Axon growth model (Diehl et al. 2016)

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The model describes the elongation over time of an axon from a small neurite to its steady-state length. The elongation depends on the availability of tubulin dimers in the growth cone. The dimers are produced in the soma and then transported along the axon to the growth cone. Mathematically the model consists of a partial differential equation coupled with two nonlinear ordinary differential equations. The code implements a spatial scaling to deal with the growing (and shrinking) domain and a temporal scaling to deal with evolutions on different time scales. Further, the numerical scheme is chosen to fully utilize the structure of the problems. To summarize, this results in fast and reliable axon growth simulations.
1 . Diehl S, Henningsson E, Heyden A (2016) Efficient simulations of tubulin-driven axonal growth. J Comput Neurosci 41:45-63 [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):
Gap Junctions:
Simulation Environment: MATLAB;
Model Concept(s): Parameter sensitivity; Development;
Implementer(s): Henningson, Erik [erikh at];
% parameter_studies.m
% This script gives an example on how the code can be used to perform
% parameter studies. This code will run the main file five times for
% different values on the degredation rate g and reproduce Fig. 9 of 
% the original paper.
% Note: For faster simulations for the extreme values of g
% the preallocation guess is increased in the main file:
%   axon_growth_simulations_with_time_and_space_scaling.m
%   line 129 is selected: where N_guess is round(2000/k);
% The code will take several minutes to run since, for big values of g, the
% axon never growths very long and therefore really big time steps (in
% original time) are never taken. A solution might be to run these 
% simulations with a bigger time step (in scaled time), denoted by k in the
% main file.
% Erik Henningsson
% May, 2016
% Lund University, Sweden

close all

gs = [1/2 1 2 4 8]*5e-7;

hold on
colors = 'bcrgm';
for iii = 1:length(gs)
    g = gs(iii);
    disp(['Starting simulation with g = ' num2str(g) '.'])
    hold_off = true; % prevents clearing and closing in axon_...
    hold on
    plot(t/24/3600, l*1000, colors(iii))

title('Fig 9')
xlabel('Time [days]')
ylabel('Axon length [mm]')

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