Shape-tension coupling produces nematic order in an epithelium vertex model

TL;DR

This study extends an epithelial vertex model to include shape-tension coupling, revealing how active forces induce nematic order and defects, potentially explaining spontaneous tissue polarity without chemical cues.

Contribution

The paper introduces a novel coupling between cell shape and tension in a vertex model, demonstrating its role in generating nematic order and defects in epithelial tissues.

Findings

Coupling induces nematic order and +1 defects.

Defects influence cell shape, size, and coordination.

Tissue polarity can emerge from mechanical forces alone.

Abstract

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived $+1$ defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.