User manual THE MATHWORKS SIMBIOLOGY 3

[. . . ] SimBiology® 3 User's Guide How to Contact MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. SimBiology® User's Guide © COPYRIGHT 2005­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] Name 1 2 3 4 5 6 Receptor-ligand interaction Heterotrimeric G protein formation G protein activation Receptor synthesis and degradation Receptor-ligand degradation G protein inactivation Reaction L + R <-> RL Gd + Gbg -> G RL + G -> Ga + Gbg + RL Rate Parameters kRL, kRLm kG1 kGa kRdo, kRs kRD1 kGd R <-> null RL -> null Ga -> Gd 3-37 3 Analysis Assume that you are calculating the sensitivity of species Ga with respect to every parameter in the model. Thus, you want to calculate the time-dependent derivatives: ( Ga ) ( Ga ) ( Ga ) (Ga) , , , . . . ( kRLm ) ( kRL ) ( kG1) ( kGa ) To calculate these sensitivities: 1 Load the model and set the SpeciesOutputs property to Ga. 2 Set the ParameterInputFactors property to all the parameters in the model. 3 Set the SensitivityAnalysis property to true and simulate the model. 4 Plot the data. The following sections explain the details of the procedure. See also the following demo: Parameter Scanning, Parameter Estimation, and Sensitivity Analysis in the Yeast Heterotrimeric G Protein Cycle Loading and Configuring the Model for Sensitivity Analysis 1 The project gprotein_norules. sbproj contains two models: one for the wild-type strain (stored in variable m1), and one for the mutant strain (stored in variable m2). Load the G protein model for the wild-type strain. sbioloadproject gprotein_norules m1 2 The options for sensitivity analysis are in the configuration set object. Get the configuration set object from the model. csObj = getconfigset(m1); 3 Set the SpeciesOutputs property to calculate the sensitivities for the species Ga in m1. You can display the model species using 3-38 Command-Line Example -- Calculating Sensitivities m1. Compartments(1). Species, which shows that species Ga is listed as the 6th species in the model. Ga = m1. Compartments(1). Species(6); set(csObj. SensitivityAnalysisOptions, 'SpeciesOutputs', Ga); 4 Retrieve all the parameters in the model and store the vector in a variable. % The function sbioselect allows you to query by Type pif = sbioselect(m1, 'Type', 'parameter'); 5 Set the ParameterInputFactors property of the SensitivityAnalysisOptions object to the variable containing the parameters. set(csObj. SensitivityAnalysisOptions, 'ParameterInputFactors', pif); Performing Sensitivity Analysis 1 Enable sensitivity analysis in the configuration set object (csObj) by setting the SensitivityAnalysis option to true. set(csObj. SolverOptions, 'SensitivityAnalysis', true); 2 Set the Normalization property of the SensitivityAnalysisOptions object to perform 'Full' normalization. set(csObj. SensitivityAnalysisOptions, 'Normalization', 'Full'); 3 Simulate the model and return the data to a SimData object (simDataObj). simDataObj = sbiosimulate(m1); For more information about normalization see Normalization in the SimBiology Reference. Extracting and Plotting Sensitivity Data You can extract sensitivity results using the getsensmatrix method. In this example, R is the sensitivity of the species Ga with respect to eight parameters. This example shows how to compare the variation of sensitivity 3-39 3 Analysis of Ga with respect to various parameters, and find the parameters that affect Ga the most. 1 Extract sensitivity data in output variables T (time), R (sensitivity data for species Ga), snames (names of the states specified for sensitivity analysis), and ifacs (names of the input factors used for sensitivity analysis). [T, R, snames, ifacs] = getsensmatrix(simDataObj); 2 Reshape R into columns of input factors to facilitate visualization and plotting. R2 = squeeze(R); 3 After extracting the data and reshaping the matrix, you can now plot the data. % Open a new figure figure; % Plot time (T) against the reshaped data R2 plot(T, R2); title('Normalized Sensitivity of Ga With Respect To Various Parameters'); xlabel('Time (seconds)'); ylabel('Normalized Sensitivity of Ga'); % Use the ifacs variable containing the % names of the input factors for the legend % Specify legend location and appearance leg = legend(ifacs, 'Location', 'NorthEastOutside'); set(leg, 'Interpreter', 'none'); 3-40 Command-Line Example -- Calculating Sensitivities From the previous plot you can see that Ga is most sensitive to parameters kGd, kRs, kRD1, and kGa. This suggests that the amounts of active G protein in the cell depends on the rate of: · Receptor synthesis · Degradation of the receptor-ligand complex · G protein activation · G protein inactivation 3-41 3 Analysis See Also For information about. . . Configuring simulation settings Normalizing the data Selecting model component objects by querying the model as shown in Step 4 in "Loading and Configuring the Model for Sensitivity Analysis" on page 3-38 See. . . "Performing Simulations at the Command Line" on page 2-2 Normalization in the SimBiology Reference sbioselect 3-42 Parameter Estimation Parameter Estimation In this section. . . "About Parameter Estimation" on page 3-43 "SimBiology Parameter Estimation" on page 3-43 About Parameter Estimation Parameter estimation lets you estimate the values of unknown parameters in a model. This is especially useful when some parameters cannot be measured experimentally . SimBiology Parameter Estimation You can estimate a single parameter or all parameters in your model using the sbioparamestim function. Parameter estimation uses the optimization functions in MATLAB, Optimization ToolboxTM, and Global Optimization Toolbox to enable estimation. Optimization Toolbox, and Global Optimization Toolbox are not required for you to use sbioparamestim. If you have these products installed, you can specify optimization methods from these toolboxes as arguments for the sbioparamestim function. If you do not have these products installed, sbioparamestim uses the MATLAB function fminsearch by default. For an example, see "Command-Line Example -- Parameter Estimation" on page 3-44 3-43 3 Analysis Command-Line Example -- Parameter Estimation In this section. . . "About the Example Model" on page 3-44 "Importing Target Experimental Data" on page 3-45 "Simulating the G Protein Model" on page 3-45 "Estimating a Parameter (kGd) in the G Protein Model" on page 3-48 "Simulating and Plotting Results Using the Estimated Parameter" on page 3-50 "Estimating Other Parameters in the G Protein Model" on page 3-51 About the Example Model This example uses a G protein model built in the "Model of the Yeast Heterotrimeric G Protein Cycle " tutorial to illustrate parameter estimation. [. . . ] To edit a response, double-click the cells in the Value column to edit them. · Column Name -- Column header in the data set containing the observed response. · Component Name -- Component in the model representing the observed response. Tip After double-clicking a cell, press the down arrow key to display a list of possible values to choose from, select a name from the list, and then press Enter. 4-95 4 Pharmacokinetic Modeling To add a response, click and then click . . [. . . ]