Title: Emergence of tissue-scale mechanics from cellular behavior
Abstract: Biological tissues gain their mechanical properties from the collective behavior of a large number of cells. Two projects will be presented that connect tissue-scale to cell-scale mechanics.The first part of the talk establishes a general geometrical framework that exactly decomposes large-scale deformation of dense 2D tissues into contributions by different kinds of cellular processes. These processes comprise cell shape changes, cell neighbor exchanges (T1 transitions), cell divisions, and cell extrusions (T2 transitions). As the key idea, we introduce a tiling of the cellular network into triangles. This allows us to define the precise contribution of each kind of cellular process to large-scale tissue deformation. Together with experimental collaborators, we apply this theoretical framework to the developing fruit fly wing. Based on deformation quantifications, we describe fly wing mechanics using a continuum model. In particular, our results suggest that active anisotropic stresses as well as a delay in tissue stress relaxation processes contribute significantly to fly wing morphogenesis. The second part of the talk focuses on vertex models, which describe 2D biological tissues as networks of polygons. Recently, a new type of disordered solid-fluid transition was discovered in these models, but the mechanisms responsible for rigidity remained unclear. In order to gain insight into this transitions and make new predictions about three-dimensional biological tissues, we have developed a fully 3D vertex model. The model takes into account surface and volume elasticity of the individual cells. We find that also the 3D model exhibits a solid-fluid transition, which is controlled by a dimensionless model parameter describing the preferred cell shape, with an accompanying structural order parameter. We furthermore show that not only the onset of rigidity, but also the properties of vertex models away from the transition point can be understood based on the behavior of this minimal surface. In particular, we show that universal relations exist between minimal average cell surface and the fluctuations in cell surface and volume, and these relations exactly predict the behavior of both shear and bulk moduli, both in 2D and 3D. This work demonstrates how universal geometrical properties of a disordered material precisely control its mechanical behavior.