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.
References:
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; Olfaction;
Implementer(s): Graham, Bruce [B.Graham at cs.stir.ac.uk];
% Continuum Model for Neurite Outgrowth
% Main m-file
% Comparison of steady-state lengths with Miller & Samuels, Table 1
% Version 1.0 (BPG & DRM 19-1-05)

% Parameters

% simulation
simp.dt = 0.01;                  % time step
simp.tmax = 2000;                  % simulation time
simp.datat = 100;                 % data collection time step
simp.N = 100;                     % number of spatial points
simp.kmax = 10000;               % maximum corrector steps
simp.mc = 0.0001;              % tolerance on C;
simp.ml = 0.0001;              % tolerance on l;

% user-defined
modp.c0 = 10;                     % concentration scale
modp.l0 = 0.01;                   % initial (min) length;
modp.D = 30000;                    % diffusion constant
modp.a = 100;                      % active transport rate
modp.g = 0.002;                    % decay rate
modp.rg = 10;                   % growth rate constant
modp.sg = 100;                   % growth rate set point (threshold)
k1 = 0.5;
k2 = 0.00001;
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);                  % soma flux-source rate
modp.el = k2*modp.rg;                   % growth cone flux-sink rate
modp.zl = k2*modp.sg;                   % growth cone flux-source rate
%modp.g = 0;                    % decay rate


% Run 1: Garfish olfactory
modp.a = 2.38*1000/24;             % active transport rate (um/hr)
T05 = 75*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.34;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp

% Run 2: Rat sciatic
modp.a = 1.2*1000/24;             % active transport rate (um/hr)
T05 = 51*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.2;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp

% Run 3: Rabbit optic
modp.a = 2*1000/24;             % active transport rate (um/hr)
T05 = 14*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.55;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp

% Run 4: Mouse optic
modp.a = 0.6*1000/24;             % active transport rate (um/hr)
T05 = 20*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.65;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp

% Run 5: Goldfish optic
modp.a = 0.4*1000/24;             % active transport rate (um/hr)
T05 = 67*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.85;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp

% Run 6: Blue whale (Alvarez et al)
modp.a = 7*1000/24;             % active transport rate (um/hr)
T05 = 730*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.14;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp

% Run 7: Blue whale (Alvarez et al) - version 2: higher production
modp.a = 4*1000/24;             % active transport rate (um/hr)
T05 = 500*24;                       % half-life (hours)
modp.g = 1/(T05/log(2));           % decay rate (per hour)
k1 = 0.006;                          % alpha_twid_h
modp.e0 = modp.g*modp.sg/(k1*modp.c0*modp.rg*modp.a);  % soma flux rate
% calculated parameters
[calcp] = CMNG_calcparams(simp, modp);
% run model for jmax time steps, linear ICs, no retraction
%[C1, C01, CN1, l1] = CMNG_rundyn(simp, modp, calcp, 0, 0);
%Ca1 = [C01 C1 CN1];
% get analytical steady-state values (note: not valid for ah=1)
[Cinfa1, linfa1] = CMNG_lCanal(simp, modp, calcp, 0);
linfa1 = linfa1*(modp.D/(modp.rg*modp.c0))/1000     % mm
Cinfa1 = Cinfa1*modp.c0;
ah1 = calcp.gamma*calcp.beta/(calcp.phi*calcp.alpha)
modp


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