% F4_3
% Carol Lucas
% Script to call L-type calcium channels to study figure 4.3 and more
% xc and xo come from equations 4.1 and 4.2
% xi = inactive state = 1-xc-xo
% xoalt (xo reduced solution for fast behavior) comes from equation 4.5
% y = xc+xo (reduced solution for slow behavior) comes from equation 4.9
% Calls ODE functions: LCfullfun (above equations )and LCtsfun (time scaled)
%
mess='Program pauses after each graph is completed.  Hit return to continue.'
k1p=0.7; k1m=0.2; k2p=0.05; k2m=0.005; cad=0.3;K1=k1m/k1p;
[t,x]=ode45('LCfullfun',[0 100],[1;0;0;1]);
xc=x(:,1);
xo=x(:,2);
xi=1-xo-xc;

xoalt=x(:,3);
xcalt=1-xoalt;

yfull=xo+xc;
ylate=x(:,4);
xlate=ylate/(1+K1);

L=length(t);


L=length(t);
figure(1);plot(t,xo,t,xoalt,t,xc,t,xcalt,t,xi);
xlabel('Time (ms)');ylabel('x values');
text(90,xc(L)+.05,'xc full');text(90,xo(L)+.05,'xo full');
text(90,xi(L)+.05,'xi full');text(90,xoalt(L)+.05,'xo fast');
text(90,xcalt(L)+.05,'xc fast');
title('Comparison of early behavior of full model and fast reduction')
pause;


figure(2);plot(t,yfull,t,ylate);axis([0 100 0 1]);
xlabel('Time (ms)');ylabel('x values');
text(90,ylate(L)+.05,'y slow');text(90,yfull(L)+.05,'y full');
title('Comparison of full xo+xc sum and approximation after slow reduction');pause;

ICa=5*xo*(20-60);

figure(3);plot(t,ICa);
xlabel('Time (ms)');ylabel('ICa2+');
title('Estimated Calcium flow based on open channels--see Figure 4.1');
pause;

figure(4);plot(t,xo,t,xlate);
xlabel('Time (ms)');ylabel('x values');
text(5,.5,'xo full');text(10,.75,'xo slow=y / (1+K1)');
title('Comparison of full model xo and xo based on reduced slow:  y=xo+xc');pause; 

[ts,xs]=ode45('LCtsfun',[0 1],[1;0]);
xots=xs(:,1);
xcts=xs(:,2);

figure(5);subplot(211);plot(ts,xots,ts,xcts);
title('time scaled: tnorm=k2m*t=.005t=t/200');
subplot(212);plot(ts/k2m,xots,ts/k2m,xcts,t,xc,t,xo);title('comparison');