All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes.

Using theory and experiments, we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane. The midplane tilt at the interdomain edge forces splay, which, in turn, manifests as spontaneous edge curvature with energetics controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at interdomain edges explains a number of experimental observations, including annularly shaped long-rod domains, and a nonmonotonic dependence of edge twist on domain radius. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids gives rise to complex shapes of fluid domains, analogous to shape transitions in 3D fluid vesicles.

Force-Induced Formation of Twisted Chiral Ribbons.

We demonstrate that an achiral stretching force transforms disk-shaped colloidal membranes composed of chiral rods into twisted ribbons with handedness opposite the preferred twist of the rods. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and the ribbon shape. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve and the force-induced twisted shape.

Hierarchical Assembly of DNA Nanostructures Based on Four-Way Toehold-Mediated Strand Displacement.

Because of its attractive cost and yield, hierarchical assembly, in which constituent structures of lower hierarchy share a majority of components, is an appealing approach to scale up DNA self-assembly. A few strategies have already been investigated to combine preformed DNA nanostructures. In this study, we present a new hierarchical assembly method based on four-way toehold-mediated strand displacement to facilitate the combination of preformed DNA structural units. Employing such a method, we have constructed a series of higher-order structures composed of 5, 7, 9, 11, 13, and 15 preformed units respectively.

Self-assembly of complex two-dimensional shapes from single-stranded DNA tiles.

Current methods in DNA nano-architecture have successfully engineered a variety of 2D and 3D structures using principles of self-assembly. In this article, we describe detailed protocols on how to fabricate sophisticated 2D shapes through the self-assembly of uniquely addressable single-stranded DNA tiles which act as molecular pixels on a molecular canvas. Each single-stranded tile (SST) is a 42-nucleotide DNA strand composed of four concatenated modular domains which bind to four neighbors during self-assembly. The molecular canvas is a rectangle structure self-assembled from SSTs. A prescribed complex 2D shape is formed by selecting the constituent molecular pixels (SSTs) from a 310-pixel molecular canvas and then subjecting the corresponding strands to one-pot annealing. Due to the modular nature of the SST approach we demonstrate the scalability, versatility and robustness of this method. Compared with alternative methods, the SST method enables a wider selection of information polymers and sequences through the use of de novo designed and synthesized short DNA strands.