Abstract
Cancer stem cells (CSCs) have been identified in primary breast cancer tissues and cell lines. The CSC population varies widely among cancerous tissues and cell lines, and is often associated with aggressive breast cancers. Despite of intensive research, how the CSC population is regulated within a tumor is still not well understood so far. In this paper, we present a mathematical model to explore the growth kinetics of CSC population both in vitro and in vivo. Our mathematical models and supporting experiments suggest that there exist non-linear growth kinetics of CSCs and negative feedback mechanisms to control the balance between the population of CSCs and that of non-stem cancer cells. The model predictions can help us explain a few long-standing questions in the field of cancer stem cell research, and can be potentially used to predict the efficicacy of anti-cancer therapy.