Interplay of curvature and rigidity in shape-based models of confluent tissue

Daniel M Sussman

doi:10.1103/physrevresearch.2.023417

Abstract

Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This implies that cells can collectively rigidify by growing the size of the sphere, i.e. by tuning the curvature of their domain. Finite-temperature studies indicate that cell motility is affected well away from the zero-temperature transition point.

Highlights

Recent years have seen a growing interest in the way that mechanical interactions between cells play a fundamental role in structural and dynamical processes in biology [1,2]
We focus on vertex models, which represent confluent monolayers as polygonal or polyhedral tilings of space; each geometrical unit corresponds to a coarse-grained cell [12] and the degrees of freedom are the vertices of the geometrical units
We first directly probe the athermal rigidity transition of the spherical vertex model as a function of N and p0; for simplicity, here we first focus on the kr = 0 limit of Eq (2)

Summary

Introduction

Recent years have seen a growing interest in the way that mechanical interactions between cells play a fundamental role in structural and dynamical processes in biology [1,2]. Vertex models attempt to explicitly represent mechanical interactions between neighboring cells by force laws that depend on the local geometry of the system, and they have been used to model biophysical processes covering morphogenesis and wound healing and tumor metastasis [13,14,15,16,17,18,19,20]. Such models have received attention for their appealing geometrical coarse-graining of clearly complex biological systems and for the unusual properties such models can support.

Methods

Results

Conclusion