A multiple timescale analysis of a mathematical model of the Wnt/β-catenin signalling pathway

Mirams, Gary R.; Byrne, Helen M.; King, John R.

Abstract

The Wnt signalling pathway is involved in stem cell maintenance, differentiation and tissue development. Its disregulation has also been implicated in many cancers. β-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 β-catenin are controlled by the proteins which make up the Wnt/β-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 β-catenin in response to a Wnt stimulus. © Springer-Verlag 2009.

Citation

Mirams, G. R., Byrne, H. M., & King, J. R. (2010). A multiple timescale analysis of a mathematical model of the Wnt/β-catenin signalling pathway. Journal of Mathematical Biology, 60(1), 131-160. https://doi.org/10.1007/s00285-009-0262-y

• Journal Article Type: Article
• Online Publication Date: Mar 14, 2009
• Publication Date: 2010-01
• Deposit Date: Jan 14, 2020
• Journal: Journal of Mathematical Biology
• Print ISSN: 0303-6812
• Electronic ISSN: 1432-1416
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 60
• Issue: 1
• Pages: 131-160
• DOI: https://doi.org/10.1007/s00285-009-0262-y
• Public URL: https://nottingham-repository.worktribe.com/output/3217744
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00285-009-0262-y