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

Journal of Mathematical Biology

Volumn 60, Issue 1, 2010, Pages 131-160

  Mirams, Gary R ^a   Byrne, Helen M ^a   King, John R ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Catenin; APC; Asymptotic analysis; ODE model; Wnt

Indexed keywords

BETA CATENIN; WNT PROTEIN;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; FEEDBACK SYSTEM; HUMAN; MATHEMATICAL PHENOMENA; METABOLISM; PHYSIOLOGY; SIGNAL TRANSDUCTION;

ANIMALS; BETA CATENIN; FEEDBACK, PHYSIOLOGICAL; HUMANS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; SIGNAL TRANSDUCTION; WNT PROTEINS;

EID: 70350233329     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-009-0262-y     Document Type: Article

References (24)

1. Cho KH, Baek S, Sung MH (2006) Wnt pathway mutations selected by optimal β-catenin signaling for tumorigenesis. FEBS Lett 580: 3665-3670. doi:10.1016/j.febslet.2006.05.053.
2. Church VL, Francis-West P (2002) Wnt signalling during limb development. Int J Dev Biol 46: 927-936.
3. Giles RH, van Ea JH, Clevers H (2003) Caught up in a Wnt storm: Wnt signalling in cancer. BBA 1653: 1-24. doi:10.1016/S0304-419X(03)00005-2.
4. Hall AC, Lucas FR, Salinas PC (2000) Axonal remodeling and synaptic differentiation in the cerebellum is regulated by WNT-7a signaling. Cell 100: 525-535. doi:10.1016/S0092-8674(00)80689-3.
5. Harris TJ, Peifer M (2005) Decisions, decisions: beta-catenin chooses between adhesion and transcription. Trends Cell Biol 15: 234-237. doi:10.1016/j.tcb.2005.03.002.
6. Hinck L, Nelson WJ, Papkoff J (1994) Wnt-1 modulates cell-cell adhesion in mammalian cells by stabilizing β-catenin binding to the cell adhesion protein cadherin. J Cell Biol 124: 729-741. doi:10.1083/jcb.124.5.729.
7. Holmes MH (1995) Introduction to perturbation methods. Springer, Berlin.
8. Ilyas M (2005) Wnt signalling and the mechanistic basis of tumour development. J Pathol 205: 130-144. doi:10.1002/path.1692.
9. Jho E, Zhang T, Domon C, Joo C, Freund J, Costantini F (2002) Wnt/β-Catenin/Tcf signaling induces the transcription of Axin2, a negative regulator of the signaling pathway. Mol Cell Biol 22: 1172-1183. doi:10.1128/MCB.22.4.1172G1183.
10. Kevorkian J, Cole JD (1981) Perturbation methods in applied mathematics. Applied mathematical sciences, vol. 34. Springer, Berlin.
11. Kim D, Rath O, Kolch W, Cho KH (2007) A hidden oncogenic positive feedback loop caused by crosstalk between Wnt and ERK pathways. Oncogene 26: 4571-4579. doi:101038/sj.onc.1210230.
12. Kruger R, Heinrich R (2004) Model reduction and analysis of robustness for the Wnt/β-catenin signal transduction pathway. Gen Inf 15: 138-148.
13. Lee E, Salic A, Kruger R, Heinrich R, Kirschner MW (2003) The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway. PLoS Biol 1: 116-132. doi:10.1371/journal.pbio.0000010.
14. Logan CY, Nusse R (2004) The Wnt signaling pathway in development and disease. Annu Rev Cell Dev Biol 20: 781-810. doi:10.1146/annurev.cellbio.20.010403.113126.
15. Mirams GR (2008) Subcellular phenomena in colorectal cancer. PhD thesis, University of Nottingham.
16. Nelson WJ, Nusse R (2004) Convergence of Wnt, β-catenin, and Cadherin pathways. Science 303: 1483-1487. doi:10.1126/science.1094291.
17. Pinto D, Clevers H (2005) Wnt control of stem cells and differentiation in the intestinal epithelium. Exp Cell Res 306: 357-363. doi:10.1016/j.yexcr.2005.02.022.
18. Reya T, Clevers H (2005) Wnt signalling in stem cells and cancer. Nature 434: 843-850. doi:10.1038/nature03319.
19. Rowan AJ, Lamlum H, Ilyas M (2000) APC mutations in sporadic colorectal tumors: a mutational 'hotspot' and interdependence of the 'two hits'. PNAS 97: 3352-3357. doi:10.1073/pnas.97.7.3352.
20. Städeli R, Hoffmans R, Basler K (2006) Transcription under the control of nuclear Arm/β-catenin. Curr Biol 16: R378-R385. doi:10.1016/j.cub.2006.04.019.
21. Tolwinski NS, Wieschaus E (2004) Rethinking WNT signaling. Trends Genet 20: 177-81. doi:10.1016/j.tig.2004.02.003.
22. van Leeuwen IMM, Byrne HM, Jensen OE, King JR (2007) Elucidating the interactions between the adhesive and transcriptional functions of β-catenin in normal and cancerous cells. J Theor Biol 247: 77-102. doi:10.1016/j.jtbi.2007.01.019.
23. Verhulst F (2005) Methods and applications of singular perturbations: boundary layers and multiple timescale dynamics. Texts in applied mathematics, vol 50. Springer, Berlin.
24. Wawra C, Kühl M, Kestler HA (2007) Extended analyses of the Wnt/β-catenin pathway: robustness and oscillatory behaviour. FEBS Lett 581: 4043-4048. doi:10.1016/j.febslet.2007.07.043.