Volumetric self-assembly of addressable DNA frames

The ability to organize distinct molecular components at prescribed positions throughout a three-dimensional volume remains a central challenge in programmable self-assembly. Although DNA nanotechnology has enabled both highly addressable structures and assemblies of considerable size, combining these capabilities is limited by the growing number of unintended interactions between components. Here, we develop a sequence-encoded strategy for the volumetric assembly of uniquely addressed DNA origami cubes. Each cube carries 24 programmable address codes that determine its position through cooperative interactions with neighboring cubes. We formulate address generation as a coding problem, derive its theoretical capacity and develop computational methods to identify and suppress incorrect multivalent binding configurations. Using this approach, we assemble a range of three-dimensional architectures, including a 6 × 6 × 6 cuboid that contains 216 unique cubes, spans 300 nm and is encoded by a single scaffold and 361 distinct oligonucleotides. We further demonstrate site-specific organization of 18-nm gold nanoparticles into prescribed three-dimensional patterns and use single-molecule DNA-PAINT to resolve spatially encoded features at the level of individual cubes. These results establish a framework for large-scale volumetric self-assembly in which molecular identity, spatial position and cargo placement can be independently programmed, providing a route toward aperiodic nanomaterials with designed three-dimensional organization.