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

Vanderbilt University Department of Mathematics 1326 Stevenson Center, Nashville, TN 37240, USA

^⋆ E-mail: georgi.i.kapitanov@vanderbilt.edu

Abstract

There is evidence that cancer develops when cells acquire a sequence of mutations that alter 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 another cell 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 of the 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 cancer pathogenesis: a very small fraction of the cancer cell population is responsible for the cancer growth and development. Also, according to the model, the nature of mutation accumulation 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 reasonable time frame, cancer cells need to exhibit a higher proliferation rate than normal cells.