%%% --- Biophysics of Macromolecules   --- %%%
%%% --- LMU - Sommersemester 2020      --- %%%
%%% --- Prof. Lipfert                  --- %%%
%%%
%%% Solutions to 
%%% Problem set 3, Problem 2
%%% Plot Hill equation for n = 2

x = 0.01:0.001:100;

n = 2;
y = x.^n./(1 + x.^n);

%%% Simply binding model w/o cooperativity
y_bind = x./(1 + x);

figure(1); clf; hold on; box on;
plot(x,y, 'b-', 'linewidth', 2)
plot(x,y_bind, 'k--', 'linewidth', 2)
legend('Hill, n=2', 'Simply binding', 'location', 'southeast')

set(gca,'LineWidth', 1,'FontSize', 25, 'FontWeight', 'bold', 'TickLength',[0.02 0.02])
ylabel('Fraction bound');
xlabel('Concentration Duper');
title('Linear plot')
axis([0 10 -0.05 1.05])

print(gcf,'-r300','-dpng', 'Hill_n2_LINEAR.png');



figure(2); clf; hold on; box on;
plot(x,y, 'b-', 'linewidth', 2)
plot(x,y_bind, 'k--', 'linewidth', 2)
legend('Hill, n=2', 'Simply binding', 'location', 'northwest')


set(gca, 'xscale', 'log')

set(gca,'LineWidth', 1,'FontSize', 25, 'FontWeight', 'bold', 'TickLength',[0.02 0.02])
ylabel('Fraction bound');
xlabel('Concentration Duper');
title('Log-Linear plot')
axis([0.01 100 -0.05 1.05])
set(gca, 'xtick', [0.01 0.1 1 10 100])
print(gcf,'-r300','-dpng', 'Hill_n2_LOGLINEAR.png');


figure(3); clf; hold on; box on;
plot(log(x),log(y./(1-y)), 'b-', 'linewidth', 2)
plot(log(x),log(y_bind./(1-y_bind)), 'k--', 'linewidth', 2)
legend('Hill, n=2', 'Simply binding', 'location', 'northwest')

line([-20 20], [0 0], 'color', [0 0 0], 'linestyle', '-')
%set(gca, 'xscale', 'log')
%set(gca, 'yscale', 'log')

set(gca,'LineWidth', 1,'FontSize', 25, 'FontWeight', 'bold', 'TickLength',[0.02 0.02])
ylabel('log(Y / (1-Y))');
xlabel('log(Concentration Duper)');
title('Hill plot')
axis([-3 3 -10 10])
%set(gca, 'xtick', [0.01 0.1 1 10 100])
print(gcf,'-r300','-dpng', 'Hill_n2_HILL.png');