DNA origami single crystals with Wulff shapes

DNA origami technology has proven to be an excellent tool for precisely manipulating molecules and colloidal elements in a three-dimensional manner. However, fabrication of single crystals with well-defined facets from highly programmable, complex DNA origami units is a great challenge. Here, we report the successful fabrication of DNA origami single crystals with Wulff shapes and high yield. By regulating the symmetries and binding modes of the DNA origami building blocks, the crystalline shapes can be designed and well-controlled. The single crystals are then used to induce precise growth of an ultrathin layer of silica on the edges, resulting in mechanically reinforced silica-DNA hybrid structures that preserve the details of the single crystals without distortion. The silica-infused microcrystals can be directly observed in the dry state, which allows meticulous analysis of the crystal facets and tomographic 3D reconstruction of the single crystals by high-resolution electron microscopy.

Anisotropic liquid drop models

We introduce and study certain variants of Gamow’s liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotropic. In sharp contrast, Wulff shapes are the unique minimizers for certain crystalline surface tensions. We also introduce and study several related liquid drop models with anisotropic repulsion for which the Wulff shape is the minimizer in the small mass regime.

New stability results for spheres and Wulff shapes

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp-sense is W2,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].