Mathematical modeling of stem cells related to cancer

Cancer and Stem Cells

Volumn , Issue , 2008, Pages 11-35

  Piotrowska, Monika Joanna ^a,b   Enderling, Heiko ^c   an der Heiden, Uwe ^a   Mackey, Michael C ^d  

^a UNIVERSITY OF WITTEN HERDECKE   (Germany)

^b UNIVERSITY OF WARSAW   (Poland)

^c TUFTS UNIVERSITY SCHOOL OF MEDICINE   (United States)

^d MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85043219821     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (70)

1. Dick, J. E. (2003). Breast cancer stem cells revealed. Proc. Natl. Acad. Sci. USA, 100 (7), 3547-3549.
2. Dontu, G., Al-Hajj M., Abdallah, W.M., Clarke, M. F. and Wicha, M. S. (2003). Stem cells in normal breast development and breast cancer. Cell Prolif., 36, 59-72.
3. Brown, M. D., Gilmore, P. E., Hart, C. A., Samuel, J. D., Ramani, V. A., George, N. J., Clarke, N. W. (2007). Characterization of benign and malignant prostate epithelial Hoechst 33342 side populations. Prostate, 67(13), 1384-1396.
4. Alison, M. R. (2005). Liver stem cells: implications for hepatocarcinogenesis. Stem Cell Rev, 1(3), 253-60.
5. Warner, J. K., Wang, J. C. Y., Hope, K. J., Jin, L., Dick, J. E. (2004). Concepts of human leukemic development. Oncogene, 23, 7164-7177.
6. Clarke, M. F. (2004). Neurobiology: at the root of brain cancer. Nature, 432, 281-282.
7. Pardal, R., Clarke, M.F. and Morrison, S.J. (2003). Applying the principes of stem-cell biology to cancer. Nature Rev. Cancer, 3, 895-902.
8. Reya, T., Morrison, S.J., Clarke M.F. and Weissman, I.L. (2001). Stem cells, cancer, and cancer stem cells. Nature, 414, 101-115.
9. Sell, S and Pierce, G.B. (1994). Maduration arrest of stem cell differentiation is a common pathway for the cellular origin of teratocarcinomas and epithelial cancers. Lab Invest., 70, 6-22.
10. Ganguly, R. and Puri, I. K. (2006). Mathematical model for the cancer stem cell hypothesis. Cell Prolif, 39, 3-14.
11. Solyani, G. I., Berezetskaya, N. M., Bulkiewicz, R. I., and Kulik, G. I. (1995). Different growth patterns of a cancer cell population as a function of its starting growth characteristics. Analysis by mathematical modelling. Cell Prolif, 28, 263-278.
12. Gamer, A. L., Lau, Y. Y., Jordan, D. W., Uhler, M. D. and Gilgenbach, R. M. (2006). Implications of a simple mathematical model to cancer cell population dynamics. Cell Proli/., 39, 15-28.
13. Wallen, C. A., Higashicubo, R. and Dethlefsen, L. A. (1984). Murine mammary tumour cells in vitro. I. The development of a quiescent state. Cell Tissue Kinet, 17, 65-77.
14. Wallen, C. A., Higashicubo, R. and Dethlefsen, L. A. (1984). Murine mammary tumour cells in vitro. II. Recruitment of quiescent state. Cell Tissue Kinet, 17, 79-89.
15. Widera, D., Mikenberg, I., Kaus, A., Kaltschmidt, C. and Kaltschmid, B. (2006). Nuclear factor-kappaB controls the reaggregation of 3D neurosphere cultures in vitro. Eur. Cell Mater., 11, 76-84.
16. Piotrowska, M. J., Widera, D., Kaltschmidt, B., an der Heiden, U. and Kaltschmidt, C. (2006). Mathematical model for NF-KB-driven proliferation of adult neural stem cells. Cell Prolif, 39, 441-455.
17. Bonizzi, G. and Karin, M. (2004). The two NF-kappaB activation pathways and their role in innate and adaptive immunity. Trends Immunol, 25, 280-288.
18. Ghosh, S. and Karin, M. (2002). Missing pieces in the NF-kappaB puzzle. Cell, 109, S81-S96.
19. Kaltschmidt, B., Widera, D. and Kaltschmidt, C. (2005). Signaling via NF-kappaB in the nervous system. Biochim. Biophys. Acta, 1745, 287-299.
20. Guttridge, D. C., Albanese, C., Reuther, J. Y., Pestell, R. G. and Baldwin, A. S. Jr. (1999). NF-kappaB controls cell growth and differentiation through transcriptional regulation of cyclin D1. Mol. Cell Biol., 19, 5785-5799.
21. Baud, V. and Karin, M. (2001). Signal transduction by tumor necrosis factor and its relatives. Trends Cell Biol., 11, 372-377.
22. Michaelis L., Menten M. (1913). Die Kinetik der Invertinwirkung, Biochem. Z. 49:333-369.
23. Hoffmann, A., Levchenko, A., Scott, M. L. and Baltimore, D. (2002). The IkappaB- NF-kappaB signaling module: temporal control and selective gene activation. Science, 298, 1241-1245.
24. Cheong, R., Bergmann, A., Werner, S. L., Regal, J., Hoffmann, A. and Levchenko, A. (2006) Transient IkappaB kinase activity mediates temporal NF-kappaB dynamics in response to a wide range of tumor necrosis factor-alpha doses. J. Biol. Chem., 281, 2945-2950.
25. Lipniacki, T., Paszek, P., Brasier, A. R., Luxon, B., Kimmel, M. (2004). Mathematical model of NF-kappaB regulatory module. J. Theor. Biol., 228, 195-215.
26. Singh, S. K., Hawkins, C., Clarke, I. D., Squire, J.A., Bayani, J., Hide, T., Henkelman, R. M., Cusimano, M. D. and Dirks, P. B. (2004). Identification of human brain tumour initiating cells. Nature, 432, 396-401.
27. Hinz, M., Krappmann, D., Eichten, A., Heder, A., Scheidereit, C. and Strauss, M. (1999). NF-kappaB function in growth control: regulation of cyclin D1 expression and G0/G1-to-S-phase transition. Mol. Cell Biol., 19, 2690-2698.
28. Kaltschmidt, B., Kaltschmidt, C., Hehner, S. P., Droge, W. and Schmitz, M. L. (1999). Repression of NF-kappaB impairs HeLa cell proliferation by functional interference with cell cycle checkpoint regulators. Oncogene, 18, 3213-3225.
29. Henderson, E. S., Lister, T. A. and Greaves, M. F., eds. (1996). Leukemia. Saunders.
30. Fortin, P. and Mackey, M. (1999). Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and etiological implications. Brit. J. Haematol, 104, 336-245.
31. Guerry, D., Dale, C., D., Omine, M., Perry, and S. Wolff, S. M. (1973). Periodic hematopoiesis in human cyclic neutropenia. J. Clin. Inves, 52, 3220-3230.
32. Haurie, C., Mackey, M. C. and Dale, D. C. (1998). Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models. Blood, 92, 2629-2640.
33. Hammond, W. P., Price, T. H., Souza, L. M. and Dale, D. C. (1989). Treatment of cyclic neutropenia with granulocyte colony stimulating factor. New Eng. J. Med., 320, 1306-1311.
34. Haurie, C., Person, R., Dale, D. C. and Mackey, M. (1999). Haematopoietic dynamics in grey collies. Exper. Hematol, 27, 1139-1148.
35. Pujo-Menjouet, L., Bernard, S. and Mackey, M. (2001). Long period oscillations in a gomodel of hematopoietic stem cells. SIAM, 4, 312-332.
36. Bernard, S., Belair, J. and Mackey, M. (2003). Oscillations in cyclical neutropenia: New evidence based on mathematical modeling. J. Theor. Biol., 223, 283-298.
37. Go, R. S. (2005). Ideopathic cyclic thrombocytopenia. Blood Reviews, 19, 53-59.
38. Swinburne, J. and Mackey, M. C. (2000). Cyclical thrombocytopenia: Characterisation by spectral analysis and a review. J. Theor. Med, 2, 81-91.
39. Cohen, T. and Cooney, D. P. (1974). Cyclic thrombocytopenia. Case report and Review of literature. Scand. J. Haematol, 12, 9-17.
40. Santillan, M., Mahaffy, J., Belair, J. and Mackey, M. (2000). Regulation of platelet production: the normal response to perturbation and cyclical platelet disease. J. Theor. Biol, 206, 585-603.
41. Von Schulthess, G. K. and Gessner, U. (1986). Oscillating platelet counts in healthy individuals: Experimental investigation and quantitative evaluation of thrombocytopenic feedback control. Scand. J. Haematol, 36, 473-479.
42. Hearn, T., Haurie, C. and Mackey, M. (1998). Cyclical neutropenia and the peripherial control of white blood cell production. J. theor. Biol, 192, 167-181.
43. Haurie, C. and Mackey, M. (2000). Modeling complex neutrophil dynamics in the grey collie. J. theor. Biol., 204, 504-519.
44. Mackey, M. C. (1979). Periodic auto-immune hemolytic anemia: An induced dynamical disease. Bull. Math. Biol., 41, 829-834.
45. Bélair, J., Mackey, M. and Mahaffy, J. (1995). Age-structured and two-delay models for erythropoiesis. Math. Biosci, 128, 317-346.
46. Mahaffy, J., Belair, J. and Mackey, M. (1998). Hematopoietic model with moving boundary condition and state dependent delay: Applications in erythropoiesis. J. Theor. Biol., 190, 135-146.
47. Bélair, J. and Mackey, M. (1987). A model for the regulation of mammalian platelet. Ann. N.Y. Acad. Sci., 504, 280-282.
48. Colijn, C. and Mackey, M. C. (2005). A mathematical model of hematopoiesis: Periodic chronic myelogenous leukemia, part I. J. Theor. Biol, 237, 117-132.
49. Mackey, M. C. (1978). A unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis. Blood, 51, 941-956.
50. Mackey, M. C. (1979). Dynamic haematological disorders of stem cell origin. In: Vassileva-Popova, J. G. and Jensen, E. V., eds., Biophysical and Biochemical Information Transfer in Recognition, 373-409. New York: Plenum Publishing Corp.
51. Mackey, M. C. (2000). Cell kinetic status of haematopoietic stem cells. Cell Prolif, 34, 71-83.
52. Colijn, C. and Mackey, M. C. (2005). A mathematical model of hematopoiesis: Cyclical neutropenia, part II. J. Theor. Biol., 237, 133-146.
53. Lomb, N. R. (1976). Least-squares frequency analysis of unequally spaced data. Astrophysics and space. Science, 39, 447-462.
54. Apostu, R. and Mackey, M. (2007, in press). Understanding cyclical thrombocytopenia: A mathematical modeling approach. J. Theor. Biol.
55. Anderson, A. R. A., Weaver, A. M., Cummings, P.T. and Quaranta, V. (2006). Tumor Morphology and Phenotypic Evolution Driven by Selective Pressure from the Microenvironment. Cell 127, 905-915.
56. Kansal, A. R., Torquato S., Harsh GR IV, Chiocca E. A. and Deisboeck T. S. (2000). Simulated Brain Tumor growth dynamics using a three-dimensional cellular automaton. J. Theor. Biol, 203(4), 367-382.
57. Agur Z., Daniel Y. and Ginosar Y. (2002). The universal properties of stem cells as pinpointed by a simple discrete model. J. Math. Biol, 44(1), 79-86.
58. Enderling H., Hlatky, L. and Hahnfeldt, P. (2007). Agent-based modeling of stem cell dynamics and tissue homeostasis. in preparation.
59. Moran P. A. P. (1962). The statistical processes of evolutionary theory. Oxford: Clarendon Press. 200 p.
60. Clarke, R. B. (2005). Isolation and characterization of human mammary stem cells. Cell Prolif. 38 (6), 375-386.
61. Wright E. G., Lord B. I., Dexter T. M. and Lajtha L. G. (1979). Mechanisms of haemopoietic stem cell proliferation control. Blood Cells. 1979 Jun 15;5(2):247-258.
62. Al-Hajj M., Wicha M. S., Benito-Hernandez A., Morrison S. J. and Clarke M. F. (2003). Prospective identification of tumorigenic breast cancer cells. Proc. Natl. Acad. Sci. USA. 100(7), 3983-3988.
63. Bonnet D. and Dick J. E. (1997). Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat. Med, 3, 730-737.
64. Lapidot T., Sirard C. and Vormoor J. (1994) A cell initiating human acute myeloid leukemia after transplantation into SCID mice. Nature, 17, 645-648.
65. Galli R., Binda E. and Orfanelli U. (2004). Isolation and characterization of tumorigenic, stem-like neural precursors from human glioblastoma. Cancer Res., 64, 7011-7021.
66. Hemmati H. D., Nakano I. and Lazareff J. A. (2003). Cancerous stem cells arise from pediatric brain tumors. Proc. Natl. Acad. Sci. USA, 100, 15178-15183.
67. Li C., Heidt D. G., Dalerba P., Burant C. F., Zhang L., Adsay V., Wicha M., Clarke M. F. and Simeone D. M. (2007). Identification of pancreatic cancer stem cells. Cancer Res., 1030-1037.
68. Dingli D. and Michor F. (2006) Successful therapy must eradicate cancer stem cells. Stem Cells, 24, 2603-2610.
69. Phillips T. M., McBride W. H. and Pajonk F. (2006). The response of CD24(- /low)/CD44+ breast cancer-initiating cells to radiation. J. Natl. Cancer Inst. 98(24):1777-1785.
70. Bao S., Wu Q., McLendon R. E., Hao Y., Shi Q., Hjelmeland A. B., Dewhirst M. W., Bigner D. D. and Rich J. N. (2006). Glioma stem cells promote radioresistance by preferential activation of the DNA damage response. Nature. 444(7120), 756-760.