Title: Comparison of reaction networks of Wnt signaling

Abstract: Wnt signaling is a vital biological mechanism that regulates crucial development processes and maintenance of tissue homeostasis. Here, we extended the parameter-free analysis of four mathematical models of the beta-catenin-dependent Wnt signaling pathway performed by MacLean et al. (PNAS USA 2015) using chemical reaction network theory. We showed that the reaction networks of the four models considered (Lee, Schmitz, MacLean, and Feinberg) coincide in basic structural and kinetic properties except in their mono-stationarity/multi-stationarity, and their capacity for admitting a degenerate equilibrium. Moreover, we showed that the embedded networks of the Lee and Feinberg models are very similar, and the discordance of the Lee network limits its mono-stationarity to mass action kinetics, which challenge the absoluteness of model discrimination into mono-stationarity versus multi-stationarity alone. Focusing, henceforth, on the three multi-stationary networks, we showed that their finest independent decompositions are very different and can be used to study further similarities and differences among them. We also determined equilibria parametrizations of the networks and inferred the presence of species with absolute concentration robustness. Finally, direct comparison of the Schmitz and Feinberg networks with the MacLean network yielded new results in three aspects: structural/kinetic relationships between embedded networks relative to their set of common species, connections between the positive equilibria of the subnetwork of common reactions and the positive equilibria of the whole networks, and construction of maximal concordant subnetwork containing the common reactions of the networks under comparison. Thus, this work can provide general insights in comparing mathematical models of the same or closely-related systems.