Skip Navigation


Mathematical Medicine and Biology Advance Access originally published online on May 3, 2006
Mathematical Medicine and Biology 2006 23(2):101-117; doi:10.1093/imammb/dql010
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
23/2/101    most recent
dql010v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by McLean, D. R.
Right arrow Articles by Graham, B. P.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by McLean, D. R.
Right arrow Articles by Graham, B. P.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Stability in a mathematical model of neurite elongation

Douglas R. McLean** and Bruce P. Graham

Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, UK

** Email: drm{at}maths.stir.ac.uk

We have developed a continuum partial differential equation model of tubulin-driven neurite elongation and solved the steady problem. For non-zero values of the decay coefficient, the authors identified three different regimes of steady neurite growth, small, moderate and large, dependent on the strength of the tubulin flux into the neurite at the soma. Solution of the fully time-dependent moving boundary problem is, however, hampered by its analytical intractibility. A linear instability analysis, novel to moving boundary problems in this context, is possible and reduces to finding the zeros of an eigen-condition function. One of the system parameters is small and this permits solutions to the eigen-condition equation in terms of asymptotic series in each growth regime. Linear instability is demonstrated to be absent from the neurite growth model and a Newton–Raphson root-finding algorithm is then shown to corroborate the asymptotic results for some selected examples. By numerically integrating the fully non-linear time-dependent system, we show how the steady solutions are non-linearly stable in each of the three growth regimes with decay and oscillatory behaviour being as predicted by the linear eigenvalue analysis.

Keywords: neurite elongation; tubulin; moving boundary problem; linear instability; non-linear stability

Received on 5 September 2005. revised on 6 February 2006. accepted on 29 March 2006.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.