% filename: mm.m

close all;
clear;

k1=1e3; 			% units 1/(Ms)
k_1=0.1; 			    % units 1/s
k2=0.05; 		    % units 1/s
E0=0.5e-3;          % units M
S0=0.001;           % units M
options=[];

[t y]=ode23('mmfunc',[0 100],[S0 0 0],options,k1,k_1,k2,E0);

S=y(:,1);
ES=y(:,2);
E=E0-ES;
P=y(:,3);
plot(t,S,'.-r',t,E,'.-b',t,ES,'.-g',t,P,'.-c');
legend('S','E','ES','P',0);
xlabel('Time (s)');
ylabel('Concentration (M)');

figure
vmax=k2*E0;
Km=(k_1+k2)/k1;
v_real=k2*ES;
v_predicted=(k2*E0*S)./(Km+S);

plot(t,v_real,'.-r',t,v_predicted,'.-b');
legend('Calculatd turnover rate v','Predicted turnover rate v0',0);
xlabel('Time (s)');
ylabel('Turn-over rate (M/s)');