Abstract
The Wnt signaling pathway plays a critical role in various biochemical processes, including embryonic development, tissue homeostasis, and cancer progression. In this paper, we conduct a comparative analysis of $\beta$-catenin-dependent Wnt signaling
reaction networks, which we refer to as Feinberg, Schmitz, and MacLean models, based on the previous study by MacLean et al. (PNAS USA 2015). Using the methods of finest independent decomposition (FID) and Equilibria Parametrizations (EP),
along with our newly developed Common Reactions Equilibria (CORE) and Concordance Profile (CP) analyses, we uncover three interesting results. Firstly, employing FID and EP reveals that both the Schmitz and MacLean
models lack absolute concentration robustness (ACR) property, whereas the Feinberg model demonstrates ACR in a single species. Second, utilizing FID and CORE unveils significant relationships within the equilibria sets of augmented Schmitz
and MacLean models, while also highlighting the lack of substantial associations between Feinberg and MacLean models. Finally, based on concordance levels, CP analysis indicates greater similarity between MacLean and Schmitz models compared
to MacLean and Feinberg models. Therefore, the methods could detect differences between models that are not evident in the standard reaction network analysis.
