% small metab network
% S -> P -> A -> degrade
% A inhibite S -> P

global Vmax_msp
%global Ca
global Kmsp
global Vmaxpa
global Kmap
global B
global V

global Ns   % initial S
global Np_init   % initial P
global Na_init   % initial A


Vmax_msp = 1;
Ca_init = 0.2;
Kmsp = 0.2;
Vmaxpa = 1;
Kmap = 0.2;
B = 0.05;
V = 1;

Ns = 1;
%Ns = 10;
%Ns = 100;
Np_init = 0;
Na_init = 0;


% dataset
t_data = [0.11 2.2 4.3 7.5 9.3];
Na_data = [0.018 0.87 1.16 1.34 1.39];


P0 = Ca_init;    % initial guess

p_opt = fminsearch(@met_nw_rss,P0,[],t_data,Na_data);

Ca = p_opt;

tstart = 0;
tend = 10;

v_init(1) = Np_init;
v_init(2) = Na_init;

[t,v] = ode45(@met_network2,[tstart tend],v_init,[],Ca);

Na_pred = v(:,2);

plot(t_data,Na_data,'o',t,Na_pred,'-')