Reentrant Rigidity Transition in Planar Epithelia with Volume- and Area Elasticity

TL;DR

This study uncovers a reentrant rigidity transition in 3D epithelial tissues driven by volume and area elasticity, showing both softening and stiffening behaviors and a phase diagram with distinct mechanical states.

Contribution

It introduces a novel framework mapping 3D epithelial mechanics onto a 2D elasticity model, revealing complex reentrant transitions and critical behavior.

Findings

Reentrant transition between columnar and squamous states

Presence of floppy states with zero shear and bulk moduli

Discontinuous transition driven by lateral tension

Abstract

We find a reentrant columnar-to-squamous rigidity transition in 3D epithelia, governed by volume- and area elasticity. Our framework maps onto the classic 2D Area- and Perimeter-Elasticity model but, unlike its 2D counterpart, exhibits both softening and stiffening depending on the initial state. The phase diagram reveals floppy states with vanishing shear and in-plane bulk moduli, alongside a lateral-tension-driven discontinuous columnar-to-squamous transition. The critical behavior underlying the emergence of the reentrant transition belongs to the mean-field universality class.