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Travelling waves in a model of quasi-active dendrites with active spines

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Timofeeva, Yulia. (2010) Travelling waves in a model of quasi-active dendrites with active spines. Physica D: Nonlinear Phenomena, Vol.239 (No.9). pp. 494-503. ISSN 0167-2789

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Official URL: http://dx.doi.org/10.1016/j.physd.2010.01.004

Abstract

Dendrites, the major components of neurons, have many different types of branching structures and are involved in receiving and integrating thousands of synaptic inputs from other neurons. Dendritic spines with excitable channels can be present in large densities on the dendrites of many cells. The recently proposed Spike-Diffuse-Spike (SDS) model that is described by a system of point hot-spots (with an integrate-and-fire process) embedded throughout a passive tree has been shown to provide a reasonable caricature of a dendritic tree with supra-threshold dynamics. Interestingly, real dendrites equipped with voltage-gated ion channels can exhibit not only supra-threshold responses, but also sub-threshold dynamics. This sub-threshold resonant-like oscillatory behaviour has already been shown to be adequately described by a quasi-active membrane. In this paper we introduce a mathematical model of a branched dendritic tree based upon a generalisation of the SDS model where the active spines are assumed to be distributed along a quasi-active dendritic structure. We demonstrate how solitary and periodic travelling wave solutions can be constructed for both continuous and discrete spine distributions. In both cases the speed of such waves is calculated as a function of system parameters. We also illustrate that the model can be naturally generalised to an arbitrary branched dendritic geometry whilst remaining computationally simple. The spatio-temporal patterns of neuronal activity are shown to be significantly influenced by the properties of the quasi-active membrane. Active (sub- and supra-threshold) properties of dendrites are known to vary considerably among cell types and animal species, and this theoretical framework can be used in studying the combined role of complex dendritic morphologies and active conductances in rich neuronal dynamics.

Item Type:	Journal Article
Subjects:	R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
Divisions:	Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH):	Dendrites -- Research, Membranes (Biology) -- Electric properties, Synapses -- Research, Neural transmission, Neural circuitry
Journal or Publication Title:	Physica D: Nonlinear Phenomena
Publisher:	Elsevier BV
ISSN:	0167-2789
Date:	1 March 2010
Volume:	Vol.239
Number:	No.9
Page Range:	pp. 494-503
Identification Number:	10.1016/j.physd.2010.01.004
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/3176