MATLAB code from haptosen.m file
%Function to define the non-dimensionalised system of ODEs describing the
%binding between Haptoglobin and Haemoglobin. u is a 4 dimensional vector
%where;
% u(1)=Hp (Haptoglobin concentration)
% u(2)=alphaHemo (Free Hemoglobin)
% u(3)=alphaHemo/Hapto complex (Haptoglobin + alphaHemo complex)
% u(4)=Hemo/Hapto complex (Full hemo/hapto complex).
% t is the time that the simulation is run over.
% lambda represents the parameter in the system determined by binding rates nd initial concentration of haemoglobin.
% gamma represents the parameter in the system determined by binding rates.
function f = haptosen(t,u,lambda,gamma);
% define the system of ODEs by setting the vector f = left hand side of the system.
f = [u(3)-lambda.*u(1)*u(2);
    u(3)-lambda.*u(1)*u(2);
    -u(3)+lambda.*u(1)*u(2)-gamma.*u(3);
    gamma.*u(3)];
% The function is then ended.

end
% This function can then be called in the run_haptosen.m file by using
% @haptosen command.





   
MATLAB code from run_haptosen.m file
File to perform sensitivity analysis for Haptoglobin and Haemoglobin
% binding model.
% a is the number of values chosen for each of the ranges of parameters.
% Therefore 100 different values were chosen.
a=100;
%Lambda1 is the range of values for the parameter Lambda, chosen with the
%expected value of (100/317)*0.3878494524 as the mean value.
lambda1=linspace(0,((100/317)*0.3878494524)*2,a);
%Gamma1 is the range of values for the parameter Gamma, chosen with the
%expected value of (83/317) as the mean value.
gamma1=linspace(0,(83/317)*2,a);
%T is the final time of the simulation.
T=30;
% Store sets an empty matrix for the final concentrations of the complex
% with the varied parameter values.
Store = zeros(a,a);
%figure(1) calls up a new figure.
figure(1)
% The for loop solves the ode system defined in haptosen function using ode23 for the range of values for both
% parameters.
for i=1:a
    for j=1:a
        [t,u]=ode23(@haptosen,[0 T],[4.17 1 0 0],[],lambda1(a+1-i),gamma1(j));
        Store(i,j) = u(end,4);
%         Store(i,j) = (u(3,4)-u(2,4))/(t(3)-t(2));
    end
end
%imagesc plots the surf plot of the parameters and the complex
%concentration.
imagesc(Store)
% xlabel and ylabel add labels to the plot.
xlabel('Increasing \lambda','FontSize',15,'FontWeight','bold');
ylabel('Increasing \gamma','FontSize',15,'FontWeight','bold');
%set removes the x and y axis
set(gca,'YTick',[],'XTick',[]);
% The following lines add a colour bar with defined labal and text.
c=colorbar('Ticks',[0,0.99],'TickLabels',{'None','High'},'FontSize',15,'FontWeight','bold');
c.Label.String = 'Complex Concentration';
%the following lines add a text arrow to allow for annotation of the graph with defined colours positions and width.
ta1 = annotation('textarrow', [0.13 0.79], [0.13 0.92]);
h = text(0.5,0.5,'Complex Formation');
s = h.FontSize;
h.FontSize = 12;
j = h.Rotation;
h.Rotation=45;
k = h.Position;
h.Position = [0.5 0.5 0];
b = ta1.Color;
d=ta1.LineWidth;
ta1.Color = 'red';
ta1.LineWidth= 4;

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