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Toward a minimal model of a large spiking cell

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Experimentalists will soon be able to ascertain the highly nonuniform morphology and channel distributions of the large, pyramidal cells that populate the mammalian cortex. This advance is captured and quantified via tens of thousands of coupled nonlinear ordinary differential equations, per cell. The circuit modeler then asks, "How many of these equations must I keep in order to guarantee a fixed level of accuracy in the input-output map?" We demonstrate that the combined application of Balanced Truncation [1] to the weakly excitable portion of the tree and Principal Orthogonal Decomposition and the Discrete Empirical Interpolation Method [2] to the strongly excitable portion of the cell permit one to reduce the system size by more than one order of magnitude and decrease simulation time by a factor of 5 without sacrificing synaptic specificity in space or time.

References

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    Kellems AR, Roos D, Xiao N, Cox SJ: Low-dimensional, morphologically accurate models of subthreshold membrane potential. J Comput Neurosci. 2009, 27: 161-176. 10.1007/s10827-008-0134-2.

  2. 2.

    Kellems AR, Chaturantabut S, Sorensen DC, Cox SJ: Morphologically accurate reduced order modeling of spiking neurons,. TR09-12, CAAM, Rice U. 2009, [http://www.caam.rice.edu/tech_reports/2009/TR09-12.pdf]

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Acknowledgements

NIBIB Grant No. 1T32EB006350-01A1

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Correspondence to Steven J Cox.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kellems, A.R., Cox, S.J. Toward a minimal model of a large spiking cell. BMC Neurosci 11, P145 (2010) doi:10.1186/1471-2202-11-S1-P145

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Keywords

  • Pyramidal Cell
  • Minimal Model
  • Circuit Model
  • Channel Distribution
  • Combine Application