A reduced cell-based phase model for tissue polarity alignment through global anisotropic cues.

Ordered polarity alignment of cell populations plays vital roles in biology, such as in hair follicle alignment and asymmetric cell division. Although cell polarity is uniformly oriented along a tissue axis in many tissues, its mechanism is not well understood. In this paper, we propose a theoretical framework to understand the generic dynamical properties of polarity alignment in interacting cellular units, where each cell is described by a reaction-diffusion system, and the cells further interact with one another through the contacting surfaces between them. Using a perturbation method under the assumption of weak coupling between cells, we derive a reduced model in which polarity of each cell is described by only one variable. Essential dynamical properties including the effects of cell shape, coupling heterogeneity, external signal and noise can be clarified analytically. In particular, we show that the anisotropicity of the system, such as oriented cell elongation and axial asymmetry in the coupling strength, can serve as a global cue that drives the uniform orientation of cell polarity along a certain axis. Our study bridges the gap between detailed and phenomenological models, and it is expected to facilitate the study of polarity dynamics in various nonequilibrium systems.