Journal of Mathematical Biology

, Volume 44, Issue 1, pp 79–86

The universal properties of stem cells as pinpointed by a simple discrete model


  • Zvia Agur
    • Institute for Medical Biomathematics, POB 282, 60991, Bene-Ataroth, Israel. e-mail:
  • Yoaz Daniel
    • Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel.
  • Yuval Ginosar
    • Institute for Medical Biomathematics, POB 282, 60991, Bene-Ataroth, Israel. e-mail:

DOI: 10.1007/s002850100115

Cite this article as:
Agur, Z., Daniel, Y. & Ginosar, Y. J Math Biol (2002) 44: 79. doi:10.1007/s002850100115


 The ability of a few stem-cells to repopulate a severely damaged bone marrow (BM) guarantees the stability of our physical existence, and facilitates successful BM transplantations. What are the basic properties of stem cells that enable the maintenance of the systems homeostasis? In the present work we attempt to answer this question by investigating a discrete (in time and phase-space) dynamical system. The model we present is shown to retrieve the essential properties of homeostasis, as reflected in BM functioning, namely, (a) to produce a constant amount of mature cells, and (b) to be capable of returning to this production after very large perturbations. The mechanism guaranteeing the fulfillment of these properties is extrinsic - negative feedback control in the micro-environment - and does not need additional stochastic assumptions. Nevertheless, the existence of a simple intrinsic control mechanism, a clock which determines the switch to differentiation, ascertains that the system does not admit non-trivial extinction states. This result may help clarifying some of the controversy about extrinsic versus intrinsic control over stem cell fate. It should be stressed that all conclusions are valid for any system containing progenitor and maturing cells.

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© Springer-Verlag Berlin Heidelberg 2002