[. . . ] 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 .
. [. . . ]