%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DMT1’s binary switching mechanism                              %
% L. Cegarra, A. Colins, Z.P. Gerdtzen, M.T. Nunez, J.C. Salgado %
% Santiago, Chile. Jan 2019                                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
close all
clc
format long g
global Vin Vout Vv endo ci

%%%%%%%%%%%%%%%%%%%%%%%%%
%%% System Parameters %%%
%%%%%%%%%%%%%%%%%%%%%%%%%
endo=1;     %%% The model is initialized in the endocytic mode
Vin=1000;   %%% Volume of cellular and basolateral medium 
Vout=200;   %%% Volume of apical medium
Vv=2.5e-10; %%% Volume of vesicles containing DMT1

k12=5.305749117015200253*10^-6;
k23=0.91039996585642;
k34=2.219297159129719;
k41=0.373081091241254;
k14=11.27031436970608;
k45=0.0629846041336298;
k54=0.649235352679672;
Nprot=566.1;

%%%% simulation time %%%%%
t0=0;   %initial time (min)
t1c=15; %duration of the first iron challenge (min)
t2c=15; %duration of the second iron challenge (min)

%%%%% vector of initial conditions for the system %%%%%
x10=1;           %P1(0)
x20=0;           %P2(0)
x30=0;           %P3(0)
x40=0;           %P4(0)
x50=0;           %P5(0)
x60=0;           %FeIn(0) Apical iron concentration
x70=20;          %FeOut(0) Iron concentration in the intracellular-basolateral space

ci=x60; % Initial condition of apical iron concentration for the first challenge

pa=[k12 k14 k41 k23 k34 k45 k54 Nprot];
x01=[x10 x20 x30 x40 x50 x60 x70];

%%%%%%%%%%%%%%
%%% System %%%
%%%%%%%%%%%%%%
options = odeset('maxstep',0.001,'initialstep',0.001,'RelTol',1e-9,'AbsTol',1e-9,'Refine',10);
[t,salr]=ode45(@S1_Appendix_b,[t0 t1c],x01,options,pa); 
x0=[salr(end,1) salr(end,2) salr(end,3) salr(end,4) salr(end,5) salr(end,6) x70];

ci=salr(end,6); %%% Initial condition of apical iron concentration for the second challenge
endo=1;         %%% The model is initialized in the endocytic mode
[t3,sal3]=ode45(@S1_Appendix_b,[t1c t1c+t2c],x0,options,pa);
tff=t1c+t2c;

%%%%%%%%%%%%%%%%
%%% Graphics %%%
%%%%%%%%%%%%%%%%

%%%%%%%%%%%% FRACTIONS OF PROTEIN %%%%%%%%%%%%%
figure (1)
plot(t,salr(:,1)+salr(:,2)+salr(:,3)+salr(:,4)+salr(:,5),'k','LineWidth',1.5)
hold on
plot(t,salr(:,1)+salr(:,2)+salr(:,3)+salr(:,4),'b','LineWidth',1.5)
hold on
plot(t,salr(:,5),'r','LineWidth',1.5)
hold on
plot(t3,sal3(:,1)+sal3(:,2)+sal3(:,3)+sal3(:,4)+sal3(:,5),'k','LineWidth',1.5)
hold on
plot(t3,sal3(:,1)+sal3(:,2)+sal3(:,3)+sal3(:,4),'b','LineWidth',1.5)
hold on
plot(t3,sal3(:,5),'r','LineWidth',1.5)
xlim([0 tff])
ylim([0 1.3])
legend('total DMT1','DMT1 in apical membrane','DMT1 in vesicles')
xlabel('Time [min]')
ylabel('Total fraction of DMT1')
title('DMT1 endocytic cycling behavior - DMT1’s binary switching mechanism')

%%%%%%%%%%%%% Apical iron uptake %%%%%%%%%%%%%
figure(2)
plot(t,salr(:,6)*1000,'k','LineWidth',1.5)
d1=[6.2392,8.499,7.4954,13.597,19.849;6.102,8.9715,9.9409,15.469,12.848;7.0755,5.2364,10.715,17.475,16.549];
d2=mean(d1);
des1=std(d1);
des1=[0,des1]';
tp=[0 3 6 9 12 15];
yp=[0,d2];
pmol =[2.46759481517043,4.14786365818531,4.09385501680269,11.1797887662026,14.7179548727796;2.08353336533845,3.31733077292367,4.00024003840615,12.5492078732597,15.1668266922708;2.08353336533845,1.67666826692271,3.26452232357177,12.617618819011,13.0952952472396];
prom2=mean(pmol);
prom2=prom2+yp(end);
des=std(pmol);
yx=prom2;
hold on
tx=[18 21 24 27 30];
% tx=tx+tl
plot(tx,yx,'rs','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','r','MarkerSize',5)
hold on
errorbar(tp,yp',des1,'.g','LineWidth',1.5)
hold on
errorbar(tx,prom2',des,'.r','LineWidth',1.5)
hold on
plot(tp,yp,'rs','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',5)
hold on
plot(t3,sal3(:,6)*1000,'k','LineWidth',1.5)
hold on
plot(tx,yx,'rs','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','r','MarkerSize',5)
xlim([0 tff])
ylim([0 35])
xlabel('Time [min]')
ylabel('Apical iron uptake [pmol/inserto]')
title('Apical iron uptake - DMT1’s binary switching mechanism')




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DMT1’s binary switching mechanism                              %
% L. Cegarra, A. Colins, Z.P. Gerdtzen, M.T. Nunez, J.C. Salgado %
% Santiago, Chile. Jan 2019                                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function xdot=S1_Appendix_b(t,x,pa)
global Vin Vout Vv endo ci

%%% Parameters
k12=pa(1);
k14=pa(2);
k41=pa(3);
k23=pa(4);
k34=pa(5);
k45=pa(6);
k54=pa(7);
Nprot=pa(8);
alphaDMT1_E=0.989;
alphaDMT1_M=0.978;

xdot = zeros(7,1);

DMT1endo=x(5);                %Fraction of DMT1 in the endocyted state DMT1endo DMT1
DMT1memb=x(4)+x(3)+x(2)+x(1); %Fraction of DMT1 in the apical membrane

%For the first iron challenge
if(ci==0)
    if((DMT1endo>alphaDMT1_E)&(endo==1))
        endo=0;
    end
    if((DMT1memb>alphaDMT1_M)&(endo==0))
        endo=1;
    end
end

% For the second iron challenge
if(ci>0)
    if((DMT1endo>(alphaDMT1_E))&(endo==1))
        endo=0;
    end
    if(((DMT1memb>(alphaDMT1_M))&(endo==0)))
        endo=1;
    end
end

k45=pa(6)*(endo);
k54=pa(7)*(1-endo);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%                 DMT1’s binary switching mechanism                 %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xdot(1)=(-k12*x(1)*x(7)-k14*x(1)+k41*x(4));                   %P1
xdot(2)=(k12*x(1)*x(7)-k23*x(2));                             %P2
xdot(3)=(k23*x(2)-k34*x(3));                                  %P3
xdot(4)=(k34*x(3)+k14*x(1)+k54*x(5)-k41*x(4)-k45*x(4)*x(7));  %P4
xdot(5)=(k45*x(4)*(x(7))-k54*x(5));                           %P5
xdot(6)=(Nprot*k34*x(3)+(Vv)*(1/Vin)*Nprot*k54*x(5));         %FeIn+2
xdot(7)=(-Vin/Vout)*((Nprot*k34*x(3)-(Vv)*(1/Vin)*Nprot*k54*x(5)));%FeOut+2
return