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

Abstract

There is evidence that cancer develops when cells acquire a sequence of mutations. 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 acquisition and growth. The model compares the rate of population growth of cancer cells versus normal cells. It also examines the role of stem cells in the cell population dynamics. The results, both analytical and numerical, support the hypothesis of the cancer stem cell: a very small fraction of the cancer cell population can be responsible for the cancer growth and development. Approved