My code is running too long

Below you will find my code. I am having a problem running the code for more than 100 seconds (tlast). For 100 seconds I get a graph in my output. However, for more than 100 seconds it keeps running and does not give me any output. What is wrong with my code?

tic
global k1 kminus1 k2 kminus2
k1 = 0.1 ;
kminus1 = 0.1 ;
k2 = 0.3 ;
kminus2 = 0.05 ;

% dt = 0.001 ;
tlast = 100 ;
% iterations = round(tlast/dt) ;

S = 1.0 ;
E = 0.1 ;
ES = 0 ;
P = 0 ;

X = [S;E;ES;P] ;

% time = dt*(0:iterations-1) ;

[time2,X_all2] = ode45(@dXdt2,[0,tlast],X) ;

S_all = X_all2(:,1) ;
E_all = X_all2(:,2) ;
ES_all = X_all2(:,3) ;
P_all = X_all2(:,4) ;

figure
hold on
plot(time2,X_all2(:,1),'k','LineWidth',2)
plot(time2,X_all2(:,2),'g','LineWidth',2)
plot(time2,X_all2(:,3),'b','LineWidth',2)
plot(time2,X_all2(:,4),'r','LineWidth',2)
xlabel('time (s)')
ylabel('Concentration (uM)')
sgtitle ('Concentration vs. Time')
legend('S','E','ES','P')

toc

Elapsed time is 0.611294 seconds.

Below is the function used to pull the numbers for the plot:

function dX_2 = dXdt2 (t,X)

global k1 kminus1 k2 kminus2

S = X(1) ;
E = X(2) ;
ES = X(3) ;
P = X(4) ;

dS = -k1*S*E + kminus1*ES ;
dE = -k1*S*E + kminus1*ES + k2*ES -kminus2*E*P ;
dES = k1*S*E - kminus1*ES + kminus2*E*P ;
dP = k2*ES - kminus2*E*P ;

dX_2 = [dS;dE;dES;dP] ;

end

[Walter Roberson]

Try ode23s() as I suspect that your system is stiff.

[MARIA]

Hello!

I tried doing that for 300 seconds but it gave me the following error:

Warning: Failure at t=2.469706e+02. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (8.774157e-13) at time t.

[Torsten]

Did you see above that the concentration of "ES" blows up ?

[MARIA]

Hello!

Yes, that should be correct since I am trying to model the conversion of Enzyme and Product back to an Enzyme-Substrate Complex. I'm modeling it as a reversible reaction.

[Torsten]

But 3.5e7 mol/m^3 seems a little high after t=100 :-)