  Cell migration is important in many biological processes, including embryonic
development, cancer metastasis, and wound healing. In these tissues, a cell's
motion is often strongly constrained by its neighbors, leading to glassy
dynamics. While self-propelled particle models exhibit a density-driven glass
transition, this does not explain liquid-to-solid transitions in confluent
tissues, where there are no gaps between cells and therefore the density is
constant. Here we demonstrate the existence of a new type of rigidity
transition that occurs in the well-studied vertex model for confluent tissue
monolayers at constant density. We find the onset of rigidity is governed by a
model parameter that encodes single-cell properties such as cell-cell adhesion
and cortical tension, providing an explanation for a liquid-to-solid
transitions in confluent tissues and making testable predictions about how
these transitions differ from those in particulate matter.
