Transfer of correlations in neural oscillators

Abstract

Event Abstract Back to Event Transfer of correlations in neural oscillators Populations of neurons in a variety of brain regions show temporal correlations between their spike trains. A potential source of such correlations is common external input, which is transformed onto correlated output through the neural dynamics. We are interested in how particular neural dynamics will affect how these inputs are mapped into outputs; in this study we examine correlation transfer in pairs of uncoupled oscillators receiving partially correlated input. METHODS We consider two uncoupled cells, driven by both independent and common noise. As a measure of input correlation we take the fraction of noise variance that is in common, c. As a measure of output correlations we look at the normalized covariance of spike counts in a finite time window T, Rho_T. We start with a neuron model driven by sufficient background current to be intrinsically oscillating, and consider its reduction to a scalar equation for the phase characterized by a phase-resetting curve (PRC). Specifically, we consider a one-parameter set of PRCs given by the linear combination of two prototypical examples: the theta model PRC, typical of Class I excitable neurons, and the PRC near a Hopf bifurcation for a Class II excitable neuron, as demonstrated by Ermentrout (Neural Computation 1996) and Ermentrout and Kopell (SIAM J. Math Analysis 1984), among others: Z(theta) = a * (1-cos(theta)) + (1-a)*(-sin(theta)) We examine the correlation coefficient between spike counts over a time window T. For very long time (T -> infinity) we use linear response theory for renewal processes to write this quantity as the ratio of integrals related to exit time moments. We show that for a large class of models, including those under consideration, these can be computed by simple quadrature of smooth functions. We check our computations by comparison with the quadratic integrate-and-fire neuron, which is known to be equivalent to the theta model. A related procedure, in progress, will allow us to compute the same quantities for finite T. RESULTS: We find that correlation transfer over long time scales exhibits striking differences from the short-time (synchrony) correlation levels computed by Marella and Ermentrout (PRE 2008); they also differ qualitatively from the results on the linear integrate-and-fire neuron presented in de la Rocha et al. (Nature 2007, PRL 2008). We find that correlation transfer for neural oscillators is nearly independent of both input statistics (mean variance of afferent currents) and output statistics (firing rate and CV). Moreover, Class I neurons maintain a positive limiting correlation coefficient; correlation in the Class II case decays to near zero. These findings may have consequences for coding by neural oscillators over long time scales, in that stimuli that affect firing rates would nonetheless produce stimulus-independent correlations. This contrasts with the strong stimulus-dependence that holds in the excitable regime, or for neural oscillators over short time scales. REFERENCES: Full text of references is provided in the supplementary material. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Transfer of correlations in neural oscillators. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.327 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 04 Feb 2009; Published Online: 04 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.