IGEM:IMPERIAL/2009/M3/Modelling/old/Codes/celldeath

=Function code=

function dy=ty_celldeath(t,y)

%%

global T km1 km2 k1 k2 k11 n1 n2 de dm growth death

%%

%equations

activating_hill_temperature =(k1*(T^n1))/(T^n1+km1^n1); %activating

dy(1)= activating_hill_temperature - dm*y(1);

dy(2)= k2*y(1) - de*y(2);

hill_function_death = (k11*(y(2)^n2))/(y(2)^n2+km2^n2); %activating

dy(3)= growth*y(3) - death * hill_function_death * y(3);

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

=Call=

%function call

clear all;

clc;

%%

global T km1 km2 k1 k2 k11 n1 n2 de dm death growth E

%T=1

km1 =1;

km2 =1;

k1 =0.5;

k2 =1;

k11 =1;

n1 =1;

n2 =1;

de =1;

dm =1;

growth=1;

E =1; %enzyme

%death=3;

i=1; %%

death=1;

for T=[0:1:4]

[T,Y]=ode45(@ty_celldeath,[0:0.01:10], [0 0 1000]); %initially, has population of 1000

A1(:,i) = Y(:,1); %mRNA conc

A2(:,i) = Y(:,2); %killing enzyme conc

A3(:,i) = Y(:,3); %population

i=i+1;

end

figure(1);subplot(1,3,1);plot(T,A1); TITLE('mRNA');xlabel('time');legend('T=0','T=1','T=2','T=3','T=4');

figure(1);subplot(1,3,2);plot(T,A2); TITLE('Enzyme');xlabel('time');legend('T=0','T=1','T=2','T=3','T=4');

figure(1);subplot(1,3,3);plot(T,A3); TITLE('Cell population');xlabel('time'); legend('T=0','T=1','T=2','T=3','T=4');

%%

death=2;

for T=[0:1:4]

[T,Y]=ode45(@ty_celldeath,[0:0.01:10], [0 0 1000]); %initially, has population of 1000

A12(:,i) = Y(:,1); %mRNA conc

A22(:,i) = Y(:,2); %killing enzyme conc

A32(:,i) = Y(:,3); %population

i=i+1;

end

figure(2);subplot(1,3,1);plot(T,A12); TITLE('mRNA');xlabel('time');legend('T=0','T=1','T=2','T=3','T=4');

figure(2);subplot(1,3,2);plot(T,A22); TITLE('Enzyme');xlabel('time');legend('T=0','T=1','T=2','T=3','T=4');

figure(2);subplot(1,3,3);plot(T,A32); TITLE('Cell population');xlabel('time'); legend('T=0','T=1','T=2','T=3','T=4');

%%

death=3;

for T=[0:0.01:0.04]

[T,Y]=ode45(@ty_celldeath,[0:0.01:10], [0 0 1000]); %initially, has population of 1000

A13(:,i) = Y(:,1); %mRNA conc

A23(:,i) = Y(:,2); %killing enzyme conc

A33(:,i) = Y(:,3); %population

i=i+1;

end

figure(3);subplot(1,3,1);plot(T,A13); TITLE('mRNA');xlabel('time');legend('T=0','T=1','T=2','T=3','T=4');

figure(3);subplot(1,3,2);plot(T,A23); TITLE('Enzyme');xlabel('time');legend('T=0','T=1','T=2','T=3','T=4');

figure(3);subplot(1,3,3);plot(T,A33); TITLE('Cell population');xlabel('time'); legend('T=0','T=1','T=2','T=3','T=4');

=Results=



=Discussion=

We can see from the simulation that as temperatures increase, there'll be an increase in production of enzyme and mRNA of TaqI and DpnII, the restriction enzymes that are involved in cell killing. As we make the death term greater than the growth term, we'll see increasing cell death, with increasing temperatures.