The homeostasis of epithelial tissue relies on a balance between the
self-renewal of stem cell populations, cellular differentiation, and loss.
Although this balance needs to be tightly regulated to avoid pathologies, such
as tumor growth, the regulatory mechanisms, both cell-intrinsic and collective,
which ensure tissue steady-state are still poorly understood. Here, we develop
a computational model that incorporates basic assumptions of stem cell renewal
into distinct populations and mechanical interactions between cells. We find
that the model generates unexpected dynamic features: stem cells repel each
other in the bulk tissue and are thus found rather isolated, as in a number of
in vivo contexts. By mapping the system onto a gas of passive Brownian
particles with effective repulsive interactions, that arise from the generated
flows of differentiated cells, we show that we can quantitatively describe such
stem cell distribution in tissues. The interaction potential between a pair of
stem cells decays exponentially with a characteristic length that spans several
cell sizes, corresponding to the volume of cells generated per stem cell
division. Our findings may help understanding the dynamics of normal and
cancerous epithelial tissues