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.
Categories: cond-mat.soft cond-mat.stat-mech physics.bio-ph