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Updated: Jun 24, 2026

The Power of Simplicity: Sea Urchin Embryos as in Vivo Developmental Models for Studying Complex Cell-to-cell Signaling Network Interactions
Published on: February 16, 2017
A multiple timescale analysis of a mathematical model of the Wnt/beta-catenin signalling pathway
Gary R Mirams1, Helen M Byrne, John R King
1Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. gary.mirams@dpag.ox.ac.uk
Abstract:
The Wnt signalling pathway is involved in stem cell maintenance, differentiation and tissue development. Its disregulation has also been implicated in many cancers. Beta-catenin is a protein that regulates both transcription of many genes and cell-cell adhesion; in response to an external Wnt stimulus the intracellular levels of beta-catenin are controlled by the proteins which make up the Wnt/beta-catenin signalling pathway. In this paper we present a systematic asymptotic analysis of an existing model of the Wnt signalling pathway due to Lee et al. (PLoS Biol 1:116-132, 2003), highlighting the operation of different pathway components over different timescales. Guided by this analysis we derive a simplified model which is shown to retain the essential behaviour of the full Wnt pathway, recreating the accumulation and degradation of beta-catenin in response to a Wnt stimulus.
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