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Team:Colombia/Modeling/Scripting
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Scripting
RALSTONIA DIFFERENTIAL EQUATION SOLUTION
These scripts create the differential equations, find the steady state concetrations and then solve them by a 4th order Runge Kutta:
DIFFERANTIAL EQUATIONS DECLARATIONS
%THIS CODE CREATE ALL THE DIFFERENTIAL EQUATIONS FOR THE SYSTEM FOR %RASTONIA
function y=ecuaDifR(t,v)
%---------Parameters------%
global alfS %Basal concentration of the sensor phcS
global alfRA %Basal concnetration of the comple pchA-pchR
global alfR %Basal concentration of LuxR
global alfI %Basal concentration of CI
global alfCI %Basal concentration of CI
global alfHA %Basal concnetration of HipA7
global alfHB %Basal concnetration of HipB
global alfAS %Basal concnetration of Salycilic acid
global gammaS %Degradation of the sensor pchS
global gammaRA %Degradation of the complex pchR-pchA
global gammaR %Degradation of LuxR
global gammaI %Degradation of LuxI
global gammaCI %Degradation of CI
global gammaHA %Degradation of HipA7
global gammaHB %Degradation of HipB
global gammaAS %Dergradation of Salycilic acid
global mOHS %Kinetic constant for the detection of 3-OH-PAME by the sensor pchS (phosphorylation)
global mSFR %Kinetic constant for the phosphorylation of the complex pchR-pchA by the sensor
global mA %Kinetic constant for the activation of the promoter by the pchA
global mIR %Kinetic constant for the formation of the complex LuxILuxR
global mI %Constant that represent the union of the complex LuxILuxR with the promoter
global mHAHB %Kinetic constant for the inhibition of HipA7
global betaI %Max production of LuxI
global betaCI %Max production of CI
global betaHB %Max peoduction of HipB
global betaHA %Max production of HipA7
global betaAS %Max production of Salicylic acid
global kA %Constant k of the hill ecuation for the promoter promoted by pchA
global kIR %Constant k of the hill equiation for the promorer prmoted by the complex luxIluxR
global kCI %Constant k of the hill equation for the promoter promoted by CI
global hA %Hill constant for the promoters promoted by pchA
global hIR %Hill constant for the promoter promoted by the complex IR
global hCI %Hill constant fot the promoter CI
global eI %Export factor of LuxI
global jI %Import factor of LuxI
global deltaI %Difusion of LuxI outside the cell
global eAS %Export of Salicylic acid
global numcel %number of cells
if (t<(10) || ((t)>20))
OH=0;
else
OH=15;
end
%------ Variables%------
S=v(1); %Cocentration of the sensor pchS the cell
SF=v(2); %Concentration of phosphorylated sensor the cell
RA=v(3); %Concentration of the comple pchR-pchA
A=v(4); %Concentratio of the promoter avtivator pchA
Ii=v(5); %Concentration of LuxI inside the cell
Io=v(6); %Concentration of LuI outsied the cell
IR=v(7); %Concentration of the complex LuxI-LuxR
R=v(8);%Concentration of the protein CI
CI=v(9);%Concentration of HipA7
HB=v(10);%Concnetratio of HipB
HA=v(11);%Concentration of salicylic acid
AS=v(12); %Concentratio of quitin monomers
%---Equations---%
dS=alfS- gammaS*S - mOHS*OH*S; %Change of the sensor pchS
dSF = mOHS *OH*S - mSFR *SF*RA ; %Change of phosphorylated sensor
dRA=alfRA - gammaRA*RA - mSFR*SF*RA;%Change of the comple pchR-pchA
dA= mSFR*SF*RA-mA*A; %Change of the activator pchA inside the cell
dIi= alfI+ (betaI*(A^hA))/(kA^hA+(A^hA)) -gammaI*Ii +jI*Io- eI*Ii- mIR*Ii*R; %Change of LuxI inside the cell
dIo= numcel*(eI*Ii-jI*Io)-deltaI*Io; %Change of LuxI outside the cell
dIR= mIR*Ii*R - mI*IR; %Change of the complex LuxI luxR
dR= alfR-gammaR*R -mIR*Ii*R +(betaI*(A^hA))/(kA^hA+(A^hA)); %Change of LuxR
dCI= alfCI -gammaCI*CI+ (betaCI*(CI^hCI))/(kCI^hCI+(CI^hCI)) +(betaCI*(IR^hIR))/(kIR^hIR+(IR^hIR));%Change of CI
dHB=alfHB-gammaHB*HB+(betaHB*(CI^hCI))/(kCI^hCI+(CI^hCI))+(betaHB*(IR^hIR))/(kIR^hIR+(IR^hIR))-mHAHB*HA^2*HB^2; %Chanche of HipB
dHA=alfHA-gammaHA*HA+ (betaHA*(CI^hCI))/(kCI^hCI+(CI^hCI))-mHAHB*HA^2*HB^2; %Change of HipA7
dAS=alfAS-gammaAS*AS +(betaAS*(CI^hCI))/(kCI^hCI+(CI^hCI))-eAS*AS+(betaAS*(IR^hIR))/(kIR^hIR+(IR^hIR)); %Change of Salicylic acid
y1(1)=dS;
y1(2)=dSF;
y1(3)=dRA;
y1(4)=dA;
y1(5)=dIi;
y1(6)=dIo;
y1(7)=dIR;
y1(8)=dR;
y1(9)=dCI;
y1(10)=dHB;
y1(11)=dHA;
y1(12)=dAS;
y=y1';
end
RUNGE KUTTA
%FILE THAT SOLVES THE DIFFERENTIAL EQUATION AND GRAPHS THEM alfS=0.9; %Basal concentration of the sensor pchS alfRA=0.9; %Basal concnetration of the complez pchA-pchR alfR=0.6; %Basal concentration of LuxR alfI=0.4; %Basal concentration of LuxI alfCI=0.5; %Basal concentration of CI alfHA=1; %Basal concnetration of HipA7 alfHB=0.4; %Basal concnetration of HipB alfAS=0.4; %Basal concnetration of Salycilic acid gammaS=1; %Degradation of Chitinase inside the cell gammaRA=1; %Degradation of chitoporin gammaR=1; %Degradation of LuxR gammaI=1; %Degradation of LuxI gammaCI=1; %Degradation of CI gammaHA=1; %Degradation of HipA7 gammaHB=4; %Degradation of HipB gammaAS=1; %Dergradation of Salycilic acid mOHS=4; %Kinetic constant for the formation of the phoshorilation of the sensor mSFR=2.6; %Kinetic constant of the reaction of the phosphorilarion of the comple R mA=3.5; %Kinetic constant for the activation by A mIR=3; %Kinetic constant for the formation of the complex LuxILuxR mI=3; %Constant that represent the union of the complex LuxILuxR with the promoter mHAHB=12; %Kinetic constant for the inhibition of HipA7 betaI=10; %Max production of LuxI betaCI=9.96; %Max production of CI betaHB=9.95; %Max production of HipB betaHA=10; %Max production of HipA7 betaAS=11.2; %Max production of Salicylic acid kA=0.1; %Constant k of the hill ecuation for the promoter promoted by S kIR=0.39; %Constant k of the hill equiation for the promorer prmoted by the complex luxIluxR kCI=0.055; %Cosntant k of the hill equation for the promoter promoted by CI hA=1.2; %Hill constant for the promoters promoted by S hIR=3.4; %Hill constant for the promoter promoted by the complex IR hCI=2.3; %Hill constant fot the promoter CI eI=0.5; %Export factor of LuxI jI=0.8; %Import factor of LuxI deltaI=0.2;%Difusion of LuxI outside the cell eAS=0.8; numcel=1; %number of cells %----%
h=100; %Tiempo maximo m=0.01; %Longitud de paso [s] t=0:m:h; %Vector tiempo xi=[1,1,1,1,1,1,1,1,1,1,1,1]; y=fsolve(@CondInR,xi);
conInd=y;
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
OH=zeros(1,length(l));
x(1,:)=conInd;
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=ecuaDifR(l(k),xk); %Primera pendiente del metodo de RK4
k2=ecuaDifR(l(k)+m/2,xk+(m/2*k1)'); %Segunda pendiente del metodo de RK4
k3=ecuaDifR(l(k)+m/2,xk+(m/2*k2)'); %Tercera pendiente del metodo de RK4
k4=ecuaDifR(l(k)+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
%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
for j=1:length(l)
if (l(j)<(10) || l(j)>(20))
OH(j)=0;
else
OH(j)=15;
end
end
S=x(:,1); SF=x(:,2); RA=x(:,3); A=x(:,4); Ii=x(:,5); Io=x(:,6); IR=x(:,7); R=x(:,8); CI=x(:,9); HB=x(:,10); HA=x(:,11); AS=x(:,12);
figure(1)
plot(l,S,l,SF)
legend('Sensor (pchS)',' Phosporilated pchS')
xlabel('Time')
ylabel('Concetratio (micromolar)')
title('Response of Sensor pchS')
figure(5)
plot(l,RA,l,A)
legend('Complex pchR-pchA','Activator pchA')
xlabel('Time')
ylabel('Concetration (micromolar)')
title('Activator response')
figure(2)
plot (l,R,l,Ii,l,Io,l,IR)
legend('LuxR','LuxI nside the cell','LuxI outside the cell','Complex(Lux-LuxR)')
xlabel('Time')
ylabel('Concetration (micromolar)')
title('LuxI-LuxR system response')
figure(3)
plot (l,HA,l,HB)
legend('Toxin HipA7','Antitoxin HipB')
xlabel('Time')
ylabel('Concetration (micromolar)')
title('Toxin-Antitoxin module')
figure(4)
plot (l,OH,l,AS,l,CI)
legend('3-OH-PAME','Salicylic acid','CI')
xlabel('Time')
ylabel('Concetration (micromolar)')
title('CI and Salicylic Acid response')
