Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions

Article

Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2009. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions." Journal of Mathematical Biology. 59 (6), pp. 761-808. https://doi.org/10.1007/s00285-009-0251-1
Article Title

Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions

ERA Journal ID929
Article CategoryArticle
AuthorsLanglands, Trevor (Author), Henry, B. I. (Author) and Wearne, S. L. (Author)
Journal TitleJournal of Mathematical Biology
Journal Citation59 (6), pp. 761-808
Number of Pages48
Year2009
Place of PublicationGermany
ISSN0303-6812
1432-1416
Digital Object Identifier (DOI)https://doi.org/10.1007/s00285-009-0251-1
Web Address (URL)https://link.springer.com/article/10.1007/s00285-009-0251-1
Abstract

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates
are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.

Keywordsdendrite, cable equation, anomalous diffusion, fractional derivative
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
490410. Partial differential equations
490102. Biological mathematics
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsUniversity of New South Wales
Icahn School of Medicine at Mount Sinai, United States
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