Curved edges in the vertex model increase tissue fluidity

TL;DR

This study explores how incorporating curved edges in the vertex model of epithelial tissues affects tissue fluidity, showing that curvature causes tissues to become fluid-like at lower target perimeters than traditional straight-edge models.

Contribution

The paper demonstrates that modeling cell junctions with curved edges shifts the solid-to-fluid transition point, providing a more realistic understanding of tissue mechanics.

Findings

Curved edges lower the transition point from solid to fluid.

Tissues with curved edges fluidize at lower target perimeters.

Curved edges alter equilibrium cell shapes and mechanical properties.

Abstract

The Vertex Model for epithelia models the apical surface of the tissue by a tiling, with polygons representing cells and edges representing cell-cell junctions. The mechanics are described by an energy governed by deviations from a target area and perimeter for each cell. It has been shown that the target perimeter, p0, governs a solid-to-fluid phase transition: when the target perimeter is low there is an energy barrier to rearrangement, and when it is high cells may rearrange for free and the tissue can flow like a liquid. One simplification often made is modelling junctions using straight edges. However, the Young-Laplace equation states that interfaces should be circular arcs, with the curvature being equal to the pressure difference between the neighbouring cells divided by the interfacial tension. Here, we investigate how including curved edges alters the mechanical properties of the vertex model and equilibrium shape of individual cells. Importantly, we show how curved edges shift the solid-to-fluid transition point, from $p0 = 3.81$ to $p0 = 3.73$, allowing tissues to fluidise sooner than in the traditional model with straight edges.