The effect of model rescaling and normalization on sensitivity analysis on an example of a MAPK pathway model

Abstract

Background: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. Methods: 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: 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. Conclusion: 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.

Mathematical investigation of innate immune responses to lung cancer: The role of macrophages with mixed phenotypes

“…In eq. (4) we do not normalise the sensitivity index [39]. This is mainly because when we investigate local sensitivity to the initial conditions, Tumour sensitivity to initial conditions.…”

Mathematical modeling of the relocation of the divalent metal transporter DMT1 in the intestinal iron absorption process

“…The negative sensitivity coefficients shown in Tables 4 and 5 reflect that an increase in the parameter value is associated with a decrease in the model’s output () and vice versa [87]. Most parameters fall in the regular/high influence categories for both iron absorption models (Tables 4 and 5).…”

The Physics behind Systems Biology

“…In this topical issue, the network view is illustrated by [99], where a 3D chromosomal structure is derived from a contact network of genomic locations, and by [98], where time-resolved transcriptome profiles are mapped onto a transcriptional regulatory network. Robustness is discussed from the perspective of sensitivity analysis for ODE models of biological systems using the example of the MAPK pathway [60]. The notion of minimal models is nicely illustrated in the methodological comparison of modeling approaches of varying levels of detail in [30].…”

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