Testing of the 5U-R-RL model

Verify against MuPad "analysis" document: 5U_R_RL_analysis.html Run in "Publish" mode to have a report.

9/8/17 - suitable for testing vectorized analytical models

Contents

close all
clear all

Set input parameters

model_name='5U-R-RL';

% Set some meaningful parameters matching settings of MuPad analysis
% document
LRratio_array=[0.0001 : 0.05 : 1.5]'; % Array of L/R

Rtotal_array=1e-3*ones(length(LRratio_array),1); % Receptor concentration, M



K_B_1_p_1=2;
K_B_1_p_2=2.1;
K_B_1_p_3=2.2;
K_B_1_p_4=2.3;
K_B_1_p_5=2.4;

K_A_p_1=1e5;
K_A_p_2=2e5;
K_A_p_3=3e5;
K_A_p_4=4e5;
K_A_p_5=5e5;

K_B_2_p_1=3;

% Set appropriate options for the model (see model file for details)
% model_numeric_solver='fminbnd'  ;
%
% model_numeric_options=optimset('Diagnostics','off', ...
%                     'Display','off',...
%                     'TolX',1e-9,...
%                     'MaxFunEvals', 1e9);

The important option here is "TolX" that sets termination tolerance on free ligand concentation in molar units. With our solution concentrations in 1e-3 range TolX should be set to some 1e-9.

Compute arrays for populations and plot

Call as non-vectorized:

concentrations_array=[];
tic
for counter=1:length(LRratio_array)
    % compute
    [concentrations species_names] = equilibrium_thermodynamic_equations.a5U_R_RL_model(...
        Rtotal_array(counter), LRratio_array(counter),...
                             K_B_1_p_1, K_B_1_p_2,  K_B_1_p_3, K_B_1_p_4,  K_B_1_p_5, ...
                             K_A_p_1,   K_A_p_2,    K_A_p_3,   K_A_p_4,    K_A_p_5, ...
                             K_B_2_p_1, ...
                            'analytical', 'none');
    % collect
    concentrations_array = [concentrations_array ; concentrations];
end
toc

Elapsed time is 0.017052 seconds.

Plot

Figure_title= model_name;
X_range=[0 max(LRratio_array)+0.1 ]; % extend X just a bit past last point
Y_range=[ ]; % keep automatic scaling for Y
% display figure
figure_handle=equilibrium_thermodynamic_equations.plot_populations(...
    Rtotal_array, LRratio_array, concentrations_array, species_names, Figure_title, X_range, Y_range);

Observations The result matches simulations in the 'analysis' MuPad notebook. The code is correct.

Test vectorization (if analytical model was vectorized!)

Call as vectorized:

tic
[concentrations_array species_names] = equilibrium_thermodynamic_equations.a5U_R_RL_model(...
        Rtotal_array, LRratio_array,...
                             K_B_1_p_1, K_B_1_p_2,  K_B_1_p_3, K_B_1_p_4,  K_B_1_p_5, ...
                             K_A_p_1,   K_A_p_2,    K_A_p_3,   K_A_p_4,    K_A_p_5, ...
                             K_B_2_p_1, ...
                            'analytical', 'none');
toc

Figure_title= sprintf(' %s - vectorized version', model_name);
X_range=[0 max(LRratio_array)+0.1 ]; % extend X just a bit past last point
Y_range=[ ]; % keep automatic scaling for Y
% display figure
figure_handle=equilibrium_thermodynamic_equations.plot_populations(...
    Rtotal_array, LRratio_array, concentrations_array, species_names, Figure_title, X_range, Y_range);

Elapsed time is 0.009924 seconds.

Conclusions

Both vectorized and non-vectorized calls work well.

Published with MATLAB® R2014b