%%% --- Biophysics of Macromolecules --- %%% %%% --- LMU - Sommersemester 2017 --- %%% %%% --- Prof. Lipfert & Prof. Jungmann --- %%% %%% %%% Solutions to %%% Problem set 4, Problem 2 %%% Ligand receptor binding, free vs. bound ligand clc;clf;clear; %%% Read the data from an excel file %%% Make sure the xlsx file is in the same directory data = xlsread('Maeda_2000_Figure1A_DATA.xlsx'); c_core = data(:,1); %%% Core enzyme concentration, nM p_bound = data(:,2)/100; %%% Fraction bound --- convert from %-bound %%% Fit simple binding model to the data %%% This pretend that free ligand = total ligand [Kd res exitflag] = fminsearch(@(Kd) norm(p_bound - (1./(1+Kd./c_core))), [0.4]); xfit = 0:0.01:1; yfit = xfit./(xfit+Kd); %%% Fit binding model that takes into account the total ligand and receptor concentration %%% Kdt is the Kd constant determined for the model that takes into account %%% total concentrations Rtot = 0.4; %%% in nM Ltot = c_core; %%% in nM [Kdt res exitflag] = fminsearch(@(Kdt) norm(p_bound - ( ((Rtot+Ltot+Kdt)-sqrt((Rtot+Ltot+Kdt).^2 - 4*Rtot*Ltot))./(2*Rtot) ) ), [0.2]); yfitt = ( ((Rtot+xfit+Kdt)-sqrt((Rtot+xfit+Kdt).^2 - 4*Rtot*xfit))./(2*Rtot) ); %%% Plot the results figure(1); clf; hold on; box on; plot(xfit, yfit, 'b--', 'linewidth', 2) plot(xfit, yfitt, 'b-', 'linewidth', 2) plot(c_core, p_bound, 'ks', 'linewidth', 2, 'markersize', 20) legend('L_{tot} = L_{free} model','L_{tot}, R_{tot} model', 'location', 'southeast') set(gca,'LineWidth', 1,'FontSize', 25, 'FontWeight', 'bold', 'TickLength',[0.02 0.02]) ylabel('Fraction bound sigma'); xlabel('Core enzyme (nM)'); axis([-0.1 1.1 -0.1 1.1]) %%% Show the fitted Kd constants in the title of the graph title(['Simple Kd = ' num2str(Kd,2) ' nM; Correct Kd = ' num2str(Kdt,2) ' nM' ]) %%% Print the results to eps print(gcf,'-r600','-depsc', 'Ltot_BindingModels.eps');