IGEM:IMPERIAL/2009/Encapsulation/Modelling/Timer2/code

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matlab code

%timer design 2

function dy=ty_timer_AND(t,y)


%variables

global IN PAI dm1 kp1 dp1 dm2 kp2 dp2 k1 k2 n1 n2

%PAI = PAI concentration

%IN = input concentration


%dm1 = rate of degradation of mRNA 1

%kp1 = rate of translation of protein 1

%dp1 = rate of degradation of protein 1


%dm2 = rate of degradation of mRNA 2

%kp2 = rate of translation of protein 2

%dp2 = rate of degradation of protein 2


%k1,k2 are parameters of the activator

%n1, n2 are hill functions of the activator


%equations

dy(1)=IN-dm1*y(1);


dy(2)= kp1*y(1)-dp1*y(2);


%%hill functions

A1=PAI.^n2./(k2.^n2+PAI.^n2);

act=((y(2).^n1).*A1)./(k1.^n1+(y(2).^n1).*A1)


dy(3)=act - dm2*y(3);


dy(4)=kp2*y(3)-dp2*y(4);



dy=[dy(1);dy(2);dy(3);dy(4)];

matlab calling code

%to call dy=ty_timer_AND(t,y)

clear all;

clc;


global IN PAI dm1 kp1 dp1 dm2 kp2 dp2 k1 k2 n1 n2;


%IN=50;

%PAI=0;


dm1=1;

kp1=1;

dp1=1;


dm2=1;

kp2=1;

dp2=1;


k1=1;

%k2=1;


%n1=3;

%n2=3;




i=1; %loop counter


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%

PAI=0;

k2=1;

n1=3;

n2=3;


for IN=[0:0.1:0.5];


[T,Y] = ode45(@ty_timer_AND,[0:1:200], [0 0 0 0]);


%loop counter to save all solutions for y2

a2(:,i)=Y(:,2);

a4(:,i)=Y(:,4);

i=i+1;

end


%subplot(2,3,1); plot(T,Y(:,1));

figure(1); subplot(1,2,1); plot(T,a2); TITLE('protein 1'); xlabel('time'); legend('IN=0','IN=0.1','IN=0.2','IN=0.3','IN=0.4','IN=0.5')

%subplot(2,3,3); plot(T,Y(:,3));

figure(1); subplot(1,2,2); plot(T,a4);TITLE('LuxR, variable input'); xlabel('time'); legend('IN=0','IN=0.1','IN=0.2','IN=0.3','IN=0.4','IN=0.5')


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%

k2=1

IN=5;

n1=3;

n2=3;


for PAI=[0:1:5];


[T,Y] = ode45(@ty_timer_AND,[0:0.01:2], [0 0 0 0]);


%loop counter to save all solutions for y2

a1(:,i)=Y(:,2);

a3(:,i)=Y(:,4);

i=i+1;

end


figure(2);subplot(1,2,1); plot(T,a1); TITLE('protein 1'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');

figure(2); subplot(1,2,2); plot(T,a3);TITLE('LuxR - output(n2=3)'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

IN=5;

PAI=1;

n1=3;

n2=3;


for k2=[0:1:5]


[T,Y] = ode45(@ty_timer_AND,[0:1:200], [0 0 0 0]);


%loop counter to save all solutions for y2

a5(:,i)=Y(:,2);

a6(:,i)=Y(:,4);

i=i+1;

end


figure(3);subplot(1,2,1); plot(T,a5); TITLE('protein 1'); xlabel('time');

figure(3); subplot(1,2,2); plot(T,a6);TITLE('LuxR - output (variable k2)'); xlabel('time');

legend('k2=0','k2=1','k2=2','k2=3','k2=4','k2=5');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

IN=5;

PAI=1;

n1=1;

k2=1;


for n2=[0:1:3]


[T,Y] = ode45(@ty_timer_AND,[0:0.1:10], [0 0 0 0]);


%loop counter to save all solutions for y2

a7(:,i)=Y(:,2);

a8(:,i)=Y(:,4);

i=i+1;

end


figure(4);subplot(1,2,1); plot(T,a7); TITLE('protein 1'); xlabel('time');

legend('n2=0','n2=1','n2=2','n2=3');

figure(4); subplot(1,2,2); plot(T,a8);TITLE('LuxR - output (varable hill exponent)'); xlabel('time');

legend('n2=0','n2=1','n2=2','n2=3');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


k2=1

IN=5;

n1=3;

n2=2;


for PAI=[0:1:5];


[T,Y] = ode45(@ty_timer_AND,[0:0.01:2], [0 0 0 0]);


%loop counter to save all solutions for y2

a9(:,i)=Y(:,2);

a10(:,i)=Y(:,4);

i=i+1;

end


figure(5);subplot(1,2,1); plot(T,a9); TITLE('protein 1'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');

figure(5); subplot(1,2,2); plot(T,a10);TITLE('LuxR - output (n2=2)'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


k2=2.5;

IN=10;

n1=1;

n2=1;


for PAI=[0:1:5];


[T,Y] = ode45(@ty_timer_AND,[0:0.01:20], [0 0 0 0]);


%loop counter to save all solutions for y2

a11(:,i)=Y(:,2);

a12(:,i)=Y(:,4);

i=i+1;

end


%figure(6);subplot(1,2,1); plot(T,a11); TITLE('protein 1'); xlabel('time');

%legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');

figure(6); subplot(1,2,2); plot(T,a12);TITLE('LuxR - output (k2=2.5)'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%


k2=1.5;

IN=10;

n1=1;

n2=1;


for PAI=[0:1:5];


[T,Y] = ode45(@ty_timer_AND,[0:0.01:20], [0 0 0 0]);


%loop counter to save all solutions for y2

a13(:,i)=Y(:,2);

a14(:,i)=Y(:,4);

i=i+1;

end


%figure(7);subplot(1,2,1); plot(T,a13); TITLE('protein 1'); xlabel('time');

%legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');

figure(7); subplot(1,2,2); plot(T,a14);TITLE('LuxR - output (k2=1.5)'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


k2=0.5;

IN=10;

n1=1;

n2=1;


for PAI=[0:1:5];


[T,Y] = ode45(@ty_timer_AND,[0:0.01:20], [0 0 0 0]);


%loop counter to save all solutions for y2

a13(:,i)=Y(:,2);

a14(:,i)=Y(:,4);

i=i+1;

end


%figure(8);subplot(1,2,1); plot(T,a13); TITLE('protein 1'); xlabel('time');

%legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');

figure(8); subplot(1,2,2); plot(T,a14);TITLE('LuxR - output (k2=0.5)'); xlabel('time');

legend('PAI=0','PAI=1','PAI=2','PAI=3','PAI=4','PAI=5');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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