Sensitivity analysis example
The method description could be found in the section Sensitivity Analysis. Here we give an example of the method application and using in BioUML.
Consider the model of p53 and Mdm2 proteins regulation described by Geva-Zatorsky et al. [1]. The model includes the negative feedback loop in which p53 transcriptionally activates an Mdm2 precursor (pMdm2) representing, for example Mdm2 mRNA, and produces subsequent synthesis of Mdm2. Active Mdm2 increases the degradation rate of p53. The list of the model reactions is done in the table below, where x, y and y0 denote concentrations of p53, Mdm2 and pMdm2 respectively.
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Assume βx = 0.3, βy = 0.4, α0 = αy = 0.1 and αxy = 3.2, and solve the algebraic system:
As a result we obtain the following steady state of the model:
Exploring the unscaled sensitivity of this state to perturbations of parameters βx, βy, α0, αxy and αy, we can find the matrix of partial derivatives:
Substituting the values of the investigated parameters, we get:
Scaled sensitivities could be found by the following way:
Reproducing the method in BioUML
To reproduce this example in BioUML workbench you first need to go to the Analysis tab in navigation pane and then follow to analyses > Methods > DAE models.
After double click on Sensitivity Analysis, a new tab with analysis settings opens.
You can select a path to the input diagram used in the example above:
data/Examples/DAE models/Data/Diagrams/Geva_Zatorsky_2006_Model_I
and select a path to save results of analysis:
data/Collaboration/Demo/Data/Sensitivity Analysis Results
Than your click to the run button and calculations are completed, you can see the results of the analysis represented by two tables including scaled and unscaled sensitivities.
References
- Geva-Zatorsky N., Rosenfeld N., Itzkovitz S., Milo R., Sigal A., Dekel E., Yarnitzky T., Liron Y., Polak P., Lahav G., Alon U. Oscillations and variability in the p53 system. Molecular Systems Biology. 2006. V. 2, № 2006.0033.
