Unusual interfaces and anomalous glassy behavior in biological matter

What can we learn about dense biological tissue by viewing it as a soft, active material? The mechanical and dynamical properties of dense collections of cells help govern processes ranging from wound healing to embryonic development to cancer progression, and an outstanding challenge is developing tractable models that can predict and explain the amazing variety of complex phenomena that even simple cellular systems can exhibit. Recent experiments have shown, for example, that many tissues lie close to a collective rigidity transition, and I will discuss how simple coarse-grained models of dense, disordered tissue can support unusual forms of low-temperature rigidity. I will then show that these models exhibit anomalous interfacial properties where different measurements of the surface tension between two tissues types can differ by orders of magnitude. This departure from equilibrium behavior can be understood as a generic consequence of certain topological features of the cell-cell interactions, and I will discuss the potential relevance of this mechanism for both biological processes (such as cell sorting and compartmentalization) and for designing new materials with exotic bulk and boundary behavior.