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Exact solutions to cable equations in branching neurons with tapering dendrites
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Yihe, Lu and Timofeeva, Yulia (2020) Exact solutions to cable equations in branching neurons with tapering dendrites. Journal of mathematical neuroscience, 10 (1). 1. doi:10.1186/s13408-020-0078-z ISSN 2190-8567.
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Official URL: https://doi.org/10.1186/s13408-020-0078-z
Abstract
Neurons are biological cells with uniquely complex dendritic morphologies that are not present in other cell types. Electrical signals in a neuron with branching dendrites can be studied by cable theory which provides a general mathematical modelling framework of spatio-temporal voltage dynamics. Typically such models need to be solved numerically unless the cell membrane is modelled either by passive or quasi-active dynamics, in which cases analytical solutions can be reduced to calculation of the Green's function describing the fundamental input-output relationship in a given morphology. Such analytically tractable models often assume individual dendritic segments to be cylinders. However, it is known that dendritic segments in many types of neurons taper, i.e. their radii decline from proximal to distal ends. Here we consider a generalised form of cable theory which takes into account both branching and tapering structures of dendritic trees. We demonstrate that analytical solutions can be found in compact algebraic forms in an arbitrary branching neuron with a class of tapering dendrites studied earlier in the context of single neuronal cables by Poznanski (Bull. Math. Biol. 53(3):457-467, 1991). We apply this extended framework to a number of simplified neuronal models and contrast their output dynamics in the presence of tapering versus cylindrical segments.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QP Physiology | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||
SWORD Depositor: | Library Publications Router | ||||||
Library of Congress Subject Headings (LCSH): | Neurons -- Mathematical models, Neurons, Computational neuroscience | ||||||
Journal or Publication Title: | Journal of mathematical neuroscience | ||||||
Publisher: | Springer UK | ||||||
ISSN: | 2190-8567 | ||||||
Official Date: | 28 January 2020 | ||||||
Dates: |
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Volume: | 10 | ||||||
Number: | 1 | ||||||
Article Number: | 1 | ||||||
DOI: | 10.1186/s13408-020-0078-z | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | ** From Europe PMC via Jisc Publications Router ** History: ppub 01-01-2020; epub 28-01-2020. ** Licence for this article: cc by | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 6 March 2020 | ||||||
Date of first compliant Open Access: | 6 March 2020 | ||||||
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