Team:Colombia Uniandes/Scripting

Scripting

Glucocorticoid Detection System

Deterministic model

Equations

function y = EcuacionesGluco(t,x) global gammaGR mGRIR mCC deltaGRI alfaR deltaR deltaCC betaCC k n deltaS H

%---------Parameters------%

GRO=funcImpulso(t);

%------ Variables%------%

GRI= x(1); %Glucocorticoid inside the cell R=x(2); %Receptor in the cytoplasm CC=x(3); %Receptor -Glucocorticoid complex V=x(4); %Violacein

%---Equations---% dGRI=gammaGR*(GRO-GRI)-mGRIR*GRI*R+mCC*CC-deltaGRI*GRI; dR=alfaR-mGRIR*GRI*R+mCC*CC-deltaR*R; dCC=mGRIR*GRI*R-mCC*CC-deltaCC*CC-(betaCC*CC.^n)/(k^n+CC.^n);%Revisar dV=H*(betaCC*CC^n)/(k^n+CC^n)-deltaS*V;

y1(1)=dGRI; y1(2)=dR; y1(3)=dCC; y1(4)=dV;

y= y1';

end

Equation solver

%global gammaGR mGRIR mCC deltaGRI alfaR deltaR deltaCC betaCC k n deltaS H
%
%
gammaGR= 0.1;    %Diffussion rate of glucocorticoid inside the cell (mm/min)
%
mGRIR=1.080e-3;        % GRI-R complex formation kinetic constant (1/umol min)
%
mCC=1.14*10^-8;    %GRI-R Complex formation reverse  kinetic constant (1/min)
%
deltaGRI=0.00833;  %Glucocorticoids Destruction rate inside the cell (1/min)
%
alfaR= 0.8e3;           %Basal production rate of the receptor (umol/min) 
%
deltaR=0.004166;          %Receptor destruction rate inside the cell (1/min)
deltaCC=0.004166;  % GRI-R complex Destruction rate (1/min)
betaCC=0.5e3;     % GRI-R complex maximum expression rate (umol/min)
k=0.05e3;          %Hill's constant for the GRI-R complex dimmer binding to his respective region (umol)
n=2;               %Hill coefficient (cooperation constant)
deltaS=0.04166;   %Signal destruction rate (1/min)
H=2;               %Correction constant for the signal
%
%
%
h=60; %Tiempo maximo
%
m=0.01; %Longitud de paso [s]
%
t=0:m:h; %Vector tiempo
%
xi=[0 0 0 0];
%
y=fsolve(@CondIndGluco,xi,optimset('algorithm','levenberg-marquardt','maxiter',100000,'tolfun',1e-9));
%
conInd=y;

assignin('base','conInd',conInd); l=(0:m:h)'; %Vector de tiempo

x=zeros(length(l),length(conInd)); %Matriz de variables, en las columnas varia %la variable y en las filas varia el tiempo

GRO=zeros(1,length(l));

x(1,:)=conInd;

for u=1:length(l)-1

   xk=x(u,:); %Captura de la ultima posicion de la matirz, es decir, los
   %valores actuales de las variables
   
   k1=EcuacionesGluco(l(u),xk); %Primera pendiente del metodo de RK4
   k2=EcuacionesGluco(l(u)+m/2,xk+(m/2*k1)'); %Segunda pendiente del metodo de RK4
   k3=EcuacionesGluco(l(u)+m/2,xk+(m/2*k2)'); %Tercera pendiente del metodo de RK4
   k4=EcuacionesGluco(l(u)+m,xk+(m*k3)'); %Cuarta pendiente del metodo de RK4
   
   xk1=xk+m/6*(k1+2*k2+2*k3+k4)'; %Calculo de nuevos valores para las
   %variables
   
      
   xk2=zeros(1,length(xk1));
   
   
   for p=1:length(xk1)
       
       if(xk1(p)<0.00000001)
           
           xk2(p)=0;
       else
           
           xk2(p)=xk1(p);
       end
       
   end
   
   
   x(u+1,:)=xk2; %Actualizacion del nuevo vector de variables en la matriz
   
   
   
   
   

end

for j=1:length(l)

   if (l(j)<(10) || l(j)>(30))
       
       GRO(j)=155;
       
   else
       
       GRO(j)=155*1.3;
       
       
   end
   
   

end

GRI=x(:,1); R=x(:,2); CC=x(:,3); V=x(:,4);

figure(1) plot(l,R)%,l,GRO)%,l,CC,l,V) legend('Receptor')%,'Glucocorticoid') %, 'Complex', 'Signal') xlabel('Time') ylabel('Concetration (micromolar)') title('Glucocorticoid model')

figure(2) plot(l,CC)%,l,GRO) legend('Complejo')%,'Glucocorticoid')

figure(3) plot(l,V)%,l,GRO) legend('Senal')%,'Glucocorticoid')

figure(4) plot(l,GRI)%,l,GRO) legend('GRI')%,'Glucocorticoid')

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