Rigidity and flocking transitions in dense tissues
The mechanical properties of epithelial tissues, which are typically composed of a single layer of tightly bound cells, play an important role in development and disease. Our goal is to develop theoretical and computational tools to help explain collective cell migration patterns and mechanical behavior in these tissues. In this talk, I will highlight the interplay between tissue rigidity and collective cell migration using two different models. The first model augments a Self-Propelled Voronoi model that describes epithelial cells in dense tissue as motile polygons covering the plane by introducing a local feedback that aligns cell polarization with the cell velocity. This alignment promotes solidification and drives transitions to both flocking liquid and solid states, qualitatively affecting the morphology of dynamical heterogeneities near the onset of tissue rigidity. This is akin to what observed in jammed epithelial monolayers, which are unjammed by the addition of endocytic proteins. Next, I will describe a hydrodynamic model for bulk tissues that couples cell shapes, tissue rigidity, and cell-substrate interactions by assuming that cells exert traction forces preferentially along gradients in the in-plane tissue stiffness, as suggested by recent experiments. An analysis of the steady states of the model leads to the identification a new “morphotactic” parameter that controls pattern formation in real tissues.