# SimBiology.SensitivityAnalysisOptions

Specify sensitivity analysis options for SimBiology models

## Description

This object contains options for local sensitivity
analysis. The object is a property of a `SimBiology.Configset`

object.

Local sensitivity analysis is supported only for deterministic (ODE) simulations. To enable or disable local sensitivity analysis, use the SensitivityAnalysis property.

You can add a number of configuration set objects with different
`SensitivityAnalysisOptions`

to the model object with the `addconfigset`

method. Only one configuration set object in the model object can
have the `Active`

property set to
`true`

at any given time.

## Creation

Use `addconfigset`

or `getconfigset`

to get a `configset`

object of a SimBiology model
first. Then use dot notation `configsetObj.SensitivityAnalysisOptions`

to get
the options object.

## Properties

`Inputs`

— Sensitivity inputs

`[]`

(default) | `SimBiology.Species`

| `SimBiology.Parameter`

| `SimBiology.Compartment`

| array

Sensitivity inputs with respect to which you want to compute the sensitivities of
species or parameter states in your model, specified as a
`SimBiology.Species`

, `SimBiology.Parameter`

,
`SimBiology.Compartment`

, or array of such objects.

SimBiology^{®} calculates sensitivities with respect to the values of parameters,
compartments, and species specified in the `Inputs`

property. When you
simulate a model with `SensitivityAnalysis`

enabled in the active
`configset`

object, sensitivity analysis returns the computed
sensitivities of the species and parameters specified in the
`Outputs`

property.

**Note**

If a species, parameter, or compartment is determined by a repeated assignment rule, then you cannot use it as a sensitivity input.

To be a sensitivity input, a compartment must have a constant capacity, that is, its

`Constant`

property must be set to`true`

.If a parameter is referenced by the

`LagParameterName`

or`DurationParameterName`

property of a`SimBiology.RepeatDose`

, the parameter must be constant to be an input for sensitivity analysis.If a parameter is referenced by any other

`SimBiology.RepeatDose`

properties, namely,`Amount`

,`Rate`

,`Interval`

,`StartTime`

, and`RepeatCount`

, you cannot use the parameter as an input for sensitivity analysis.If you have any species, parameter, or compartment affecting a parameterized

`RepeatDose`

or`ScheduleDose`

object, directly or indirectly via a rule, you cannot use such a quantity as an input for sensitivity analysis.The sensitivities are zero for any sensitivity input that is determined by an initial assignment.

`Outputs`

— Sensitivity outputs

`[]`

(default) | `SimBiology.Species`

| `SimBiology.Parameter`

| array | ...

Sensitivity outputs, specified as a `SimBiology.Species`

,
`SimBiology.Parameter`

, or array of such objects. The property defines
species and parameter states that you want to compute sensitivities for.

SimBiology calculates sensitivities with respect to the values of the parameters and
the initial amounts of the species specified in the `Inputs`

property. When you simulate a model with `SensitivityAnalysis`

enabled
in the active `SimBiology.configset`

object, sensitivity analysis returns
the computed sensitivities of the species and parameters specified in the
`Outputs`

property.

**Note**

If a species or parameter is determined by a repeated assignment rule, then you cannot use it as a sensitivity output.

`Normalization`

— Normalization type for local sensitivity analysis

`"None"`

(default) | `"Half"`

`"Full"`

Normalization type for local sensitivity analysis, specified as
`"None"`

, `"Half"`

, or
`"Full"`

.

The following equations show you how sensitivities of a species `x`

with respect to an input parameter `k`

are calculated for each
normalization type. In each equation, the numerator is a sensitivity output and the
denominator is a sensitivity input.

`"Full"`

specifies that the data should be made dimensionless.$$\left(\frac{k}{x(t)}\right)\left(\frac{\partial x(t)}{\partial k}\right)$$

Use this option if you want to compute the relative change in a sensitivity output,

`x(t)`

, with respect to the relative change in a sensitivity input,`k`

. This option is useful to compare different sensitivities where the respective sensitivity inputs have different units and respective sensitivity outputs have different units as well.`"Half"`

specifies normalization relative to the numerator (sensitivity output) only.$$\left(\frac{1}{x(t)}\right)\left(\frac{\partial x(t)}{\partial k}\right)$$

Use this option if you want to compute the relative change in a sensitivity output,

`x(t)`

, with respect to the absolute change in a sensitivity input,`k`

. This option is useful to compare different sensitivities when the sensitivity outputs have different units while the inputs have the same units.`"None"`

specifies no normalization.$$\frac{\partial x(t)}{\partial k}$$

Use this option if you want to compute the absolute change in a sensitivity output,

`x(t)`

, with respect to the absolute change in a sensitivity input,`k`

. This option is useful to compare different sensitivities when all sensitivity inputs have the same units and all sensitivity outputs have the same units.

**Tip**

Intuitively, you might want to normalize even if the units are the same when the inputs and/or outputs are at very different scales. For instance, one species might have a concentration of around 1 mM while another has a concentration around 100 mM. Using the full normalization lets you compare the relative (percentage) change, such as 1%, to both sensitivity inputs and outputs. However, if you want to compare the sensitivities of an absolute change, such as 0.1 nM, to both inputs and outputs, use no normalization.

**Data Types: **`char`

| `string`

## Examples

### Calculate Sensitivities Using sbiosimulate

This example performs local sensitivity analysis on a Model of the Yeast Heterotrimeric G Protein Cycle to find parameters that influence the amount of active G protein. 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:

$$\frac{\partial (Ga)}{\partial \left(kRLm\right)},\frac{\partial \left(Ga\right)}{\partial \left(kRL\right)},\frac{\partial \left(Ga\right)}{\partial \left(kG1\right)},\frac{\partial \left(Ga\right)}{\partial \left(kGa\right)}...$$

**Load G-protein Model**

The provided SimBiology project `gprotein_norules.sbproj`

contains a model that represents the wild-type strain (stored in variable `m1`

).

sbioloadproject gprotein_norules.sbproj m1

**Set up Sensitivity Analysis Options**

The options for sensitivity analysis are in the `configset`

object of the model.

csObj = getconfigset(m1);

Use the `sbioselect`

function, which lets you query by type, to retrieve the `Ga`

species from the model.

Ga = sbioselect(m1,'Name','Ga');

Set the `Outputs`

property of the `SensitivityAnalysisOptions`

object to the `Ga`

species.

csObj.SensitivityAnalysisOptions.Outputs = Ga;

Retrieve all the parameters from the model and store the vector in a variable, `pif`

.

pif = sbioselect(m1,'Type','parameter');

Set the `Inputs`

property of the `SensitivityAnalysisOptions`

object to the `pif`

variable containing the parameters.

csObj.SensitivityAnalysisOptions.Inputs = pif;

Enable sensitivity analysis in the `configset`

object by setting the `SensitivityAnalysis`

option to `true`

.

csObj.SolverOptions.SensitivityAnalysis = true;

Set the `Normalization`

property of the `SensitivityAnalysisOptions`

object to perform `'Full'`

normalization.

`csObj.SensitivityAnalysisOptions.Normalization = 'Full';`

**Calculate Sensitivities**

Simulate the model and return the data to a `SimData object`

:

simDataObj = sbiosimulate(m1);

**Extract and Plot Sensitivity Data**

You can extract sensitivity results using the `getsensmatrix`

method of a `SimData object`

. 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 of `Ga`

with respect to various parameters, and find the parameters that affect `Ga`

the most.

[T, R, snames, ifacs] = getsensmatrix(simDataObj);

Because `R`

is a 3-D array with dimensions corresponding to times, output factors, and input factors, reshape `R`

into columns of input factors to facilitate visualization and plotting:

R2 = squeeze(R);

After extracting the data and reshaping the matrix, plot the data:

figure; plot(T,R2); title('Normalized Sensitivity of Ga With Respect To Various Parameters'); xlabel('Time (seconds)'); ylabel('Normalized Sensitivity of Ga'); leg = legend(ifacs, 'Location', 'NorthEastOutside'); set(leg, 'Interpreter', 'none');

From the 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

## Version History

**Introduced in R2006a**

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