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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. 

Self-assembling DNA crystals have emerged over the last two decades as an efficient and effective means of organizing matter at the nanoscale, but functionalization of these lattices has proved challenging as physiological buffer conditions are required to maintain structural integrity. In this manuscript, we demonstrate the silicification of porous DNA crystals using sol-gel chemistry. We identify reaction conditions that produce the minimum coating thickness to confer environmental protection, and subsequently measure the protective ability of the silica coating to various stressors, including heat, low ionic strength solution, organic solvents, and unprotected flash freezing. By soaking ions and dyes into the lattice after silica coating, we demonstrate that the crystals maintain their pores, and that the major groove of the DNA can still be used as a site-specific template for chemical modifications. We image a library of different crystal motifs by electron microscopy and confirm the presence of silica using energy dispersive spectroscopy. Finally, we perform X-ray diffraction on these crystals, both with and without cryoprotection and determine the structure of the DNA frame, underscoring the conserved molecular order after coating. We anticipate these mesoporous silica composites for use in applications involving extreme, non-physiological conditions and for experiments which utilize the DNA glass described here as a template for surface science. 

Topology has emerged as a field for describing and controlling order and matter, and thereby the physical properties of materials. There are several largely disparate fields focused on examining and manipulating topology. One of these arenas is in the realm of real space, manipulating systems in terms of their spatial properties, to control the corresponding structural, mechanical, and self- assembling responses. Much of the work in soft matter topology falls within this domain. A second arena is in the domain of momentum or k-space wherein topology controls the features of the electronic band structure of materials, and topologically non-trivial features result in the development of materials with truly unique properties. This work focuses squarely on the realm of condensed matter physics. Here, we review concepts of real- and k-space topology and propose areas for convergence between these two disparate fields. 

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. 

Tertiary chirality describes the handedness of supramolecular assemblies and relies not only on the primary and secondary structures of the building blocks but also on topological driving forces that have been sparsely characterized. Helical biopolymers, especially DNA, have been extensively investigated as they possess intrinsic chirality that determines the optical, mechanical, and physical properties of the ensuing material. Here, we employ the DNA tensegrity triangle as a model system to locate the tipping points in chirality inversion at the tertiary level by X-ray diffraction. We engineer tensegrity triangle crystals with incremental rotational steps between immobile junctions from 3 to 28 base pairs (bp). We construct a mathematical model that accurately predicts and explains the molecular configurations in both this work and previous studies. Our design framework is extendable to other supramolecular assemblies of helical biopolymers and can be used in the design of chiral nanomaterials, optically active molecules, and mesoporous frameworks, all of which are of interest to physical, biological, and chemical nanoscience. 

Abstract The rational design of molecular electronics remains a grand challenge of materials science. DNA nanotechnology has offered unmatched control over molecular geometry, but direct electronic functionalization is a challenge. Here a generalized method is presented for tuning the local band structure of DNA using transmetalation in metal‐mediated base pairs (mmDNA). A method is developed for time‐resolved X‐ray diffraction using self‐assembling DNA crystals to establish the exchange of Ag⁺ and Hg²⁺ in T:T base pairs driven by pH exchange. Transmetalation is tracked over six reaction phases as crystal pH is changed from pH 8.0 to 11.0, and vice versa. A detailed computational analysis of the electronic configuration and transmission in the ensuing crystal structures is then performed. This findings reveal a high conductance contrast in the lowest unoccupied molecular orbitals (LUMO) as a result of metalation. The ability to exchange single transition metal ions as a result of environmental stimuli heralds a means of modulating the conductance of DNA‐based molecular electronics. In this way, both theoretical and experimental basis are established by which mmDNA can be leveraged to build rewritable memory devices and nanoelectronics. 

Abstract Non‐canonical interactions in DNA remain under‐explored in DNA nanotechnology. Recently, many structures with non‐canonical motifs have been discovered, notably a hexagonal arrangement of typically rhombohedral DNA tensegrity triangles that forms through non‐canonical sticky end interactions. Here, we find a series of mechanisms to program a hexagonal arrangement using: the sticky end sequence; triangle edge torsional stress; and crystallization condition. We showcase cross‐talking between Watson–Crick and non‐canonical sticky ends in which the ratio between the two dictates segregation by crystal forms or combination into composite crystals. Finally, we develop a method for reconfiguring the long‐range geometry of formed crystals from rhombohedral to hexagonal and vice versa. These data demonstrate fine control over non‐canonical motifs and their topological self‐assembly. This will vastly increase the programmability, functionality, and versatility of rationally designed DNA constructs.