Multi-scale Modelling for Threshold Dependent Differentiation

A. Q. Cai; Y. Peng; J. Wells; X. Dai; Q. Nie

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 4, page 103-117
  • ISSN: 0973-5348

Abstract

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The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator c-Myc, its threshold dependent differentiation, and feedback regulation on maintaining a stable stem cell population are investigated.

How to cite

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Cai, A. Q., et al. "Multi-scale Modelling for Threshold Dependent Differentiation." Mathematical Modelling of Natural Phenomena 4.4 (2009): 103-117. <http://eudml.org/doc/222372>.

@article{Cai2009,
abstract = { The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator c-Myc, its threshold dependent differentiation, and feedback regulation on maintaining a stable stem cell population are investigated. },
author = {Cai, A. Q., Peng, Y., Wells, J., Dai, X., Nie, Q.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {cell division; cell differentiation; stem cells; threshold; cell population balance model; c-Myc; epidermal development; cell population balance model},
language = {eng},
month = {7},
number = {4},
pages = {103-117},
publisher = {EDP Sciences},
title = {Multi-scale Modelling for Threshold Dependent Differentiation},
url = {http://eudml.org/doc/222372},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Cai, A. Q.
AU - Peng, Y.
AU - Wells, J.
AU - Dai, X.
AU - Nie, Q.
TI - Multi-scale Modelling for Threshold Dependent Differentiation
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/7//
PB - EDP Sciences
VL - 4
IS - 4
SP - 103
EP - 117
AB - The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator c-Myc, its threshold dependent differentiation, and feedback regulation on maintaining a stable stem cell population are investigated.
LA - eng
KW - cell division; cell differentiation; stem cells; threshold; cell population balance model; c-Myc; epidermal development; cell population balance model
UR - http://eudml.org/doc/222372
ER -

References

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  1. M. Abercrombie. The crawling movement of metazoan cells. Proc. R. Soc. Lond. B. Biol. Sci., 207 (1980), No. 1167, 129–147.  
  2. I. Arnold, F. M. Watt. c-Myc activation in transgenic mouse epidermis results in mobilization of stem cells and differentiation of their progeny. Curr. Biol., 11 (2001), No. 8, 558–568.  
  3. B. Basse, B. C. Baguley, E. S. Marshall, W. R. Joseph, B. van Brunt, G. C. Wake, D. J. N. Wall. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. J. Math. Biol., 47 (2003), No. 4, 295–312.  Zbl1050.92028
  4. S. Bernard, L. Pujo-Menjouet, M. C. Mackey. Analysis of cell kinetics using a cell division marker: Mathematical modeling of experimental data. Biophys. J., 84 (2003), 3414–3424.  
  5. B. van Brunt, G. C. Wake, H. K. Kim. On a singular Sturm-Liouville problem involving an advanced functional differential equation. European J. Appl. Math., 12 (2001), 625–644.  Zbl1017.34068
  6. A. Q. Cai, K. A. Landman, B. D. Hughes, C. M. Witt. T cell development in the thymus: From periodic seeding to constant output. J. Theor. Biol., 249 (2007), No. 2, 384–394, 2007.  
  7. E. Clayton, D. P. Doupé, A. M. Klein, D. J. Winton, B. D. Simons, P. H. Jones. A single type of progenitor cell maintains normal epidermis. Nature, 446 (2007), 185–189.  
  8. E. Fuchs, S. Raghavan. Getting under the skin of epidermal morphogenesis. Nat. Rev. Genet., 3 (2002), 199–209.  
  9. A. B. Glick, A. B. Kulkarni, T. Tennenbaum, H. Hennings, K. C. Flanders, M. O'Reily, M. B. Sporn, S. Karlsson, S. H. Yuspa. Loss of expression of transforming growth factor β in skin and skin tumors is associated with hyperproliferation and a high risk for malignant conversion. Proc. Natl. Acad. Sci. USA, 90 (1993), 6076–6080.  
  10. M. A. Hjortsø. Population balances in biomedical engineering: Segregation through the distribution of the cell states. McGraw-Hill, 2006.  
  11. M. D. Johnston, C. M. Edwards, W. F. Bodmer, P. K. Maini, S. J. Chapman. Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer. Proc. Natl. Acad. Sci. USA, 104 (2008), No. 10, 4008–4013.  
  12. W.-C. Lo, C.-S. Chou, K. K. Gokoffski, F. Y.-M. Wan, A. D. Lander, A. L. Calof, Q. Nie. Feedback regulation in multistage cell lineages. Math. Biosci. Eng., 6 (2008), No. 1, 59–82.  Zbl1159.92013
  13. T. Luzyanina, D. Roose, T. Schenkel, M. Sester, S. Ehl, A. Meyerhans, G. Bocharov Numerical modelling of label-structured cell population growth using CFSE distribution data. Theor. Biol. Med. Model., 4 (2007), No. 26.  
  14. M. Mangel, M. B. Bonsall. Phenotypic evolutionary models in stem cell biology: replacement, quiescence, and variability. PLoS one, 3 (2008), No. 2, e1591.  
  15. N. V. Mantzaris. Single-cell gene-switching networks and heterogeneous cell population phenotypes. Comput. Chem. Eng., 29 (2005), 631–643.  
  16. J. D. Murray. Mathematical biology, Vol. 1, New York: Springer, 2002.  Zbl1006.92001
  17. M. Nair, A. Teng, V. Bilanchone, A. Agrawal, B. Li, X. Dai. Ovol1 regulates the growth arrest of embryonic epidermal progenitor cells and represses c-Myc transcription. J. Cell. Biol., 173 (2006), No. 2, 253–264.  
  18. S. Pelengaris, T. Littlewood, M. Khan, G. Elia, G. Evan. Reversible activation of c-Myc in skin: induction of a complex neoplastic phenotype by a single oncogenic lesion. Mol. Cell, 3 (1999), No. 5, 565–577.  
  19. L. F. Shampine. Solving hyperbolic PDEs in Matlab. Appl. Num. Anal. Comp. Math., 2 (2005), No. 3, 346–358.  Zbl1085.65514
  20. I. P. Tomlinson, W. F. Bodmer. Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models. Proc. Nat. Acad. Sci. USA, 92 (1995), 11130–11134.  
  21. R. L. Waikel, Y. Kawachi, P. A. Waikel, X.-J. Wang, D. R. Roop. Deregulated expression of c-Myc depletes epidermal stem cells. Nat. Genet., 28 (2001), No. 2, 165–168.  
  22. G. Wang. Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development. J. Math. Biol., 54 (2007), 761–786.  Zbl1145.92020
  23. F. M. Watt, M. Frye, S. A. Benitah. Myc in mammalian epidermis: how can an oncogene stimulate differentiation?. Nat. Rev. Cancer, 8 (2008), 234–242.  
  24. J. J. Willie Jr, M. R. Pittelkow, G. D. Shipley, R. E. Scott. Integrated control of growth and differentiation of normal human prokeratinocytes cultures in serum-free medium: clonal analyses, growth kinetics and cell cycle studies. J. Cell. Physiol, 121 (1984), 31–44.  
  25. A. Wilson, M. J. Murphy, T. Oskarsson, K. Kaloulis, M. D. Bettess, G. M. Oser, A.-C. Pasche, C. Knabenhans, H. R. MacDonald, A. Trumpp. c-Myc controls the balance between hematopoietic stem cell self-renewal and differentiation. Genes. Dev, 18 (2004), 2747–2763.  

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