An embedded network approach for scale-up of fluctuation-driven systems with preservation of spike information

David Cai, Louis Tao, David W. McLaughlin

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Abstract

To address computational "scale-up" issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information and, thus, cannot be used to investigate, e.g., cortical mechanisms that are encoded through detailed spike-timing statistics. To retain high-order statistical information of spikes, we develop a hybrid theoretical framework that embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We use a newly developed kinetic theory for the description of the coarse-grained background, in combination with a Poisson spike reconstruction procedure to ensure that our method applies to the fluctuation-driven regime as well as to the mean-driven regime. This embedded-network approach is verified to be dynamically accurate and numerically efficient. As an example, we use this embedded representation to construct "reverse-time correlations" as spiked-triggered averages in a ring model of orientation-tuning dynamics.

Original languageEnglish (US)
Pages (from-to)14288-14293
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume101
Issue number39
DOIs
StatePublished - Sep 28 2004

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Neurons

ASJC Scopus subject areas

  • Genetics
  • General

Cite this

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abstract = "To address computational {"}scale-up{"} issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information and, thus, cannot be used to investigate, e.g., cortical mechanisms that are encoded through detailed spike-timing statistics. To retain high-order statistical information of spikes, we develop a hybrid theoretical framework that embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We use a newly developed kinetic theory for the description of the coarse-grained background, in combination with a Poisson spike reconstruction procedure to ensure that our method applies to the fluctuation-driven regime as well as to the mean-driven regime. This embedded-network approach is verified to be dynamically accurate and numerically efficient. As an example, we use this embedded representation to construct {"}reverse-time correlations{"} as spiked-triggered averages in a ring model of orientation-tuning dynamics.",
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