Viscous vertex model for active epithelial tissues

TL;DR

This paper introduces a viscous vertex model for active epithelial tissues that incorporates cortical and bulk dissipation, enabling the study of tissue rheology and defect formation.

Contribution

The authors develop a rotationally invariant viscous vertex model with boundary condition flexibility and a protocol to measure tissue shear viscosity.

Findings

Viscosity influences cell-shape textures and defect stability.

The model remains well-posed at zero substrate friction, suitable for free-floating tissues.

A new rheology protocol effectively extracts tissue shear viscosity.

Abstract

We present a rotationally invariant viscous vertex model that accounts for both cortical and bulk dissipation of cells. The vanishing substrate-friction limit is enforced via Lagrange multipliers, which also provides a framework for implementing various boundary conditions, such as fixed boundaries and prescribed tractions. Building on this formulation, we introduce a slab-shear rheology protocol to extract an effective, coarse-grained tissue shear viscosity. Under polar or nematic activity, viscosity regulates the formation of elongated, spatially correlated cell-shape textures and stabilizes well-defined topological defects. Because the model remains well-posed at zero substrate friction, it is naturally suited to describing free-floating epithelia and organoids.