function dx =
modele(t,x)
% This function defines the ordinary differential
equations that provide
% a large scale description of our system.
%
% CALL: [dx] = modele(t, x)
% t = scalar value, time
% x = vector representing the concentrations of
the genes ( 5 genes )
% dx =
derivative of the concentrations
%
% This function uses the following formalism
dx=x'=f(x)
%
% x(1) : FlhDC
% x(2) : FliA
% x(3) : Z1 / FliL
% x(4) :
Z2 / FlgA
% x(5) :
Z3 / FlhB
% x(6) :
AHL - interieur
% x(7) :
AHL - exterieur
% x(8) : mTetR
% x(9) : TetR
%% Parameters
%prop=1e8;
% Beta3=400;
% k=0.1;
g=1;%
degradation rate
Beta(1)=50;
Beta(2)=1200;
Beta(3)=150;
Beta(4)=100;
Beta2(1)=0;
Beta2(2)=250;
Beta2(3)=300;
Beta2(4)=350;
kappa=20;
n=1;
ks0=1;
ks1=0.01;
eta=2;
kse=0;
etaext=2;
BetaTet=1;
%% Auxilliary Function, describing a decreasing step
function
function xs = f(x)
seuil=20000;
Beta3=100;%ptet activity in the
absence of repressor
if x>seuil
xs=0;
else
xs=Beta3;
end
end
%% ODE%
% x(1) : FlhDC
% x(2) : FliA
% x(3) : Z1 / FliL
% x(4) : Z2 / FlgA
% x(5) : Z3 / FlhB
% x(6) :
AHL - interieur
% x(7) :
AHL - exterieur
% x(8) : mTetR
% x(9) : TetR
x=max(x,0);
dx(1)=-g*x(1)+f(x(5));
dx(2)=Beta2(1)*x(2) + Beta(1)*x(1) - g*x(2);
dx(3)=Beta2(2)*x(2) + Beta(2)*x(1) - g*x(3);
dx(4)=Beta2(3)*x(2) + Beta(3)*x(1) - g*x(4);
dx(5)=Beta2(4)*x(2) + Beta(4)*x(1) - g*x(5);
dx(6)=-ks0*x(6) +
ks1*x(5) - eta * (x(6) - x(7));
dx(7)= -kse*x(7) +
etaext * (x(6)-x(7));
dx(8)=-x(8) +
kappa * x(6) /( 1 + x(6));
dx(9)=BetaTet*(x(8)-x(9));
dx=dx(:);
end
"
