Cellular signalling pathways consolidate multiple molecular interactions into working models of signal propagation, amplification, and modulation. They are described and visualized as networks. Adjusting network topologies to experimental data is a key goal of systems biology. While network reconstruction algorithms like nested effects models are well established tools of computational biology, their data requirements can be prohibitive for their practical use. In this paper we suggest focussing on well defined aspects of a pathway and develop the computational tools to do so. We adapt the framework of nested effect models to focus on a specific aspect of activated Wnt signalling in HCT116 colon cancer cells: Does the activation of Wnt target genes depend on the secretion of Wnt ligands or do mutations in the signalling molecule β-catenin make this activation independent from them? We framed this question into two competing classes of models: Models that depend on Wnt ligands secretion versus those that do not. The model classes translate into restrictions of the pathways in the network topology. Wnt dependent models are more flexible than Wnt independent models. Bayes factors are the standard Bayesian tool to compare different models fairly on the data evidence. In our analysis, the Bayes factors depend on the number of potential Wnt signalling target genes included in the models. Stability analysis with respect to this number showed that the data strongly favours Wnt ligands dependent models for all realistic numbers of target genes.
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