Team:Paris/Modeling/modele

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