Radial percolation reveals that cancer stem cells are trapped in the core of colonies

Abstract

Using geometrical arguments, it is shown that Cancer Stem Cells (CSCs) must be con-fined inside solid tumors under natural conditions. Aided by an agent-based model and percolation theory, the probability of a CSC being positioned at the border of a colony is estimated. This probability is estimated as a function of the CSC self-renewal probability ps; i.e., the chance that a CSC remains undifferentiated after mitosis. In the most common situations ps is low, and most CSCs produce differentiated cells at a very low rate. The results presented here show that CSCs form a small core in the center of a cancer cell colony; they become quiescent due to the lack of space to proliferate, which stabilizes their population size. This result provides a simple explanation for the CSC niche size, dispensing with the need for quorum sensing or other proposed signaling mechanisms. It also supports the hypothesis that metastases are likely to start at the very beginning of tumor development.