Abstract
The Wnt/\(\beta \)-catenin pathway plays a crucial role in stem cell renewal and differentiation in the normal human colonic crypt. The balance between \(\beta \)-catenin and APC along the crypt axis determines its normal functionality. The mechanism that deregulates this balance may give insight into the initiation of colorectal cancer. This is significant because the spatial dysregulation of \(\beta \)-catenin by the mutated tumor suppressor gene/protein APC in human colonic crypts is responsible for the initiation and growth of colorectal cancer. We consider a regulatory function that promotes APC synthesis within the cell and its effect on the accumulation of the Wnt target protein, \(\beta \)-catenin. It is evident that an APC gradient exists along the crypt axis; however, the mechanism by which APC expression is regulated within the cell is not well known. We investigate the dynamics of an APC regulatory mechanism with an increased level of Axin at the subcellular level. Model output shows an increase of APC for a diminished Wnt signal, which explains the APC gradient along the crypt. We find that the dynamic interplay between \(\beta \)-catenin, APC, and Axin produces oscillatory behavior, which is controlled by the Wnt stimulus. In the presence of reduced functional APC, the oscillations are amplified, which suggests that the cell remains in a more proliferative state for longer periods of time. Increased Axin levels (typical of mammalian cells) reduce oscillatory behavior and minimize the levels of \(\beta \)-catenin within the cell while raising the levels of APC.
Similar content being viewed by others
References
Aberle H, Bauer A, Stappert J (1997) Beta-catenin is a target for the ubiquitin–proteasome pathway. Embo J 16:3797–3804
Albuquerque C, Breukel C, van der Lujit R, Fidalgo P, Lagel P, Slors FJM, Leitao CN, Fodde R, Smits R (2002) The ‘just-right’ signaling model: APC somatic mutations are selected based on a specific level of activation of the beta-catenin signaling cascade. Hum Mol Genet 11:1549–1560
Boman BM, Huang E (2008) Human colon cancer stem cells: a new paradigm in gastrointestinal oncology. J Clin Oncol 26:2828–2838
Boman BM, Fields JZ (2013) An APC: WNT counter-current-like mechanism regulates cell division along the human colonic crypt axis: A mechanism that explains how apc mutations induce proliferative abnormalities that drive colon cancer development. Front Oncol 3(244):1–15
Boman BM, Wicha MS, Fields JZ, Runquist OA (2007) Symmetric division of cancer stem cells—a key mechanism in tumor growth that should be targeted in future therapeutic approaches. Clin Pharmacol Ther 81(6):893–898
Cho KH, Baek S, Sung MH (2006) Wnt pathway mutations selected by optimal beta-catenin signaling for tumorigenesis. FEBS Lett 580:3665–3670
Clevers H, Nusse R (2012) Wnt/beta-catenin signaling and disease. Cell 149:1192–1204
Cliffe A, Hamada F, Bienz M (2003) A role of Dishevelled in relocating Axin to the plasma membrane during wingless signaling. Curr Biol 13:960–966
Fearnhead NS, Wilding JL, Bodmer WF (2001) Genetics of colorectal cancer: hereditary aspects and overview of colorectal tumorigenesis. Br Med Bull 64:27–43
Gaspar C, Fodde R (2004) APC dosage effects in tumorigenesis and stem cell differentiation. Int J Dev Biol 48:377–386
Hadjihannas MV, Bernkopf DB, Bruckner M, Behrens J (2003) Beta-catenin regulation during the cell cycle: implications in G2/M and apoptosis. Mol Biol Cell 14:2844–2860
Huang EH, Hynes MJ, Ahang T, Ginestier C, Dontu G, Appelman H, Fields JZ, Wicha MS, Boman BM (2009) Aldehyde dehydrogenase 1 is a marker for normal and malignant human colonic stem cells (SC) and tracks SC overpopulation during colon tumorigenesis. Cancer Res 69:3382–3389
Kikuchi A, Yamamoto H (2007) Regulation of Wnt signalling by receptor-mediated enocytosis. J Biochem 141:443–451
Kosiniski C, Li VSW, Chan ASY, Zhang J, Ho C, Tsui WY, Chan TL, Mifflin RC, Powell DW, Yuen ST, Leung SY, Chen X (2007) Gene expression patterns of human colon tops and basal crypts and BMP antagonists as intestinal stem cell niche factors antagonists as intestinal stem cell niche factors. Proc Natl Acad Sci 4:15418–15423
Kruger R, Heinrich R (2004) Model reduction and analysis of robustness for the Wnt/beta-catenin signal transduction pathway. Genome Inform 15(1):138–148
Kunttas-Tatli E, Roberts DM, McCartney BM (2014) Self-association of the apc tumor supressor is required for the assembly, stability, and activity of the wnt signaling destruction complex. Mol Biol Cell 25:3424–3436
Latres E, Chiaur DS, Pagano M (1999) The human F box protein beta-Trcp associates with the Cul 1/Skp 1 complex and regulates the stability of beta-catenin. Oncogene 18:849–854
Lee E, Salic A, Kirschner MW (2001) Physiological regulation of beta-catenin stability by Tcf3 and CK1epsilon. J Cell Biol 154:983–993
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
Leeuwen IMM, Mirams GR, Walter A, Fletcher A, Murray P (2010) An integrative computational model for intestinal tissue renewal. Cell Prolif 42:617–636
Liu C, Kato Y, Zhang Z (1999) Beta-Trcp couples beta-catenin phophorylation-degradation and regulates Xenopus axis formation. Proc Natl Acad Sci 96:6273–6278
Lloyd-Lewis B, Fletcher AG, Dale TC, Byrne HM (2013) Toward a quantitative understanding of the Wnt/beta-catenin pathway through simulation and experiment. WIREs Syst Biol Med 5(4):391–407
MacDonald BT, Tamai K, He X (2009) Wnt/beta-catenin signaling: components, mechanisms, and diseases. Dev Cell 17(1):9–26
Mirams GR, Byrne HM, King JR (2010) A multiple time scale analysis of a mathematical model of the Wnt/beta-catenin signaling pathway. J Math Biol 60:131–160
Murray PJ, Edwards CM, Tindall MJ, Maini PK (2009) From a discrete to a continuum model of cell dynamics in one dimension. Phys Rev 80:031912
Murray PJ, Kang J, Mirams GR, Shin S, Byrne HM, Maini PK, Cho KH (2010) Modelling spatially regulated beta-catenin dynamics and invasion in intestinal crypts. Biophys J 99:716–725
Murray PJ, Walter A, Fletcher AG, Edwards CM, Tindall MJ, Maini PK (2011) Comparing a discrete and continuum model of the intestinal crypt. Phys Biol 8:026011
Nishimura S, Wakabayashi N, Toyoda K, Kashima K, Mitsufuji S (2003) Expression of Musashi-1 in human normal colon crypt cells. Dig Dis Sci 48:1523–1529
Nusse R (2005) Wnt signaling in disease and in development. Cell Res 15(1):28–32
Orford K, Crockett C, Jensen JP, Weissman AM, Byers SW (1997) Serine phosphorylation-regulated ubiquitination and degradation of beta-catenin. J Biol Chem 272:24735–24738
Potten CS, Loeffler M (1990) Stem cells: attributes, cycles, spirals, pitfalls, and uncertainties: lessons for and from the crypt. J Cell Sci 115:2381–2388
Pronobis MI, Rusan NM, Peifer M (2015) A novel gsk3-regulated apc:axin interaction regulates wnt signaling by driving a catalytic cycle of efficient \(\beta \)-catenin destruction. eLife 4(e08022):1–31
Tan CW, Gardiner BS, Hirokawa Y, Layton MJ, Smith DW, Burgess AW (2012) Wnt signalling pathway parameters for mammalian cells. PLoS ONE 7(2):e31882. doi:10.1371/journal.pone.0031882
Vries RGJ, Huch M, Clevers H (2010) Stem cells and cancer of the stomach and intestine. Mol Oncol 4:373–384
Wasan HS, Park HS, Liu KC, Mandir NK, Winnett A, Sasieni P, Bodmer WF, Goodlad RA, Wright NA (1998) APC in the regulation of intestinal crypt fission. J Pathol 185:246–255
Wawra C, Kuhl M, Kestler HA (2007) Extended analyses of the Wnt/beta-catenin pathway: robustness and oscillatory behaviour. FEBS Lett 581:4043–4048
Weinberg RA (2007) The biology of cancer. Garland Science, New York
Wodarz D, Komarova NL (2005) Computational biology of cancer: lecture notes and mathematical modeling. World Scientific Publishing, Hackensack, NJ
Zhang T, Fields JZ, Opdenaker L, Otevrel T, Masuda E, Palazzo JP, Isenberg GA, Goldstein SD, Bland M, Boman BM (2010) Survivin-induced Aurora-B Kinase activation—a mechanism by which APC mutations contribute to increased mitoses during colon cancer development. Am J Pathol 177:2816–2826
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Emerick, B., Schleiniger, G. & Boman, B.M. A kinetic model to study the regulation of \(\beta \)-catenin, APC, and Axin in the human colonic crypt. J. Math. Biol. 75, 1171–1202 (2017). https://doi.org/10.1007/s00285-017-1112-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-017-1112-y