Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-10T15:20:02.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics

Published online by Cambridge University Press:  25 January 2012

T. Stiehl  and
A. Marciniak-Czochra
Get access

Abstract

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts. Using linear stability analysis we derive conditions necessary and sufficient for expansion of malignant cell clones, based on fundamental cellular properties. This approach reveals different scenarios of cancer initiation and provides qualitative hints to possible treatment strategies.

Keywords

multi-compartmental modelsstem cell differentiationenvironmental signalingleukemiacancer stem cellsleukemic stem cellslinear stability analysis
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 1: Cancer modeling , 2012 , pp. 166 - 202
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablain, J., de The, H.. Revisiting the differentiation paradigm in acute promyelocytic leukemia. Blood, 117 (2008), No. 22, 5795–5802. CrossRefGoogle ScholarPubMed
Adimy, M., Crauste, F.. Modeling and asymptotic stability of a growth factor- dependent stem cell dynamics model with distributed delay. Discrete Contin. Dyn. Syst. Ser. B, 8 (2007), No. 1, 19–38. Google Scholar
Adimy, M., Crauste, F., Ruan, S.. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math., 65 (2005), No. 4, 1328–1352. CrossRefGoogle Scholar
Adimy, M., Crauste, F., Ruan, S.. Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol., 68 (2006), No. 8, 2321–2351. CrossRefGoogle ScholarPubMed
Aglietta, M., Piacibello, W., Sanavio, F., Stacchini, A., Apra, F., Schena, M., Mossetti, C., Carnino, F., Caligaris-Cappio, F., Gavosto, F.. Kinetics of human hemopoietic cells after in vivo administration of granulocyte-macrophage colony-stimulating factor. J. Clin. Invest., 83 (1989), No. 2, 551–557. CrossRefGoogle ScholarPubMed
T. Alarcon, P. Getto, A. Marciniak-Czochra, MdM. Vivanco. A model for stem cell population dynamics with regulated maturation delay. Discr. Cont. Dyn. Systems B (2011), to appear.
Andrey, L.. Chaos in cancer. Med. Hypotheses, 28 (1989), No. 3, 143–144. CrossRefGoogle Scholar
Arino, O., Kimmel, M.. Stability analysis of models of cell production systems. Math. Modelling, 7 (1986), No. 9-12, 1269–1300. CrossRefGoogle Scholar
Baum, M., Chaplain, MA., Anderson, AR., Douek, M., Vaidya, JS.. Does breast cancer exist in a state of chaos ? Eur. J. Cancer, 35 (1999), No. 6, 886–891. CrossRefGoogle Scholar
Bejar, R., Levine, R., and Ebert, B. L.. Unraveling the molecular pathophysiology of myelodysplastic syndromes. J. Clin. Oncol., 29 (2011), No. 5, 504–514. CrossRefGoogle ScholarPubMed
Belair, J., Mackey, MC., Mahaffy, J. M.. Age-structured and two-delay models for erythropoiesis. Math. Biosci., 128 (1995), No. 1-2, 317–346. CrossRefGoogle ScholarPubMed
Bellan, C., Stefano, L., Giulia, dF., Rogena, E. A., Lorenzo, L.. Burkitt lymphoma versus diffuse large B-cell lymphoma : a practical approach. Hematol. Oncol., 28 (2010), No. 2, 53–56. Google ScholarPubMed
Bocker, MT., Hellwig, I., Breiling, A., Eckstein, V., Ho, A. D., Lyko, F.. Genome-wide promoter DNA methylation dynamics of human hematopoietic progenitor cells during differentiation and aging. Blood, 117 (2011), No. 19 : e182–e189. CrossRefGoogle ScholarPubMed
Bogner, V., Keil, L., Kanz, KG., Kirchhoff, C., Leidel, B. A., Mutschler, W., Biberthaler, P.. Very early posttraumatic serum alterations are signiïňĄcantly associated to initial massive RBC substitution, injury severity, multiple organ failure and adverse clinical outcome in multiple injured patients. Eur. J. Med. Res., 14 (2009), No. 7, 284–291. CrossRefGoogle ScholarPubMed
Bonnet, D., Dick, J. E.. Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat. Med., 3 (1997), No. 7, 730–737. CrossRefGoogle ScholarPubMed
Bryan, J., Jabbour, E., Prescott, H., Garcia-Manero, G., Issa, J. P., Kantarjian, H.. Current and future management options for myelodysplastic syndromes. Drugs, 70 (2010), No. 11, 1381– 1394. CrossRefGoogle ScholarPubMed
Buss, EC., Ho, A. D.. Leukemia stem cells. Int. J. Cancer., 129 (2011), No. 10, 2328–2336. CrossRefGoogle ScholarPubMed
Chen, SY., Huang, YC., Liu, SP, Tsai, FJ, Shyu, WC, Lin, SZ. An overview of concepts for cancer stem cells. Cell Transplant., 20 (2011), No. 1, 113–120. CrossRefGoogle ScholarPubMed
Cheson, BD.. Standard and low-dose chemotherapy for the treatment of myelodysplastic syndromes. Leuk. Res., Suppl. 1 (1998), S17–S21. CrossRefGoogle Scholar
Clevers, H.. The cancer stem cell : premises, promises and challenges. Nat Med., 17 (2011), No. 3, 313–319. CrossRefGoogle ScholarPubMed
Coffey, D.S.. Self-organization, complexity and chaos : the new biology for medicine. Nat. Med., 4 (1998), No. 8, 882–885. CrossRefGoogle ScholarPubMed
Colijn, C., Mackey, M.C.. A mathematical model of hematopoiesis –I. periodic chronic myelogenous leukemia. J. Theor. Biol., 237 (2005), No. 2, 117–132. CrossRefGoogle ScholarPubMed
D. Dingli, JM. Pacheco. Stochastic dynamics and the evolution of mutations in stem cells. BMC Biol., 9 :41 (2011).
Doumic-Jauffret, M., Kim, PS., Perthame, B.. Stability analysis of a simplied yet complete model for chronic myelogenous leukemia. Bull. Math. Biol., 72 (2010), No. 7, 1732–1759. CrossRefGoogle Scholar
Doumic-Jauffret, M., Marciniak-Czochra, A., Perthame, B., Zubelli, JP.. A Structured Population Model of Cell Differentiation. SIAM J. Appl. Math., 71 (2011), 1918–1940. CrossRefGoogle Scholar
Fenaux, P., Mufti, GJ., Hellstrom-Lindberg, E., Santini, V., Finelli, C., Giagounidis, A., Schoch, R., Gattermann, N., Sanz, G., List, A., Gore, SD., Seymour, JF., Bennett, JM., Byrd, J., Backstrom, J., Zimmerman, L., McKenzie, D., Beach, C., Silverman, LR.; International Vidaza High-Risk MDS Survival Study Group. Efficacy of azacitidine compared with that of conventional care regimens in the treatment of higher-risk myelodysplastic syndromes : a randomised, open-label, phase III study. Lancet Oncol., 10 (2009), No. 3, 223–232. CrossRefGoogle ScholarPubMed
Foley, C., Bernard, S., Mackey, MC.. Cost-effective G-CSF therapy strategies for cyclical neutropenia : Mathematical modelling based hypotheses. J. Theor. Biol., 238 (2006), No. 4, 754–763. CrossRefGoogle ScholarPubMed
Fried, W.. Erythropoietin and erythropoiesis. Exp. Hematol., 37 (2009), No. 9, 1007–1015. CrossRefGoogle ScholarPubMed
FR. Gantmacher. The theory of matrices 2. Chelsea Publishing, New York, 1964.
P. Getto, A. Marciniak-Czochra, Y. Nakata, MdM. Vivanco. Global dynamics of two compartment models for cell production systems with regulatory mechanisms. (2011), submitted.
J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York, 2002.
Haeno, H., Levine, RL., Gilliland, DG., Michor, F.. A progenitor cell origin of myeloid malignancies. PNAS, 106 (2009), No. 39, 16616–16621. CrossRefGoogle ScholarPubMed
Hope, KJ., Jin, L., Dick, JE.. Acute myeloid leukemia originates from a hierarchy of leukemic stem cell classes that differ in self-renewal capacity. Nat. Immun., 5 (2004), No. 7, 738–743. CrossRefGoogle ScholarPubMed
JH. Jandl (ed), Textbook of Hematology, Little Brown, Boston, MA, 1996.
Janz, S., Potter, M., Rabkin, CS.. Lymphoma- and leukemia-associated chromosomal translocations in healthy individuals. Genes Chromosomes Cancer, 36 (2003), No. 3, 211–223. CrossRefGoogle ScholarPubMed
Kantarjian, H., Oki, Y., Garcia-Manero, G., Huang, X., OBrien, S., Cortes, J., Faderl, S., Bueso-Ramos, C., Ravandi, F., Estrov, Z., Ferrajoli, A., Wierda, W., Shan, J., Davis, J., Giles, F., Saba, HI., Issa, JP.. Results of a randomized study of 3 schedules of low- dose decitabine in higher-risk myelodysplastic syndrome and chronic myelomonocytic leukemia. Blood, 109 (2007), No. 1, 52–57. CrossRefGoogle ScholarPubMed
Knipp, S., Hildebrand, B., Kündgen, A., Giagounidis, A., Kobbe, G., Haas, R., Aul, C., termann, N. Gat-, Germing, U.. Intensive chemotherapy is not recommended for patients aged > 60 years who have myelodysplastic syndromes or acute myeloid leukemia with high-risk karyotypes. Cancer, 110 (2007), No. 2, 345–352. CrossRefGoogle ScholarPubMed
Korde, N., Kristinsson, SY., Landgren, O.. Monoclonal gammopathy of undetermined signiïňĄcance (MGUS) and smoldering multiple myeloma (Smm) : novel biological insights and development of early treatment strategies. Blood, 117 (2011), No. 21, 5573–5581. CrossRefGoogle ScholarPubMed
Lander, A., Gokoffski, K., Wan, F., Nie, Q., Calof, A.. Cell lineages and the logic of proliferative control. PLoS biology, 7 (2009), No. 1, 84–100. CrossRefGoogle ScholarPubMed
Lange, SS., Takata, K., Wood, RD.. DNA polymerases and cancer. Nat. Rev. Cancer, 11 (2011), No. 2, 96–110. CrossRefGoogle ScholarPubMed
Lansdorp, PM.. Stem cell biology for the transfusionist. Vox Sang., 74 Suppl. 2 (1998), 91–94. CrossRefGoogle ScholarPubMed
Layton, JE., Hockman, H., Sheridan, WP., Morstyn, G.. Evidence for a novel in vivo control mechanism of granulopoiesis : mature cell-related control of a regulatory growth factor. Blood, 74 (1989), No. 4, 1303–1307. Google ScholarPubMed
Lo, W., Chou, C., Gokoffski, K., Wan, F., Lander, A., Calof, A., Nie, Q.. Feedback regulation in multistage cell lineages. Math. Biosci. Eng., 6 (2009), No. 1, 59–82. CrossRefGoogle ScholarPubMed
MMackey, C.. Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood, 51 (1978), No. 5, 941–956. Google ScholarPubMed
Mackey, MC., Glass, L., Oscillation and chaos in physiological control systems. Science, 197 (1977), No. 4300, 287–289. CrossRefGoogle ScholarPubMed
A. Marciniak-Czochra, T.Stiehl. Mathematical models of hematopoietic reconstitution after stem cell transplantation. In HG. Bock, T. Carraro, W. Jäger, S. Koerkel, R. Rannacher, JP. Schloeder (eds), Model Based Parameter Estimation : Theory and Applications. Springer, Heidelberg, 2011.
Marciniak-Czochra, A., Stiehl, T., Jäger, W., Ho, AD., Wagner, W.. Modeling of asymmetric cell division in hematopoietic stem cells – regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev., 18 (2009), No. 3, 377–385. CrossRefGoogle ScholarPubMed
Marciniak-Czochra, A., Stiehl, T., Wagner, W.. Modeling of replicative senescence in hematopoietic development. Aging (Albany NY), 1 (2009), No. 8, 723–732. CrossRefGoogle ScholarPubMed
Metcalf, D.. Hematopoietic cytokines. Blood, 111 (2008), No. 2, 485–491. CrossRefGoogle ScholarPubMed
Michor, F., Hughes, TP., Iwasa, Y., Branford, S., Shah, NP., Sawyers, CL., Nowak, MA.. Dynamics of chronic myeloid leukaemia. Nature, 435 (2005), No. 7046, 1267–1270. CrossRefGoogle ScholarPubMed
Moore, KA., Lemischka, IR.. Stem cells and their niches. Science, 311 (2006), No. 5769, 1880–1805. CrossRefGoogle ScholarPubMed
D. Morgan, A. Murray, T. Hunt, P. Nurse. In : Alberts Molecular Biology of the Cell, 4th Edition, Garland Science, New York, 2002.
Munk Pedersen, I., Reed, J.. Microenvironmental interactions and survival of CLL B-cells. Leuk. Lymphoma, 45 (2004), No. 12, 2365–2372. CrossRefGoogle ScholarPubMed
Nakata, Y., Getto, P., Marciniak-Czochra, A., Alarcon, T.. Stability analysis of multi-compartment models for cell production systems. J. Biol. Dyn., (2011), doi : 10.1080/17513758.2011.558214. Google ScholarPubMed
Pujo-Menjouet, L., Bernard, S., Mackey, MC.. Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Syst, 4 (2005), No. 2, 312–332. CrossRefGoogle Scholar
Reya, T., Morrison, SJ., Clarke, MF., Weissman, IL.. Stem cells, cancer, and cancer stem cells. Nature, 414 (2001), No. 6859, 105–111. CrossRefGoogle ScholarPubMed
Roeder, I., Herberg, M., Horn, M.. An age-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bull. Math. Biol., 71 (2009), No. 3, 602–626. CrossRefGoogle ScholarPubMed
Roeder, I., Horn, M., Glauche, I., Hochhaus, A., Mueller, MC., Loeffler, M.. Dynamic modeling of imatinib-treated chronic myeloid leukemia : functional insights and clinical implications. Nat. Med., 12 (2006), No. 10, 1181–1184. CrossRefGoogle ScholarPubMed
Roeder, I., Loeffler, M.. A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp. Hematol., 30 (2002), 853–861. CrossRefGoogle ScholarPubMed
R. Rudnicki. Chaoticity of the blood cell production system. Chaos, doi : 10.1063/1.3258364, 2009.
Schueler, F., Hirt, C., Doelken, G.. Chromosomal translocation t (14 ;18) in healthy individuals. Semin. Cancer. Biol., 13 (2003), 3, 203–209. CrossRefGoogle Scholar
Shinjo, K., Takeshita, A., Ohnishi, K., Ohno, R.. Granulocyte colony-stimulating factor receptor at various stages of normal and leukemic hematopoietic cells. Leuk. Lymphoma, 25 (1997), No. 1-2, 37–46. CrossRefGoogle ScholarPubMed
Soltanian, S., Matin, MM.. Cancer stem cells and cancer therapy. Tumour Biol., 32 (2011), No. 3, 425–440. CrossRefGoogle ScholarPubMed
Stiehl, T., Marciniak-Czochra, A.. Characterization of stem cells using mathematical models of multistage cell lineages. Mathematical and Computer Modelling, 53 (2011), No. 7-8, 1505–1517. CrossRefGoogle Scholar
Till, JE., Siminovitch, L., McCulloch, EA.. Stochastic Model of Stem Cell Proliferation Based on Growth of Spleen Colony-Forming Cells. PNAS, 51 (1964), 29–49. CrossRefGoogle ScholarPubMed
Tomasetti, C., Levy, D.. Role of symmetric and asymmetric division of stem cells in developing drug resistance. PNAS., 107 (2010), No. 39. 16766-16771. CrossRefGoogle ScholarPubMed
Tormo, M., Marugan, I., Calabuig, M.. Myelodysplastic syndromes : an update on molecular pathology. Clin. Transl. Oncol., 12 (2010), No. 10, 652–661.CrossRefGoogle ScholarPubMed