Shape Programming in Entropic Tissues

TL;DR

This paper explores how directed active T1 cell rearrangements can actively shape tissues, linking tissue mechanics to entropic spring physics and providing a framework for shape programming in biological tissues.

Contribution

It demonstrates that active T1 cell rearrangements can be used to program tissue shapes, connecting tissue mechanics with entropic spring physics through a vertex model approach.

Findings

Directed T1 rearrangements can actively shape tissues.

A connection between tissue active rearrangements and entropic springs is established.

A simple vertex model captures shape programming parameters.

Abstract

Epithelial morphogenesis, a signature problem of tissue biology and tissue mechanics, continues to inspire biologists and physicists alike. Many treatments focus on tissue fluidization, apical/basal ratio changes, or mechanical instabilities. In contrast to these approaches, shape-programmable materials, where the local lengths in the material change in a prescribed way, offer an appealing analogy. In this analogy, certain in-plane collective cell behaviors could also actively alter the local lengths in a tissue and therefore provide the ingredients necessary for shape programming. In this Letter we demonstrate that this is indeed the case for directed, active T1 rearrangements of cells. We determine the required shape programming parameters associated to tissue patches with both fixed numbers of rearrangements and patches at steady state between directed T1 events and counterbalancing randomly oriented ones using a simple free-boundary vertex model approach. Along the way we uncover a surprising connection between tissues with active T1 events and the central limit theorem, and through it, the physics of entropic springs.