% PROTEIN EXPRESSION ANALYSIS IN PBAD/ARAC INDUCIBLE MODEL

clear all;

% Parameters definition

D = 2;%min-1
    % Vc ratio
    Vcel = 1.1e-9; % uL
    Vext = 1e-3; % uL
Vc = Vcel/Vext;
Ku =10; %
Kd = 100; %
Kb = Ku/Kd;
K = 8; % min-1
alfa = 0.01;
p = 0:0.2:10; % min-1
dm = 0.247; % min-1
dp = 0.0063; % min-1
darab = 1e-6; % min-1
mu = 0.017; % min-1 
cn = 500; % molec
Kmax = 1.62e8;%cel


%Initial conditions
arab0 = 0:1e6:1e8; % molec
vol = 2e-5; % mL (200 uL)
Mm = 150.3; % g/mol
NA = 6.022e23; % molec/mol. Avogadro number
perc = 1000*(100*arab0*Mm./(NA*vol)); % Concentration: 100.m(mg)/V(mL)



for i=1:length(p)
    for j=1:length(arab0)
        n0 = [0 arab0(j) 0 1 1 1]';
        param = [D Vc Ku Kd K alfa p(i) dm darab dp mu cn Kmax];
        %ODE options
        options = odeset('RelTol',1e-6,'Stats','off','Abstol',1e-6);
        [t,n] = ode23t(@mi_araC_simplest,[0 400],n0,options,param);
        PoI(i,j) = n(end,5); % Stationary value of PoI for each p and K values
    end
end
%%
% PoI 3D surf 
figure
surf(perc,p,PoI,'FaceAlpha',0.6)
title("Protein expression PoI changing L-arabinose concentration arab_0 and translation rate p",'FontName','Lato','FontSize',14)
ylabel("p (min^{-1})",'FontName','Lato','FontSize',12)
xlabel("arab_0 (%)",'FontName','Lato','FontSize',12)
zlabel("PoI (molecules)")
colorbar