function diffusion_stp

% ADJUST THIS TO MINIMIZE SSE
geometry = 0.190;                 % geometric diffusion factor of microcarriers
             
% bulk parameters
V_b = 1.008;                      % volume of bulk solution (cm^3)              
n = 16000;                        % number of microcarriers in bulk volume

% ligand properties (streptavidin)
m_L0 = 40;                        % mass of ligand (ug)
MW_L = 55000;                     % molecular weight of ligand (g/mol)
D_LW = 6.2e-7;                    % ligand diffusion coeff. in water (cm^2/s)
a = 1;                            % rxn stoic coeff (L per R)

% fixed carrier properties
R = 0.01275;                      % microcarrier radius (cm)
C_R0 = 3403;                      % receptor density in carriers (pM/cm^3, nM)
D_L_app = D_LW * geometry * 60;   % effective diffusion coeff (cm^2/min)

% init
t_0 = 0;                          % initial time (min)
t_f = 65;                         % final time (min)

alpha = 0.999999999999;           % fudge factor to prevent MATLAB implosion
r_i0 = R * alpha;                 % init. interfatial radius in microcarrier (cm)

C_Lb0 = m_L0 / MW_L * 1e6 / V_b;  % init. conc. of ligand in bulk (pmol/cm^3, nM)

% y1 = r_i, y2 = C_Lb
dydt = @(t,y) [
    ((R * D_L_app * y(2) / a)) / (C_R0 * y(1) * (y(1) - R));
    (4 * pi * n * D_L_app * y(2) * R * y(1)) / (V_b * (y(1) - R))];

[t,Y] = ode45(dydt, [t_0 t_f], [r_i0 C_Lb0]);

r_i = Y(:, 1);                    % interfacial radius (cm)
C_Lb = Y(:, 2);                   % bulk ligand concentration (pmol/cm^3, nM)

% fluxes (pmol/cm^2/min)
N_L = (D_L_app * C_Lb .* r_i) ./ (R^2 * (r_i /  R + (-1)));

% NOTE: flow rates (pmol/min) will be the same at interface and at r=R due 
% to pseudo-steady state assumption
w_L = -(4 * pi * R^2 * N_L);

% concentration profiles (nM) as function of interfacial radius
C_r = diff(cumtrapz(t, -w_L)) ./ diff(4 / 3 * pi * r_i.^3);

% total bound mass (ug)
m_bt_L = trapz(t, w_L) * MW_L / 1e6 * n;

disp(['total bound mass at ', num2str(t(end)),' min']);
disp([num2str(m_bt_L), ' ug, ', num2str(m_bt_L / m_L0 * 100), '% (ligand)']);

% experimental data
exp_time1 = [7.5 15 30 60];
exp_time2 = [15 20 25 30];
exp_conc1 = [20.20 17.15 13.78 13.99]; % bulk concentration in ug/ml
exp_conc2 = [18.73 16.74 14.91 14.75];

figure;
plot(exp_time1,exp_conc1, '.');
hold on;
plot(exp_time2,exp_conc2, '.');
plot(t, C_Lb * MW_L / 1e6);
hold off;
xlabel('t (min)');
ylabel('concentration (ug/ml)');
legend('exp1', 'exp2', 'ligand');
title ('bulk concentration');

% fitting to experimental data (least squares algorithm)
e1 = interp1(t, C_Lb, exp_time1) * MW_L / 1e6 - exp_conc1;
e2 = interp1(t, C_Lb, exp_time2) * MW_L / 1e6 - exp_conc2;

% MINIMIZE THIS (SSE)
disp(['SSE: ', num2str(sum([e1 e2].^2))]);

end