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

TL;DR

This paper introduces a simple, generic theoretical model for cellular polarity alignment, capturing the influence of cell geometry, external signals, and noise, and providing a tractable framework for studying polarity in biological systems.

Contribution

It derives a reduced phase model from reaction-diffusion systems that incorporates geometric effects, enabling analytical and numerical analysis of cellular polarity alignment.

Findings

Model captures geometric dependencies of polarity alignment.

Reduced model resembles an XY model with novel geometric terms.

Analytical and numerical tractability facilitates future studies.

Abstract

Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of 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 their proximal surfaces. The system behavior is shown to be strongly dependent on geometric properties such as cell alignment and cell shape. Using a perturbative method under the assumption of weak coupling between cells, we derive a reduced model in which each cell is described by just one variable, the phase. The reduced model resembles an XY model but contains novel terms that possesses geometric information, which enables the understanding of the geometric dependencies as well as the effects of external signal and noise. The model is simple, generic, and analytically and numerically tractable, and is therefore expected to facilitates studies on cellular polarity alignment in various nonequilibrium systems.