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Clicking on the donut icon will load a page at altmetric. Find more information on the Altmetric Attention Score and how the score is calculated. Structural DNA nanotechnology plays an ever-increasing role in advanced biomolecular applications. Here, we present a computational method to analyze structured DNA assemblies rapidly at near-atomic resolution. Both high computational efficiency and molecular-level accuracy are achieved by developing a multiscale analysis framework.
The sequence-dependent relative geometry and mechanical properties of DNA motifs are characterized by the all-atom molecular dynamics simulation and incorporated into the structural finite element model successfully without significant loss of atomic information.
The proposed method can predict the three-dimensional shape, equilibrium dynamic properties, and mechanical rigidities of monomeric to hierarchically assembled DNA structures at near-atomic resolution without adjusting any model parameters. The calculation takes less than only 15 min for most origami-scale DNA nanostructures consisting of — base-pairs. Hence, it is expected to be highly utilized in an iterative design—analysis—revision process for structured DNA assemblies.
Figure 1. Overview of the multiscale analysis framework. A structured DNA assembly is subdivided into structural motifs classified according to the topological connection of bases: three types of BP steps, two types of CO steps, and the ssDNA part. Structural elements are developed to incorporate the sequence-dependent intrinsic properties of structural motifs that are precalculated and stored in the property library.
The electrostatic repulsive forces between BPs are applied through electrostatic elements. From an input design, structural motifs are identified from the topological connectivity and the initial configuration is determined. The global stiffness matrix of the entire assembly is constructed from the element stiffness matrices of structural and electrostatic elements.
The intrinsic properties of a structural motif are assigned from the property library according to its type and sequence. Through an automated solution procedure, the results including the three-dimensional shape, dynamic properties in equilibrium, and mechanical rigidities are calculated rapidly at near-atomic resolution. Figure 2. Analysis of monomeric DNA nanostructures. Four 32HB structures, 24 whose CO spacing was systematically designed to be 21, 42, 63, and 84 BPs along the helical axis, were analyzed.
Interhelical distances increase with the CO spacing due to the electrostatic repulsive forces. The structural or electrostatic elements were generated between two finite element nodes. Included angles of 10 polymorphic 12HB structures 22 were measured. For the quarter Q and half H circle designs 36 by BP insertion and deletion, the radius of curvature and angle of curvature were quantified by fitting a circle to BP positions in the predicted structures.
Left-handed L and right-handed R twist structures 4 were analyzed. Their twist angle and axial length were obtained using the principal axes of cross-sectional planes in the predicted structure. The node-to-node distance of polymeric ribbons in the experiment was estimated as the axial length divided by the twist angle. Twist angles of 6HB structures 23 controlled by sequence-dependent torsional and bending rigidities of nicked BP steps were predicted.
Two pairs of stiff, moderate, and flexible structures are represented as S1 and S2, M1 and M2, and F1 and F2, respectively. Figure 3. Analysis of hierarchical DNA nanostructures. Two asymmetric substructures with spacer helices comprise a V-brick. The ring assembly was obtained by minimizing the distance between interlocking surfaces of predicted V-bricks. They were obtained by joining the shape-complementary planar surfaces of ring assemblies using the same approach to obtaining rings from V-bricks.
Distortion was hardly seen in the tube consisting of twist-corrected V-bricks where some BPs were deliberately removed green. The twist-corrected triangle brick, embossed V-brick, and connector brick were designed to be assembled into a 3-fold assembly structure via shape complementary at the interfaces. Three opening angles of the embossed V-bricks were designed to be The three-dimensional shape of self-limiting tetrahedron, hexahedron, and dodecahedron was analyzed.
Figure 4. Structural details at near-atomic resolution. The root-mean-square deviation with respect to the experimental cryo-EM structure 38 was 1. Almost the same length of the structure in the helical axis Lz was predicted, while its width and height in two transverse directions Lx and Ly were slightly underestimated compared to the experimental structure.
Three representative CO angles were calculated following the previous definition 38 using the vectors connecting six points: two mean positions of CO-nick BP steps gray circles and four points in each lag located two BPs away from the CO other circles. The mean and standard deviation of these angles were calculated using those measured for all CO steps in the structure. The predicted translational and rotational parameters 40 of all BP steps in the structure were consistent with the experimental results.
Figure 5. Dynamic properties in equilibrium. BP index green arrow represents the nodal positions of BPs along the helical axis. The overlap coefficient between RMSF profiles predicted by the proposed method and the 50 ns long all-atom MD simulation 22 was 0.
The upper-left and lower-right triangles represent the correlation coefficients obtained from the MD simulation and the present framework, respectively. With the proposed multiscale analysis framework, the calculation could be completed in 1 min using a single PC with an Intel i 3. Figure 6. Global mechanical rigidities.
To predict the bending and torsional persistence lengths, 10 DNA bundle structures were designed with various numbers of comprising helices and cross-sectional shapes on the honeycomb HC or square SQ lattice.
The predicted torsional persistence lengths were comparable to previously reported values 44 and followed the minimum trend dashed line of the theoretically formulated range. Such files may be downloaded by article for research use if there is a public use license linked to the relevant article, that license may permit other uses.
More by Jae Young Lee. More by Jae Gyung Lee. More by Giseok Yun. More by Chanseok Lee. More by Young-Joo Kim. More by Kyung Soo Kim. More by Tae Hwi Kim. More by Do-Nyun Kim. Cite this: ACS Nano , 15 , 1 , — Published by American Chemical Society. Article Views Altmetric -. Abstract High Resolution Image. Structural DNA nanotechnology enables the engineering of molecular structures with programmable shapes and properties.
While modeling and simulation approaches have been proposed, there has been a trade-off between computational efficiency and prediction accuracy. To reduce the computational cost, the development of coarse-grained models has been fueled through modeling the essential properties of DNA.
Although this model has a major advantage in describing the detailed characteristics such as the hybridization process and thermal dissociation, it is inherently based on time integration, and thus, it requires still day to week scale time to reach a reasonable equilibrium of a largely deformable structure.
Alternatively, a recent multiresolution model, MrDNA, 28 employs a low-resolution model to perform rapid relaxation of a DNA nanostructure and gradually increases the modeling resolution to predict structural features at the atomic level, achieving significant computational efficiency of hour scale for DNA origami structures. On the other hand, a continuum or structural model, CanDo, 24 approximating DNA as a continuous medium or beam-like structure can predict the shape and physical properties of a structure quickly within an hour for most DNA nanostructures.
However, it has empirical model parameters to be adjusted to fit a certain target property. Also, the electrostatic interaction and sequence dependence of intrinsic geometry and mechanical properties of DNA are usually ignored. Here, we present a computational method for the rapid analysis of structured DNA assemblies at near-atomic resolution that can be effectively used in the design process.
A multiscale analysis framework, integrating the intrinsic properties of DNA at the atomic level to the continuum description serially, 29 was employed so as to exploit both the efficiency of structural models and the accuracy of MD approaches.
Structural motifs constituting structured DNA assemblies were first defined carefully, and their sequence-dependent geometric and mechanical properties were characterized thoroughly using all-atom MD simulations. These properties as well as the electrostatic interaction among DNA helices were incorporated into a finite-element-based structural model that we developed without significant loss of atomic information. The three-dimensional shape at near-atomic resolution, the conformational dynamic properties in equilibrium, and the mechanical rigidities of an assembly were then obtained accurately and swiftly within 15 min on a single PC for most origami-scale monomeric structures without any adjustment of parameters, as demonstrated for a comprehensive set of DNA origami designs.
Results and Discussion. A BP step represents two BPs connected successively within a helix, categorized into regular and nicked BP steps where one of the backbones is broken in nicked ones. Two BPs connected across helices by the same backbone were referred to as a CO step. Antiparallel crossovers were only considered in this work. They were not specified for ssDNA, as its mechanical role as an entropic spring is governed by its end-to-end distance and contour length while its sequence dependence was assumed to be negligible.
High Resolution Image. The sequence-dependent relative geometry and mechanical properties of these motifs in equilibrium were quantified from the MD trajectories Figure 1 b. The relative motion was recorded over time and converted to a covariance matrix providing its elastic properties under quasi-harmonic approximation. The measured properties agree quantitatively well with known characteristics of DNA including the helical rise of 0. Note that the structural element considers all of the geometry and mechanical properties between two BPs axial length, shearing distances, and twisting and bending angles obtained by MD simulations without further approximation as well as their sequence dependence unlike the simplified beam model used in CanDo.
For the analysis of structured nucleic acids, it is important to model the electrostatic interaction among negatively charged BPs in an ionic solution to capture the deformation due to interhelical repulsion. Noting that the intrinsic properties of the BP or CO steps including electrostatic interactions from MD simulation were already incorporated in structural elements, we considered electrostatic repulsion between distant BPs in adjacent helices rather than inside the helix.
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Computational Analysis and Design of Bridge Structures covers the general aspects of bridges, bridge behavior and the modeling of bridges, and special topics on.
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Masonry structures, although classically suitable to withstand gravitational loads, are sensibly vulnerable if subjected to extraordinary actions such as earthquakes, exhibiting cracks even for events of moderate intensity compared to other structural typologies like as reinforced concrete or steel buildings.
The methods for their computational analysis and design range from approximate to refined analyses, and rapidly improving computer technology has made the more refined and complex methods of analyses more commonplace.
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ReplyThe methods for their computational analysis and design range from approximate to refined analyses, and rapidly improving computer technology has made the more refined and complex methods of analyses more commonplace.
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