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

Abstract

The dynamics of a genetically-labelled 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 their spatial distribution. Yet, if the spatial behaviour 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 in the physical system. 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 behaviour 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 behaviour 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.

Dynamic heterogeneity as a strategy of stem cell self-renewal

“…However, even under these conditions (considered in ref. 45), the dynamics of the lattice H model are qualitatively the same and phase-separated domains of cell types grow (see Supporting Information and Fig. S4).…”

“…12 has been studied for the balanced case Δ = 0 in ref. 45. There it was shown that the system coarsens over time and becomes increasingly inhomogeneous: The layer phase separates into A-and B-cell-rich domains that grow over time (see also Fig.…”

“…By contrast, the lattice H model translates to a voter model, in which cells are stochastically and irreversible replaced by neighboring cells, following the transitions ↑ ↓ → ↑ ↑ or ↑ ↓ → ↓ ↓, respectively, with equal probability (47). The latter model is nonergodic, exhibiting coarsening and phase separation into large irregular domains of cell states that grow over time (45,47). This dynamics does not support a homeostatic state.…”

“…43 and 44 for niche-based regulation mechanisms). To illustrate this point, in the following we consider two concrete examples: (i) one-dimensional layers of progenitor cells, where the lowest layer is stem-like (A cells) and higher layers are prone to differentiation (B cells) and (ii) a 2D epithelial sheet, as originally conceived for the H model in its application to basal interfollicular epidermis (45). One-dimensional layers.…”

Patterning as a signature of human epidermal stem cell regulation

“…To develop a cell-based model that incorporates many of the features of a stochastic cell population, we adopt the approach described in Kein et al [32]. We model the basal layer as a two-dimensional (hexagonal) lattice where each site may host one of the three cell types or may be vacant ().…”