DNA can be programmed to self-assemble into high molecular weight 3D assemblies with precise nanometer-scale structural features. Although numerous sequence design strategies exist to realize these assemblies in solution, there is currently no computational framework to predict their 3D structures on the basis of programmed underlying multi-way junction topologies constrained by DNA duplexes. Here, we introduce such an approach and apply it to assemblies designed using the canonical immobile four-way junction. The procedure is used to predict the 3D structure of high molecular weight planar and spherical ring-like origami objects, a tile-based sheet-like ribbon, and a 3D crystalline tensegrity motif, in quantitative agreement with experiments. Our framework provides a new approach to predict programmed nucleic acid 3D structure on the basis of prescribed secondary structure motifs, with possible application to the design of such assemblies for use in biomolecular and materials science.

The control of enzymatic reactions using nanoscale DNA devices offers a powerful application of DNA nanotechnology uniquely derived from actuation. However, previous characterization of enzymatic reaction rates using bulk biochemical assays reported suboptimal function of DNA devices such as tweezers. To gain mechanistic insight into this deficiency and to identify design rules to improve their function, here we exploit the synergy of single molecule imaging and computational modeling to characterize the three-dimensional structures and catalytic functions of DNA tweezer-actuated nanoreactors. Our analysis revealed two important deficiencies--incomplete closure upon actuation and conformational heterogeneity. Upon rational redesign of the Holliday junctions located at their hinge and arms, we found that the DNA tweezers could be more completely and uniformly closed. A novel single molecule enzyme assay was developed to demonstrate that our design improvements yield significant, independent enhancements in the fraction of active enzyme nanoreactors and their individual substrate turnover frequencies. The sequence-level design strategies explored here may aid more broadly in improving the performance of DNA-based nanodevices including biological and chemical sensors.

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Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.