4.4 Article

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

Journal

JOURNAL OF MATHEMATICAL BIOLOGY
Volume 60, Issue 1, Pages 131-160

Publisher

SPRINGER HEIDELBERG
DOI: 10.1007/s00285-009-0262-y

Keywords

Wnt; APC; beta-Catenin; ODE model; Asymptotic analysis

Funding

  1. EPRSC [GR/572023/01]
  2. Royal Society
  3. Wolfson Foundation

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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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