The University of Southampton
University of Southampton Institutional Repository

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials
A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials
By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson–Nernst–Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin–Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies
action potential, matched asymptotic expansions, electrolyte, hodgkin–huxley model, poisson–nernst–planck equations
1477-8599
201-224
Richardson, G.
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Richardson, G.
3fd8e08f-e615-42bb-a1ff-3346c5847b91

Richardson, G. (2009) A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials. Mathematical Medicine and Biology, 26 (3), 201-224. (doi:10.1093/imammb/dqn027). (PMID:19273492)

Record type: Article

Abstract

By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson–Nernst–Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin–Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies

Text
Mathematical_Medicine_and_Biology_2009_Richardson.pdf - Other
Download (1MB)

More information

Published date: September 2009
Keywords: action potential, matched asymptotic expansions, electrolyte, hodgkin–huxley model, poisson–nernst–planck equations
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 69572
URI: http://eprints.soton.ac.uk/id/eprint/69572
ISSN: 1477-8599
PURE UUID: 72577bc4-7d9a-43ed-bd97-6d97b5b165d5

Catalogue record

Date deposited: 19 Nov 2009
Last modified: 07 Jan 2022 23:41

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×