A multiple timescale analysis of a mathematical model of the Wnt/beta-catenin signalling pathway.
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.
Mirams
Gary R
GR
Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. gary.mirams@dpag.ox.ac.uk
Byrne
Helen M
HM
King
John R
JR
D000818:Animals; D025461:Feedback, Physiological; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D015398:Signal Transduction / Q000502:physiology*; D051153:Wnt Proteins / Q000378:metabolism*; D051176:beta Catenin / Q000378:metabolism*
D051153:Wnt Proteins; D051176:beta Catenin