Mechanism of murine epidermal maintenance: cell division and the voter model

The dynamics of a genetically labeled cell population may be used to infer the laws of cell division in mammalian tissue. Recently, we showed that in mouse tail skin, where proliferating cells are confined to a two-dimensional layer, cells proliferate and differentiate according to a simple stochastic model of cell division involving just one type of proliferating cell that may divide both symmetrically and asymmetrically. Curiously, these simple rules provide excellent predictions of the cell population dynamics without having to address the cells' spatial distribution. Yet, if the spatial behavior of cells is addressed by allowing cells to diffuse at random, one deduces that density fluctuations destroy tissue confluence, implying some hidden degree of spatial regulation of cell division. To infer the mechanism of spatial regulation, we consider a two-dimensional model of cell fate that preserves the overall population dynamics. By identifying the resulting behavior with a three-species variation of the voter model, we predict that proliferating cells in the basal layer should cluster. Analysis of empirical correlations of cells stained for proliferation activity confirms that the expected clustering behavior is indeed seen in nature. As well as explaining how cells maintain a uniform two-dimensional density, these findings present an interesting experimental example of voter-model statistics in biology.