Shape-Shifting Droplet Networks

Taking a cue from biology, researchers have engineered materials that, through self-assembly, fold into designated geometries. Recent work showed that sheets of aqueous droplets can assemble into a variety of three-dimensional shapes. Expanding on this result, Mark Bowick and collaborators at Syracuse University, have now demonstrated theoretically that such droplet networks can be programmed to reversibly switch between different shapes. This finding is a step toward biologically inspired robots that can change their shape according to their environment.

Endocytosis in Yeast

We have constructed a theoretical model of endocytosis in yeast. Recent experiments on endocytosis in yeast demonstrate that the actin cytoskeleton plays a crucial role in the deformation of the cell membrane. However, competing ideas remain as to precisely how the actin cytoskeleton organizes itself to help drive the deformation. To begin to resolve this controversy, we mathematically model clathrin-mediated endocytosis in yeast using variational methods and Monte Carlo simulations. Our results also suggest that the pinch-off mechanism may be assisted by a pearling-like instability. 

Mechanics of Anisotropic Spring Networks

The actin cytoskeleton gives the cell shape and support, is crucial for cell locomotion, and participates in cell division. To study the mechanical properties of the actin cytoskeleton as modeled by rigidity percolation (disordered spring networks), we have analytically and numerically studied disordered spring networks with an underlying anisotropy, i.e. where the filaments are preferentially oriented along one direction. We found, for example, that the increasing the anisotropy, increases the filament density required for a nonzero shear modulus (rigidity).