Emergent order in epithelial sheets by interplay of cell divisions and cell fate regulation

The fate choices of stem cells between self-renewal and differentiation are often tightly regulated by paracrine (cell-cell) signalling. Here, we assess how the interplay between cell division, differentiation, and short range paracrine signalling can affect the macroscopic ordering of cell types in self-renewing epithelial sheets, by studying a simple spatial cell fate model with cells being arranged on a 2D lattice. We show in this model that if cells commit to their fate directly upon cell division, macroscopic domains of cells of the same type emerge, if at least a small proportion of divisions are symmetric, except if signalling interactions are laterally inhibiting. In contrast, if cells are first licensed to differentiate, yet retaining the possibility to return to their naive state, macroscopic order only emerges if the signalling strength exceeds a critical threshold: if then the signalling interactions are laterally inducing, macroscopic domains emerge as well. Lateral inhibition, on the other hand, can in that case generate macroscopic patterns of alternating cell types (checkerboard pattern), yet only if the proportion of symmetric divisions is sufficiently low. These results can be understood theoretically by an analogy to phase transitions in spin systems known from statistical physics. Author summaryA fundamental question in stem cell biology is how a cells choice to differentiate or not (cell fate choices), is regulated through communication with other cells in a tissue, and whether these choices are a one-way path or to some degree reversible. However, measuring this in living animals is very difficult and often impossible, since this requires to make videos of cells inside the body with a microscope. Here, we employ a simple mathematical model for the fate choices of stem cells when they are regulated by communication with nearby cells in the tissue. We show that different means of cell fate choice and cell communication can lead to qualitatively different patterns of cell types: macroscopic domains, checkerboard patterns, or randomly disordered distributions, depending on the character of cell communication, and whether cell fate is one-way or reversible. Our analysis therefore shows that those aspects of stem cell activity, which are otherwise difficult to measure, can be distinguished by observing macroscopic patterns of cell types.