Continuum model of tubulin-driven neurite elongation (Graham et al 2006)

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Accession:59581
This model investigates the elongation over time of a single developing neurite (axon or dendrite). Our neurite growth model describes the elongation of a single,unbranched neurite in terms of the rate of extension of the microtubule cytoskeleton. The cytoskeleton is not explicitly modelled, but its construction is assumed to depend on the available free tubulin at the growing neurite tip.
Reference:
1 . Graham BP, Lauchlan K, McLean DR (2006) Dynamics of outgrowth in a continuum model of neurite elongation. J Comput Neurosci 20:43-60 [PubMed]
2 . Graham BP, van Ooyen A (2006) Mathematical modelling and numerical simulation of the morphological development of neurons. BMC Neurosci 7 Suppl 1:S9 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Axon; Dendrite;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Development;
Implementer(s): Graham, Bruce [B.Graham at cs.stir.ac.uk];
  
Continuum model of tubulin-driven neurite elongation
----------------------------------------------------

This model investigates the elongation over time of a single
developing neurite (axon or dendrite).  The dynamics of outgrowth,
determined by numerical integration of the model, are explored in
the paper (to be referred to as GLM):

Bruce P. Graham, Karen Lauchlan and Douglas R. McLean, "Dynamics
of outgrowth in a continuum model of neurite elongation", Journal
of Computational Neuroscience, to appear.

Our neurite growth model describes the elongation of a single,
unbranched neurite in terms of the rate of extension of the
microtubule cytoskeleton. The cytoskeleton is not explicitly
modelled, but its construction is assumed to depend on the
available free tubulin at the growing neurite tip. A site of
tubulin production in the cell body (soma) results in a flux of
tubulin across the soma/neurite interface from where tubulin is
transported along the neurite by active transport and diffusion.
A constant, slow active transport rate is assumed. At the
distal neurite tip tubulin is consumed by microtubule assembly,
which represents the average assembly of all available
microtubules. If assembly exceeds disassembly, then the
population of microtubules increases in length, on average.  
To incorporate the effect of
somatic tubulin concentration on tubulin synthesis into the model,
the flux of tubulin across the soma/neurite interface may be
continuously autoregulated by the tubulin concentration there.
Finally, tubulin is assumed everywhere to degrade with a fixed
time constant. For simplicity we assume that this single
``degradation'' process encompasses degradation of the tubulin
dimers, a constant consumption of tubulin by microtubule assembly
along the length of the neurite, and also allows for local
synthesis of new tubulin in the neurite leading to an apparent
increase in the tubulin half-life. Microtubule
assembly proximal to the neurite tip is assumed not to contribute
to neurite elongation.

Full mathematical details of the model and the algorithm for
its numerical solution using a finite difference scheme are
given in GLM. A novelty here is that the neurite length changes
dynamically, so stretching of the spatial discretization must
be incorporated.

Steady-state analysis of the model can be found in:
McLean & Graham, Proc. Roy. Soc. Lond. A. 460:2437-2456, 2004.
McLean, Lauchlan & Graham, WSEAS Trans. Biol. and Biomed.
2:98-105, 2005.

The numerical code was developed using Matlab version 7.

Example Main Matlab file: CMNG_exampmain.m

GUI Version: CMNG_gui.fig and CMNG_gui.m

Runnable m-files for each figure in the JCN paper 
e.g. GLMpap_Figs2_3.m etc


Graham BP, Lauchlan K, McLean DR (2006) Dynamics of outgrowth in a continuum model of neurite elongation. J Comput Neurosci 20:43-60[PubMed]

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Diehl S, Henningsson E, Heyden A (2016) Efficient simulations of tubulin-driven axonal growth. J Comput Neurosci [Journal] [PubMed]

   Axon growth model (Diehl et al. 2016) [Model]

Graham BP, van Ooyen A (2006) Mathematical modelling and numerical simulation of the morphological development of neurons. BMC Neurosci 7 Suppl 1:S9 [PubMed]

   Continuum model of tubulin-driven neurite elongation (Graham et al 2006) [Model]
   Compartmental models of growing neurites (Graham and van Ooyen 2004) [Model]

Sterratt D, Graham B, Gillies A, Willshaw D (2011) Principles of Computational Modelling in Neuroscience, Cambridge University Press :1-401 [Journal]

   Principles of Computational Modelling in Neuroscience (Book) (Sterratt et al. 2011) [Model]

(58 refs)

Graham BP, van Ooyen A (2006) Mathematical modelling and numerical simulation of the morphological development of neurons. BMC Neurosci 7 Suppl 1:S9[PubMed]

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References and models that cite this paper

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Alvarez J, Giuditta A, Koenig E (2000) Protein synthesis in axons and terminals: significance for maintenance, plasticity and regulation of phenotype. With a critique of slow transport theory. Prog Neurobiol 62:1-62 [PubMed]

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   Continuum model of tubulin-driven neurite elongation (Graham et al 2006) [Model]

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   Compartmental models of growing neurites (Graham and van Ooyen 2004) [Model]

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Van Veen MP, Van Pelt J (1994) Neuritic growth rate described by modeling microtubule dynamics. Bull Math Biol 56:249-73 [PubMed]

van_Ooyen A (2003) Modeling Neural Development

Van_ooyen A, Graham B, Ramakers G (2001) Competition for tubulin between growing neurites during development Neurocomputing 38:73-78

van_Ooyen A, van_Pelt J (2002) Competition in neuronal morphogenesis and the development of nerve connections Computational Neuroanatomy: Principles and Methods, Ascoli G, ed. pp.219

Van_Pelt J, Graham B, Uylings H (2003) Formation of dendriticbranching patterns Modeling Neural Development (chapter 4), van_Ooyan A, ed. pp.75

van_Veen M, van_Pelt J (1992) A model for outgrowth of branching neurites J Theor Biol 159:1-23

Willshaw D, Price D (2003) Models for topographic map formation Modeling Neural Development, van_Ooyen A, ed. pp.213

Diehl S, Henningsson E, Heyden A (2016) Efficient simulations of tubulin-driven axonal growth. J Comput Neurosci [Journal] [PubMed]

   Axon growth model (Diehl et al. 2016) [Model]

Sterratt D, Graham B, Gillies A, Willshaw D (2011) Principles of Computational Modelling in Neuroscience, Cambridge University Press :1-401 [Journal]

   Principles of Computational Modelling in Neuroscience (Book) (Sterratt et al. 2011) [Model]

(61 refs)