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A one-dimensional moving-boundary model for tubulin-driven axonal growth.

Diehl, Stefan LU ; Henningsson, Erik LU ; Heyden, Anders LU and Perna, S (2014) In Journal of Theoretical Biology 358(Online 21 June 2014). p.194-207
Abstract
A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential equation models the dynamic and the spatial behaviour of the concentration of tubulin that is transported along the axon from the soma to the growth cone. Two ordinary differential equations describe the time-variation of the concentration of free tubulin in the growth cone and the speed of elongation. All steady-state solutions of the model are categorized. Given a set of the biological parameter values, it is shown how one easily can infer whether there exist zero, one or two steady-state solutions and... (More)
A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential equation models the dynamic and the spatial behaviour of the concentration of tubulin that is transported along the axon from the soma to the growth cone. Two ordinary differential equations describe the time-variation of the concentration of free tubulin in the growth cone and the speed of elongation. All steady-state solutions of the model are categorized. Given a set of the biological parameter values, it is shown how one easily can infer whether there exist zero, one or two steady-state solutions and directly determine the possible steady-state lengths of the axon. Explicit expressions are given for each stationary concentration distribution. It is thereby easy to examine the influence of each biological parameter on a steady state. Numerical simulations indicate that when there exist two steady states, the one with shorter axon length is unstable and the longer is stable. Another result is that, for nominal parameter values extracted from the literature, in a large portion of a fully grown axon the concentration of free tubulin is lower than both concentrations in the soma and in the growth cone. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Neurite elongation, Partial differential equation, Steady state, Polymerization, Microtubule cytoskeleton
in
Journal of Theoretical Biology
volume
358
issue
Online 21 June 2014
pages
194 - 207
publisher
Academic Press
external identifiers
  • pmid:24956328
  • wos:000340336900016
  • scopus:84905394413
ISSN
1095-8541
DOI
10.1016/j.jtbi.2014.06.019
language
English
LU publication?
yes
id
a8661f91-1cda-494b-8966-e4f4e3d55461 (old id 4527068)
date added to LUP
2014-08-21 15:31:55
date last changed
2017-02-13 13:14:09
@article{a8661f91-1cda-494b-8966-e4f4e3d55461,
  abstract     = {A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential equation models the dynamic and the spatial behaviour of the concentration of tubulin that is transported along the axon from the soma to the growth cone. Two ordinary differential equations describe the time-variation of the concentration of free tubulin in the growth cone and the speed of elongation. All steady-state solutions of the model are categorized. Given a set of the biological parameter values, it is shown how one easily can infer whether there exist zero, one or two steady-state solutions and directly determine the possible steady-state lengths of the axon. Explicit expressions are given for each stationary concentration distribution. It is thereby easy to examine the influence of each biological parameter on a steady state. Numerical simulations indicate that when there exist two steady states, the one with shorter axon length is unstable and the longer is stable. Another result is that, for nominal parameter values extracted from the literature, in a large portion of a fully grown axon the concentration of free tubulin is lower than both concentrations in the soma and in the growth cone.},
  author       = {Diehl, Stefan and Henningsson, Erik and Heyden, Anders and Perna, S},
  issn         = {1095-8541},
  keyword      = {Neurite elongation,Partial differential equation,Steady state,Polymerization,Microtubule cytoskeleton},
  language     = {eng},
  number       = {Online 21 June 2014},
  pages        = {194--207},
  publisher    = {Academic Press},
  series       = {Journal of Theoretical Biology},
  title        = {A one-dimensional moving-boundary model for tubulin-driven axonal growth.},
  url          = {http://dx.doi.org/10.1016/j.jtbi.2014.06.019},
  volume       = {358},
  year         = {2014},
}