Parameter-free methods distinguish Wnt pathway models and guide design of experiments

TL;DR

This paper compares existing Wnt pathway models with a new spatial localization model using Bayesian and algebraic methods, revealing a bistable switch and guiding minimal experimental design.

Contribution

Introduces a new mechanistic Wnt model with spatial localization, and applies algebraic and Bayesian methods for model analysis and experimental guidance.

Findings

The new model allows bistability via control of shuttling and degradation.

All models can fit mammalian Wnt signaling data.

Algebraic methods identify key variables for model discrimination.

Abstract

The canonical Wnt signaling pathway, mediated by $\beta$-catenin, is crucially involved in development, adult stem cell tissue maintenance and a host of diseases including cancer. We undertake analysis of different mathematical models of Wnt from the literature, and compare them to a new mechanistic model of Wnt signaling that targets spatial localization of key molecules. Using Bayesian methods we infer parameters for each of the models to mammalian Wnt signaling data and find that all models can fit this time course. We are able to overcome this lack of data by appealing to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into Wnt signaling: The new model (unlike any other investigated) permits a bistable switch in the system via control of shuttling and degradation parameters, corresponding to stem-like vs committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that must be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.