Rigidity and glass transitions in collections of cells and fiber networks

In biological processes like embryonic development and in cancer metastasis, collective groups of cells must dramatically reorganize and move over substantial distances like a fluid. In other cases, such as the mature lining of the human lung, it is functionally important for the cells to behave as an intact solid, and still other tissues appear to straddle a disordered fluid-solid transition. First, I will discuss a theory for the origin of rigidity and the scaling laws that occur in a broad class of models for biological tissues (including vertex models for confluent cell aggregates and spring network models for extra-cellular matrix), and then I will discuss the anomalous glassy behavior that arises in such models in the presence of thermal or active fluctuations.