The effect of model rescaling and normalization on sensitivity analysis on an example of a MAPK pathway model
Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, Stuttgart, 70569, Germany
* e-mail: email@example.com
Accepted: 7 April 2016
Published online: 10 May 2016
The description of intracellular processes based on chemical reaction kinetics has become a standard approach in the last decades, and parameter estimation poses several challenges. Sensitivity analysis is a powerful tool in model development that can aid model calibration in various ways. Results can for example be used to simplify the model by elimination or fixation of parameters that have a negligible influence on relevant model outputs. However, models are usually subject to rescaling and normalization to reference experiments, which changes the variance of the output. Thus, the results of the sensitivity analysis may change depending on the choice of these rescaling factors and reference experiments. Although it might intuitively be clear, this fact has not been addressed in the literature so far.
In this study we investigate the effect of model rescaling and additional normalization to a reference experiment on the outcome of two different sensitivity analyses. Results are exemplified on a model for the MAPK pathway module in PC-12 cell lines. For this purpose we apply local sensitivity analysis and a global variance-based method based on Sobol sensitivity coefficients, and compare the results for differently scaled and normalized model versions.
Results indicate that both sensitivity analyses are invariant under simple rescaling of variables and parameters with constant factors, provided that sensitivity coefficients are normalized and that the parameter space is appropriately chosen for Sobol’s method. By contrast, normalization to a reference experiment that also depends on parameters has a large impact on the results of any sensitivity analysis, and in particular complicates the interpretation.
This work shows that, in order to perform sensitivity analysis, it is necessary to take into account the dependency on parameters of the reference condition when working with normalized model versions.
Key words: Global sensitivity analysis / Sobol indices / Model rescaling / MAPK signaling pathway
© Kirch et al., 2016