% INDUCIBLE MODEL PBAD/ARAC RESOLUTION:
clear all;

% Parameters definition
D = 2; % min-1
 % Vc ratio:
    Vcel = 1.1e-9; % uL
    Vext = 1e-3; % uL
Vc = Vcel/Vext;
Ku = 100; % min-1
Kd = 10; % molec
K = 2; % min-1
alfa = 0.1;
p = 2.4; % min-1
dm = 0.247; % min-1
darab = 1e-6; % min-1
dp = 0.156; % min-1
mu = 0.017; % min-1 
cn = 500; % molec
Kmax = 1.62e8; % cel

param = [D Vc Ku Kd K alfa p dm darab dp mu cn Kmax];

% Initial conditions
    % arab0
vol = 2e-5; % mL (200 uL)
perc = 0.002; % Concentration: 100.m(g)/V(mL)
Mm = 150.3; % g/mol
NA = 6.022e23; % molec/mol. Avogadro number
arab0 = NA*vol*(perc./100)/Mm;  % molec

n0 = [0 arab0 0 1 1 1]';

% ODE options 
options = odeset('RelTol',1e-6,'Stats','off','Abstol',1e-6);
[t,n]=ode23t(@mi_araC_simplest,[0 400],n0,options,param);

% Graphs
fig = figure('Color','w');
hold on
subplot(2,3,1)
plot(t,n(:,1),'k')
xlabel('Tiempo (min)','FontName','Lato')
ylabel('(P_{BAD}.araC.arab_i) (molec)','FontName','Lato')
title('(P_{BAD}.araC.arab_i) vs Time','FontName','Lato','FontSize',14)
hold on
subplot(2,3,2)
plot(t,n(:,2),'r')
xlabel('Time (min)','FontName','Lato')
ylabel('arab_e (molec)','FontName','Lato')
title('arab_e vs Time','FontName','Lato','FontSize',14)
hold on
subplot(2,3,3)
plot(t,n(:,3),'r')
xlabel('Time (min)','FontName','Lato')
ylabel('arab_i (molec)','FontName','Lato')
title('arab_i vs Time','FontName','Lato','FontSize',14)
hold on
subplot(2,3,4)
plot(t,n(:,4),'r')
xlabel('Time (min)','FontName','Lato')
ylabel('mRNA (molec)','FontName','Lato')
title('mRNA vs Time','FontName','Lato','FontSize',14)
hold on
subplot(2,3,5)
plot(t,n(:,5),'b')
xlabel('Time (min)','FontName','Lato')
ylabel('PoI (molec)','FontName','Lato')
title('PoI  vs Time','FontName','Lato','FontSize',14)
hold on
subplot(2,3,6)
plot(t,n(:,6),'k')
xlabel('Time (min)','FontName','Lato')
ylabel('Cells','FontName','Lato')
title('Number of cells vs Time','FontName','Lato','FontSize',14)
hold on