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A Mathematical Model of Cancer Stem Cell Lineage PopulationDynamics with Mutation Accumulation and Telomere Length Hierarchies

Published online by Cambridge University Press:  25 January 2012

G. Kapitanov
G. Kapitanov*
Affiliation:
Vanderbilt University Department of Mathematics 1326 Stevenson Center, Nashville, TN 37240, USA
*
⋆E-mail: [email protected]
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Abstract

There is evidence that cancer develops when cells acquire a sequence of mutations thatalter normal cell characteristics. This sequence determines a hierarchy among the cells,based on how many more mutations they need to accumulate in order to become cancerous.When cells divide, they exhibit telomere loss and differentiate, which defines anothercell hierarchy, on top of which is the stem cell. We propose a mutation-generation model,which combines the mutation-accumulation hierarchy with the differentiation hierarchy ofthe cells, allowing us to take a step further in examining cancer development and growth.The results of the model support the hypothesis of the cancer stem cell’s role in cancerpathogenesis: a very small fraction of the cancer cell population is responsible for thecancer growth and development. Also, according to the model, the nature of mutationaccumulation is sufficient to explain the faster growth of the cancer cell population.However, numerical results show that in order for a cancer to develop within a reasonabletime frame, cancer cells need to exhibit a higher proliferation rate than normalcells.

Keywords

cancerstem cellscancer stem cellmathematical modelmutationtelomere shortening
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 1: Cancer modeling , 2012 , pp. 136 - 165
Copyright
© EDP Sciences, 2012

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