Radial percolation reveals that Cancer Stem Cells are trapped in the core of colonies

Lucas Barberis

doi:10.4279/pip.130002

Abstract

Using geometrical arguments, it is shown that Cancer Stem Cells (CSCs) must be confined 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.

Highlights

Cancer Stem Cells (CSCs) are responsible for driving tumor growth due to their ability to make copies of themselves and differentiate into cells with more specific functions [1]
Metastasis is an intriguing feature of cancer invasion
If this could be observed in the laboratory, the experiments that reveal a CSC preference for hypoxic environments could be explained by this fact

Summary

Introduction

Cancer Stem Cells (CSCs) are responsible for driving tumor growth due to their ability to make copies of themselves (self-renewal) and differentiate into cells with more specific functions [1]. CSC duplication could have three possible outcomes: stem cell replication (self-renewal), asymmetric differentiation and symmetric differentiation To model such a feature mathematically, we can assume that the three outcomes will occur with probabilities ps, pa and pd, respectively. Li et al report that hypoxia plays an important role in the de-differentiation of cells [14] These results indicate that a hypoxic environment will increase the numbers of CSCs. The aim of this work is to simulate colony growth by means of an Agent-Based Model (ABM) that mimics basic features of CSC proliferation, with emphasis on its geometrical properties. In these examples we set ps = 0.5 and started with a CSC seed depicted in yellow.

Total CSC

Percolation theory

To roughly estimate z we built up a tree graph

Conclusions

Quiescent CSC