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

Abstract

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (<i>η</i>) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (<i>ϕ</i>_<i>S</i>). The increase in <i>η</i> up to <i>ϕ</i>_<i>S</i> is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, <i>η</i> is a constant above <i>ϕ</i>_<i>S</i>. To determine the mechanism of this unusual dependence of <i>η</i> on <i>ϕ</i>, 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 <i>ϕ</i>_<i>S</i> but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.