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main.m
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main.m
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% A simplified implementation version of the model from:
% A Model for Growth of a Single Fungal Hypha Based on Well-Mixed Tanks
% in Series: Simulation of Nutrient and Vesicle Transport in Aerial Reproductive Hyphae
% AUTHORS: Balmant, W. et al., PLoS One 10, e0120307 (2015).
% ________________________________________________________________________
% Implementation by: Leandro A. Scholz (leandro dot a dot scholz at gmail dot com)
% MSc. in Chemical Engineering
% Federal University of Paraná
% Date: September 28th 2018
%
% ________________________________________________________________________
% KEY INPUT PARAMETERS
%
% N - Initial number of tanks
% Nv - Number of vesicle producing tanks
N = 50;
Nv = 30;
% OTHER INPUT PARAMETERS
%
% A - Cross sectional area of the hypha - dm^2
A = 1e-8;
% A0 - Cross sectional area of the source tank - dm^2
% D - Difusivity of nutrient inside the hypha - dm^2.h^-1
D = 2.48e-4;
% kc - maximum rate of vesicle consumption - g-vesicles.h^-1
kc = 2e-8;
% Kc - saturation constant for vesicle consumption - g-vesicles.dm^-3
Kc = 400;
% kp - Maximum rate of vesicle production - g-vesicles.dm^-3.h^-1
kp = 1000;
% Kp - saturation constant for vesicle production - g-vesicles.dm^-3
Kp = 10;
% m - maintenance coefficient of the hypha for nutrient - g-nutrient.g-biomass^-1.h^-1
m = 1.8e-3;
% w0 - concentration of nutrient in the source tank - g-nutrient.dm^-3
w0 = 5;
% v - convective velocity inside the hypha - dm.h^-1
v = 0.026;
% Yl - extension of hyphal length per mass of vesicles consumed - dm.g-vesicles^-1
Yl = 1e6;
% Yphi - Yield coefficient for production of vesicles from nutrient - g-vesicles.g-nutrient^-1
Yphi = 0.5;
% Deltax - length of the side of each cubic tank - dm
Deltax = 1e-4;
% lambda - Maximum possible length of the vesicle producing zone - micrometers
lambda = Nv * Deltax;
% rhox - biomass dry weight per volume - g-biomass.dm^-3
rhox = 100;
% psi - velocity of active transport of vesicles inside the hypha - dm.h^-1
psi = 0.05;
%
%_________________________________________________________________________
% VARIABLES
%
% L - length of the tip tank
% wi - concentration of nutrient in tank i
% phi_i - concentration of vesicles in tank i
% n - number of tanks present in the hypha at any time at time t=0 -> n=N
%
% The number of equations to solve depends on n
% Number of equations = 2*n + 1
% anonymous function that is just a function of t and the variables to solve
% for, not the input parameters.
F=@(t,y) HyphalTanks(t,y,N,Nv,A,D,kc,Kc,kp,Kp,m,w0,v,Yl,Yphi,Deltax,rhox,psi);
% initial conditions
y0=zeros(1,2*N+1);
y0(end)= Deltax;
%time span
tspan=0:0.01:0.3;
[t,y,]=ode45(F, tspan, y0);