Abstract
A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell density (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, 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 density. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
We have changed the abstract and the introduction suitable for a broad audience and we also have changed the title.