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

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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.

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