Testing of the U-5R model

Verify against MuPad "analysis" document: U-2R_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='U-5R';

% 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_A   = 1e6;
K_B_s_1 = 2;
K_B_s_2 = 3;
K_B_s_3 = 4;
K_B_s_4 = 5;
K_B_s_5 = 6;

% 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.U_5R_model(...
        Rtotal_array(counter), LRratio_array(counter), K_A,...
        K_B_s_1, K_B_s_2, K_B_s_3, K_B_s_4, K_B_s_5,...
        'analytical', 'none');
    % collect
    concentrations_array = [concentrations_array ; concentrations];
end
toc
Elapsed time is 0.006076 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.U_5R_model(...
        Rtotal_array, LRratio_array, K_A,...
        K_B_s_1, K_B_s_2, K_B_s_3, K_B_s_4, K_B_s_5,...
        '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 0.002769 seconds.

Conclusions

Both vectorized and non-vectorized calls work well.