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In many adult tissues, stem cells and differentiated cells are nothomogeneously distributed : stem cells are arranged in periodic "niches", anddifferentiated cells are constantly produced and migrate out of these niches.In this article, we provide a general theoretical framework to study mixturesof dividing and actively migrating particles, which we apply to biologicaltissues. We show in particular that the interplay between the stresses arisingfrom active cell migration and stem cell division give rise to robust stem cellpatterns. The instability of the tissue leads to spatial patterns which areeither steady or oscillating in time. The wavelength of the instability has anorder of magnitude consistent with the biological observations. We also discussthe implications of these results for future in vitro and in vivo experiments.

An interplay of migratory and division forces as a generic mechanism for stem cell patterns