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Issue Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008
Special issue dedicated to Glenn Webb
Page(s) 78 - 89
DOI 10.1051/mmnp:2008042
Published online 23 October 2008

Math. Model. Nat. Phenom. Vol. 3, No. 7, 2008, pp. 78-89
DOI: 10.1051/mmnp:2008042

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

O. U. Kirnasovsky, Y. Kogan and Z. Agur

Institute for Medical BioMathematics, 10 Hate'ena St., P.O.B. 282, 60991 Bene Ataroth, Israel

agur@imbm.org

Published online: 23 October 2008

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


Mathematics Subject Classification. 92B05, 92C15, 92C37, 37N25

Key words: proliferation -- differentiation -- intracellular pathways -- Wnt -- Notch -- cell signalling





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