A multiple timescale analysis of a mathematical model of the Wnt/β-catenin signalling pathway
Open accessAbstract
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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All other simulation studies either used wet-lab data from other publications or did not explicitly refer to wet-lab data at all [29, 30, 33, 34, 39, 41, 53].
“All other simulation studies either used wet-lab data from other publications or did not explicitly refer to wet-lab data at all [29, 30, 33, 34, 39, 41, 53].”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
In all provenance graphs but the one by Mirams et al. (2010) [41], at least one Qualitative Model was used by a Building Simulation Model activity to produce the first Simulation Model.
“In all provenance graphs but the one by Mirams et al. (2010) [41], at least one Qualitative Model was used by a Building Simulation Model activity to produce the first Simulation Model.”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
Two simulation studies ([35, 41]) show disconnected graphs.
“Two simulation studies ([35, 41]) show disconnected graphs.”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
The simulation models developed in [29, 32, 34-36, 39, 41] had neither been calibrated nor validated explicitly, because they used parameter values from other studies.
“The simulations models developed in [29, 32, 34–36, 39, 41] had neither been calibrated nor validated explicitly, because they used parameter values from other studies.”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
Some simulation studies resulted in the development of multiple simulation models that are neither extensions nor compositions but rather form a revision or alternative to other simulation models developed in the same study: [33, 39, 41, 46, 48, 49].
“Some simulation studies resulted in the development of multiple simulation models that are neither extensions nor compositions but rather form a revision or alternative to other simulation models developed in the same study: [33, 39, 41, 46, 48, 49].”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
Some studies develop a story line where a simulation model has been successively refined, extended, or composed ([28, 33, 34, 36, 41, 46, 48, 49, 51, 56]).
“Some studies develop a story line where a simulation model has been successively refined, extended, or composed ([28, 33, 34, 36, 41, 46, 48, 49, 51, 56]).”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
The central cluster includes the Wnt model by Lee et al. (2003) as well as the studies [30, 34, 35, 41].
“The central cluster includes the Wnt model by Lee et al. (2003) [28] as well as the studies [30, 34, 35, 41].”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [41]
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References 28 · Cited by 53
- Authors
- Mirams, G. R., Byrne, H. M., & King, J. R.
- Affiliations
- University of Nottingham (GB)
- Corresponding author
- Mirams, Gary R.
- Venue
- Journal of Mathematical Biology
- Published
- 2009-03-14
- Volume
- 60
- Issue
- 1
- Pages
- 131-160
- ISSN
- 0303-6812 (ISSN-L)
- 1432-1416
- OpenAlex
- W2060200034
- Cited by
- 53
- References
- 28
- Citations by year
- 2025: 2 · 2023: 1 · 2022: 1 · 2021: 5 · 2020: 2 · 2019: 2 · 2018: 5 · 2017: 5 · 2015: 6 · 2014: 3 · 2013: 8 · 2012: 4
- FWCI
- 1.62
- Type
- journal article
- Language
- en
- Open access
- Licence
- Locations
- Journal of Mathematical Biology (publishedVersion)
- PubMed (publishedVersion)
- Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
- Repository@Nottingham (University of Nottingham) (submittedVersion)
- Funders
- Royal Society
- Wolfson Foundation
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Wnt/β-catenin signaling in development and cancer
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
- Keywords
- Wnt/β-catenin signaling, asymptotic analysis, model reduction, stem cell maintenance, cancer
- MeSH terms
- Animals, Humans, Models, Biological, Signal Transduction, Feedback, Physiological, Wnt Proteins, beta Catenin, Mathematical Concepts
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