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Democratization in a passive dendritic tree : an analytical investigation

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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. ISSN 0929-5313

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Official URL: http://dx.doi.org/10.1007/s10827-008-0075-9

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

Identification Number:

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)

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