Mathematical Modeling of Mutation Acquisition in Hierarchical Tissues: Quantification of the Cancer Stem Cell Hypothesis.

Abstract

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. 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.

Cancer stem cells have been identified and characterized in several forms of malignancy, but the specific multi-step process that causes their formation is uncertain. In this dissertation, a mathematical model is developed to investigate the role of cancer stem cells in tumorigenesis. With the application of a maturity-structured model, three primary aspects of cancer dynamics are discussed: (1) the sequential order of mutations that causes the fastest emergence of cancer stem cells, (2) the impact of deregulated mechanisms that normally govern homeostasis in hierarchical tissue, and (3) the evolving tissue composition as disease progresses with particular focus on the cancer stem cell population. Model predictions suggest that unbalanced stem-cell self-renewal and inhibition of progenitor differentiation contribute to aggressive forms of cancer. In addition, the continuous maturity structure is a novel feature of this model that is particularly effective in capturing the dynamics of immature blast accumulation in the progression of Chronic Myelogenous Leukemia. Simulating this specific form of cancer highlights potential modeling contributions to the scientific community, as the mathematical framework may be used to investigate additional forms of malignancy in hierarchical tissues.