Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

TL;DR

This study uses simulations to show that free volume saturation in non-confluent tissues explains the sharp increase and plateau in viscosity during morphogenesis, revealing a glass-like cell dynamics behavior.

Contribution

It introduces a free volume theory-based explanation for viscosity behavior in non-confluent tissues, supported by agent-based simulations.

Findings

Viscosity sharply increases until a critical packing fraction.

Beyond this point, viscosity remains constant despite increased cell density.

Free volume saturation explains the viscosity plateau and sluggish cell dynamics.

Abstract

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity ({\eta}) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction ({\phi}S). The increase in {\eta} up to {\phi}S is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, {\eta} is a constant above {\phi}S. To determine the mechanism of this unusual dependence of {\eta} on {\phi}, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above {\phi}S but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.