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In this study, we investigate the topological adaptability and structural resilience of periodic soft matter entanglements using the DNA tensegrity triangle, a foundational motif in structural DNA nanotechnology, as a model system. By simulating the Reidemeister moves from knot theory, which describe a series of “moves” by which the knot equivalence is preserved, we demonstrate that many variants of the tensegrity triangle maintain their lattice geometry, underscoring the motif’s inherent topological robustness. Using granular deformations in a series of closely related motifs, we systematically twist the helices and slide their ends relative to junction crossings to yield 48 distinct crystal structures. Notably, we Identify a novel poke-DX feature (PDX), which introduces rigid crossover configurations with enhanced crystallographic resolution and site-specific metal ion coordination. Further exploration reveals the formation of semi-junctions – a new class of four-arm junctions held together by a single rotatable bond, which feature relaxed torsional strain and altered crossover geometries. These configurations support lattice transformations into tetragonal and distorted rhombohedral forms as well as facilitate topological inversion between left- and right- handed triangles. Altogether, these findings illustrate how controlled topological operations at the molecular level can tune local flexibility and stiffness at key sites to affect long-range lattice geometry. This work positions DNA-based frameworks as a programmable platform for the design of architected materials, topological metamaterials, and nanoscale devices with tunable structural and functional properties. 

DNA nanotechnology leverages the molecular design resolution of the DNA double helix to fold and tile matter into designer architectures. Recent advances in bioinorganic chemistry have exploited the affinity of soft nucleobase functional groups for silver ions in order to template the growth of silver nanoclusters by templated reduction. The coupling of the spatial resolution of DNA nanotechnology and the atomic precision of DNA-based nanocluster synthesis has not been realized. Here we develop a method using 3D DNA crystals to employ silver-ion-mediated base pairs as nucleation sites for atomically-precise nanocluster growth. By leveraging the topology of DNA tensegrity triangles, we provide a mesoporous 3D lattice that is robust to reducing conditions, enabling precise spatial templating. Use of in situ confocal fluorescence microscopy allows for the direct observation of reaction kinetics and reconstruction of the optical bandgap. Control over reaction time and stoichiometry, base pair identity, and buffer composition enable precise tuning of the atomic composition and optical properties of the ensuing nanoclusters. The resulting crystals are of diffraction quality, yielding molecular structures of Ag4 and Ag6 in 3D. Inter-cluster distances of less than 2 nm show strong plasmonic coupling, with red shifting observed relative to literature standards. We anticipate that these results will yield advances in materials synthesis, DNA-based plasmonic crystals, and optically-active nanoelectronics.