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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
*
tjacks@umich.edu
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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

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