Settings file

A place for the user to define all the relevant properties of model simulation that are not stored in SBtab. This are usually things that need to change during optimizations or model development.

These settings files can be found can be found on the respective model repository in the directory “Matlab/Settings”, in the example model from our main repository in the directory “Matlab/model/Model_Example/Matlab/Settings”, or by following these links:

• Example model settings files

• Fujita_2010 model settings files

• Nair_2016 model settings files

• Viswan_2018 model settings files

Default settings code

function [stg] = default_settings()
% This function returns a structure "stg" containing default settings for a
% model analysis and optimization workflow. The structure includes settings
% related to model import, analysis, simulation, diagnostics, plotting,
% sensitivity analysis, and optimization. Inputs and outputs for the
% function are as follows:
%
%   Inputs: None
%
%   Outputs:
%     - stg: A structure containing fields for various settings, which
%            include import options, analysis options, simulation options,
%            diagnostics settings, plotting options, sensitivity analysis
%            options, and optimization settings.
%
%   Functions called: None
%
%   Loaded variables: None
%
% To understand the function better, please read the comments within the
% code for a detailed explanation of each setting and their default values.

% stg.exprun: Lists experiments to run (example experiment 1 to 3 and
% experiment 6)
% 
% stg.useLog: Determines the scoring method choice (check documentation)
% (Use logarithm)
% 
% stg.optmc: Specifies whether to use multi-core wherever available
% (Optimization Multi-core)
% 
% stg.rseed: Sets the random seed value (Random seed)
% 
% stg.simcsl: Indicates whether to display simulation diagnostics in the
% console (Simulation Console)
% 
% stg.optcsl: Specifies whether to display optimization results in the
% console (Optimization console)
% 
% stg.save_results: Specifies whether to save results (Save results)
% 
% stg.simdetail: Specifies whether to run detailed simulation for plots
% 
% stg.maxt: Sets the maximum time for each individual function to run in
% seconds (Maximum time)
% 
% stg.eqt: Defines the equilibration time (Equilibration time)
% 
% stg.dimenanal: Specifies whether to perform Dimensional Analysis
% (Dimensional Analysis)
% 
% stg.UnitConversion: Specifies whether to perform Unit conversion (Unit
% conversion)
% 
% stg.abstolscale: Specifies whether to apply Absolute Tolerance Scaling
% (Absolute Tolerance Scaling)
% 
% stg.reltol: Assigns the value of Relative tolerance (Relative tolerance)
% 
% stg.abstol: Assigns the value of Absolute tolerance (Absolute tolerance)
% 
% stg.simtime: Specifies the time units for simulation (Simulation time)
% 
% stg.sbioacc: Specifies whether to run sbioaccelerate (sbioaccelerate)
% 
% stg.abstolstepsize_eq: Provides the absolute tolerance step size for
% equilibration (Absolute tolerance step size for equilibration)
% 
% stg.maxstep: Max step size in the simulation (if empty, MATLAB decides
% what's best) (Maximum step)
% 
% stg.maxstepeq: Sets the max step size in the simulation (if empty, MATLAB
% decides what's best) (Maximum step)
% 
% stg.maxstepdetail: Sets the max step size in the detailed plots (if
% empty, MATLAB decides what's best) (Maximum step)
% 
% stg.errorscore: Specifies the default score when there is a simulation
% error, required to keep optimizations working (error score)
% 
% stg.parnum: Specifies the number of parameters to optimize (Parameter
% number)
% 
% stg.lb: Assigns the array with the lower bound of all parameters (Lower
% bound)
% 
% stg.ub: Assigns the array with the upper bound of all parameters (Upper
% bound)
% 
% stg.partest: Choice of what parameters in the array to test, the indices
% correspond to the parameters in the model and the numbers correspond to
% the parameters in the optimization array (Parameters to test)
% 
% stg.pat: Defines the parameter array to test (Parameter array to test)
% 
% stg.pa: Contains all the parameter arrays (parameters here are in log10
% space) (Parameter arrays)
% 
% stg.bestpa: Provides the best parameter array found so far for the model
% (Best parameter array)
% 
% stg.plot: Specifies whether to plot results (Plots)
% 
% stg.plotoln: Specifies whether to use long names in the title
% 
% stg.sansamples: Sets the number of samples to use in Sensitivity Analysis
% (Sensitivity analysis number of samples)
% 
% stg.sasubmean: Specifies whether to subtract the mean before calculating
% SI and SIT in Sensitivity Analysis (Sensitivity analysis subtract mean)
% 
% stg.sasamplemode: Determines the sampling mode for Sensitivity Analysis
% (Sensitivity analysis sampling mode)
% 
% stg.sasamplesigma: Defines the sigma for creating the normal distribution
% of parameters to perform Sensitivity Analysis (Sensitivity analysis
% sampling sigma)
% 
% stg.optt: Sets the time for the optimization in seconds (Optimization
% time)
% 
% stg.popsize: Defines the population size for the algorithms that use
% populations (Population size)
% 
% stg.osm: Chooses the optimization start method (Optimization start
% method)
% 
% stg.dbs: Specifies the distance from the best parameter array to be used
% in stg.osm method 2 (Distance from best parameter array)
% 
% stg.mst: Specifies whether to use Multistart (Multistart)
% 
% stg.msts: Provides the Multistart size
% 
% stg.optplots: Specifies whether to display Plots (Plots don't work if
% using multistart) (Optimization plots)
% 
% stg.fmincon: Indicates whether to run fmincon (fmincon)
% 
% stg.fm_options: Sets options for fmincon (fmincon options)
% 
% stg.sa: Specifies whether to run simulated annealing (Simulated
% annealing)
% 
% stg.sa_options: Provides options for simulated annealing (Simulated
% annealing options)
% 
% stg.psearch: Specifies whether to run Pattern search (Pattern search)
% 
% stg.psearch_options: Sets options for Pattern search (Pattern search
% options)
% 
% stg.ga: Specifies whether to run Genetic algorithm (Genetic algorithm)
% 
% stg.ga_options: Options for Genetic algorithm (Genetic algorithm options)
% 
% stg.pswarm: Specifies whether to run Particle swarm (Particle swarm)
% 
% stg.pswarm_options: Sets options for Particle swarm (Particle swarm
% options)
% 
% stg.sopt: Specifies whether to run Surrogate optimization (Surrogate
% optimization)
% 
% stg.sopt_options: Provides options for Surrogate optimization (Surrogate
% optimization options)

%% Analysis

% Lists experiments to run (example experiment 1 to 3 and experiment 6)
stg.exprun = [1:3,6];

% Determines the scoring method choice (check documentation) (Use
% logarithm)
stg.useLog = 4;

% Specifies whether to use multicore wherever available (Optimization
% Multicore)
stg.optmc = true;

% Sets the random seed value (Random seed)
stg.rseed = 1;

% Indicates whether to display simulation diagnostics in the console
% (Simulation Console)
stg.simcsl = false;

% Specifies whether to display optimization results in the console
% (Optimization console)
stg.optcsl = false;

% Specifies whether to save results (Save results)
stg.save_results = true;

% Specifies whether to run detailed simulation for plots
stg.simdetail = true;

%% Simulation

% Sets the maximum time for each individual function to run in seconds
% (Maximum time)
stg.maxt = 10;

% Defines the equilibration time (Equilibration time)
stg.eqt  = 50000;

% Specifies whether to perform Dimensional Analysis (Dimensional Analysis)
stg.dimenanal = false;

% Specifies whether to perform Unit conversion (Unit conversion)
stg.UnitConversion = false;

% Specifies whether to apply Absolute Tolerance Scaling (Absolute Tolerance
% Scaling)
stg.abstolscale = true;

% Assigns the value of Relative tolerance (Relative tolerance)
stg.reltol = 1.0E-3;

% Value of Relative tolerance minimum
% (Relative tolerance minimum)
stg.reltol_min = 1.0E-3;

% Value of Absolute tolerance
% (Absolute tolerance)
stg.abstol = 1.0E-6;

% Value of Absolute tolerance minimum
% (Absolute tolerance minimum)
stg.abstol_min = 1.0E-6;

% Specifies the time units for simulation (Simulation time)
stg.simtime = "second";

% Specifies whether to run sbioaccelerate (after changing this value you
% need to run "clear functions" to see an effect) (sbioaccelerate)
stg.sbioacc = true;

% Provides the absolute tolerance step size for equilibration (Absolute
% tolerance step size for equilibration)
stg.abstolstepsize_eq = [];

% Max step size in the simulation (if empty MATLAB decides whats best)
% (Maximum step)
stg.maxstep = 10;

% Sets the max step size in the simulation (if empty, MATLAB decides what's
% best) (Maximum step)
stg.maxstepeq = 2;

% Sets the max step size in the detailed plots (if empty, MATLAB decides
% what's best) (Maximum step)
stg.maxstepdetail = 2;

% Specifies the default score when there is a simulation error, required to
% keep optimizations working (error score)
stg.errorscore = 10^10;
%% Model

% Specifies the number of parameters to optimize (Parameter number)
stg.parnum = 5;

% Provides the array with the lower bound of all parameters
original_parameter_set = zeros(1,10);

% Assigns the array with the lower bound of all parameters  (Lower bound)
stg.lb = original_parameter_set-5;

% Assigns the array with the upper bound of all parameters (Upper bound)
stg.ub = original_parameter_set+5;

%% Diagnostics

% Choice of what parameters in the array to test, the indices correspond to
% the parameters in the model and the numbers correspond to the parameters
% in the optimization array, usually not all parameters are optimized so
% there needs to be a match between one and the other. (Parameters to test)
% In this example there are ten parameters in this imaginary model and we
% are only interested in parameter 2,4,8,9, and 10. Note that stg.parnum is
% five because of this and not ten
stg.partest(:,1) = [0,1,0,2,0,0,0,3,4,5];

% Defines the parameter array to test (Parameter array to test)
stg.pat = 1:2;

% Contains all the parameter arrays (parameters here are in log10 space)
% (Parameter arrays)
stg.pa(1,:) = [1,1,1,1,1];
stg.pa(1,:) = [1,0,1,2,1];

% Provides the best parameter array found so far for the model (Best
% parameter array)
stg.bestpa = stg.pa(1,:);

%% Plots

stg.lsa_samples = 1000;
stg.lsa_range_from_best = 0.25;

% Specifies whether to plot results (Plots)
stg.plot = true;

% Specifies whether to use long names in the title of the output plots in
% f_plot_outputs.m (Plot outputs long names)
stg.plotoln = true;


stg.in_plot_trim = 1;

%% Sensitivity analysis

% Sets the number of samples to use in Sensitivity Analysis (Sensitivity
% analysis number of samples)
stg.sansamples = 100;

% Specifies whether to subtract the mean before calculating SI and SIT in
% Sensitivity Analysis (Sensitivity analysis subtract mean)
stg.sasubmean = true;

% Determines the sampling mode for Sensitivity Analysis; 0 Log uniform
% distribution truncated at the parameter bounds 1 Log normal distribution
% with mu as the best value for a parameter and sigma as stg.sasamplesigma
% truncated at the parameter bounds 2 same as 1 without truncation 3 Log
% normal distribution centered at the mean of the parameter bounds and
% sigma as stg.sasamplesigma truncated at the parameter bounds 4 same as 3
% without truncation. (Sensitivity analysis sampling mode)
stg.sasamplemode = 2;

% Defines the sigma for creating the normal distribution of parameters to
% perform Sensitivity Analysis (Sensitivity analysis sampling sigma)
stg.sasamplesigma = 0.1;


stg.gsabootstrapsize = ceil(sqrt(stg.sansamples));

%% Profile Likelihood

% Parameter(optimization array) that is being worked on in a specific
% iteration of PL (if -1 no parameter is being worked in PL)
% (Profile Likelihood Index)
stg.PLind = -1;

% Which parameters to do PL on, it should be all parameters but can also be
% a subset for testing purposes
% (Profile Likelihood parameters to Test)
stg.pltest = [1:6];

% How many points to do for each parameter in the PL
% (Profile Likelihood Resolution)
stg.plres = 50;

% True or false to decide whether to do plots after calculating PL
% (Profile Likelihood Plots)
stg.plplot = true;

% (Profile likelihood simulated annealing opptimization to start)
stg.plsaots = optimoptions(@simulannealbnd,'Display','off', ...
    'InitialTemperature',...
    ones(1,stg.parnum-1)*1,'MaxTime',15,'ReannealInterval',40);

% (Profile Likelihood optimization threshold value)
stg.plotv = 0.99;

% Ratio between the value of the first try of a point in PLA and the
% previous point,if above this ratio an intermediate value is picked up to
% 2 times
stg.ratio = 2;

% Profile Likelihood re-optimize optimization number
stg.plroptn = 30;

% Profile Likelihood display current optimization status
stg.pldcos = 0;

% True or false to decide whether to run simulated annealing
% (Profile Likelihood Simulated Annealing)
stg.plsa = true;

% Options for simulated annealing
% (Profile Likelihood Simulated Annealing options)
stg.plsao = optimoptions(@simulannealbnd,'Display','off', ...
    'InitialTemperature',...
    ones(1,stg.parnum-1)*1,'MaxTime',10,'ReannealInterval',40);

% (Profile Likelihood Simulated Annealing options start)
stg.plsaos = optimoptions(@simulannealbnd,'Display','off', ...
        'InitialTemperature',...
        ones(1,stg.parnum-1)*1,'MaxTime',60,'ReannealInterval',40);

% True or false to decide whether to run Pattern search
% (Profile Likelihood Pattern search)
stg.plps = true;

% Options for Pattern search
% (Pattern search options)
stg.plpso = optimoptions(@patternsearch,'Display','off',...
    'MaxTime',9,...
    'UseCompletePoll',false,'UseCompleteSearch',false,...
    'MaxMeshSize',1,'MaxFunctionEvaluations',10000);

stg.plpsos = optimoptions(@patternsearch,'Display','off',...
    'MaxTime',60,...
    'UseCompletePoll',false,'UseCompleteSearch',false,...
    'MaxMeshSize',1,'MaxFunctionEvaluations',10000);

% True or false to decide whether to run surrogate optimization
% (Profile Likelihood surrogate optimization)
stg.plfm = true;

% Options for surrogate optimization
% (Profile Likelihood surrogate optimization options)
stg.plfmo = optimoptions(@simulannealbnd,'Display','off', ...
    'InitialTemperature',...
    ones(1,stg.parnum-1)*1,'MaxTime',10,'ReannealInterval',40);

% (Profile Likelihood surrogate optimization options start)
stg.plfmos = optimoptions(@simulannealbnd,'Display','off', ...
        'InitialTemperature',...
        ones(1,stg.parnum-1)*1,'MaxTime',60,'ReannealInterval',40);

%% Optimization

% Sets the time for the optimization in seconds (fmincon does not respect
% this time!!) (Optimization time)
stg.optt = 60*5;

% Defines the population size for the algorithms that use populations
% (Population size)
stg.popsize = 144;

% Chooses the optimization start method: 1 for random starting point(s)
% inside bounds, 2 for random starting point(s) near the best point
% (Optimization start method)
stg.osm = 1;

% Specifies the distance from the best parameter array to be used in
% stg.osm method 2 (Distance from best parameter array)
stg.dbpa = 0.1;

% Specifies whether to use Multistart (Multistart)
stg.mst = false;

% Provides the Multistart size
stg.msts = 1;

% Specifies whether to display Plots (Plots don't work if using multistart)
% (Optimization plots)
stg.optplots = true;

% Indicates whether to run fmincon (no gradient, so this doesn't work well;
% no max time!!) (fmincon)
stg.fmincon = false;

% Sets options for fmincon (fmincon options)
stg.fm_options = optimoptions('fmincon', 'Algorithm', 'interior-point',...
    'MaxIterations', 10, 'OptimalityTolerance', 0, 'StepTolerance', 1e-6,...
    'FiniteDifferenceType', 'central', 'MaxFunctionEvaluations', 10000);

% Specifies whether to run simulated annealing (Simulated annealing)
stg.sa = false;

% Provides options for simulated annealing (Simulated annealing options)
stg.sa_options = optimoptions(@simulannealbnd, 'MaxTime', stg.optt,...
    'ReannealInterval', 40);

% Specifies whether to run Pattern search (Pattern search)
stg.psearch = false;

% Sets options for Pattern search (Pattern search options)
stg.psearch_options = optimoptions(@patternsearch, 'MaxTime', stg.optt,...
    'UseParallel', stg.optmc, 'UseCompletePoll', true,...
    'UseCompleteSearch', true, 'MaxMeshSize',2, ...
    'MaxFunctionEvaluations', 2000);

% Specifies whether to run Genetic algorithm (Genetic algorithm)
stg.ga = false;

% Options for Genetic algorithm (Genetic algorithm options)
stg.ga_options = optimoptions(@ga, 'MaxGenerations', 200, ...
    'MaxTime', stg.optt,'UseParallel', stg.optmc, ...
    'PopulationSize', stg.popsize,'MutationFcn', 'mutationadaptfeasible', ...
    'HybridFcn',{@patternsearch,stg.psearch_options});

% Specifies whether to run Particle swarm (Particle swarm)
stg.pswarm = false;

% Sets options for Particle swarm (Particle swarm options)
stg.pswarm_options = optimoptions('particleswarm', 'MaxTime', stg.optt,...
    'UseParallel', stg.optmc, 'MaxIterations', 200, ...
    'SwarmSize', stg.popsize);
    
% Specifies whether to run Surrogate optimization (Surrogate optimization)
stg.sopt = false;

% Provides options for Surrogate optimization (Surrogate optimization
% options)
stg.sopt_options = optimoptions('surrogateopt', 'MaxTime', stg.optt,...
    'UseVectorized', stg.optmc, 'MaxFunctionEvaluations', 5000,...
    'MinSampleDistance', 0.2, 'MinSurrogatePoints', 32*2+1);
end

Example settings code

Import

Default settings code

Example settings code

• stg.import - (logical) Decide whether to run import functions

• stg.sbtab_excel_name - (string) Name of the Excel file with the SBtab

• stg.name - (string) Name of the model

• stg.cname - (string) Name of the default model compartment

• stg.sbtab_name - (string) Name of the SBtab saved in .mat format

Analysis

Default settings code

% Lists experiments to run (example experiment 1 to 3 and experiment 6)
stg.exprun = [1:3,6];

% Determines the scoring method choice (check documentation) (Use
% logarithm)
stg.useLog = 4;

% Specifies whether to use multicore wherever available (Optimization
% Multicore)
stg.optmc = true;

% Sets the random seed value (Random seed)
stg.rseed = 1;

% Indicates whether to display simulation diagnostics in the console
% (Simulation Console)
stg.simcsl = false;

% Specifies whether to display optimization results in the console
% (Optimization console)
stg.optcsl = false;

% Specifies whether to save results (Save results)
stg.save_results = true;

% Specifies whether to run detailed simulation for plots
stg.simdetail = true;

Example settings code

• stg.exprun - (double) Experiments to run

• stg.useLog - (double) Choice between 0,1,2 and 3 to change either and how to apply log10 to the scores, check results:

• stg.optmc - (logical) Decide whether to use multicore everywhere it is available

• stg.rseed - (double) Choice of random seed

• stg.simcsl - (logical) Decide whether to display simulation diagnostics in the console

• stg.optcsl - (logical) Decide whether to display optimization results on console

• stg.save_results - (logical) Decide whether to save results

• stg.simdetail - (logical) Decide whether to run detailed simulation for plots

Simulation

Default settings code

% Sets the maximum time for each individual function to run in seconds
% (Maximum time)
stg.maxt = 10;

% Defines the equilibration time (Equilibration time)
stg.eqt  = 50000;

% Specifies whether to perform Dimensional Analysis (Dimensional Analysis)
stg.dimenanal = false;

% Specifies whether to perform Unit conversion (Unit conversion)
stg.UnitConversion = false;

% Specifies whether to apply Absolute Tolerance Scaling (Absolute Tolerance
% Scaling)
stg.abstolscale = true;

% Assigns the value of Relative tolerance (Relative tolerance)
stg.reltol = 1.0E-3;

% Value of Relative tolerance minimum
% (Relative tolerance minimum)
stg.reltol_min = 1.0E-3;

% Value of Absolute tolerance
% (Absolute tolerance)
stg.abstol = 1.0E-6;

% Value of Absolute tolerance minimum
% (Absolute tolerance minimum)
stg.abstol_min = 1.0E-6;

% Specifies the time units for simulation (Simulation time)
stg.simtime = "second";

% Specifies whether to run sbioaccelerate (after changing this value you
% need to run "clear functions" to see an effect) (sbioaccelerate)
stg.sbioacc = true;

% Provides the absolute tolerance step size for equilibration (Absolute
% tolerance step size for equilibration)
stg.abstolstepsize_eq = [];

% Max step size in the simulation (if empty MATLAB decides whats best)
% (Maximum step)
stg.maxstep = 10;

% Sets the max step size in the simulation (if empty, MATLAB decides what's
% best) (Maximum step)
stg.maxstepeq = 2;

% Sets the max step size in the detailed plots (if empty, MATLAB decides
% what's best) (Maximum step)
stg.maxstepdetail = 2;

% Specifies the default score when there is a simulation error, required to
% keep optimizations working (error score)
stg.errorscore = 10^10;

Example settings code

• stg.maxt - (double) Maximum time for each individual function has to run in seconds

• stg.eqt - (double) Equilibration time in seconds

• stg.dimenanal - (logical) Decide whether to do Dimensional Analysis

• stg.UnitConversion - (logical) Decide whether to do Unit conversion

• stg.abstolscale - (logical) Decide whether to do Absolute Tolerance Scaling

• stg.reltol - (double) Value of Relative tolerance

• stg.abstol - (double) Value of Absolute tolerance

• stg.simtime - (string) Time units for simulation

• stg.sbioacc - (logical) Decide whether to run sbioaccelerate (after changing this value you need to run “clear functions” to see an effect)

• stg.abstolstepsize_eq - (double) Absolute tolerance step size for equilibration (if empty MATLAB® decides whats best)

• stg.maxstep - (double) Max step size in the simulation (if empty MATLAB® decides what’s best)

• stg.maxstepeq - (double) Max step size in the equilibration (if empty MATLAB® decides whats best)

• stg.maxstepdetail - (double) Max step size in the detailed plots (if empty MATLAB® decides whats best)

• stg.errorscore - (double) Default score when there is a simulation error, this is needed to keep the optimizations working.

Model

Default settings code

% Specifies the number of parameters to optimize (Parameter number)
stg.parnum = 5;

% Provides the array with the lower bound of all parameters
original_parameter_set = zeros(1,10);

% Assigns the array with the lower bound of all parameters  (Lower bound)
stg.lb = original_parameter_set-5;

% Assigns the array with the upper bound of all parameters (Upper bound)
stg.ub = original_parameter_set+5;

Example settings code

• stg.parnum - (double) Number of parameters to optimize

• stg.tci - (double) Index for the parameters that have thermodynamic constraints

• stg.tcm - (double) Parameters to multiply to the first parameter (in stg.partest to get to the correct thermodynamic constraint formula)

• stg.tcd - (double) Parameters to divide to the first parameter (in stg.partest to get to the correct thermodynamic constraint formula)

• stg.lb - (double) Lower bound of all parameters

  \[stg.lb = \begin{bmatrix} lb_{1} & lb_{2} & ... & lb_{i} \end{bmatrix}\]

  • \(i =\) Parameter index

• stg.ub - (double) Upper bound of all parameters

  \[stg.up = \begin{bmatrix} ub_{1} & ub_{2} & ... & ub_{i} \end{bmatrix}\]

  • \(i =\) Parameter index

Diagnostics

Default settings code

% Choice of what parameters in the array to test, the indices correspond to
% the parameters in the model and the numbers correspond to the parameters
% in the optimization array, usually not all parameters are optimized so
% there needs to be a match between one and the other. (Parameters to test)
% In this example there are ten parameters in this imaginary model and we
% are only interested in parameter 2,4,8,9, and 10. Note that stg.parnum is
% five because of this and not ten
stg.partest(:,1) = [0,1,0,2,0,0,0,3,4,5];

% Defines the parameter array to test (Parameter array to test)
stg.pat = 1:2;

% Contains all the parameter arrays (parameters here are in log10 space)
% (Parameter arrays)
stg.pa(1,:) = [1,1,1,1,1];
stg.pa(1,:) = [1,0,1,2,1];

% Provides the best parameter array found so far for the model (Best
% parameter array)
stg.bestpa = stg.pa(1,:);

Example settings code

• stg.partest - (double) Choice of which parameters to work on, since depending on the task, not all SBtab parameters are worked on. k indices correspond to the parameters in the SBtab and numbers up to i correspond to the parameters in the work set. This is the set that actually gets used for diagnostics, optimization, and sensitivity analyis.

  \[stg.partest_k = \begin{bmatrix} 1_{k_1} & 2_{k_2} & ... & i_{k_{end}} \end{bmatrix}\]

  In our example model parameter 216 from the SBtab is parameter number 1 of the work set, parameter 217 from the SBtab is parameter number 2 of the work set, and successively.

  \[stg.partest_{[216:227]} = \begin{bmatrix} 1_{216} & 2_{217} & ... & 6_{221} & 1_{222} & 2_{223} & ... & 6_{227} \end{bmatrix}\]

• stg.pat - (double) Index(\(j\)) of the parameter set to work on

• stg.pa - (double) All the parameter sets

  \[\begin{split}stg.pa = \begin{bmatrix} x_{1,1} & x_{2,1} & ... & x_{i,1} \\ x_{1,2} & x_{2,2} & ... & x_{i,2} \\ ... & ... & ... & ... \\ x_{1,j} & x_{2,j} & ... & x_{i,j} \end{bmatrix}\end{split}\]

• stg.bestpa - (double) Best parameter set found so far during optimization

  \[stg.bestx = \begin{bmatrix} bestx_{1} & bestx_{2} & ... & bestx_{i} \end{bmatrix}\]

  • \(x =\) Parameters being worked on

  • \(i =\) Index of Parameters being worked on

  • \(k =\) Index of the parameters in SBtab

  • \(j =\) Index of the Parameter set to work on

Plots

Default settings code

stg.lsa_samples = 1000;
stg.lsa_range_from_best = 0.25;

% Specifies whether to plot results (Plots)
stg.plot = true;

% Specifies whether to use long names in the title of the output plots in
% f_plot_outputs.m (Plot outputs long names)
stg.plotoln = true;


stg.in_plot_trim = 1;

Example settings code

• stg.plot - (logical) Decide whether to plot results

• stg.plotoln - (logical) Decide whether to use long names in the title of the output plots in f_plot_outputs.m

Global Sensitivity Analysis (GSA)

Default settings code

% Sets the number of samples to use in Sensitivity Analysis (Sensitivity
% analysis number of samples)
stg.sansamples = 100;

% Specifies whether to subtract the mean before calculating SI and SIT in
% Sensitivity Analysis (Sensitivity analysis subtract mean)
stg.sasubmean = true;

% Determines the sampling mode for Sensitivity Analysis; 0 Log uniform
% distribution truncated at the parameter bounds 1 Log normal distribution
% with mu as the best value for a parameter and sigma as stg.sasamplesigma
% truncated at the parameter bounds 2 same as 1 without truncation 3 Log
% normal distribution centered at the mean of the parameter bounds and
% sigma as stg.sasamplesigma truncated at the parameter bounds 4 same as 3
% without truncation. (Sensitivity analysis sampling mode)
stg.sasamplemode = 2;

% Defines the sigma for creating the normal distribution of parameters to
% perform Sensitivity Analysis (Sensitivity analysis sampling sigma)
stg.sasamplesigma = 0.1;


stg.gsabootstrapsize = ceil(sqrt(stg.sansamples));

%% Profile Likelihood

% Parameter(optimization array) that is being worked on in a specific
% iteration of PL (if -1 no parameter is being worked in PL)
% (Profile Likelihood Index)
stg.PLind = -1;

% Which parameters to do PL on, it should be all parameters but can also be
% a subset for testing purposes
% (Profile Likelihood parameters to Test)
stg.pltest = [1:6];

% How many points to do for each parameter in the PL
% (Profile Likelihood Resolution)
stg.plres = 50;

% True or false to decide whether to do plots after calculating PL
% (Profile Likelihood Plots)
stg.plplot = true;

% (Profile likelihood simulated annealing opptimization to start)
stg.plsaots = optimoptions(@simulannealbnd,'Display','off', ...
    'InitialTemperature',...
    ones(1,stg.parnum-1)*1,'MaxTime',15,'ReannealInterval',40);

% (Profile Likelihood optimization threshold value)
stg.plotv = 0.99;

% Ratio between the value of the first try of a point in PLA and the
% previous point,if above this ratio an intermediate value is picked up to
% 2 times
stg.ratio = 2;

% Profile Likelihood re-optimize optimization number
stg.plroptn = 30;

% Profile Likelihood display current optimization status
stg.pldcos = 0;

% True or false to decide whether to run simulated annealing
% (Profile Likelihood Simulated Annealing)
stg.plsa = true;

% Options for simulated annealing
% (Profile Likelihood Simulated Annealing options)
stg.plsao = optimoptions(@simulannealbnd,'Display','off', ...
    'InitialTemperature',...
    ones(1,stg.parnum-1)*1,'MaxTime',10,'ReannealInterval',40);

% (Profile Likelihood Simulated Annealing options start)
stg.plsaos = optimoptions(@simulannealbnd,'Display','off', ...
        'InitialTemperature',...
        ones(1,stg.parnum-1)*1,'MaxTime',60,'ReannealInterval',40);

% True or false to decide whether to run Pattern search
% (Profile Likelihood Pattern search)
stg.plps = true;

% Options for Pattern search
% (Pattern search options)
stg.plpso = optimoptions(@patternsearch,'Display','off',...
    'MaxTime',9,...
    'UseCompletePoll',false,'UseCompleteSearch',false,...
    'MaxMeshSize',1,'MaxFunctionEvaluations',10000);

stg.plpsos = optimoptions(@patternsearch,'Display','off',...
    'MaxTime',60,...
    'UseCompletePoll',false,'UseCompleteSearch',false,...
    'MaxMeshSize',1,'MaxFunctionEvaluations',10000);

% True or false to decide whether to run surrogate optimization
% (Profile Likelihood surrogate optimization)
stg.plfm = true;

% Options for surrogate optimization
% (Profile Likelihood surrogate optimization options)
stg.plfmo = optimoptions(@simulannealbnd,'Display','off', ...
    'InitialTemperature',...
    ones(1,stg.parnum-1)*1,'MaxTime',10,'ReannealInterval',40);

% (Profile Likelihood surrogate optimization options start)
stg.plfmos = optimoptions(@simulannealbnd,'Display','off', ...
        'InitialTemperature',...
        ones(1,stg.parnum-1)*1,'MaxTime',60,'ReannealInterval',40);

Example settings code

• stg.sansamples - (double) Number of samples to use in GSA (in total (2+npars)*sansamples simulations will be performed, where npars are the number of parameters).

• stg.sasubmean - (logical) Decide whether to subtract mean before calculating SI and STI, see Halnes et al 2009.

• stg.sasamplemode - (double) Choose the way you want to obtain the samples of the parameters for performing the GSA;

0. Reciprocal (log uniform) distribution

\(X_{i} \sim Reciprocal(a_{i},b_{i})\)

• \(i =\) Parameter index

• \(a_{i} = stg.lb_{i}\)

• \(b_{i} = stg.ub_{i}\)

Example distribution with \(a = -1, b = 1\)

1. Log normal distribution with μ corresponding to the best value for a parameter, as recieved from the optimization, and σ as stg.sasamplesigma truncated at the parameter bounds

\(X_{i} \sim TruncatedLogNormal(μ_{i}, σ, a_{i}, b_{i})\)

• \(i =\) Parameter index

• \(μ_{i} = bestx_{i}\)

• \(σ = stg.sasamplesigma\)

• \(a_{i} = stg.lb_{i}\)

• \(b_{i} = stg.ub_{i}\)

Example distribution with \(μ = 0.5, σ = 1, a = -1, b = 1\)

2. same as 1 without truncation

\(X_{i} \sim LogNormal(μ, σ)\)

• \(i =\) Parameter index

• \(μ_{i} = bestx_{i}\)

• \(σ = stg.sasamplesigma\)

Example distribution with \(μ = 0.5, σ = 1\)

3. Log normal distribution with μ corresponding to the mean of the parameter bounds and σ as stg.sasamplesigma but truncated at the parameter bounds

\(X_{i} \sim TruncatedLogNormal(μ_{i}, σ, a_{i}, b_{i})\)

• \(i =\) Parameter index

• \(μ_{i} = \frac{stg.lb_{i} + (stg.ub_{i} - stg.lb_{i})}{2}\)

• \(σ = stg.sasamplesigma\)

• \(a_{i} = stg.lb_{i}\)

• \(b_{i} = stg.ub_{i}\)

Example distribution with \(μ = \frac{a+(b-a)}{2}, σ = 1, a = -1, b = 1\)

4. same as 3 without truncation.

\(X_{i} \sim LogNormal(mu_{i}, σ)\)

• \(i =\) Parameter index

• \(μ_{i} = \frac{stg.lb_{i} + (stg.ub_{i} - stg.lb_{i})}{2}\)

• \(σ = stg.sasamplesigma\)

Example distribution with \(μ = \frac{a+(b-a)}{2}, σ = 1, a = -1, b = 1\)

• stg.sasamplesigma - (double) σ for creating the normal distribution of parameters to perform sensitivity analysis

Optimization

Default settings code

% Sets the time for the optimization in seconds (fmincon does not respect
% this time!!) (Optimization time)
stg.optt = 60*5;

% Defines the population size for the algorithms that use populations
% (Population size)
stg.popsize = 144;

% Chooses the optimization start method: 1 for random starting point(s)
% inside bounds, 2 for random starting point(s) near the best point
% (Optimization start method)
stg.osm = 1;

% Specifies the distance from the best parameter array to be used in
% stg.osm method 2 (Distance from best parameter array)
stg.dbpa = 0.1;

% Specifies whether to use Multistart (Multistart)
stg.mst = false;

% Provides the Multistart size
stg.msts = 1;

% Specifies whether to display Plots (Plots don't work if using multistart)
% (Optimization plots)
stg.optplots = true;

% Indicates whether to run fmincon (no gradient, so this doesn't work well;
% no max time!!) (fmincon)
stg.fmincon = false;

% Sets options for fmincon (fmincon options)
stg.fm_options = optimoptions('fmincon', 'Algorithm', 'interior-point',...
    'MaxIterations', 10, 'OptimalityTolerance', 0, 'StepTolerance', 1e-6,...
    'FiniteDifferenceType', 'central', 'MaxFunctionEvaluations', 10000);

% Specifies whether to run simulated annealing (Simulated annealing)
stg.sa = false;

% Provides options for simulated annealing (Simulated annealing options)
stg.sa_options = optimoptions(@simulannealbnd, 'MaxTime', stg.optt,...
    'ReannealInterval', 40);

% Specifies whether to run Pattern search (Pattern search)
stg.psearch = false;

% Sets options for Pattern search (Pattern search options)
stg.psearch_options = optimoptions(@patternsearch, 'MaxTime', stg.optt,...
    'UseParallel', stg.optmc, 'UseCompletePoll', true,...
    'UseCompleteSearch', true, 'MaxMeshSize',2, ...
    'MaxFunctionEvaluations', 2000);

% Specifies whether to run Genetic algorithm (Genetic algorithm)
stg.ga = false;

% Options for Genetic algorithm (Genetic algorithm options)
stg.ga_options = optimoptions(@ga, 'MaxGenerations', 200, ...
    'MaxTime', stg.optt,'UseParallel', stg.optmc, ...
    'PopulationSize', stg.popsize,'MutationFcn', 'mutationadaptfeasible', ...
    'HybridFcn',{@patternsearch,stg.psearch_options});

% Specifies whether to run Particle swarm (Particle swarm)
stg.pswarm = false;

% Sets options for Particle swarm (Particle swarm options)
stg.pswarm_options = optimoptions('particleswarm', 'MaxTime', stg.optt,...
    'UseParallel', stg.optmc, 'MaxIterations', 200, ...
    'SwarmSize', stg.popsize);
    
% Specifies whether to run Surrogate optimization (Surrogate optimization)
stg.sopt = false;

% Provides options for Surrogate optimization (Surrogate optimization
% options)
stg.sopt_options = optimoptions('surrogateopt', 'MaxTime', stg.optt,...
    'UseVectorized', stg.optmc, 'MaxFunctionEvaluations', 5000,...
    'MinSampleDistance', 0.2, 'MinSurrogatePoints', 32*2+1);
end

Example settings code

• stg.optt - (double) Time for the optimization in seconds (fmincon does not respect this time!!)

• stg.popsize - (double) Population size (for the algorithms that use populations)

• stg.osm - (double) optimization start method, choose between

  1. Get a random starting parameter set or group of starting parameter sets inside the bounds

  2. Get a random starting parameter set or group of starting parameter sets near the best parameter set

• stg.dbpa - (double) Distance from best parameter set to be used in stg.osm method 2

• stg.mst - (logical) Decide whether to use one or multiple starting parameter sets for the optimization

• stg.msts - (double) Number of starting parameter sets for the optimizations

• stg.optplots - (logical) Decide whether to display optimiazation plots (They aren’t ploted if running the code in multicore)

• stg.fmincon - (logical) Decide whether to run fmincon (no gradient in our models so this doesn’t work very well, does not respect time set for the optimization!!)

• stg.fm_options - (optim.options.Fmincon) Options for fmincon

• stg.sa - (logical) Decide whether to run simulated annealing

• stg.sa_options - (optim.options.SimulannealbndOptions) Options for simulated annealing

• stg.psearch - (logical) Decide whether to run Pattern search

• stg.psearch_options - (optim.options.PatternsearchOptions) Options for Pattern search

• stg.ga - (logical) Decide whether to run Genetic algorithm

• stg.ga_options - (optim.options.GaOptions) Options for Genetic algorithm

• stg.pswarm - (logical) Decide whether to run Particle swarm

• stg.pswarm_options - (optim.options.Particleswarm) Options for Particle swarm

• stg.sopt - (logical) Decide whether to run Surrogate optimization

• stg.sopt_options - (optim.options.Surrogateopt) Options for Surrogate optimization

Automatically generated at Import

• stg.expn - (double) Total number of experiments stored in the SBtab

• stg.outn - (double) Total number of experimental outputs specified in the SBtab

References

Halnes, G., Ulfhielm, E., Ljunggren, E.E., Kotaleski, J.H. and Rospars, J.P., 2009. Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of Computational Neuroscience, 27(3), p.471.