MATLAB code from chromate.m file
% Function to define the system of ODEs describing the modified chromate pathway.
%% Section 1: Function to define the system of ODEs describing the modified chromate pathway.
% The vector u has seven dimensions where;
% u(1) = ChrB protein concentration,
% u(2) = ChrB dimer concentration,
% u(3) = Cv, the hexavalent chromate added to the system concentration,
% u(4) = Dimer and Cv complex concentration,
% u(5) = Pc, the closed (bound and non-functioning) promoter concentration,
% u(6) = Po. the open (unbound and functioning) promoter concentration,
% u(7) = GFP output concentration.
% Parameter t is time that the simulation runs over. 
% Parameters k1..k8 represent the kinetic rates of the system.
function f=chromate(t,u);
k1 = 1;
k2 = 1;
k3 = 1;
km3 = 1;
k4 = 1;
km4 = 1;
k5 = 1;
k6 = 1;
km6=1;
k7 = 1;
% k8 divided by 60 as in minutes not hours.
k8=(0.25/60);
% Set S1 and S2 at specific times which represent whether chromate is present or not
% S is the signal input.

S1=0;
S2=1;
if (t<500)% Where time is less than 500 seconds.
    S=S1;

else if (t>500) && (t<3100)% Where time is more than 500 seconds and less than 3100 seconds.
        S=S2;

    else if (t>3100)% Where time is more than 3100 seconds.
            S=S1;
        end
    end
end % If and else if loop sets the times when chromate is present or absent from the system.
% Define f as a vector where the input is the right hand side of the systems of ODEs representing the pathway with signal input incorporated.
f=[k1 - k2*u(1)+km3*u(2)-k3*u(1)*u(1);
    k3*u(1)*u(1)-km3*u(2)+(km4*u(4))-(k4*u(2)*u(3)*S)-k5*u(2)+(km6*u(5)*S)-k6*u(2)*u(6);
    -k4*u(2)*u(3)*S+km4*u(4);
     k4*u(2)*u(3)*S-km4*u(4);
     k6*u(6)*u(2)-km6*u(5)*S;
     -k6*u(6)*u(2)+km6*u(5)*S;
     k7*u(6)*S-k8*u(7)];
 % End function.
end
% This function can then be called using the @chromate command in run_chromate.m file.
% END OF SECTION
%
%
%% Function to define the system of ODEs describing the original chromate pathway.
% Function to define the system of ODEs describing the modified chromate pathway.
%% Section 1: Function to define the system of ODEs describing the modified chromate pathway.
% The vector u has seven dimensions where;
% u(1) = ChrB protein concentration,
% u(2) = ChrB dimer concentration,
% u(3) = Cv, the hexavalent chromate added to the system concentration,
% u(4) = Dimer and Cv complex concentration,
% u(5) = Pc, the closed (bound and non-functioning) promoter concentration,
% u(6) = Po. the open (unbound and functioning) promoter concentration,
% u(7) = GFP output concentration.
% Parameter t is time that the simulation runs over. 
% Parameters k1..k8 represent the kinetic rates of the system.
function f=chrom_wt(t1,u1);
k2 = 1;
k3 = 1;
km3 = 1;
k4 = 1;
km4 = 1;
k5 = 1;
k6 = 1;
km6=1;
k7 = 1;
% k8 divided by 60 as in minutes not hours.
k8=(0.25/60);
% Set S1 and S2 at specific times which represent whether chromate is present or not.
% S is the signal input.

S1=0;
S2=1;
if (t1<500)% Where time is less than 500 seconds.
    S=S1;

else if (t1>500) && (t1<3100)% Where time is more than 500 seconds and less than 3100 seconds.
        S=S2;

    else if (t1>3100)% Where time is more than 3100 seconds.
            S=S1;
        end
    end
end % If and else if loop sets the times when chromate is present or absent from the system.
% Define f as a vector where the input is the right hand side of the systems of ODEs representing the pathway with signal input incorporated.
f=[k7*u1(6)-k2*u1(1)+km3*u1(2)-k3*u1(1)*u1(1);
    k3*u1(1)*u1(1)-km3*u1(2)+(km4*u1(4))-(k4*u1(2)*u1(3)*S)-k5*u1(2)+(km6*u1(5)*S)-k6*u1(2)*u1(6);
    -k4*u1(2)*u1(3)*S+km4*u1(4);
     k4*u1(2)*u1(3)*S-km4*u1(4);
     k6*u1(6)*u1(2)-km6*u1(5)*S;
     -k6*u1(6)*u1(2)+km6*u1(5)*S;
     k7*u1(6)*S-k8*u1(7)];
 % End function.
end
% This function can then be called using the @chrom_wt command in run_chromate.m file
%
%
% END OF FILE




 MATLAB code from run_chromate.m file
%% File to solve chromate functions.
%% Section 1: Solving the modified system to investigate GFP production with chromate added and removed at specific times.
% a = Initial ChrB protein concentration.
a = 1;
% b = Initial ChrB dimer concentration.
b = 1;
% c = Initial Cv, chromate, concentration.
c =1;
% d = Initial Cv and dimer complex concentration.
d = 0;
% e = Initial Pc, closed promoter, concentration.
e = 0;
% f = Initial Po, open promoter, concentration.
f = 1;
% g = Initial GFP concentration.
g = 0.01;
% T = Final time of simulation, in seconds.
T=3600;
% Solve the function using ode23 solver with set time range and defined initial conditions.
% Save time values in vector t and u(1)..u(7) values in matrix u.
[t,u]=ode23(@chromate,[0,T],[a,b,c,d,e,f,g],[]);

% Call up empty figure 1 to prevent overwriting figures.
figure1=figure(1)
% Plot t vector against the 7th column of the u matrix, that is the GFP concentration, and set linewidth to 3 so that it is easily read.
plot(t,u(:,7), 'LineWidth',3);
% Ensure that axis fits the data by using axis tight command.
axis tight
% Remove the values on the x and y axis as they are not relevant.
set(gca,'YTick',[],'XTick',[]);
% Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration.
annotation(figure1,'arrow',[0.133928571428571 0.914285714285714],...
    [0.0466190476190482 0.0476190476190482],'LineWidth',4);
annotation(figure1,'arrow',[0.0982142857142857 0.0982142857142857],...
    [0.103761904761905 0.919047619047619],'LineWidth',4);
% Annotate the figure by adding text arrow to highlight where the chromate is added and removed.
annotation(figure1,'textarrow',[0.3875 0.25],...
    [0.346619047619048 0.119047619047619],'Color',[1 0 0],...
    'String',{'Chromate Added'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
annotation(figure1,'textarrow',[0.682142857142857 0.789285714285714],...
    [0.779952380952381 0.919047619047619],'Color',[1 0 0],...
    'String',{'Chromate Removed'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
% Set the labels of the x and y axis to Time and Concentration, respectively.
xlabel ('Increasing Time', 'FontSize', 15);
ylabel ('Increasing Concentration','FontSize', 15);
% Add a legend for GFP Concentration.
legend1=legend('GFP Concentration');
% Make the box around legend bold and make font bigger, also position legend so that it is easily read.
set(legend1,...
    'Position',[0.468154768530456 0.149603206588803 0.360714277944395 0.0626984112082966],...
    'LineWidth',2,...
    'FontWeight','bold',...
    'FontSize',12);
% END OF SECTION
%
%

%% Section 2: Sensitivity analysis on effect of chromate added to GFP production in modified pathway.
% n = Number of different values of chromate evaluated.
n=10;
% T = Final time of simulation, in seconds.
T=3600;
% c1 = The range of values used for initial chromate concentration, with minimum at 0 and maximum at 400.
c1=linspace(0,400,n);
% Call up figure 2 to ensure no figures are overwritten.
figure2=figure(2)
% Set hold on so that multiple lines will be plotted on same figure.
hold on
% Set a for loop so that the n values for chromate are evaluated individually and the system solved for each of them.
for i=1:n
 % Solve the chromate function using ode23 solver over set time range and same initial conditions for all variables except chromate.
    % The initial concentration of chromate will depend on the value of i within the for loop.
    % The values will be stored in the t vector and u matrix.
    [t,u]=ode23(@chromate,[0,T],[a,b,c1(i),d,e,f,g],[]);
    % Plot the GFP concentration over time.
    plot(t,u(:,7), 'LineWidth',2);
% End the for loop.
end
% Then switch hold off so that no more lines are plotted on figure.
hold off
% Set axis to tight so that plot fits the data.
axis tight
% Add a rectangle onto the graph to highlight the section that will be zoomed in on in figure 3.
annotation('rectangle',[0.236714285714286 0.561904761904762 0.213285714285714 0.354761904761906], 'LineStyle','--');
% Remove the values of the x and y axis as they are not necessary.
set(gca,'YTick',[],'XTick',[]);
% Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration.
annotation(figure2,'arrow',[0.133928571428571 0.914285714285714],...
    [0.0466190476190482 0.0476190476190482],'LineWidth',4);
annotation(figure2,'arrow',[0.0982142857142857 0.0982142857142857],...
    [0.103761904761905 0.919047619047619],'LineWidth',4);
% Annotate the figure by adding text arrow to highlight where the chromate is added and removed.
annotation(figure2,'textarrow',[0.3875 0.25],...
    [0.346619047619048 0.119047619047619],'Color',[1 0 0],...
    'String',{'Chromate Added'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
annotation(figure2,'textarrow',[0.682142857142857 0.789285714285714],...
    [0.779952380952381 0.919047619047619],'Color',[1 0 0],...
    'String',{'Chromate Removed'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
% Set the labels of the x and y axis to Time and Concentration, respectively.
xlabel ('Increasing Time', 'FontSize', 15);
ylabel ('Increasing Concentration','FontSize', 15);
%
% We will now replot figure 2 but zoom in on a specific section for clarity.
%
%
% Call up empty figure 3 to prevent overwriting figures.
figure3=figure(3)
% Set hold on so that multiple lines will be plotted on same figure.
 hold on
 % Set a for loop so that the n values for chromate are evaluated individually and the system solved for each of them.
 for i=1:n
 % Solve the chromate function using ode23 solver over set time range and same initial conditions for all variables except chromate.
   
    % The initial concentration of chromate will depend on the value of i within the for loop.
    % The values will be stored in the t vector and u matrix.
    [t,u]=ode23(@chromate,[0,T],[a,b,c1(i),d,e,f,g],[]);
    % Plot the GFP concentration over time.
    plot(t,u(:,7), 'LineWidth',2);
% End the for loop.
 end
 % set hold off, so that no more lines are plotted.
hold off
% Ensure that axis fits the data by using axis tight command.
axis tight
% Remove the values on the x and y axis as they are not relevant and set the x and y limits so that we get a zoomed in section of the plot.
set(gca,'YTick',[],'XTick',[], 'XLim',[909.850230414748 1359.85023041475],'YLim',[163.478891218168 187.138947135872]);
% Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration.
annotation(figure3,'arrow',[0.133928571428571 0.914285714285714],...
    [0.0466190476190482 0.0476190476190482],'LineWidth',4);
annotation(figure3,'arrow',[0.0982142857142857 0.0982142857142857],...
    [0.103761904761905 0.919047619047619],'LineWidth',4);
% Add a 3rd arrow to the plot to show increasing initial concentration of Cv in the legend.
annotation(figure3,'arrow',[0.817857142857141 0.817857142857143],...
    [0.597619047619051 0.238095238095238],'LineWidth',4);
% Set legend as just lines with no text, as text will be added later using paint (see wiki figures).
legend2=legend('','','','','','','','','','');
% Set the position of the legend and the width of the box line.
set(legend2,...
    'Position',[0.631547602609266 0.207142857142858 0.255952397390734 0.413492042689934],...
    'LineWidth',2);
% Set the labels of the x and y axis to Time and Concentration, respectively.
xlabel ('Increasing Time', 'FontSize', 15);
ylabel ('Increasing Concentration','FontSize', 15);
% END OF SECTION
%
%



%% Section 3: Solving the original system to investigate GFP production with chromate added and removed at specific times.
% The same initial conditions are used as modified systems so they do not need to be redefined.
% Solve the chrom_wt function using ode23 solver with set time range and defined initial conditions.
% Save time values in vector t and u(1)..u1(7) values in matrix u.
[t,u]=ode23(@chrom_wt,[0,T],[a,b,c,d,e,f,g],[]);
% Call up a new figure to ensure figures are not overwritten.
figure4=figure(4)
% Plot t vector against the 7th column of the u matrix, that is the GFP
% concentration, and set linewidth to 3 so that it is easily read.
plot(t,u(:,7), 'LineWidth',3);
% Ensure that axis fits the data by using axis tight command.
axis tight
% Remove the values on the x and y axis as they are not relevant.
set(gca,'YTick',[],'XTick',[]);
% Annotate the figure by adding arrows along the x and y axis to represent
% increasing time and concentration.
annotation(figure4,'arrow',[0.133928571428571 0.914285714285714],...
    [0.0466190476190482 0.0476190476190482],'LineWidth',4);
annotation(figure4,'arrow',[0.0982142857142857 0.0982142857142857],...
    [0.103761904761905 0.919047619047619],'LineWidth',4);
% Annotate the figure by adding text arrow to highlight where the chromate
% is added and removed.
annotation(figure4,'textarrow',[0.3875 0.25],...
    [0.346619047619048 0.119047619047619],'Color',[1 0 0],...
    'String',{'Chromate Added'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
annotation(figure4,'textarrow',[0.682142857142857 0.789285714285714],...
    [0.779952380952381 0.919047619047619],'Color',[1 0 0],...
    'String',{'Chromate Removed'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
% Set the x and y labels to Increasing Time and Increasing concentration.
xlabel ('Increasing Time', 'FontSize', 15);
ylabel ('Increasing Concentration','FontSize', 15);
% Add a legend for GFP Concentration.
legend3=legend('GFP Concentration');
% Set the legend position, box line width and font size/style.
set(legend3,...
    'Position',[0.468154768530456 0.149603206588803 0.360714277944395 0.0626984112082966],...
    'LineWidth',2,...
    'FontWeight','bold',...
    'FontSize',12);
% END OF SECTION
%
%

figure4 = 

  Figure (4) with properties:

      Number: 4
        Name: ''
       Color: [0.9400 0.9400 0.9400]
    Position: [403 246 560 420]
       Units: 'pixels'

  Use GET to show all properties

Section 4: Sensitivity analysis on effect of chromate added to GFP production in original pathway.

Again set n as the number of values used for initial chromate.

n=10;
% T = Final time of simulation, in seconds.
T=3600;
% c1 = The range of values used for initial chromate concentration, with
% minimum at 0 and maximum at 400.
c1=linspace(0,400,n);
% Call up figure 5 to ensure no figures are overwritten.
figure5=figure(5)
% Set hold on so that multiple lines will be plotted on same figure.
hold on
% Set a for loop so that the n values for chromate are evaluated
% individually and the system solved for each of them.
for i=1:n
 % Solve the chromate function using ode23 solver over set time range
    % and same initial conditions for all variables except chromate.
    % The initial concentration of chromate will depend on the value of i
    % within the for loop.
    % The values will be stored in the t vector and u matrix.
    [t,u]=ode23(@chrom_wt,[0,T],[a,b,c1(i),d,e,f,g],[]);
    % Plot the GFP concentration over time.
    plot(t,u(:,7), 'LineWidth',2);
% End the for loop.
end
% Then switch hold off so that no more lines are plotted on figure.
hold off
% Set the axis to tight so that the data fits the plot.
axis tight
% Add a rectangle onto the graph to highlight the section that will be
% zoomed in on in figure 6.
annotation('rectangle',[0.236714285714286 0.561904761904762 0.213285714285714 0.354761904761906], 'LineStyle', '--');
% Remove the values on the x and y axis as they are not relevant.
set(gca,'YTick',[],'XTick',[]);
% Annotate the figure by adding arrows along the x and y axis to represent
% increasing time and concentration.
annotation(figure5,'arrow',[0.133928571428571 0.914285714285714],...
    [0.0466190476190482 0.0476190476190482],'LineWidth',4);
annotation(figure5,'arrow',[0.0982142857142857 0.0982142857142857],...
    [0.103761904761905 0.919047619047619],'LineWidth',4);
% Annotate the figure by adding text arrow to highlight where the chromate
% is added and removed.
annotation(figure5,'textarrow',[0.3875 0.25],...
    [0.346619047619048 0.119047619047619],'Color',[1 0 0],...
    'String',{'Chromate Added'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
annotation(figure5,'textarrow',[0.682142857142857 0.789285714285714],...
    [0.779952380952381 0.919047619047619],'Color',[1 0 0],...
    'String',{'Chromate Removed'},...
    'LineWidth',4,...
    'FontWeight','bold',...
    'FontSize',12);
% Set the x and y labels as increasing Time and Increasing Concentration
% respectively.
xlabel ('Increasing Time', 'FontSize', 15);
ylabel ('Increasing Concentration','FontSize', 15);
%
% We now want to replot figure 5 with a section zoomed in.
%
% Call up figure 6 so that no other plots are overwritten.
figure6=figure(6)
% Set hold on so that multiple line can be plotted on one graph.
 hold on
 % Set a for loop so that the n values for chromate are evaluated
% individually and the system solved for each of them.
 for i=1:n
 % Solve the chromate function using ode23 solver over set time range
    % and same initial conditions for all variables except chromate.
    % The initial concentration of chromate will depend on the value of i
    % within the for loop.
    % The values will be stored in the t vector and u matrix.
    [t,u]=ode23(@chrom_wt,[0,T],[a,b,c1(i),d,e,f,g],[]);
    % Plot the GFP concentration over time.
    plot(t,u(:,7), 'LineWidth',2);
% End the for loop.
 end
 % Set hold off so that no more lines are plotted on the figure.
hold off
% Ensure that axis fits the data by using axis tight command.
axis tight
% Remove the values on the x and y axis as they are not relevant and set the x and y limits so that we get a zoomed in section of the plot.
set(gca,'YTick',[],'XTick',[], 'XLim',[909.850230414748 1359.85023041475],'YLim',[163.478891218168 187.138947135872]);
% Annotate the figure by adding arrows along the x and y axis to represent
% increasing time and concentration.
annotation(figure6,'arrow',[0.133928571428571 0.914285714285714],...
    [0.0466190476190482 0.0476190476190482],'LineWidth',4);
annotation(figure6,'arrow',[0.0982142857142857 0.0982142857142857],...
    [0.103761904761905 0.919047619047619],'LineWidth',4);
% Add a 3rd arrow to the plot to show increasing initial concentration of
% Cv in the legend.
annotation(figure6,'arrow',[0.817857142857141 0.817857142857143],...
    [0.597619047619051 0.238095238095238],'LineWidth',4);
% Set legend as just lines with no text, as text will be added later using
% paint (see wiki figures).
legend4=legend('','','','','','','','','','');
% Set the position of the legend and the width of the box line.
set(legend4,...
    'Position',[0.631547602609266 0.207142857142858 0.255952397390734 0.413492042689934],...
    'LineWidth',2);
% Set the x and y labels to Increasing Time and Increasing Concentration
% respectively.
xlabel ('Increasing Time', 'FontSize', 15);
ylabel ('Increasing Concentration','FontSize', 15);
%
%
% END OF FILE