Quantitative approaches to cancer stem cells and epithelial-mesenchymal transition.

The last decade has witnessed significant advances in the application of mathematical and computational models to biological systems, especially to cancer biology. Here, we present stochastic and deterministic models describing tumour growth based on the cancer stem cell hypothesis, and discuss the application of these models to the epithelial-mesenchymal transition. In particular, we discuss how such quantitative approaches can be used to validate different possible scenarios that can lead to an increase in stem cell activity following induction of epithelial-mesenchymal transition, observed in recent experimental studies on human breast cancer and related cell lines. The utility of comparing mammosphere data to computational mammosphere simulations in elucidating the growth characteristics of mammary (cancer) stem cells is discussed as well.