A Maturity-Structured Mathematical Model of Mutation Acquisition in the Absence of Homeostatic Regulation

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 in certain malignancies. 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. Although identified and characterized in several forms of malignancy, the specific multi-step process that causes the formation of cancer stem cells is uncertain. Here, a maturity-structured mathematical model is developed to investigate the sequential order of mutations that causes the fastest emergence of cancer stem cells. Using model predictions, we discuss conditions for which genetic instability significantly speeds cancer onset and suggest that unbalanced stem-cell self-renewal and inhibition of progenitor differentiation contribute to aggressive forms of cancer. To our knowledge, this is the first continuous maturity-structured mathematical model used to investigate mutation acquisition within hierarchical tissue in order to address implications of cancer stem cells in tumorigenesis.