  Vertex models are a popular approach to modeling the mechanical and dynamical
properties of dense biological tissues, describing the tissue as a network of
connected polygons representing the cells. Recently a class of two-dimensional
vertex models was shown to exhibit a disordered rigidity transition controlled
by the preferred cellular geometry, echoing experimental findings. An
attractive variant of these models uses a Voronoi tessellation to describe the
cells and endows them with a non-equilibrium model of cellular motility,
leading to rich, glassy behavior. This glassy behavior was suggested to be
inextricably linked to an underlying jamming transition. We test this
conjecture, exploring the low-effective-temperature limit of the Voronoi model
by studying cell trajectories from detailed dynamical simulations in
combination with rigidity measurements of energy-minimized disordered cell
configurations. We find that the zero-temperature limit of this model has no
unjamming transition.
