Energy barriers and cell migration in confluent tissues

Biological processes such as embryogensis, tumorigenesis and wound healing require cells to move within a tissue. While the migration of single cells has been extensively studied, it has remained unclear how single cell properties control migration through a confluent tissue. We develop numerical and theoretical models to calculate energy barriers to cell rearrangements, which govern cell motility. In contrast to sheared foams where energy barriers are power-law distributed, energy barriers in tissues are exponentially distributed and depend systematically on the cell's number of neighbors. Using simple extensions of `trap' and `Soft Glassy Rheology' models, we demonstrate that these energy barrier distributions give rise to glassy behavior and use the models to make testable predictions for two-time correlation functions and caging times. We incorporate these ideas into a continuum model that combines glassy rheology with active polarization to better understand collective migration in epithelial sheets.