A theoretical framework for jamming in confluent biological tissues

For important biological functions such as wound healing, embryonic development, and cancer tumorogenesis, cells must initially rearrange and move over relatively large distances, like a liquid. Subsequently, these same tissues must undergo buckling and support shear stresses, like a solid. Our work suggests that biological tissues can accommodate these disparate requirements because the tissues are close to glass or jamming transition. While recent self propelled particle models generically predict a glass/jamming transition that is driven by packing density $\varphi $ and happens at some critical $\varphi $c less than unity, many biological tissues that are confluent with no gaps between cells appear to undergo a jamming transition at a constant density ($\varphi =$1). I will discuss a new theoretical framework for predicting energy barriers and rates of cell migration in 2D tissue monolayers, and show that this model predicts a novel type of rigidity transition, which takes place at~constant $\varphi =$1 and depends only on single cell properties such as cell-cell adhesion, cortical tension and cell elasticity. This model additionally predicts that an experimentally observable parameter, the ratio between a cell's perimeter and the square root of its cross-sectional area, attains a specific, critical value at the jamming transition. We show that this prediction is precisely realized in primary epithelial cultures from human patients, with implications for asthma pathology.