Geodesic
A Maturity-Structured Mathematical Model of Mutation, Acquisition in the Absence of Homeostatic Regulation
S. N. Gentry1 ; R. Ashkenazi1 ; T. L. Jackson1
1 Department of Mathematics, University of Michigan, 48109 Ann Arbor, USA
Mathematical modelling of natural phenomena, Tome 4 (2009) no. 3, pp. 156-182.

Voir la notice de l'article provenant de la source EDP Sciences

Most mammalian tissues are organized into a hierarchical structure of stem, progenitor, and differentiated cells. Tumors exhibit similar hierarchy, even if it is abnormal in comparison with healthy tissue. In particular, it is believed that a small population of cancer stem cells drives tumorigenesis in certain malignancies. These cancer stem cells are derived from transformed stem cells or mutated progenitors that have acquired stem-cell qualities, specifically the ability to self-renew. Similar to their normal counterparts, cancer stem cells are long-lived, can self-renew and differentiate, albeit aberrantly, and are capable of generating tissue, resulting in tumor formation. Although identified and characterized in several forms of malignancy, the specific multi-step process that causes the formation of cancer stem cells is uncertain. Here, a maturity-structured mathematical model is developed to investigate the sequential order of mutations that causes the fastest emergence of cancer stem cells. Using model predictions, we discuss conditions for which genetic instability significantly speeds cancer onset and suggest that unbalanced stem-cell self-renewal and inhibition of progenitor differentiation contribute to aggressive forms of cancer. To our knowledge, this is the first continuous maturity-structured mathematical model used to investigate mutation acquisition within hierarchical tissue in order to address implications of cancer stem cells in tumorigenesis.
DOI : 10.1051/mmnp/20094307

S. N. Gentry 1 ; R. Ashkenazi 1 ; T. L. Jackson 1

1 Department of Mathematics, University of Michigan, 48109 Ann Arbor, USA 
@article{MMNP_2009_4_3_a6,
     author = {S. N. Gentry and R. Ashkenazi and T. L. Jackson},
     title = {A {Maturity-Structured} {Mathematical} {Model} of {Mutation,} {Acquisition} in the {Absence} of {Homeostatic} {Regulation}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {156--182},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {2009},
     doi = {10.1051/mmnp/20094307},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094307/}
}
TY  - JOUR
AU  - S. N. Gentry
AU  - R. Ashkenazi
AU  - T. L. Jackson
TI  - A Maturity-Structured Mathematical Model of Mutation, Acquisition in the Absence of Homeostatic Regulation
JO  - Mathematical modelling of natural phenomena
PY  - 2009
SP  - 156
EP  - 182
VL  - 4
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094307/
DO  - 10.1051/mmnp/20094307
LA  - en
ID  - MMNP_2009_4_3_a6
ER  - 
%0 Journal Article
%A S. N. Gentry
%A R. Ashkenazi
%A T. L. Jackson
%T A Maturity-Structured Mathematical Model of Mutation, Acquisition in the Absence of Homeostatic Regulation
%J Mathematical modelling of natural phenomena
%D 2009
%P 156-182
%V 4
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094307/
%R 10.1051/mmnp/20094307
%G en
%F MMNP_2009_4_3_a6
S. N. Gentry; R. Ashkenazi; T. L. Jackson. A Maturity-Structured Mathematical Model of Mutation, Acquisition in the Absence of Homeostatic Regulation. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 3, pp. 156-182. doi : 10.1051/mmnp/20094307. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094307/

[1] J.L. Abkowitz, S.N. Catlin, M.T. Mccallie, P. Guttorp Blood 2002 2665 2667

[2] M. Al-Hajj, M.F. Clarke Oncogene 2004 7274 7282

[3] L.K. Andersen, M.C. Mackey J. Theor. Biol. 2001 113 130

[4] D.J. Araten, D.W. Golde, R.H. Zhang Cancer Res. 2005 8111 8117

[5] R. Ashkenazi, S.N. Gentry, T.L. Jackson. Pathways to tumorigenesis - modeling mutation acquisition in stem cells and their progeny. Neoplasia (Accepted).

[6] 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.

[7] J.C. Barrett Environ. Health Persp. 1993 9 20

[8] F. Behbod, J.M. Rosen Carcinogenesis 2005 703 711

[9] S. Bernard, J. Bélair, M.C. Mackey J. Theor. Biol. 2003 283 298

[10] J.H. Bielas, K.R. Loeb, B.P. Rubin, L.D. True, L.A. Loeb P. Natl. Acad. of Sci. USA 2006 18238 18242

[11] E. Caussinus, C. Gonzalez Nat. Genet. 2005 1125 1129

[12] S.H. Cheshier, S.J. Morrison, X. Liao, I.L. Weissman P. Natl. Acad. Sci. USA 1999 3120 3125

[13] C. Colijn, M.C. Mackey J. Theor. Biol. 2005 117 132

[14] D.L. Crowe, B. Parsa, U.K. Sinha Histol. Histopathol. 2004 505 509

[15] T.M. Fliedner, D. Graessle, C. Paulsen, K. Reimers Cancer Biother. Radio. 2002 405 426

[16] C.M. Flynn, D.S. Kaufman Blood 2007 2688 2692

[17] U. Galderisi, M. Cippollaro, A. Giordano Cell Death Differ. 2006 5 11

[18] D. Hanahan, R.A. Weinberg Cell 2000 57 70

[19] K. Hardy, J. Stark Apoptosis 2002 373 381

[20] W.J. Harrison J. Clin. Pathol. 1962 254 259

[21] B.J.P. Huntly, D.G. Gilliland Nat. Rev. Cancer 2005 311 321

[22] A.L. Jackson, L.A. Loeb Genetics 1998 1483 1490

[23] C.A. JanewayJr., P. Travers, M. Walport, M.J. Shlomchik. Immunobiology, Sixth Edition. Garland Science, 2005.

[24] F. Michor, T.P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C.L. Sawyers, M.A. Nowak Nature 2005 1267 1270

[25] F. Michor, I. Iwasa, H. Rajagopalan, C. Lengauer, M.A. Nowak Cell Cycle 2004 358 362

[26] J.D. Murray. Mathematical Biology, Second Edition. Springer, 1989.

[27] A. O'Neill, D.V. Schaffer Biotechnol. Appl. Bioc. 2004 5 16

[28] I. Ostby, H.B. Benestad Math. Biosci. 2003 1 27

[29] R. Pardal, M.F. Clarke, S.J. Morrison Nat. Rev. Cancer 2003 895 902

[30] P. Reizenstein Leukemia Res. 1990 679 681

[31] T. Reya, S.J. Morrison, M.F. Clarke, I.L. Weissman Nature 2001 105 111

[32] S.L. Spencer, M.J. Berryman, J.A. García, D. Abbott J. Theor. Biol. 2004 515 524

[33] M. Wu, H.Y. Kwon, F. Rattis, J. Blum, C. Zhao, R. Ashkenazi, T.L. Jackson, N. Gaiano, T. Oliver, T. Reya Cell Stem Cell 2007 541 554

Cité par Sources :