Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T09:26:51.089Z Has data issue: false hasContentIssue false
  • English
  • Français

A Maturity-Structured Mathematical Model of Mutation, Acquisition in theAbsence of Homeostatic Regulation

Published online by Cambridge University Press:  05 June 2009

S. N. Gentry ,
R. Ashkenazi  and
T. L. Jackson
S. N. Gentry
Affiliation:
Department of Mathematics, University of Michigan, 48109 Ann Arbor, USA
R. Ashkenazi
Affiliation:
Department of Mathematics, University of Michigan, 48109 Ann Arbor, USA
T. L. Jackson*
Affiliation:
Department of Mathematics, University of Michigan, 48109 Ann Arbor, USA
*
[email protected]
Get access

Abstract

Most mammalian tissues are organized into a hierarchical structure of stem,progenitor, and differentiated cells. Tumors exhibit similar hierarchy, even ifit is abnormal in comparison with healthy tissue. In particular, it is believedthat a small population of cancer stem cells drives tumorigenesis in certainmalignancies. These cancer stem cells are derived from transformed stem cells ormutated progenitors that have acquired stem-cell qualities, specifically theability to self-renew. Similar to their normal counterparts, cancer stem cellsare long-lived, can self-renew and differentiate, albeit aberrantly, and arecapable of generating tissue, resulting in tumor formation. Although identifiedand characterized in several forms of malignancy, the specific multi-stepprocess that causes the formation of cancer stem cells is uncertain. Here, amaturity-structured mathematical model is developed to investigate thesequential order of mutations that causes the fastest emergence of cancer stemcells. Using model predictions, we discuss conditions for which geneticinstability significantly speeds cancer onset and suggest that unbalancedstem-cell self-renewal and inhibition of progenitor differentiation contributeto aggressive forms of cancer. To our knowledge, this is the first continuousmaturity-structured mathematical model used to investigate mutation acquisitionwithin hierarchical tissue in order to address implications of cancer stem cellsin tumorigenesis.

Keywords

cancer stem cell hypothesismaturity-structured mathematical modelmutation acquisition
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 3: Cancer modelling (Part 2) , 2009 , pp. 156 - 182
Copyright
© EDP Sciences, 2009

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

Abkowitz, J.L., Catlin, S.N., McCallie, M.T., Guttorp, P.. Evidence that the number of hematopoietic stem cells per animal is conserved in mammals. Blood, 100 (2002), No. 7, 2665–2667. CrossRef
Al-Hajj, M., Clarke, M.F., MF. Self-renewal and solid tumor stem cells. Oncogene, 23 (2004), No. 43, 7274–7282. CrossRef
Andersen, L.K., Mackey, M.C., MC. Resonance in periodic chemotherapy: a case study of acute myelogenous leukemia. J. Theor. Biol., 209 (2001), No. 13, 113–130. CrossRef
Araten, D.J., Golde, D.W., Zhang, R.H., RH, H.T. Thaler, L. Gargiulo, R. Notaro, R, L. Luzzatto, L. A quantitative measurement of the human somatic mutation rate. Cancer Res., 65 (2005), No. 18, 8111–8117. CrossRef
R. Ashkenazi, S.N. Gentry, T.L. Jackson. Pathways to tumorigenesis - modeling mutation acquisition in stem cells and their progeny. Neoplasia (Accepted).
D.R. Barreda, P.C. Hanington, M. Belosevic, M Regulation of myeloid development and function by colony stimulating factors. Dev. Comp. Immunol., 28 (2004), No. 5, 509–554.
Barrett, J.C., JC. Mechanisms of multistep carcinogenesis and carcinogen risk assessment. Environ. Health Persp., 100 (1993), 9–20. CrossRef
Behbod, F., Rosen, J.M.. Will cancer stem cells provide new therapeutic targets? (Review). Carcinogenesis, 26 (2005), No. 4, 703–711. CrossRef
Bernard, S., Bélair, J., Mackey, M.C., MC. Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J. Theor. Biol., 223 (2003), No. 3, 283–298. CrossRef
Bielas, J.H., Loeb, K.R., Rubin, B.P., True, L.D., Loeb, L.A.. Human cancers express a mutator phenotype. P. Natl. Acad. of Sci. USA, 103 (2006), No. 48, 18238–18242. CrossRef
Caussinus, E., Gonzalez, C., C. Induction of tumor growth by altered stem-cell asymmetric division in Drosophila melanogaster . Nat. Genet., 37 (2005), No. 10, 1125–1129. CrossRef
Cheshier, S.H., Morrison, S.J., Liao, X., Weissman, I.L.. In vivo proliferation and cell cycle kinetics of long-term self-renewing hematopoietic stem cells. P. Natl. Acad. Sci. USA, 96 (1999), No. 6, 3120–3125. CrossRef
Colijn, C., Mackey, M.C.. A mathematical model of hematopoiesis – I. Periodic chronic myelogenous leukemia. J. Theor. Biol., 237 (2005), No. 2, 117–132. CrossRef
Crowe, D.L., Parsa, B., Sinha, U.K.. Relationships between stem cells and cancer stem cells (Review). Histol. Histopathol., 19 (2004), No. 2, 505–509.
Fliedner, T.M., Graessle, D., Paulsen, C., Reimers, K.. Structure and function of bone marrow hemopoiesis: mechanisms of response to ionizing radiation exposure. Cancer Biother. Radio., 17 (2002), No. 4, 405–426.
Flynn, C.M., Kaufman, D.S., DS. Donor cell leukemia: insight into cancer stem cells and the stem cell niche. Blood, 109 (2007), No. 7, 2688–2692.
Galderisi, U., Cippollaro, M., Giordano, A.. Stem cells and brain cancer. Cell Death Differ., 13 (2006), No. 1, 5–11. CrossRef
Hanahan, D., Weinberg, R.A.. The hallmarks of cancer (Review). Cell, 100 (2000), No. 1, 57–70. CrossRef
Hardy, K., Stark, J., J. Mathematical models of the balance between apoptosis and proliferation. Apoptosis, 7 (2002), No. 4, 373–381. CrossRefPubMed
Harrison, W.J.. The total cellularity of the bone marrow in man. J. Clin. Pathol., 15 (1962), No. 3, 254–259. CrossRef
Huntly, B.J.P., Gilliland, D.G.. Leukaemia stem cells and the evolution of cancer-stem-cell research. Nat. Rev. Cancer, 5 (2005), No. 4, 311–321. CrossRefPubMed
Jackson, A.L., Loeb, L.A.. The mutation rate and cancer. Genetics, 148 (1998), No. 4, 1483–1490.
C.A. JanewayJr., P. Travers, M. Walport, M.J. Shlomchik. Immunobiology, Sixth Edition. Garland Science, 2005.
Michor, F., Hughes, T.P., Iwasa, Y., Branford, S., Shah, N.P., Sawyers, C.L., Nowak, M.A.. Dynamics of chronic myeloid leukaemia. Nature, 435 (2005), No. 7046, 1267–1270. CrossRef
Michor, F., Iwasa, I., Rajagopalan, H., Lengauer, C., Nowak, M.A., MA. Linear model of colon cancer initiation. Cell Cycle, 3 (2004), No. 3, 358–362. CrossRef
J.D. Murray. Mathematical Biology, Second Edition. Springer, 1989.
O'Neill, A., Schaffer, D.V.. The biology and engineering of stem-cell control. Biotechnol. Appl. Bioc., 40 (2004), No. 1, 5–16.
Ostby, I., Benestad, H.B., P/ Grottum. Mathematical modeling of human granulopoiesis: the possible importance of regulated apoptosis. Math. Biosci., 186 (2003), No. 1, 1–27. CrossRef
Pardal, R., Clarke, M.F., Morrison, S.J.. Applying the principles of stem-cell biology to cancer. Nat. Rev. Cancer, 3 (2003), No. 12, 895–902. CrossRefPubMed
Reizenstein, P.. Growth of normal and malignant bone marrow cells. Leukemia Res., 14 (1990), No. 8, 679–681. CrossRef
Reya, T., Morrison, S.J., Clarke, M.F., Weissman, I.L.. Stem cells, cancer, and cancer stem cells. Nature, 414 (2001), No. 6859, 105–111. CrossRef
Spencer, S.L., Berryman, M.J., García, J.A., Abbott, D., D. An ordinary differential equation model for the multistep transformation to cancer. J. Theor. Biol., 231 (2004), No. 4, 515–524. CrossRef
Wu, M., Kwon, H.Y., Rattis, F., Blum, J., Zhao, C., Ashkenazi, R., Jackson, T.L., Gaiano, N., Oliver, T., Reya, T.. Imaging hematopoietic precursor division in real time. Cell Stem Cell, 1 (2007), No. 5, 541–554. CrossRef