MATLAB code from obp.m file
%Function to define the non-dimensionalised system of ODEs describing the folding of the Oderant Binding Protein (OBP).
% u is a 3 dimensional vector
%where;
% u(1)= alpha (Alpha Helix Concentration),
% u(2)= beta (Beta Barrel Concentration)
% u(3)= OBP (Folded OBP Concentration. )
% t is the time that the simulation is run over.
% K represents psi, the binding parameter determined by the binding rates and
% initial concentration of alpha helices.
function f = obp(t,u,K)
% define the system of ODEs by setting the vector f = left hand side of the system.
f = [u(3)-K*u(1)*u(2);
    u(3)-K*u(1)*u(2);
    -u(3)+K*u(1)*u(2)];
% The function is then ended.
end
% This function can then be called in the run_obp.m file by using
% @obp command.
% END OF FILE





MATLAB code for run_obp.m file.
%%File to perform sensitivity analysis for OBP folding model. Section 1: This section runs sensitivity analysis for both the parameter psi (K) and the ratio between beta barrels and alpha helices, D_{0} (v0).
 a is the number of datapoints in the range for both K and v0, chosen to be 50.
a=50;
% K is the range of values for K that the system will be solved over, where
% the max is twice the expected value.
K=linspace(0,(5291.005292)*2,a);
% u0 is the range of values for v0 that the system will be solved over,
% where the max is twice the expected value.
v0=linspace(0,4,a);
% T is the final time of the simulation in seconds.
T=0.001;
% Store is set as an empty matrix that will be filled by the values for the
% folded OBP concentration for each of the values of K and v0.
Store = zeros(a,a);
% Call up first empty figure to plot in.
figure(1)
% The for loop solves the function obp.m using ode23 for the range of values of
% K and v0, and stores the complex concentration values in the Store matrix.
for i=1:a
    for j=1:a
        [t,u]=ode23(@obp,[0 T],[1 v0(a-i+1) 0],[],K(j));
        Store(i,j) = u(end,3);

    end
end
%imagesc plots the complex concentration against v0 and K.
imagesc(Store)
% label function adds x labels to both the x and y axis.
xlabel('Increasing D_{0}','FontSize',15,'FontWeight','bold');
ylabel('Increasing \psi','FontSize',15,'FontWeight','bold');
% the set function removes the values from the x and y axis..
set(gca,'YTick',[],'XTick',[]);
% the color bar function adds a user defined colourbar with the label,
% 'Complex Concentration'.
c=colorbar('Ticks',[0,0.99],'TickLabels',{'None','High'},'FontSize',15,'FontWeight','bold');
c.Label.String = 'Complex Concentration';
% The resulting plot is Figure 5.
%
%
%%Section 2: This section is used to plot only v0 against complex concentration over time.
a is the number of datapoints in the range for v0, chosen to be 50.
a=50;
% v0 is the range of values for v0 that the system will be solved over
% where the max is four times the expected value.
v0=linspace(0,4,a);
% store is set as an empty matrix that will be filled by the values for the
% time values, alpha helix concentration, beta-barrel concentration and
% folded OBP concentration for each value of v0.
store = zeros(a,4,a); %1st is time, 2:4 are u.
% The for loop solves obp.m for the range of values of v0 and stores
% the values in the store matrix.
for i=1:a

    [t,u]=ode23(@spermsen,[0 0.001],[1 v0(i) 0],[],5291.005292);
    store(end-size(t,1)+1:end,1,i) = t;
    store(end-size(t,1)+1:end,2:4,i) = u;

end

% figure calls up an empty figure so that Figure 5 is not overwritten.
figure(2)
% v0 is then plotted against complex concentration, u(3).
 plot(v0,squeeze(store(end,4,:)),'LineWidth',2);
 % label function adds x labels to both the x and y axis.
 xlabel('Ratio of \beta to \alpha, D_{0}','FontSize',15,'FontWeight','bold');
ylabel('Concentration of Complex Formed','FontSize',15,'FontWeight','bold');
% annotation command allows us to add lines with specified style, width and colour
% for annotation of the graph,
% these can then be manually manipulated by using the edit plot tool.
t2 = annotation('line', [0.42 0.42], [0.15 0.91]);
b = t2.Color;
d=t2.LineWidth;
g=t2.LineStyle;
t2.Color = 'red';
t2.LineWidth= 2;
t2.LineStyle= ':';
% This plot is Figure 3.
%
%
%%Section 3: This section is used to plot only K against folded OBP over time.
% a is the number of datapoints in the range for K, chosen to be 50.
a=50;
% K is the range of values for K that the system will be solved over,
% where the max is twice the expected value.
K=linspace(0,(5291.005292)*2,a);
% store is set as an empty matrix that will be filled by the values for the
% time values, alpha helix concentration, beta-barrel concentration and
% folded OBP concentration for each value of K.
store = zeros(a,4,a); %1st is time, 2:4 are u
for i=1:a

    [t,u]=ode23(@spermsen,[0 0.001],[1.5 1 0],[],K(i));
    store(end-size(t,1)+1:end,1,i) = t;
    store(end-size(t,1)+1:end,2:4,i) = u;

end
% The for loop solves obp.m for the range of values of K and stores
% the values in the store matrix.
% figure calls up an empty figure so that Figure 6 is not overwritten.
figure(3)
% K is then plotted against complex concentration, u(3).
plot(K,squeeze(store(end,4,:)),'LineWidth',2);
% axis tight ensures the axis are not too large for the datapoints.
axis tight
% label function adds x labels to both the x and y axis.
xlabel('Increasing K','FontSize',15,'FontWeight','bold');
ylabel('Concentration of Complex Formed','FontSize',15,'FontWeight','bold');
% This plot is Figure 7.
% END OF FILE

Watch Our Introduction Video