Arbitrary Design of DNA-Programmable 3D Crystals through Symmetry Mapping

Nanoscale self-assembly offers exciting potential for creating intricate structures beyond the limits of traditional top-down nanofabrication. Despite advancements in molecularly programmable assembly, particularly utilizing DNA nanotechnology, challenges remain in defining precise assembly instructions for the formation of complex three-dimensional (3D) superlattice architectures. DNA-based self-assembly methods offer programmability through sequence-encoded addressable bonds, but the difficulty lies in reducing the complexity and number of these interactions to establish a modular, structural design strategy and streamline the assembly and component fabrication process. This work proposes a symmetry-mapping bond assignment algorithm to guide the design of arbitrarily prescribed 3D lattices self-assembled from voxels with directional, addressable bonds and capable of carrying nanocargo. The algorithm enables the minimization of the number of DNA-based voxels, thus reducing the amount of information required to encode assembly. The developed approach leverages the symmetries of the target lattices, assembled from voxels, but significantly incorporates experimentally relevant binding rules and restrictions specific to DNA-based systems. We discuss the developed algorithm and demonstrate its capability in selected examples of nanoscale analogs of zinc blende (ZnS) and cubic Laves phase (MgCu₂), as well as a lattice based on an arbitrarily designed motif (letter H). Through the established algorithm and associated software for Mapping Of Structurally Encoded aSsembly (MOSES), this inverse design approach provides a scalable solution for designing complexly organized 3D nanostructures, providing a means for programming bottom-up nanomaterial fabrication.