How to do a convolution on a graph?

Here what I've done. I want to plot the G graph that receive a concentration that already been diffuse.

%% do not edit this: urlwrite('http://web.mit.edu/20.305/www/part_composition_setup.m', ... 'part_composition_setup.m'); rehash; part_composition_setup('v6');

%% feel free to edit below: T_max = 10; % simulation length A_levels = 100; % how to vary A in linear B_levels = 100; % how to vary B in linear D_levels = 100; % how to vary D in linear E_levels = 100; % how to vary F in linear Q= 2; %Protein concentration at r=0 t= 3; %Time D= 4;%Diffusion coefficient xdistance=5; ydistance=3; r=sqrt(xdistance^2)+(ydistance^2);%Euclidean distance H=(Q/sqrt(4*pi*D*t))*exp((-r^2)/4*D*t);% Flick's Law

% parameters for the A n_A = 2; % Hill coefficient for A K_A = 10; % A binding coefficient A_SS = 70; % steady-state concentration of A

% parameters for the B n_B = 1.5; % Hill coefficient for B K_B = 10; % B binding coefficient B_SS = 70; % steady-state concentration of B

% parameters for the C n_C = 2; % Hill coefficient of C K_C = 5; % C binding coefficient C_gamma = 0.2; % C gamma

K_Cp = 100; % C production rate constant K_Cdp = 1; % C degradation rate constant

% parameters for the D n_D = 2.5; % Hill coefficient for D K_D = 10; % A binding coefficient D_SS = 70; % steady-state concentration of D

% parameters for the E: n_E = 2.2; % Hill coefficient for D K_E = 9; % A binding coefficient

K_Ep = 20; % E production rate constant K_Edp = 1; % E degradation rate constant E_gamma = 0.2; % E gamma E_SS=20;

% parameters for the F n_F = 3; % Hill coefficient for F K_F = 12; % F binding coefficient F_SS = 70; % steady-state concentration of F K_Fdp = 2; K_Fp = 30;

% parameters for the G K_Gp = 30; % G production rate constant K_Gdp = 2; % G degradation rate constant G_gamma = 0.34; % G gamma

K_G = 14; n_G = 4;

chrct = BioSystem(); dCdt = chrct.AddCompositor('XC', 0); % outputC dFdt = chrct.AddCompositor('XF', 0); % outputF dGdt = chrct.AddCompositor('XG', 0); % outputG dDiffusion1dt = chrct.AddCompositor('XDiff1', 0); % Diff dDiffusion2dt = chrct.AddCompositor('XDiff2', 0); % Diff

% linear chrct.AddConstant('A', 0); chrct.AddConstant('B', 0); chrct.AddConstant('C', 0); chrct.AddConstant('D', 0); chrct.AddConstant('E', 0); chrct.AddConstant('F', 0); chrct.AddConstant('G', 0); % chrct.AddConstant('Q', 0); chrct.AddConstant('t', 0); chrct.AddConstant('Dif', 0); chrct.AddConstant('xdistance', 0); chrct.AddConstant('ydistance', 0); chrct.AddConstant('H', 0); %constant concentration chrct.AddConstant('A_SS', A_SS); chrct.AddConstant('B_SS', B_SS); chrct.AddConstant('D_SS', D_SS); chrct.AddConstant('F_SS', F_SS); % hill constants chrct.AddConstant('n_A', n_A); chrct.AddConstant('n_B', n_B); chrct.AddConstant('n_C', n_C); chrct.AddConstant('n_D', n_D); chrct.AddConstant('n_E', n_E); chrct.AddConstant('n_F', n_F); chrct.AddConstant('n_G', n_G); %binding constant for input chrct.AddConstant('K_A', K_A); chrct.AddConstant('K_B', K_B); chrct.AddConstant('K_C', K_C); chrct.AddConstant('K_D', K_D); chrct.AddConstant('K_E', K_E); chrct.AddConstant('K_F', K_F); chrct.AddConstant('K_G', K_G); %production rate of C and E chrct.AddConstant('K_Cp', K_Cp); chrct.AddConstant('K_Cdp', K_Cdp); chrct.AddConstant('K_Ep', K_Ep); chrct.AddConstant('K_Edp', K_Edp); chrct.AddConstant('K_Fp', K_Fp); chrct.AddConstant('K_Fdp', K_Fdp); chrct.AddConstant('K_Gp', K_Gp); chrct.AddConstant('K_Gdp', K_Gdp); chrct.AddConstant('C_gamma', C_gamma); chrct.AddConstant('E_gamma', E_gamma); chrct.AddConstant('G_gamma', G_gamma);

%function y(1)= dCdt; y(2)= dFdt; y(3)= dGdt; y(4)= dDiffusiondt;

%Production of C from A OR B GATE chrct.AddPart(Part('Production of C', dCdt, ... Rate('(A^n_A)/((K_A^n_A)+(A^n_A))+(B_SS^n_B)/((K_B^n_B)+(B_SS^n_B))')));

chrct.AddPart(Part('Degradation of C', dCdt, ... Rate('-K_Cdp * XC')));

%Production of F from D AND E GATE chrct.AddPart(Part('Production of F', dFdt, ... Rate('(E^n_E)/((K_E^n_E)+(E^n_E))*(F_SS^n_D)/((K_D^n_D)+(F_SS^n_D))')));

chrct.AddPart(Part('Degradation of F', dFdt, ... Rate('-K_Fdp * XF')));

%Diffusion chrct.AddPart(Part('Diffusion of chemical', dDiffusion1dt, ... Rate('(XC/sqrt(4*pi*2*2))*exp((r^2)/4*2*2)')));

chrct.AddPart(Part('Diffusion of chemical', dDiffusion2dt, ... Rate('(XF/sqrt(4*pi*2*2))*exp((r^2)/4*2*2)')));

%Production of G from C OR F GATE chrct.AddPart(Part('Production of G', dGdt, ... Rate('(XDiff1^n_C)/((K_C^n_C)+(XDiff1^n_C))+(XDiff2^n_F)/((K_F^n_F)+(XDiff2^n_F))')));

chrct.AddPart(Part('Degradation of G', dGdt, ... Rate('-K_Gdp * XG')));

%bound C_end_levels = zeros(1, length(A_levels)); F_end_levels = zeros(1, length(A_levels)); G_end_levels = zeros(1, length(A_levels));

C_ix = chrct.CompositorIndex('XC'); F_ix = chrct.CompositorIndex('XF'); G_ix = chrct.CompositorIndex('XG');

%plot figure('position', [0, 0, 500, 900])

top1 = subplot(4, 1, 1); title(top1, 'Time behavior of [C]') top2 = subplot(4, 1, 2); title(top2, 'Time behavior of [F]') top3 = subplot(4, 1, 3); title(top3, 'Time behavior of [G]') hold(top1, 'on') hold(top2, 'on') hold(top3, 'on')

for ix = 1:length(A_SS) A = A_SS(ix); B = B_SS(ix); D = D_SS(ix); E = E_SS(ix); chrct.ChangeConstantValue('A', D); chrct.ChangeConstantValue('B', B); chrct.ChangeConstantValue('D', D); chrct.ChangeConstantValue('E', E); [T, Y] = chrct.run([0, T_max]); plot(top1, T, Y(:, C_ix), 'DisplayName', ... sprintf('A = %.1f', A)) plot(top1, T, Y(:, C_ix), 'DisplayName', ... sprintf('B = %.1f', B)) plot(top2, T, Y(:, F_ix), 'DisplayName', ... sprintf('D = %.1f', D)) plot(top3, T, Y(:, F_ix), 'DisplayName', ... sprintf('E = %.1f', E))

    C_end_levels(ix) = Y(end, C_ix);
    E_end_levels(ix) = Y(end, F_ix);
    G_end_levels(ix) = Y(end, G_ix);
end

xlabel(top1, 'Time') xlabel(top2, 'Time') xlabel(top3, 'Time') ylabel(top1, '[C]') ylabel(top2, '[G]') ylabel(top3, '[E]') legend(top1, 'Location', 'eastoutside') legend(top2, 'Location', 'eastoutside') legend(top3, 'Location', 'eastoutside') colormap(top1, jet) colormap(top2, jet) colormap(top3, jet) hold(top1, 'off') hold(top2, 'off') hold(top3, 'off')