  Cell motion inside dense tissues governs many biological processes, including
embryonic development and cancer metastasis, and recent experiments suggest
that these tissues exhibit collective glassy behavior. To make quantitative
predictions about glass transitions in tissues, we study a self-propelled
Voronoi (SPV) model that simultaneously captures polarized cell motility and
multi-body cell-cell interactions in a confluent tissue, where there are no
gaps between cells. We demonstrate that the model exhibits a jamming transition
from a solid-like state to a fluid-like state that is controlled by three
parameters: the single-cell motile speed, the persistence time of single-cell
tracks, and a target shape index that characterizes the competition between
cell-cell adhesion and cortical tension. In contrast to traditional particulate
glasses, we are able to identify an experimentally accessible structural order
parameter that specifies the entire jamming surface as a function of model
parameters. We demonstrate that a continuum Soft Glassy Rheology model
precisely captures this transition in the limit of small persistence times, and
explain how it fails in the limit of large persistence times. These results
provide a framework for understanding the collective solid-to-liquid
transitions that have been observed in embryonic development and cancer
progression, which may be associated with Epithelial-to-Mesenchymal transition
in these tissues.
