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];
% make_graphs.m
% these were not the original commands to make paper figures but
% make figures that resemble three in the paper:
% Fig 2a, 2b, 3b

%%% Axon length, l %%%

plot(t/24/3600, l*1000)
title('Fig 2a')
xlabel('Time [days]')
ylabel('Axon length [mm]')

%%% Concentration along the axon, c %%%

% Down-sampling of the solution for cheaper 3D-plot.
ndisp = 10; % In time by a factor 10.
ndispy = 10; % In space by a factor 10.

y_down = [0; y(ndispy:ndispy:end-ndispy+1); 1];
x3D = 1000*[l0; l(ndisp:ndisp:end)]*y_down';
t_down = [0; t(ndisp:ndisp:end)];
css = zeros(1,size(x3D,1));
for kk = 1:length(css)
    css(kk) = cs(t_down(kk),cs0);
c_down = [css; ...
    cinit(y_down(2:end-1)) c(ndispy:ndispy:end-ndispy+1,ndisp:ndisp:end); ...
    [cc(1); cc(ndisp:ndisp:end)]'];

mesh(x3D, t_down/24/3600, c_down')
title('Fig 2b')
xlabel('x [mm]')
ylabel('Time [days]')
zlabel('Concentration [mol/m^3]')

%%% Growth cone concentration, cc %%%

axis([0 3500 0.01 0.024])
grid on
title('Fig 3b')
xlabel('Time [s]')
ylabel('Growth cone concentration [mol/m^3]')

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