Timofeeva, Yulia, Cox, S. J., Coombes, Stephen and Josić, Krešimir (2008) Democratization in a passive dendritic tree : an analytical investigation. Journal of Computational Neuroscience, Vol.25 (No.2). pp. 228-244. doi:10.1007/s10827-008-0075-9

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH):	Dendritic trees
Journal or Publication Title:	Journal of Computational Neuroscience
Publisher:	Springer New York LLC
ISSN:	0929-5313
Official Date:	6 February 2008
Dates:	Date Event 6 February 2008 Published
Volume:	Vol.25
Number:	No.2
Page Range:	pp. 228-244
DOI:	10.1007/s10827-008-0075-9
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), National Science Foundation (U.S.) (NSF), Norman Hackerman Advanced Research Program (NHARP)
Grant number:	GR/R76219 (EPSRC), DMS-0604429 (NSF)

Data sourced from Thomson Reuters' Web of Knowledge

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