Extended analyses of the Wnt/β-catenin pathway: Robustness and oscillatory behaviour
Abstract
The Wnt/β‐catenin signalling pathway is evolutionarily conserved across many species and plays important roles during embryogenesis. The Lee–Heinrich model (to recognize the contributions of R. Heinrich we will refer to the work proposed by Lee et al. [Lee, E., Salic, A., Krüger, R., Heinrich, R., Kirschner, M.W. (2003) The roles of APC and axin derived from experimental and theoretical analysis of the Wnt pathway. PloS Biol. 1, 116–132] as the Lee–Heinrich model) describes this pathway by use of coupled ordinary differential equations. Here, we extend this model by introducing negative feedback loops of the pathway using time‐delay differential equations. Single‐ and multiple‐parameter perturbations suggest a very robust behaviour of this pathway that can also demonstrate oscillatory behaviour. These findings are of biological significance as Wnt pathway components show oscillations during vertebrate somitogenesis.
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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 [35]
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 [35]
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 [35]
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References 24 · Cited by 56
- Authors
- Wawra, C., Kühl, M., & Kestler, H. A.
- Affiliations
- Universität Ulm (DE)
- Corresponding author
- Kühl, Michael
- Kestler, Hans A.
- Venue
- FEBS Letters
- Publisher
- Wiley
- Published
- 2007-07-27
- Volume
- 581
- Issue
- 21
- Pages
- 4043-4048
- ISSN
- 0014-5793 (ISSN-L)
- 1873-3468
- OpenAlex
- W2140094325
- Cited by
- 56
- References
- 24
- Citations by year
- 2026: 1 · 2025: 2 · 2022: 1 · 2021: 1 · 2020: 1 · 2019: 2 · 2018: 1 · 2017: 4 · 2016: 2 · 2015: 3 · 2014: 5 · 2013: 5 · 2012: 6
- FWCI
- 2.11
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- FEBS Letters (publishedVersion)
- PubMed (publishedVersion)
- 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
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Developmental Biology and Gene Regulation
- Keywords
- Wnt/β-catenin signaling, delay differential equations, negative feedback loop, robustness, oscillations, APC, Axin, somitogenesis
- MeSH terms
- Animals, Biological Clocks, Models, Biological, Vertebrates, Signal Transduction, Somites, Organogenesis, Wnt Proteins, beta Catenin
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