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Sparse gamma rhythms arising through clustering in adapting neuronal networks

Kilpatrick, ZP and Ermentrout, B (2011) Sparse gamma rhythms arising through clustering in adapting neuronal networks. PLoS Computational Biology, 7 (11). ISSN 1553-734X

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Abstract

Gamma rhythms (30-100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons. © 2011 Kilpatrick, Ermentrout.

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Details

Item Type: Article
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Kilpatrick, ZP
Ermentrout, B
Contributors:
ContributionContributors NameEmailPitt UsernameORCID
EditorGutkin, Boris S.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Date: 1 November 2011
Date Type: Publication
Journal or Publication Title: PLoS Computational Biology
Volume: 7
Number: 11
DOI or Unique Handle: 10.1371/journal.pcbi.1002281
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Refereed: Yes
ISSN: 1553-734X
MeSH Headings: Action Potentials; Brain Waves--physiology; Cluster Analysis; Computer Simulation; Cortical Synchronization--physiology; Fourier Analysis; Humans; Interneurons; Least-Squares Analysis; Models, Neurological; Nerve Net--physiology; Pyramidal Cells
Other ID: NLM PMC3219625
PubMed Central ID: PMC3219625
PubMed ID: 22125486
Date Deposited: 07 Sep 2012 19:48
Last Modified: 20 Dec 2018 00:55
URI: http://d-scholarship.pitt.edu/id/eprint/13997

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