Team:Colombia Uniandes/Scripting

From 2013.igem.org

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(→Stochastic)
(→Equations)
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====Equations====
====Equations====
-
 
+
%
-
function y = EqNick(x,t)
+
function y = EqNick(x,t)
-
 
+
%
-
%--Parameters---%
+
%--Parameters---%
-
 
+
%
-
global gammaN Kp beta Kd Kx alfaR deltaR Kt deltaT n alfaP deltaP
+
global gammaN Kp beta Kd Kx alfaR deltaR Kt deltaT n alfaP deltaP
-
 
+
%
-
 
+
%
-
 
+
%
-
No=x(1); % Niquel outside the cell
+
No=x(1); % Niquel outside the cell
-
 
+
%
  %------ Variables%------%
  %------ Variables%------%
-
   
+
  %
-
Ni= x(2); %Nickel Inside the cell
+
Ni= x(2); %Nickel Inside the cell
-
R=x(3); %RcnR (Repressor)  
+
R=x(3); %RcnR (Repressor)  
-
T=x(4); %RcnR Tetramer
+
T=x(4); %RcnR Tetramer
-
P=x(5); %Porine   
+
P=x(5); %Porine   
-
   
+
  %
-
   
+
  %
-
                                %---Equations---%
+
                              %---Equations---%
-
 
+
% 
-
dNo=-gammaN*(No-Ni) - Kp*P*No;
+
dNo=-gammaN*(No-Ni) - Kp*P*No;
-
dNi=gammaN*(No-Ni) + Kp*P*No- beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
+
dNi=gammaN*(No-Ni) + Kp*P*No- beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
-
dR=alfaR-deltaR*R - Kt*R^4;
+
dR=alfaR-deltaR*R - Kt*R^4;
-
dT= Kt*R^4 - deltaT*T - beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
+
dT= Kt*R^4 - deltaT*T - beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
-
dP=alfaP - deltaP*P + beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
+
dP=alfaP - deltaP*P + beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
-
 
+
%
-
y1(1)=dNo;
+
y1(1)=dNo;
-
y1(2)=dNi;
+
y1(2)=dNi;
-
y1(3)=dR;
+
y1(3)=dR;
-
y1(4)=dT;
+
y1(4)=dT;
-
y1(5)=dP;
+
y1(5)=dP;
-
 
+
%
-
y= y1';
+
y= y1';
-
 
+
%
-
end
+
end
====Equation solver====
====Equation solver====

Revision as of 22:50, 25 September 2013


Scripting

Contents

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')
%

Stochastic

%
%Stochastic Simulation of the Chemical Reactions of the Glucocorticoid
%System
%
%
%%----Parameters of the System----
global gammaGR mGRIR mCC deltaGRI alfaR deltaR deltaCC betaCC k n deltaS H
%
%%-----Initial Conditions of the glucocorticoid system-----
%Run CondIndGluco.m with the parameters of the system.
%
con=condiciones();
%
GRO_0= round(10000); %Glucocorticoid Outside the Cell
GRI_0 = round(con(1)); %Glucocorticoid Inside the Cell
R_0= round(con(2)); %Receptor
CC_0= round(con(3)); %Receptor- Glucocorticoid Complex
V_0= round(con(4));%Signal
%
%%----Simulation Constants----
numCells = 10;
numEvents= 60000;
numCurves = 5; % Restriction(numCurves<numCells)
Step=0.1;
tMax=45; %Minutes
%
%Plot the behaviour of the molecule 1/0 for yes/no
Plot_GRO = 1;            
Plot_GRI=1;            
Plot_R =1;             
Plot_CC = 1;             
Plot_V = 1;   
PlotMean=1;          
%
%%----Stochastic Simulation----
%Variables of the System
GRO= zeros(numCells,numEvents);
GRI= zeros(numCells,numEvents);
R= zeros(numCells,numEvents);
CC= zeros(numCells,numEvents);
V = zeros(numCells,numEvents);
%
t = zeros(numCells,numEvents); %Time
tr = zeros(numCells,numEvents);
%Initial Conditions
GRO(:,1)=GRO_0*ones(numCells,1);
GRI(:,1)=GRI_0*ones(numCells,1);
R(:,1)=R_0*ones(numCells,1);
CC(:,1)=CC_0*ones(numCells,1);
V(:,1)=V_0*ones(numCells,1);
%
%Stochastic Simulation
%
for S_ns =1:numCells
%
%
    for S_ne = 1:numEvents
        %Random numbers drawn from uniform distribution between zero and
        %one
        rand1 = rand(1); %This determine time
        rand2 = rand(1); %This determine Event
%
        %Events (Description in attached document)
        e1= gammaGR*GRO(S_ns,S_ne);
        e2= gammaGR*GRI(S_ns,S_ne);
        e3= mGRIR*GRI(S_ns,S_ne)*R(S_ns,S_ne);
        e4= mCC*CC(S_ns,S_ne);
        e5= deltaGRI*GRI(S_ns,S_ne);
        e6= alfaR;
        e7= deltaR*R(S_ns,S_ne);
        e8= deltaCC*CC(S_ns,S_ne);
        %e8= (betaCC*((CC(S_ns,S_ne))^n))/(k^n)+ ((CC(S_ns,S_ne))^n);
        e9= H*((betaCC*((CC(S_ns,S_ne))^n))/((k^n)+ ((CC(S_ns,S_ne))^n)));
        e10= deltaS*V(S_ns,S_ne);
%
        %Vector of Events
        vecEvents = [e1,e2,e3,e4,e5,e6,e7,e8,e9,e10];
%
        %Sum of Events
        sumEvents = sum(vecEvents);
%
        %Waitiing time until the next ocurrence of a reaction time
        %Probabilistic Distribution
        time= (1/sumEvents)*log(1/rand1);
        tr(S_ns,S_ne)=time;
        t(S_ns,S_ne+1)= t(S_ns,S_ne)+ time;
%
%
        %Glucocorticoid outside the cell        
%
        GRO(S_ns,S_ne+1)=funcImpulso(t(S_ns,S_ne+1));
        if(t(S_ns,S_ne)<130)
            GRI(S_ns,S_ne)=funcImpulso(t(S_ns,S_ne+1))*957/2575;
        end
%
        %Simulation Creation/Destruction of each molecule
        if rand2<(vecEvents(1)/sumEvents)
%
            GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne)+1;
            R(S_ns, S_ne+1)= R(S_ns,S_ne);
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
        elseif rand2< (sum(vecEvents(1:2)))/sumEvents
            if GRI(S_ns,S_ne)<=0
%
                GRI(S_ns,S_ne+1)= 0;
            else
                GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne)-1;
            end
%
            R(S_ns, S_ne+1)= R(S_ns,S_ne);
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
%
        elseif rand2< (sum(vecEvents(1:3)))/sumEvents
%
            if R(S_ns,S_ne)<=0 || GRI(S_ns,S_ne)<=0
               CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
               R(S_ns, S_ne+1)= R(S_ns,S_ne);
               GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
            else
               CC(S_ns, S_ne+1)= CC(S_ns,S_ne)+1;
               R(S_ns, S_ne+1)= R(S_ns,S_ne)-1;
               GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne)-1;
            end
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
%
        elseif rand2< (sum(vecEvents(1:4)))/sumEvents
%
            if CC(S_ns,S_ne)<=50
               CC(S_ns,S_ne+1)=0;
               GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
               R(S_ns, S_ne+1)= R(S_ns,S_ne); 
            else
               CC(S_ns, S_ne+1)= CC(S_ns,S_ne)-50;
               GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne)+50;
               R(S_ns, S_ne+1)= R(S_ns,S_ne)+50; 
            end
%
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
        elseif rand2< (sum(vecEvents(1:5)))/sumEvents
%
            if GRI(S_ns,S_ne)<=0
               GRI(S_ns,S_ne+1)=0;
            else
               GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne)-10;
            end
%
%
            R(S_ns, S_ne+1)= R(S_ns,S_ne);
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
            V(S_ns, S_ne+1) = V(S_ns,S_ne); 
%
        elseif rand2< (sum(vecEvents(1:6)))/sumEvents
%
            GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
            R(S_ns, S_ne+1)= R(S_ns,S_ne)+600;
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
        elseif rand2< (sum(vecEvents(1:7)))/sumEvents
%
            if R(S_ns,S_ne)<=0
                   R(S_ns,S_ne+1)=0;
            else
                R(S_ns, S_ne+1)= R(S_ns,S_ne)-300;
            end
%
%
            GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
        elseif rand2< (sum(vecEvents(1:8)))/sumEvents
            if CC(S_ns,S_ne)<=35
               CC(S_ns,S_ne+1)=round(CC(S_ns,S_ne)*0.75);
            else
              CC(S_ns, S_ne+1)= CC(S_ns,S_ne)-35;
%
            end
            GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
            R(S_ns, S_ne+1)= R(S_ns,S_ne);                   
            V(S_ns, S_ne+1) = V(S_ns,S_ne);
%
        elseif rand2< (sum(vecEvents(1:9)))/sumEvents
%
            GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
            R(S_ns, S_ne+1)= R(S_ns,S_ne);
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
            V(S_ns, S_ne+1) = V(S_ns,S_ne)+1000;
%
        else
            if V(S_ns,S_ne)<=0
               V(S_ns,S_ne+1)=0;
            else
               V(S_ns, S_ne+1)= V(S_ns,S_ne)-500;
            end
%
            GRI(S_ns,S_ne+1)= GRI(S_ns,S_ne);
            R(S_ns, S_ne+1)= R(S_ns,S_ne);
            CC(S_ns, S_ne+1)= CC(S_ns,S_ne);
%
        end
    end
end
%
%% ------------- Time Regularization -----------------------------
time=t;
%
[orgTime, newGRO] = regIntervalFixed2(time, GRO, Step, tMax);
[orgTime, newGRI] = regIntervalFixed2(time,GRI, Step, tMax);
[orgTime, newR] = regIntervalFixed2(time, R, Step, tMax);
[orgTime, newCC] = regIntervalFixed2(time, CC, Step, tMax);
[orgTime, newV] = regIntervalFixed2(time, V, Step, tMax);
%
GROMean=mean(newGRO);
GRIMean=mean(newGRI);
RMean=mean(newR);
CCMean=mean(newCC);
VMean=mean(newV);
%
%
%% Plotting 
% figure(1)
% plot(t(1,:),GRI(1,:),t(1,:),GRO)
% title('GRI')
% figure(2)
% plot(t(1,:),R(1,:))
% title('R')
% figure(3)
% plot(t(1,:),V(1,:))
% title('V')
% figure(4)
% plot(t(1,:),CC(1,:))
% title('CC')
%
if Plot_GRO
    figure,
%
    for i= 1:numCurves
        stairs(orgTime,newGRO(i,:))
        hold on
    end
    %if PlotMean
        %stairs(orgTime,GROMean,'r')
    %end
    hold off 
%
    title();
    xlabel('Time(min)');
    ylabel('Glucocorticoid Outside The Cell(Molecules)');
end
%
if Plot_GRI
    figure,
    for i= 1:numCurves
        stairs(orgTime,newGRI(i,:))
%
        hold on
    end
%
    if PlotMean
        stairs(orgTime,GRIMean,'r','LineWidth',2.5)
    end
    hold off 
%
    title();
    xlabel('Time(min)');
    ylabel('Glucocorticoid Inside The Cell(Molecules)');
end
%
 if Plot_R
    figure,
    for i= 1:numCurves
        stairs(orgTime,newR(i,:))
        hold on
    end
%
    if PlotMean
        stairs(orgTime,RMean,'r','LineWidth',2.5)
    end
    hold off 
%
    title();
    xlabel('Time(min)');
    ylabel('Receptor(Molecules)');
end           
%
if Plot_CC
    figure,
    for i= 1:numCurves
        stairs(orgTime,newCC(i,:))
        hold on
    end
%
    if PlotMean
        stairs(orgTime,CCMean,'r','LineWidth',2.5)
    end
    hold off 
%
    title();
    xlabel('Time(min)');
    ylabel('Receptor-Glucocorticoid Complex(Molecules)');
end           
%
if Plot_V
    figure,
    for i= 1:numCurves
        stairs(orgTime,newV(i,:))
        hold on
    end
%
    if PlotMean
        stairs(orgTime,VMean,'r','LineWidth',2.5)
    end
    hold off 
%
    title();
    xlabel('Time(min)');
    ylabel('Signal Production(Molecules)');
end 
%
%
%
%
%
%
%
%
% 
%
% 
%
%

Nickel removal system

Deterministic model

Equations

%
function y = EqNick(x,t)
%
%--Parameters---%
%
global gammaN Kp beta Kd Kx alfaR deltaR Kt deltaT n alfaP deltaP
%
%
%
No=x(1); % Niquel outside the cell
%
%------ Variables%------%
% 
Ni= x(2); %Nickel Inside the cell
R=x(3); %RcnR (Repressor) 
T=x(4); %RcnR Tetramer
P=x(5); %Porine  
% 
%
                             %---Equations---%
%  
dNo=-gammaN*(No-Ni) - Kp*P*No;
dNi=gammaN*(No-Ni) + Kp*P*No- beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
dR=alfaR-deltaR*R - Kt*R^4;
dT= Kt*R^4 - deltaT*T - beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
dP=alfaP - deltaP*P + beta/(1 + (T/(Kd*(1+(Ni/Kx))^n)));
%
y1(1)=dNo;
y1(2)=dNi;
y1(3)=dR;
y1(4)=dT;
y1(5)=dP;
%
y= y1';
%
end

Equation solver

%
%
clear all
clc
%
%
%
%---------Parameters------%
%
%
%
global gammaN Kp beta Kd Kx alfaR deltaR Kt deltaT n alfaP deltaP
%
gammaN=0.5034e-4; %Diffussion rate of Nickel (1/min)
%
Kp=0.000634; %Dynamic constant for the entrance of nickel to the cell
%
beta=0.166; %Porine maximum expression rate (nM/min)
%
Kd=276e-3; %Association constant DNA and repressor (nM)
%
Kx=25e-3; %Association constant of the repressor with nickel (nM)
%
alfaR= 5; %Represor basal production rate (nM/min)
%
deltaR=1/1200; % Represor destruction rate (1/min)
%
Kt=820e-3;% Rate constant for the formation of the tetramer (Giraldo et al)
%
deltaT=1/1200; %Tetramer destruction rate (!/min)
%
n=1; %Hill coefficient (cooperation constant)
%
alfaP=0.031; %Porine basal production rate (nM/min)
%
deltaP=1/1200;%Porine destruction rate (1/min)
%
%
%
yo=[0 0 0 0];
%
con=fsolve(@(x)CondIniciales(x),yo, optimset('display','iter','MaxIter',1000000,'algorithm','levenberg-marquardt','tolfun',1e-9));
%
assignin('base','ini',con);
%
%
cond=abs(con);
%
h=30; %Tiempo maximo
%
m=0.01; %Paso
l=(0:m:h);%Vector de tiemp
%
condI=[9.88e3 cond];
x=zeros(length(l),length(condI));
x(1,:)=condI;
%
for k=1:length(l)-1
%    
   xk=x(k,:); %Captura de la ultima posicion de la matirz, es decir, los valores actuales de las variables
%   
   k1=EqNick(xk,l(k)); %Primera pendiente del metodo de RK4
   k2=EqNick(xk+(m/2*k1)',l(k)+m/2); %Segunda pendiente del metodo de RK4
   k3=EqNick(xk+(m/2*k2)',l(k)+m/2); %Tercera pendiente del metodo de RK4
   k4=EqNick(xk+(m*k3)',l(k)+m); %Cuarta pendiente del metodo de RK4
%  
   xk1=xk+m/6*(k1+2*k2+2*k3+k4)'; %Calculo de nuevos valores para las
   %variables
%  
   %xk1=xk+m*ecuaDif(l(k),xk)'; %Method of Newton
%   
   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(k+1,:)=xk2; %Actualizacion del nuevo vector de variables en la matriz
%    
%   
%   
%   
end
%
No=x(:,1);
Ni=x(:,2);
assignin('base','No',No);
assignin('base','Nistable',Ni(length(Ni)));
disp(Ni(length(Ni)))
R=x(:,3);
assignin('base','Rstable',R(length(R)));
T=x(:,4);
assignin('base','Tstable',T(length(T)));
P=x(:,5);
assignin('base','Pstable',P(length(P)));
cond=[R(length(R)) T(length(T)) P(length(P))];
assignin('base','cond',cond);
figure(1)
plot(l,No,l,P)
legend('No','P')
xlabel('Time (min)')
ylabel('Concentration (nM)')
figure(2)
plot(l,Ni)
legend('Ni')
xlabel('Time (min)')
ylabel('Concentration (nM)')
figure(3)
plot(l,R)
legend('R')
xlabel('Time (min)')
ylabel('Concentration (nM)')
figure(4)
plot(l,T)
legend('T')
xlabel('Time (min)')
ylabel('Concentration (nM)')
figure(5)
plot(l,P)
legend('P')
xlabel('Time (min)')
ylabel('Concentration (nM)') 
%

Stochastic

Retrieved from "http://2013.igem.org/Team:Colombia_Uniandes/Scripting"