz Schimansky-Geier

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