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Democratization in a passive dendritic tree: An analytical investigation

Timofeeva, Yulia; Cox, Steven J.; Coombes, S.; Josic, Kresimir

Authors

Yulia Timofeeva y.timofeeva@warwick.ac.uk

Steven J. Cox cox@rice.edu

Kresimir Josic josic@math.uh.edu



Abstract

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as "dendritic democracy". Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green's representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius. © Springer Science+Business Media, LLC 2008.

Citation

José, K., Cox, S. J., Timofeeva, Y., Timofeeva, Y., Cox, S. J., Coombes, S., & Josic, K. (2008). Democratization in a passive dendritic tree: An analytical investigation. Journal of Computational Neuroscience, 25(2), 228-244. https://doi.org/10.1007/s10827-008-0075-9

Journal Article Type Article
Acceptance Date Jan 16, 2008
Online Publication Date Feb 6, 2008
Publication Date Feb 6, 2008
Deposit Date Jan 18, 2008
Journal Journal of Computational Neuroscience
Print ISSN 0929-5313
Electronic ISSN 0929-5313
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 25
Issue 2
Pages 228-244
DOI https://doi.org/10.1007/s10827-008-0075-9
Keywords dendritic democracy
cable equation
shunts
Public URL http://eprints.nottingham.ac.uk/id/eprint/774
Publisher URL https://link.springer.com/article/10.1007%2Fs10827-008-0075-9
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information The original publication is available at www.springerlink.com

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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