Dense packing of cell monolayers: Jamming of deformable polygons

Collective motion in dense packings of cells occurs in wound healing,
embryonic development, and cancerous tumor growth. Most current
computational models of dense cell packings either treat the system as
collections of spherical particles or assume that the system is
confluent, with no extracellular space. We have developed a new model
for dense cell packings in two spatial dimensions, where the cells are
modeled as deformable particles that have a preferred area and
perimeter. We measure the packing fraction, φ_j at jamming onset
as a function of the asphericity, α, which is the ratio of the
perimeter square to the area of the particle. We find that the jammed
packing fraction increases monotonically with α and that the system
becomes confluent with φ_j = 1 for α > 1.16. Using surface
Voronoi analysis, we show that this value for α corresponds to the
case when the cells completely fill their Voronoi-tesselated
regions. We also demonstrate that the free area per cell obeys a
k-gamma distribution, which has been found for jammed packings of
non-deformable particles. Finally, we will describe results
from our model concerning the mobility of deformable particles
subjected to applied forces, as well as diffusion of deformable
particles subjected to active forces to discuss the effect of geometry in active jamming of deformable particles.