% 18 April: make it fit 6 state CC model

clear;

%% Set directories
main_dir = pwd;
data_dir = [main_dir '\data' filesep];
output_dir = [main_dir '\output' filesep];
storage_dir = [main_dir '\storage' filesep];


%% Define constants and volumes ( [=] pL)
R = 8.314; % unit J/mol/K
T = 310;
F = 96485;
W_i = 38;
W_e = 5.182;
N_A = 6.022e23;
x_Ks_channel = 2*5369/N_A*1e15; % channel density: unit fmol (From Pan K channel)

%% Load stoichiometric matrices  

N_f = [1	0	0	0	0; % includes GHK
0	0	0	0	0;
0	1	0	1	0;
0	0	0	0	1;
0	0	1	0	0;
0	0	0	0	0;

];

N_r = [0	0	0	0	0;
1	0	0	0	0;
0	0	0	0	0;
0	1	0	0	0;
0	0	0	1	0;
0	0	1	0	1;
];

N_fT = transpose(N_f);
N_rT = transpose(N_r);

N = N_r - N_f;
% N_T = N_rT - N_fT;

num_cols = size(N,2); % number of reactions
I = eye(num_cols); 

M = [I N_fT; I N_rT];
M_rref = rref(M);

% GHK permeability for K in Ks channel (see PSO_GHK_fitting_curve.m)
load([storage_dir 'ks_G_GHK.mat']);
P_k_ks = G_GHK/F * 1e12; % Unit pL/s

%% Set up the vectors
load([storage_dir 'ks_xs1_parameters.mat']);
params_xs1 = params_vec;

load([storage_dir 'ks_xs2_parameters.mat']);
params_xs2 = params_vec;

% unit s^-1
alpha_xs1 = params_xs1(1); % unit s^-1
beta_xs1 = params_xs1(3); % unit s^-1

alpha_xs2 = params_xs2(1); % unit s^-1
beta_xs2 = params_xs2(3); % unit s^-1

kf_Ks = [P_k_ks/x_Ks_channel; ... % R_GHK
    alpha_xs1; ... % Rx1_0
    alpha_xs1; ... % Rx1_1
    alpha_xs2; ... % Rx2_0
    alpha_xs2];    % Rx2_1

kr_Ks = [P_k_ks/x_Ks_channel; ... % R_GHK
    beta_xs1; ... % Rx1_0
    beta_xs1; ... % Rx1_1
    beta_xs2; ... % Rx2_0
    beta_xs2];    % Rx2_1

% Overall
kf = kf_Ks;
kr = kr_Ks;

k = [kf;kr];
W = [ones(size(N,2),1);
    W_i;W_e;ones(4,1)];

lambdaW = exp(pinv(M)*log(k));
lambda = lambdaW./W;
kappa = lambda(1:size(N,2));   % [=] mol/s if corresponding v [=] mol/s
K = lambda(size(N,2)+1:end);   % [=] 1/mol if corresponding q [=] mol

save([output_dir 'K_kappa_1.mat'],'kappa','K');

%% Checks
N_rref = rref(N);
R_zdvat = null(N,'r');

K_eq = kf./kr;
zero_est = R_zdvat'*K_eq;

k_est = exp(M*log(lambdaW));
diff = sum(abs((k-k_est)./k));

kdiff = [k,k_est];

if diff > 1
    warning('lol DIFF is greater than 1, nublet.');
end

%% display text for cellml
rname = {'Ks','x10','x11','x20','x21'};
Kname = {'Ki','Ke','Sa','Sb','Sc','Sd'};
for ik = 1:length(kappa)
    fprintf('var kappa_%s: fmol_per_sec {init: %g, pub: out};\n', rname{ik}, kappa(ik));
end
for ik = 1:length(K)
    fprintf('var K_%s: per_fmol {init: %g, pub: out};\n', Kname{ik}, K(ik));
end

