single pore code

matlabcode/singlepore/single_pore_demo.m

+%% A demo model to show the effect of single pore kinetics on overall assembly curve
+function main()
+%% lognormal function
+% par_ini = [20,100];
+% par_kin = [0.5]; 
+% time = [0:0.1:60];
+% N = 3;
+% pdf_fun = pdf_ini(time, par_ini , 'lognorm');
+% time_app = time_appear(N, par_ini, 'lognorm');
+% kin_fun = kin_pdf(time, par_kin);
+% kin_conv = conv(kin_fun, pdf_fun);
+% N = length(time_app);
+% [totkin, singlekin] = addpores(time, time_app, kin_fun);
+% makefigure(1, N, time, kin_fun, pdf_fun, totkin, singlekin, time_app); 
+% saveas(1, 'C:\Users\toni\Dropbox\NPCMaturation\results\singlepore\pores_N=3.png')
+% ColOrd = get(gca,'ColorOrder');
+% %%
+% N = 100;
+% pdf_fun = pdf_ini(time, par_ini , 'lognorm');
+% time_app = time_appear(N, par_ini, 'lognorm');
+% kin_fun = kin_pdf(time, par_kin);
+% kin_conv = conv(kin_fun, pdf_fun);
+% N = length(time_app);
+% [totkin, singlekin] = addpores(time, time_app, kin_fun);
+% makefigure(2, N, time, kin_fun, pdf_fun, totkin, singlekin, time_app); 
+% saveas(2, 'C:\Users\toni\Dropbox\NPCMaturation\results\singlepore\pores_N=100.png')
+% 
+% %% 
+% makefigure(3, N, time, kin_fun, pdf_fun, totkin, singlekin, time_app); 
+% plot(time, kin_conv(1:length(time))/10, '-', 'Color', ColOrd(6,:), 'LineWidth', 2);
+% saveas(3, 'C:\Users\toni\Dropbox\NPCMaturation\results\singlepore\pores_N=100_conv.png');
+
+%%
+N = 200;
+par_ini = [32, 100];
+
+par_kin = [0.5]; 
+time = [0:0.1:90];
+pdf_fun1 = pdf_ini(time, par_ini , 'lognorm');
+kin_fun1 = kin_pdf(time, par_kin);
+kin_conv1 = conv(kin_fun1, pdf_fun1);
+time_app1 = time_appear(N, par_ini, 'lognorm');
+[totkin1, singlekin1] = addpores(time, time_app1, kin_fun1);
+
+par_ini = [15,50];
+par_kin = [4]; 
+pdf_fun2 = pdf_ini(time, par_ini , 'lognorm');
+kin_fun2 = kin_pdf(time, par_kin);
+kin_conv2 = conv(kin_fun2, pdf_fun2);
+time_app2 = time_appear(N, par_ini, 'lognorm');
+[totkin2, singlekin2] = addpores(time, time_app2, kin_fun2);
+
+setupFigure(4, [100 0 400 500])
+clf
+subplot(4,3,1)
+plot(time, [kin_fun1*32; kin_fun2*32],  'LineWidth', 1.5)
+
+xlim([0 30]);
+ylabel('# proteins ')
+subplot(4,3,4:6)
+plot(time, [pdf_fun1; pdf_fun2],  'LineWidth', 1.5)
+ylabel('Probability')
+subplot(4,1,3:4)
+plot(time, [kin_conv1(1:length(time))/kin_conv1(length(time)); kin_conv2(1:length(time))/kin_conv2(length(time))], ...
+      'LineWidth', 1.5);
+
+xlabel('Time');
+ylabel('Relative intensity');
+saveas(4, 'C:\Users\toni\Dropbox\NPCMaturation\results\singlepore\pores_mix_sol.png');
+
+%% histogram of pores
+setupFigure(5, [100 0 400 500])
+clf
+subplot(3,2,1)
+
+histogram(singlekin1(time == 20, :)*32, 'BinMethod','integers', 'Normalization', 'Probability');
+xlim([-1 33])
+ylim([0 1])
+ylabel('Probability');
+subplot(3,2,3)
+histogram(singlekin1(time == 30, :)*32, 'BinMethod','integers', 'Normalization', 'Probability');
+xlim([-1 33])
+ylim([0 1])
+ylabel('Probability');
+subplot(3,2,5)
+histogram(singlekin1(time == 50, :)*32,  'BinMethod','integers', 'Normalization', 'Probability');
+xlim([-1 33])
+ylim([0 1])
+ylabel('Probability');
+xlabel('# of NUPs');
+
+ColOrd = get(gca,'ColorOrder');
+subplot(3,2,2)
+histogram(singlekin2(time == 20, :)*32, 'BinMethod','integers', 'Normalization', 'Probability', 'FaceColor', ColOrd(2,:));
+xlim([-1 33])
+ylim([0 1])
+ylabel('Probability');
+subplot(3,2,4)
+histogram(singlekin2(time == 30, :)*32, 'BinMethod','integers', 'Normalization', 'Probability','FaceColor', ColOrd(2,:));
+xlim([-1 33])
+ylim([0 1])
+ylabel('Probability');
+subplot(3,2,6)
+histogram(singlekin2(time == 50, :)*32,  'BinMethod','integers', 'Normalization', 'Probability', 'FaceColor', ColOrd(2,:));
+xlim([-1 33])
+ylim([0 1])
+ylabel('Probability');
+xlabel('# of NPC');
+xlabel('# of NUPs')
+ylabel('Probability')
+saveas(5, 'C:\Users\toni\Dropbox\NPCMaturation\results\singlepore\hist_NUPsnumber.png');
+
+
+%%
+% figure(6)
+% clf
+% subplot(3,2,1)
+% edges = [0:17]
+% [h1, edge] = histcounts(singlekin1(time == 20, :)*16, 'BinEdges',edges, 'Normalization', 'Probability');
+% hold
+% [h2, edge] = histcounts(singlekin1(time == 30, :)*16, 'BinEdges',edges, 'Normalization', 'Probability');
+% [h3, edge] = histcounts(singlekin1(time == 50, :)*16,  'BinEdges',edges, 'Normalization', 'Probability');
+% bar(edges(1:end-1),[h1;h2;h3]')
+% ylabel('Probability');
+% subplot(2,1,2)
+% 
+% edges = [0:17]
+% [h1, edge] = histcounts(singlekin2(time == 20, :)*16, 'BinEdges',edges, 'Normalization', 'Probability');
+% hold
+% [h2, edge] = histcounts(singlekin2(time == 30, :)*16, 'BinEdges',edges, 'Normalization', 'Probability');
+% [h3, edge] = histcounts(singlekin2(time == 50, :)*16,  'BinEdges',edges, 'Normalization', 'Probability');
+% bar(edges(1:end-1),[h1;h2;h3]')
+% ylabel('Probability');
+% xlabel('Number of NUPs')
+% ylabel('Probability')
+end
+
+function makefigure(hfig, N, time, kin_fun, pdf_fun, totkin, singlekin, time_app)
+setupFigure(hfig, [100 0 400 500])
+clf
+subplot(4,3,1)
+plot(time, kin_fun*32, '-k', 'LineWidth', 1.5)
+ColOrd = get(gca,'ColorOrder');
+xlim([0 10]);
+ylabel('# proteins ')
+subplot(4,3,4:6)
+plot(time, pdf_fun, '-', 'LineWidth', 1.5, 'Color', ColOrd(2,:))
+ylabel('Probability')
+subplot(4,1,3:4)
+
+plot(time, totkin/N, 'LineWidth', 1.5,  'Color', ColOrd(1,:));
+hold
+plot(time, singlekin/N, '--k');
+
+plot([time_app; time_app], repmat([0;0.1],1,size(time_app,2)), '-', 'Color', ColOrd(2,:));
+xlabel('Time');
+ylabel('Relative intensity');
+end
+
+function [totkin, singlekin] = addpores(time, time_app, kin)
+    %% Add 
+    time_app = round(time_app, 1);
+    totkin = zeros(length(time),1);
+    singlekin = zeros(length(time),length(time_app));
+    for i = 1:length(time_app)
+        pos = find(round(time,1) == time_app(i));
+        
+        totkin(pos:end) = totkin(pos:end) + kin(1:end-(pos-1))';
+        singlekin(pos:end, i) = kin(1:end-(pos-1))';
+    end
+end
+
+function [t,y] = kin(dt, par)
+%% function generating a kinetic trace of a pore starts with alpha of signal
+alpha = 1/100;
+tmin = log(alpha/(1-alpha))*par(1);
+tmax = log((1-alpha)/alpha)*par(1);
+t = [tmin:dt:tmax];
+y = 1  - 1./(1 + exp(t/par(1)));
+end
+
+function [y] = kin_pdf(time, par)
+%% function generating a kinetic trace of a pore in a time interval to be used for convolution
+alpha = 1/100;
+tmin = log(alpha/(1-alpha))*par(1);
+time = time + tmin;
+y = 1  - 1./(1 + exp(time/par(1)));
+end
+
+function inipdf = pdf_ini(time, par, dist)
+%% function generating the probability 
+switch dist
+    case 'lognorm'
+        mu = log((par(1)^2)/sqrt(par(2)+par(1)^2));
+        sigma = sqrt(log(par(2)/(par(1)^2)+1));
+        [M, V]= lognstat(mu,sigma)
+        pd = makedist('Lognormal',mu, sigma);
+        inipdf = pdf(pd, time)
+    case 'genlog'
+        inipdf = par(3)/par(2)*exp(-(time-par(1))/par(2)).*(1+exp(-(time-par(1))/par(2))).^(-par(3)-1);      
+end
+end
+
+function inicdf = cdf_ini(time, par, dist)
+%% function generating the probability 
+switch dist
+    case 'lognorm'
+        mu = log((par(1)^2)/sqrt(par(2)+par(1)^2));
+        sigma = sqrt(log(par(2)/(par(1)^2)+1));
+        [M, V]= lognstat(mu,sigma)
+        pd = makedist('Lognormal',mu, sigma);
+        inicdf = cdf(pd, time)
+    case 'genlog'
+        inicdf = (1+exp(-(time-par(1))/par(2))).^(-par(3));
+end
+end
+
+function time = invcdfgenlog(prob, par)
+%% inverse gen log cdf
+time = par(1) - log((1./prob).^(1/par(3))-1)*par(2);
+end
+
+function time = time_appear(n, par, dist)
+%% function generating a list of pore events
+switch dist
+    case 'lognorm'
+        mu = log((par(1)^2)/sqrt(par(2)+par(1)^2));
+        sigma = sqrt(log(par(2)/(par(1)^2)+1));
+        [M, V]= lognstat(mu,sigma)
+        time = lognrnd(mu, sigma, 1,n);
+    case 'genlog'
+        prob = rand(1,n);
+        time = invcdfgenlog(prob, par);
+        % remove negative values
+        time(time<0) = [];
+end
+end
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