Topological Floppy Modes in Epithelial Tissues

TL;DR

This paper investigates topologically protected floppy modes in epithelial tissues, revealing how boundary and interface modes can lead to localized soft spots, with implications for tissue morphogenesis and mechanical behavior.

Contribution

It introduces a topological analysis of epithelial tissue models, including a vertex model and an active tension network, highlighting new polarized phases with localized modes.

Findings

Topologically polarized phases with localized floppy modes in ATN

Localization occurs when cells are allowed to become concave

No localization in the simple vertex model

Abstract

Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorporates active adaptation of the cytoskeleton. By analyzing spatially periodic lattices at the Maxwell point of mechanical instability, we find topologically polarized phases with exponential localization of floppy modes and states of self-stress in the ATN when cells are allowed to become concave, but not in the VM.