Effect of cellular rearrangement time delays on the rheology of vertex models for confluent tissues

TL;DR

This study investigates how finite delays in cellular neighbor exchanges, due to molecular processes, influence tissue mechanics and fluidity in vertex models of confluent tissues, revealing delays can stiffen tissues and promote rosette formation.

Contribution

The paper introduces a vertex model incorporating fixed T1 transition delays, highlighting how molecular-scale timescales dominate tissue rheology and morphogenetic processes.

Findings

T1 delay times dominate tissue relaxation when larger than cell-shape timescales.

Increasing T1 delays leads to more rosettes and higher-fold vertices.

Tissues with longer T1 delays exhibit more elastic-like behavior.

Abstract

Large-scale tissue deformation during biological processes such as morphogenesis requires cellular rearrangements. The simplest rearrangement in confluent cellular monolayers involves neighbor exchanges among four cells, called a T1 transition, in analogy to foams. But unlike foams, cells must execute a sequence of molecular processes, such as endocytosis of adhesion molecules, to complete a T1 transition. Such processes could take a long time compared to other timescales in the tissue. In this work, we incorporate this idea by augmenting vertex models to require a fixed, finite time for T1 transitions, which we call the "T1 delay time". We study how variations in T1 delay time affect tissue mechanics, by quantifying the relaxation time of tissues in the presence of T1 delays and comparing that to the cell-shape based timescale that characterizes fluidity in the absence of any T1 delays. We show that the molecular-scale T1 delay timescale dominates over the cell shape-scale collective response timescale when the T1 delay time is the larger of the two. We extend this analysis to tissues that become anisotropic under convergent extension, finding similar results. Moreover, we find that increasing the T1 delay time increases the percentage of higher-fold coordinated vertices and rosettes, and decreases the overall number of successful T1s, contributing to a more elastic-like -- and less fluid-like -- tissue response. Our work suggests that molecular mechanisms that act as a brake on T1 transitions could stiffen global tissue mechanics and enhance rosette formation during morphogenesis.