Examining the Influence of Nondimensionalization on Partial Rank Correlation Coefficient Results when Modeling the Epithelial Mesenchymal Transition.

Partial Rank Correlation Coefficient (PRCC) is a powerful type of global sensitivity analysis. Usually performed following Latin Hypercube Sampling (LHS), this analysis can highlight the parameters in a mathematical model producing the observed results, a crucial step when using models to understand real-world phenomena and guide future experiments. Recently, Gasior et al. performed LHS and PRCC when modeling the influence of cell-cell contact and TGF- $\beta$ signaling on the epithelial mesenchymal transition (Gasior et al. in J Theor Biol 546:111160, 2022). Though their analysis provided insight into how these tumor-level factors can impact intracellular signaling during the transition, their results were potentially impacted by nondimensionalizing the model prior to performing sensitivity analysis. This work seeks to understand the true impact of nondimensionalization on sensitivity analysis by performing LHS and PRCC on both the original model that Gasior et al. proposed and seven different nondimensionalizations. Parameter ranges were kept small to capture shifts in the values that originally produced bistable behavior. By comparing these eight different iterations, this work shows that the issues from performing sensitivity analysis following nondimensionalization are two-fold: (1) nondimensionalization can obscure or exclude important parameters from in-depth analysis and (2) how a model is nondimensionalized can, potentially, change analysis results. Ultimately, this work cautions against using nondimensionalization prior to sensitivity analysis if the subsequent results are meant to guide future experiments.