%%% --- Biophysics of Macromolecules --- %%% %%% --- LMU - Sommersemester 2017 --- %%% %%% --- Prof. Lipfert & Prof. Jungmann --- %%% %%% %%% Solutions to %%% Problem set 4, Problem 1 %%% 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');