Analysis of a Mathematical Model for the Molecular Mechanismof Fate Decision in Mammary Stem Cells

Abstract

Recently, adult stem cells have become a focus of intensive biomedical research, but thecomplex regulation that allows a small population of stem cells to replenish depleted tissues is stillunknown. It has been suggested that specific tissue structures delimit the spaces where stem cellsundergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests thata feedback control of stem cells on their own proliferation and differentiation (denoted QuorumSensing) suffices for preserving homeostasis in developing tissues. In the present work we examinethis discrepancy by analyzing a mathematical model of signalling pathways in a mammary stemcell. Our work shows that the model has a unique equilibrium depending on the environmentalconditions, which is stable for appropriate parameter values. We show how this dependence onthe micro-environment can control the cell decision to either proliferate or differentiate. Our workfurther suggests that this description is sufficient for the creation of niche conditions, with no needof additional structures. The analysis also pinpoints the pathways that may serve as the QuorumSensing mechanism.