The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 353–363 | Cite as

Modelling the dynamics of stem cells in colonic crypts

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Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics

Abstract

We present a theoretical and computational framework to model the colonic crypt organisation in the human intestine. We construct a theoretical and computational framework to model the colonic crypt behaviour, using a Voronoi tessellation to represent each cell and elastic forces between them we addressed how their dynamical disfunction can lead to tumour masses and cancer. Our results indicate that for certain parameters the crypt is in a homeostatic state, but slight changes on their values can disrupt this behaviour.

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References

  1. 1.
    N. Barker, R.A. Ridgway, J.H. van Es, M. van Wetering, H. Begthel, M. van den Born, E. Danenberg, A.R. Clarke, O.J. Sansom, H. Clevers, Crypt stem cells as the cells-of-origin of intestinal cancer, Nature 457, 608 (2009)ADSCrossRefGoogle Scholar
  2. 2.
    A. d’Onofrio, I.P.M. Tomlinson, A non-linear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt, J. Theor. Biol. 244, 367 (2007)CrossRefGoogle Scholar
  3. 3.
    I.P.M. Tomlinson, W.F. Bodmer, Failure to programmed cell death and differentiation as causes of tumors: Some simple mathematical models, PNAS 92, 11130 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    P.A. Beachy, S.S. Karhadkar, D.M. Berman, Tissue repair and stem cell renewal in cancirogenesis, Nature 432, 324 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    G.R. Mirams, A.G. Fletcher, P.K. Maini, H.M. Byrne, A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt, J. Theor. Biol. 312, 143 (2012)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    S.K. Kershaw, H.M. Byrne, D.J. Gavaghan, J.M. Osborne, Colorectal cancer through simulation and experiment, IET Syst. Biol. 7, 57 (2013)CrossRefGoogle Scholar
  7. 7.
    Y. Kagawa, N. Horita, H. Taniguchi, S. Tsuneda, Modeling of stem cell dynamics in human colonic crypts in silico, J. Gastroenterol. 49, 263 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    B. Creamer, R. Shorter, J. Bamforth, The turnover and shedding of epithelial cells. i. the turnover in the gastro-intestinal tract. Gut 2, 110 (1961)Google Scholar
  9. 9.
    L.W. Peterson, D. Artis, Intestinal epithelial cells: regulators of barrier function and immune homeostasis, Nature Reviews: Immunology 14, 141 (2014)Google Scholar
  10. 10.
    A.M. Baker, B. Cereser, S. Melton, A.G. Fletcher, M. Rodriguez-Justo, P.J. Tadrous, A. Humphries, G. Elia, S.A. McDonald, N.A. Wright, B.D. Simons, M. Jansen, T.A. Graham, Quantification of crypt and stem cell evolution in the normal and neoplastic human colon, Cell Rep. 8, 940 (2014)CrossRefGoogle Scholar
  11. 11.
    S.J. Leedham, P. Rodenas-Cuadrado, K. Howarth, A. Lewis, S. Mallappa, S. Segditsas, H. Davis, R. Jeffery, M. Rodriguez-Justo, S. Keshav, S.P.L. Travis, T.A. Graham, J. East, S. Clark, I.P.M. Tomlinson, A basal gradient of wnt and stem-cell number influences regional tumour distribution in human and mouse intestinal tracts, Gut 62, 83 (2013)CrossRefGoogle Scholar
  12. 12.
    S. Frisch, H. Francis, Disruption of epithelial cell-matrix interactions induces apoptosis, J. Cell Biol. 124, 619 (1994)CrossRefGoogle Scholar
  13. 13.
    P. Kaur, C.S. Potten, Circadian variation in migration velocity in small intestinal epithelium, Cell Tissue Kinet. 19, 591 (1986)Google Scholar
  14. 14.
    S. Tsubouchi, Theoretical implications for cell migration through the crypt and the villus of labelling studies conducted at each position within the crypt, Cell Tissue Kinet. 16, 441 (1983)Google Scholar
  15. 15.
    D. Cunningham, W. Atkin, H.J. Lenz, H.T. Lynch, B. Minsky, B. Nordlinger, N. Starling, Colorectal cancer, The Lancet 375, 1030 (2010)CrossRefGoogle Scholar
  16. 16.
    X. Liu, J.M.J. Hunt, Kras gene mutation in colorectal cancer is correlated with increased proliferation and spontaneous apoptosis, Am. J. Clin. Pathol. 135, 245 (2011)CrossRefGoogle Scholar
  17. 17.
    A. Humphries, N.A. Wright, Colonic crypt organization and tumorigenesis, Nature Reviews: Cancer 8, 415 (2008)Google Scholar
  18. 18.
    A.G. Fletcher, P.J. Murray, P.K. Maini, arXiv:1506.05019v1 [q-bio.TO] (2015)
  19. 19.
    O. Voloshanenko, G. Erdmann, T.D. Dubash, I. Augustin, M. Metzig, G. Moffa, C. Hundsrucker, G. Kerr, T. Sandmann, B. Anchang, K. Demir, C. Boehm, S. Leible, C.R. Ball, H. Glimm, R. Spang, M. Boutros, Wnt secretion is required to mantain high levels of wnt activity in colon cancer cells, Nat. Commun. 4, 13 (2013)CrossRefGoogle Scholar
  20. 20.
    P. Polakis, Wnt signaling and cancer, Genes & Dev. 14, 1837 (2000)Google Scholar
  21. 21.
    C.H.F. Chan, P. Camacho-Leal, C.P. Stanners, Colorectal hyperplasia and dysplasia due to human carcinoembryonic antigen (cea) family member expression in transgenic mice, Plos One 2, e1353 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    R.A. Barrio, J.R. Romero-Arias, M.A. Noguez, E. Azpeitia, E. Ortiz-Gutiérrez, V. Hernández-Hernández, Y. Cortes-Poza, E.R. Álvarez-Buylla, Cell pattern emerge from coupled chemical and physical fields with cell proliferation dynamics: The arabidopsis thaliana root as a study system, PLOS: Comput. Biol. 9, e1003026 (2013)ADSGoogle Scholar
  23. 23.
    H. Honda, Description of cellular patterns by dirichlet domains: the two-dimensional case, J. Theor. Biol. 72, 523 (1978)MathSciNetCrossRefGoogle Scholar
  24. 24.
    N. Saitô, Asymptotic regular pattern of epidermal cells in mammalian skin, J. Theor. Biol. 95, 591 (1982)MathSciNetCrossRefGoogle Scholar
  25. 25.
    F.A. Meineke, C.S. Potten, M. Loeffler, Cell migration and organization in the intestinal crypt using a lattice-free model, Cell Prolif. 34, 253 (2001)CrossRefGoogle Scholar
  26. 26.
    J. Butcher, Numerical Methods for Ordinary Differential Equations (Wiley, 2003)Google Scholar
  27. 27.
    R.A. Barrio, C. Varea, J.L. Aragón, P.K. Maini, A two-dimensional numerical study of spatial pattern formation in interacting turing systems, Bull. Math. Biol. 61, 483 (1999)CrossRefMATHGoogle Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Instituto de Física, Universidad Nacional Autónoma de MéxicoMéxico D.F.Mexico

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