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

Proceedings of the National Academy of Sciences of the United States of America
Adam L MacLeanHeather A Harrington

Abstract

The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal 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 aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.

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Citations

Dec 10, 2015·Bulletin of Mathematical Biology·Elizabeth GrossBernd Sturmfels
Aug 3, 2016·Journal of Mathematical Biology·Michael Marcondes de FreitasCarsten Wiuf
Oct 14, 2016·Journal of the Royal Society, Interface·Elizabeth GrossHeather A Harrington
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Mar 4, 2020·Journal of Mathematical Biology·Elizabeth GrossAnne Shiu
Oct 11, 2017·Theoretical Biology & Medical Modelling·Kelsey GasiorSudin Bhattacharya
Jan 26, 2021·Computational and Structural Biotechnology Journal·Daniel WardLucia Marucci
Oct 11, 2015·Biology Open·Adam L MacLeanMichael P H Stumpf
Aug 6, 2021·PLoS Computational Biology·Kai BuddeAdelinde M Uhrmacher

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