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Multi-scale Modelling for Threshold Dependent Differentiation

  • A. Q. Cai (a1) (a2), Y. Peng (a1) (a2), J. Wells (a3), X. Dai (a3) and Q. Nie (a1) (a2)...


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.


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[1] Abercrombie, M.. The crawling movement of metazoan cells. Proc. R. Soc. Lond. B. Biol. Sci., 207 (1980), No. 1167, 129147.
[2] Arnold, I., Watt, F. M.. c-Myc activation in transgenic mouse epidermis results in mobilization of stem cells and differentiation of their progeny. Curr. Biol., 11 (2001), No. 8, 558568.
[3] Basse, B., Baguley, B. C., Marshall, E. S., Joseph, W. R., van Brunt, B., Wake, G. C., Wall, D. J. N.. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. J. Math. Biol., 47 (2003), No. 4, 295312.
[4] Bernard, S., Pujo-Menjouet, L., Mackey, M. C.. Analysis of cell kinetics using a cell division marker: Mathematical modeling of experimental data. Biophys. J., 84 (2003), 34143424.
[5] van Brunt, B., Wake, G. C., Kim, H. K.. On a singular Sturm-Liouville problem involving an advanced functional differential equation. European J. Appl. Math., 12 (2001), 625644.
[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] Clayton, E., Doupé, D. P., Klein, A. M., Winton, D. J., Simons, B. D., Jones, P. H.. A single type of progenitor cell maintains normal epidermis. Nature, 446 (2007), 185189.
[8] Fuchs, E., Raghavan, S.. Getting under the skin of epidermal morphogenesis. Nat. Rev. Genet., 3 (2002), 199209.
[9] Glick, A. B., Kulkarni, A. B., Tennenbaum, T., Hennings, H., Flanders, K. C., O'Reily, M., Sporn, M. B., Karlsson, S., Yuspa, S. H.. 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), 60766080.
[10] M. A. Hjortsø. Population balances in biomedical engineering: Segregation through the distribution of the cell states. McGraw-Hill, 2006.
[11] Johnston, M. D., Edwards, C. M., Bodmer, W. F., Maini, P. K., Chapman, S. J.. Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer. Proc. Natl. Acad. Sci. USA, 104 (2008), No. 10, 40084013.
[12] Lo, W.-C., Chou, C.-S., Gokoffski, K. K., Wan, F. Y.-M., Lander, A. D., Calof, A. L., Nie, Q.. Feedback regulation in multistage cell lineages. Math. Biosci. Eng., 6 (2008), No. 1, 5982.
[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] Mantzaris, N. V.. Single-cell gene-switching networks and heterogeneous cell population phenotypes. Comput. Chem. Eng., 29 (2005), 631643.
[16] J. D. Murray. Mathematical biology, Vol. 1, New York: Springer, 2002.
[17] Nair, M., Teng, A., Bilanchone, V., Agrawal, A., Li, B., Dai, X.. Ovol1 regulates the growth arrest of embryonic epidermal progenitor cells and represses c-Myc transcription. J. Cell. Biol., 173 (2006), No. 2, 253264.
[18] Pelengaris, S., Littlewood, T., Khan, M., Elia, G., Evan, G.. Reversible activation of c-Myc in skin: induction of a complex neoplastic phenotype by a single oncogenic lesion. Mol. Cell, 3 (1999), No. 5, 565577.
[19] Shampine, L. F.. Solving hyperbolic PDEs in Matlab. Appl. Num. Anal. Comp. Math., 2 (2005), No. 3, 346358.
[20] Tomlinson, I. P., Bodmer, W. F.. Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models. Proc. Nat. Acad. Sci. USA, 92 (1995), 1113011134.
[21] Waikel, R. L., Kawachi, Y., Waikel, P. A., Wang, X.-J., Roop, D. R.. Deregulated expression of c-Myc depletes epidermal stem cells. Nat. Genet., 28 (2001), No. 2, 165168.
[22] Wang, G.. Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development. J. Math. Biol., 54 (2007), 761786.
[23] Watt, F. M., Frye, M., Benitah, S. A.. Myc in mammalian epidermis: how can an oncogene stimulate differentiation?. Nat. Rev. Cancer, 8 (2008), 234242.
[24] Willie Jr, J. J., Pittelkow, M. R., Shipley, G. D., Scott, R. E.. 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), 3144.
[25] Wilson, A., Murphy, M. J., Oskarsson, T., Kaloulis, K., Bettess, M. D., Oser, G. M., Pasche, A.-C., Knabenhans, C., MacDonald, H. R., Trumpp, A.. c-Myc controls the balance between hematopoietic stem cell self-renewal and differentiation. Genes. Dev, 18 (2004), 27472763.



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