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Ordered polarity alignment of a cell population plays a vital role inbiology, such as in hair follicle alignment and asymmetric cell division. Here,we propose a theoretical framework for the understanding of generic dynamicalproperties of polarity alignment in interacting cellular units, where each cellis described by a reaction-diffusion system and the cells further interact withone another through their proximal surfaces. The system behavior is shown to bestrongly dependent on geometric properties such as cell alignment and cellshape. Using a perturbative method under the assumption of weak couplingbetween cells, we derive a reduced model in which each cell is described byjust one variable, the phase. The reduced model resembles an XY model butcontains novel terms that possesses geometric information, which enables theunderstanding of the geometric dependencies as well as the effects of externalsignal and noise. The model is simple, generic, and analytically andnumerically tractable, and is therefore expected to facilitates studies oncellular polarity alignment in various nonequilibrium systems.

A Simple Generic Model of Cellular Polarity Alignment: Derivation and Analysis