We just posted a very exciting new paper on the arXiv:1409.0593! This work, pioneered by first author Max Dapeng Bi, shows that the vertex model, which has been widely and successfully used to describe cell shapes and statistics in biological tissues, has an unexpected rigidity transition.  This transition, instead of being controlled by the cell density (as it is in jamming for particulate systems) is controlled by the cell shape.  Specifically, it is controlled by the cell's perimeter-to-area ratio (measured from a cross-sectional cut through a monolayer). Interestingly, this model also predicts that in confluent tissue (where there are no gaps between cells) adhesion can help make the tissue more fluid-like, which is the opposite of what happens in particulate matter.  We are currently collaborating with several biology groups to test aspects of this exciting prediction.