Large Deformation of a DNA-Origami Nanoarm Induced by the Cumulative Actuation of Tension-Adjustable Modules

Dynamic switching circuit modulated by intramolecular conformation transition of DNA translator for versatile fluorescence biosensors

It might be intriguing and desirable to explore the stimuli-responsive modulation of dynamic switching circuit (DSC) for constructing versatile fluorescence biosensors via two-step sequential independent displacement reactions. Here, a switchable DNA translator (DT) encoding three functional modules is proposed to implement DSC for interpreting specific Key triggers (i.e. DNA segment, miRNA or small molecule) by activating intramolecular conformation transition. Upon presenting Key to regulate strand displacement, the Lock-blocked DT is liberated and self-folded into "active" on-state hairpin structure, so that two ended toeholds are oriented closely to execute proximal hybridization cooperatively for Key-responsive signal readout. Benefited from fast kinetics, efficient transduction, simplified operation and flexible programming, the Key-actuated DSC strategy achieved label-free assay of various target species by employing tunable Ag nanocluster as fluorescent reporter adjacent to or away from hemin/G-quadruplex complexes, which would be more potential and applicable in versatile fluorescence biosensors, identifiable cell imaging or customized tasks than typical strand displacements.

Controlling the Hierarchical Assembly of DNA-Based Hexagonal Microstructures

This paper discusses the controlled morphology of hierarchical liquid crystalline DNA assemblies. Through a process of heating and slow cooling, double-stranded DNAs (dsDNAs) having 23 complementary bases and two base overhangs (a pair of 25mer oligonucleotides) spontaneously assemble into micro-sized hexagonal platelets in a solution containing poly(ethylene glycol) (PEG) and salt. Remarkably, the addition of a shorter dsDNA with AA/TT overhangs (a pair of 18mer oligonucleotides) to a PEG-salt solution of 25mer DNA with AA/TT overhangs results in the formation of molecular tubes, each with a central blockage. In contrast, the addition of 18mer DNA with GG/CC overhangs leads to the formation of hexagonal frames from hexagonal platelets. In the assemblies, 18mer DNA is more predominant at the edges, while the central nuclei are composed of 25mer DNA. X-ray scattering measurements reveal that both molecular tubes and hexagonal frames form hexagonal columnar liquid crystalline assemblies. These self-assemblies are thought to result from depletion attraction due to PEG and end-to-end stacking between dsDNA overhangs. Differences in the melting temperatures between longer and shorter dsDNAs enable the stepwise formation of hierarchical assemblies, while variations in overhang sequences modulate the overall morphology by altering the growth direction of the assemblies.

A Chemo-Mechanically Coupled DNA Origami Clamp Capable of Generating Robust Compression Forces

DNA nanostructures have been utilized to study biological mechanical processes and construct artificial nanosystems. Many application scenarios necessitate nanodevices able to robustly generate large single molecular forces. However, most existing dynamic DNA nanostructures are triggered by probabilistic hybridization reactions between spatially separated DNA strands, which only non-deterministically generate relatively small compression forces (≈0.4 piconewtons (pN)). Here, an intercalator-triggered dynamic DNA origami nanostructure is developed, where large amounts of local binding reactions between intercalators and the nanostructure collectively lead to the robust generation of relatively large compression forces (≈11.2 pN). Biomolecular loads with different stiffnesses, 3, 4, and 6-helix DNA bundles are efficiently bent by the compression forces. This work provides a robust and powerful force-generation tool for building highly chemo-mechanically coupled molecular machines in synthetic nanosystems.

Diverse Chiral Nanotubes Assembled from Identical DNA Strands

DNA nanotubes with controllable geometries hold a wide range of interdisciplinary applications. When preparing DNA nanotubes of varying widths or distinct chirality, existing methods require repeatedly designing and synthesizing specific DNA sequences, which can be costly and laborious. Here, we proposed an intercalator-assisted DNA tile assembly method which enables the production of DNA nanotubes of diverse widths and chirality using identical DNA strands. Through adjusting the concentration of intercalators during assembly, the twisting direction and extent of DNA tiles could be modulated, leading to the formation of DNA nanotubes featuring controllable widths and chirality. Moreover, through introducing additional intercalators and secondary annealing, right-handed nanotubes could be reconfigured into distinct left-handed nanotubes. We expect that this method could be universally applied to modulating the self-assembly pathways of various DNA tiles and other chiral materials, advancing the landscape of DNA tile assembly.

Prediction of DNA origami shape using graph neural network

Unlike proteins, which have a wealth of validated structural data, experimentally or computationally validated DNA origami datasets are limited. Here we present a graph neural network that can predict the three-dimensional conformation of DNA origami assemblies both rapidly and accurately. We develop a hybrid data-driven and physics-informed approach for model training, designed to minimize not only the data-driven loss but also the physics-informed loss. By employing an ensemble strategy, the model can successfully infer the shape of monomeric DNA origami structures almost in real time. Further refinement of the model in an unsupervised manner enables the analysis of supramolecular assemblies consisting of tens to hundreds of DNA blocks. The proposed model enables an automated inverse design of DNA origami structures for given target shapes. Our approach facilitates the real-time virtual prototyping of DNA origami, broadening its design space.

Autonomous assembly and disassembly of gliding molecular robots regulated by a DNA-based molecular controller

In recent years, there has been a growing interest in engineering dynamic and autonomous systems with robotic functionalities using biomolecules. Specifically, the ability of molecular motors to convert chemical energy to mechanical forces and the programmability of DNA are regarded as promising components for these systems. However, current systems rely on the manual addition of external stimuli, limiting the potential for autonomous molecular systems. Here, we show that DNA-based cascade reactions can act as a molecular controller that drives the autonomous assembly and disassembly of DNA-functionalized microtubules propelled by kinesins. The DNA controller is designed to produce two different DNA strands that program the interaction between the microtubules. The gliding microtubules integrated with the controller autonomously assemble to bundle-like structures and disassemble into discrete filaments without external stimuli, which is observable by fluorescence microscopy. We believe this approach to be a starting point toward more autonomous behavior of motor protein-based multicomponent systems with robotic functionalities.

Isothermal self-assembly of multicomponent and evolutive DNA nanostructures

Thermal annealing is usually needed to direct the assembly of multiple complementary DNA strands into desired entities. We show that, with a magnesium-free buffer containing NaCl, complex cocktails of DNA strands and proteins can self-assemble isothermally, at room or physiological temperature, into user-defined nanostructures, such as DNA origamis, single-stranded tile assemblies and nanogrids. In situ, time-resolved observation reveals that this self-assembly is thermodynamically controlled, proceeds through multiple folding pathways and leads to highly reconfigurable nanostructures. It allows a given system to self-select its most stable shape in a large pool of competitive DNA strands. Strikingly, upon the appearance of a new energy minimum, DNA origamis isothermally shift from one initially stable shape to a radically different one, by massive exchange of their constitutive staple strands. This method expands the repertoire of shapes and functions attainable by isothermal self-assembly and creates a basis for adaptive nanomachines and nanostructure discovery by evolution.

Versatile computer-aided design of free-form DNA nanostructures and assemblies

Recent advances in structural DNA nanotechnology have been facilitated by design tools that continue to push the limits of structural complexity while simplifying an often-tedious design process. We recently introduced the software MagicDNA, which enables design of complex 3D DNA assemblies with many components; however, the design of structures with free-form features like vertices or curvature still required iterative design guided by simulation feedback and user intuition. Here, we present an updated design tool, MagicDNA 2.0, that automates the design of free-form 3D geometries, leveraging design models informed by coarse-grained molecular dynamics simulations. Our GUI-based, stepwise design approach integrates a high level of automation with versatile control over assembly and subcomponent design parameters. We experimentally validated this approach by fabricating a range of DNA origami assemblies with complex free-form geometries, including a 3D Nozzle, G-clef, and Hilbert and Trifolium curves, confirming excellent agreement between design input, simulation, and structure formation.

Multi-Reconfigurable DNA Origami Nanolattice Driven by the Combination of Orthogonal Signals

The progress of the scaffolded DNA origami technology has enabled the construction of various dynamic nanodevices imitating the shapes and motions of mechanical elements. To further expand the achievable configurational changes, the incorporation of multiple movable joints into a single DNA origami structure and their precise control are desired. Here, we propose a multi-reconfigurable 3 × 3 lattice structure consisting of nine frames with rigid four-helix struts connected with flexible 10-nucleotide joints. The configuration of each frame is determined by the arbitrarily selected orthogonal pair of signal DNAs, resulting in the transformation of the lattice into various shapes. We also demonstrated sequential reconfiguration of the nanolattice and its assemblies from one into another via an isothermal strand displacement reaction at physiological temperatures. Our modular and scalable design approach could serve as a versatile platform for a variety of applications that require reversible and continuous shape control with nanoscale precision.

Recent Advances in DNA Origami-Engineered Nanomaterials and Applications

DNA nanotechnology is a unique field, where physics, chemistry, biology, mathematics, engineering, and materials science can elegantly converge. Since the original proposal of Nadrian Seeman, significant advances have been achieved in the past four decades. During this glory time, the DNA origami technique developed by Paul Rothemund further pushed the field forward with a vigorous momentum, fostering a plethora of concepts, models, methodologies, and applications that were not thought of before. This review focuses on the recent progress in DNA origami-engineered nanomaterials in the past five years, outlining the exciting achievements as well as the unexplored research avenues. We believe that the spirit and assets that Seeman left for scientists will continue to bring interdisciplinary innovations and useful applications to this field in the next decade.

Controllable dynamics of complex DNA nanostructures

In the past four decades, a variety of self-assembly design frameworks have led to the construction of versatile DNA nanostructures with increasing complexity and controllability. The controllable dynamics of DNA nanostructures has garnered much interest and emerged as a powerful tool for conducting sophisticated tasks at the molecular level. In this minireview, we summarized the controllable reconfigurations of complex DNA nanostructures induced by nucleic acid strands, environmental stimuli and enzymatic treatments. We also envisioned that with the optimization of response time, sensitivity and specificity, dynamic DNA nanostructures have great promise in applications ranging from nanorobotics to life sciences.

Regulating the Polymerization of DNA Structures via Allosteric Control of Monomers

Regulation of self-assembly is crucial in constructing structural biomaterials, such as tunable DNA nanostructures. Traditional tuning of self-assembled DNA nanostructures was mainly conducted by introducing external stimuli after the assembly process. Here, we explored the allosteric assembly of DNA structures via introducing external stimuli during the assembly process to produce structurally heterogeneous polymerization products. We demonstrated that ethidium bromide (EB), a DNA intercalator, could increase the left-handed out-of-plane chirality of curved DNA structures. Then, EB and double strands were introduced as competing stimuli to transform monomers into allosteric conformations, leading to three different polymerization products. The steric trap between different polymerization products promoted the polymerized structures to keep their geometric properties, like chirality, under varying intensity of external stimuli. Our strategy harnesses allosteric effects for assembly of DNA-based materials and is expected to expand the design space for advanced control in synthetic materials.

Actuating tension-loaded DNA clamps drives membrane tubulation

Membrane dynamics in living organisms can arise from proteins adhering to, assembling on, and exerting force on cell membranes. Programmable synthetic materials, such as self-assembled DNA nanostructures, offer the capability to drive membrane-remodeling events that resemble protein-mediated dynamics but with user-defined outcomes. An illustrative example is the tubular deformation of liposomes by DNA nanostructures with purposely designed shapes, surface modifications, and self-assembling properties. However, stimulus-responsive membrane tubulation mediated by DNA reconfiguration remains challenging. Here, we present the triggered formation of membrane tubes in response to specific DNA signals that actuate membrane-bound DNA clamps from an open state to various predefined closed states, releasing prestored energy to activate membrane deformation. We show that the timing and efficiency of vesicle tubulation, as well as the membrane tube widths, are modulated by the conformational change of DNA clamps, marking a solid step toward spatiotemporal control of membrane dynamics in an artificial system.

Design, Mechanical Properties, and Dynamics of Synthetic DNA Filaments

Over the past 40 years, structural and dynamic DNA nanotechnologies have undoubtedly demonstrated to be effective means for organizing matter at the nanoscale and reconfiguring equilibrium structures, in a predictable fashion and with an accuracy of a few nanometers. Recently, novel concepts and methodologies have been developed to integrate nonequilibrium dynamics into DNA nanostructures, opening the way to the construction of synthetic materials that can adapt to environmental changes and thus acquire new properties. In this Review, we summarize the strategies currently applied for the construction of synthetic DNA filaments and conclude by reporting some recent and most relevant examples of DNA filaments that can emulate typical structural and dynamic features of the cytoskeleton, such as compartmentalization in cell-like vesicles, support for active transport of cargos, sustained or transient growth, and responsiveness to external stimuli.

Nanopolymers for magnetic applications: how to choose the architecture?

Directional assembly of nanoscale objects results in morphologies that can broadly be classified as supra-molecular nanopolymers. Such morphologies, given a functional choice of the monomers used as building blocks, can be of ubiquitous utility in optical, magnetic, rheological, and medical applications. These applications, however, require a profound understanding of the interplay between monomer shape and bonding on one side, and polymeric properties - on the other. Recently, we fabricated nanopolymers using cuboid DNA nanochambers, as they not only allow fine-tuning of the resulting morphologies but can also carry magnetic nanoparticles. However, it is not known if the cuboid shape and inter-cuboid connectivity restrict the equilibrium confirmations of the resulting nanopolymers, making them less responsive to external stimuli. In this work, using Molecular Dynamics simulations, we perform an extensive comparison between various nanopolymer architectures to explore their polymeric properties, and their response to an applied magnetic field if magnetic nanoparticles are embedded. We explain the impact of monomer shape and bonding on the mechanical and magnetic properties and show that DNA nanochambers can build highly responsive and magnetically controllable nanopolymers.

Tuning curved DNA origami structures through mechanical design and chemical adducts

The bending and twisting of DNA origami structures are important features for controlling the physical properties of DNA nanodevices. It has not been fully explored yet how to finely tune the bending and twisting of curved DNA structures. Traditional tuning of the curved DNA structures was limited to controlling the in-plane-bending angle through varying the numbers of base pairs of deletions and insertions. Here, we developed two tuning strategies of curved DNA origami structures fromin silicoandin vitroaspects.In silico, the out-of-plane bending and twisting angles of curved structures were introduced, and were tuned through varying the patterns of base pair deletions and insertions.In vitro, a chemical adduct (ethidium bromide) was applied to dynamically tune a curved spiral. The 3D structural conformations, like chirality, of the curved DNA structures were finely tuned through these two strategies. The simulation and TEM results demonstrated that the patterns of base pair insertions and deletions and chemical adducts could effectively tune the bending and twisting of curved DNA origami structures. These strategies expand the programmable accuracy of curved DNA origami structures and have potential in building efficient dynamic functional nanodevices.

Stress in DNA Gridiron Facilitates the Formation of Two-Dimensional Crystalline Structures

Programmable DNA nanotechnology has generated some of the most intricate self-assembled nanostructures and has been employed in a growing number of applications, including functional nanomaterials, nanofabrication, biophysics, photonics, molecular machines, and drug delivery. An important design rule for DNA nanostructures is to minimize the mechanical stress to reduce the potential energy in these nanostructures whenever it is possible. This work revisits the DNA gridiron design consisting of Holliday junctions and compares the self-assembly of the canonical DNA gridiron with a new design of DNA gridiron, which has a higher degree of mechanical stress because of the interweaving of DNA helices. While the interweaving DNA gridiron indeed exhibits lower yield, compared to its canonical counterpart of a similar size, we discover that the mechanical stress within the interweaving gridiron can promote the formation of the two-dimensional crystalline lattice instead of nanotubes. Furthermore, tuning the design of interweaving gridiron leads to the change of overall crystal size and regularity of geometry. Interweaving DNA double helices represents a new design strategy in the self-assembly of DNA nanostructures. Furthermore, the discovery of the new role of mechanical stress in the self-assembly of DNA nanostructures provides useful knowledge to DNA nanotechnology practitioners: a more balanced view regarding mechanical stress can be considered when designing future DNA nanostructures.

Characterizing and Harnessing the Mechanical Properties of Short Single-Stranded DNA in Structured Assemblies

Precise engineering of DNA structures is of growing interest to solve challenging problems in biomolecular applications and beyond. The introduction of single-stranded DNA (ssDNA) into the DNA structure can play a pivotal role in providing high controllability of critical structural features. Herein, we present a computational model of ssDNA with structural applications to harness its characteristics. The nonlinear properties of nucleotide gaps are systematically characterized to construct a structural model of the ssDNA across length scales with the incorporation of a finite element framework. The proposed method shows the programmability of structural bending, twisting, and persistence length by implementing the ssDNA in various DNA structures with experimental validation. Our results have significant implications for DNA nanotechnology in expanding the boundary of design and analysis of structural shape and stiffness.

Sequence-dependent twist-bend coupling in DNA minicircles

Looping of double-stranded DNA molecules with 100-200 base pairs into minicircles, catenanes, and rotaxanes has been suggested as a potential tool for DNA nanotechnologies. However, sharp DNA bending into a minicircle with a diameter of several to ten nanometers occurs with alterations in the DNA helical structure and may lead to defective kink formation that hampers the use of DNA minicircles, catenanes, and rotaxanes in nanoscale DNA applications. Here, we investigated local variations of a helical twist in sharply bent DNA using microsecond-long all-atom molecular dynamics simulations of six different DNA minicircles, focusing on the sequence dependence of the coupling between DNA bending and its helical twist. Twist angles between consecutive base pairs were analyzed at different locations relative to the direction of DNA bending and, among 10 unique dinucleotide steps, we identified four dinucleotide steps with strong twist-bend coupling, the pyrimidine-purine dinucleotide steps of TA/TA, CG/CG, and CA/TG and the purine-purine dinucleotide step of GA/TC. This work suggests the sequence-dependent structural responses of DNA to strong mechanical deformation, providing new molecular-level insights into the structure and stability of sharply bent DNA minicircles for nanoscale applications.

DNA nanotechnology provides an avenue for the construction of programmable dynamic molecular systems

Self-assembled supramolecular structures in living cells and their dynamics underlie various cellular events, such as endocytosis, cell migration, intracellular transport, cell metabolism, and gene expression. Spatiotemporally regulated association/dissociation and generation/degradation of assembly components is one of the remarkable features of biological systems. The significant advancement in DNA nanotechnology over the last few decades has enabled the construction of various-shaped nanostructures via programmed self-assembly of sequence-designed oligonucleotides. These nanostructures can further be assembled into micrometer-sized structures, including ordered lattices, tubular structures, macromolecular droplets, and hydrogels. In addition to being a structural material, DNA is adopted to construct artificial molecular circuits capable of activating/inactivating or producing/decomposing target DNA molecules based on strand displacement or enzymatic reactions. In this review, we provide an overview of recent studies on artificially designed DNA-based self-assembled systems that exhibit dynamic features, such as association/dis-sociation of components, phase separation, stimulus responsivity, and DNA circuit-regulated structural formation. These biomacromolecule-based, bottom-up approaches for the construction of artificial molecular systems will not only throw light on bio-inspired nano/micro engineering, but also enable us to gain insights into how autonomy and adaptability of living systems can be realized.

3D DNA Nanostructures: The Nanoscale Architect

Structural DNA nanotechnology is a pioneering biotechnology that presents the opportunity to engineer DNA-based hardware that will mediate a profound interface to the nanoscale. To date, an enormous library of shaped 3D DNA nanostructures have been designed and assembled. Moreover, recent research has demonstrated DNA nanostructures that are not only static but can exhibit specific dynamic motion. DNA nanostructures have thus garnered significant research interest as a template for pursuing shape and motion-dependent nanoscale phenomena. Potential applications have been explored in many interdisciplinary areas spanning medicine, biosensing, nanofabrication, plasmonics, single-molecule chemistry, and facilitating biophysical studies. In this review, we begin with a brief overview of general and versatile design techniques for 3D DNA nanostructures as well as some techniques and studies that have focused on improving the stability of DNA nanostructures in diverse environments, which is pivotal for its reliable utilization in downstream applications. Our main focus will be to compile a wide body of existing research on applications of 3D DNA nanostructures that demonstrably rely on the versatility of their mechanical design. Furthermore, we frame reviewed applications into three primary categories, namely encapsulation, surface templating, and nanomechanics, that we propose to be archetypal shape- or motion-related functions of DNA nanostructures found in nanoscience applications. Our intent is to identify core concepts that may define and motivate specific directions of progress in this field as we conclude the review with some perspectives on the future.

Chemo-Mechanical Modulation of Cell Motions Using DNA Nanosprings

Cell motions such as migration and change in cellular morphology are essential activities for multicellular organism in response to environmental stimuli. These activities are a result of coordinated clustering/declustering of integrin molecules at the cell membrane. Here, we prepared DNA origami nanosprings to modulate cell motions by targeting the clustering of integrin molecules. Each nanospring was modified with arginyl-glycyl-aspartic acid (RGD) domains with a spacing such that when the nanospring is coiled, the RGD ligands trigger the clustering of integrin molecules, which changes cell motions. The coiling or uncoiling of the nanospring is controlled, respectively, by the formation or dissolution of an i-motif structure between neighboring piers in the DNA origami nanodevice. At slightly acidic pH (<6.5), the folding of the i-motif leads to the coiling of the nanospring, which inhibits the motion of HeLa cells. At neutrality (pH 7.4), the unfolding of the i-motif allows cells to resume mechanical movement as the nanospring becomes uncoiled. We anticipate that this pH-responsive DNA nanoassembly is valuable to inhibit the migration of metastatic cancer cells in acidic extracellular environment. Such a chemo-mechanical modulation provides a new mechanism for cells to mechanically respond to endogenous chemical cues.

Mechanical Flexibility of DNA: A Quintessential Tool for DNA Nanotechnology

The mechanical properties of DNA have enabled it to be a structural and sensory element in many nanotechnology applications. While specific base-pairing interactions and secondary structure formation have been the most widely utilized mechanism in designing DNA nanodevices and biosensors, the intrinsic mechanical rigidity and flexibility are often overlooked. In this article, we will discuss the biochemical and biophysical origin of double-stranded DNA rigidity and how environmental and intrinsic factors such as salt, temperature, sequence, and small molecules influence it. We will then take a critical look at three areas of applications of DNA bending rigidity. First, we will discuss how DNA's bending rigidity has been utilized to create molecular springs that regulate the activities of biomolecules and cellular processes. Second, we will discuss how the nanomechanical response induced by DNA rigidity has been used to create conformational changes as sensors for molecular force, pH, metal ions, small molecules, and protein interactions. Lastly, we will discuss how DNA's rigidity enabled its application in creating DNA-based nanostructures from DNA origami to nanomachines.

Engineering Aptamer Switches for Multifunctional Stimulus-Responsive Nanosystems

Although RNA and DNA are best known for their capacity to encode biological information, it has become increasingly clear over the past few decades that these biomolecules are also capable of performing other complex functions, such as molecular recognition (e.g., aptamers) and catalysis (e.g., ribozymes). Building on these foundations, researchers have begun to exploit the predictable base-pairing properties of RNA and DNA in order to utilize nucleic acids as functional materials that can undergo a molecular "switching" process, performing complex functions such as signaling or controlled payload release in response to external stimuli including light, pH, ligand-binding and other microenvironmental cues. Although this field is still in its infancy, these efforts offer exciting potential for the development of biologically based "smart materials". Herein, ongoing progress in the use of nucleic acids as an externally controllable switching material is reviewed. The diverse range of mechanisms that can trigger a stimulus response, and strategies for engineering those functionalities into nucleic acid materials are explored. Finally, recent progress is discussed in incorporating aptamer switches into more complex synthetic nucleic acid-based nanostructures and functionalized smart materials.

Programming the Curvatures in Reconfigurable DNA Domino Origami by Using Asymmetric Units

The DNA origami technique is a robust method for the design of DNA nanostructures with prescribed shapes, including complex curved geometries. In addition to static structures, dynamic DNA origami has been used to construct sophisticated nanomachines that can reconfigure their shapes in response to external stimuli. Here, we report a new method to design DNA origami structures that can transform between a noncurved conformation and curved conformation. The reconfigurable structures are developed on the basis of dynamic DNA domino origami, which can transform in a cascading process initiated by trigger DNA strands. The degree of curvature could be programmed by tuning the sizes of DNA units within the origami.

Computing the Elastic Mechanical Properties of Rodlike DNA Nanostructures

To study the elastic properties of rodlike DNA nanostructures, we perform long simulations of these structures using the oxDNA coarse-grained model. By analyzing the fluctuations in these trajectories, we obtain estimates of the bend and twist persistence lengths and the underlying bend and twist elastic moduli and couplings between them. Only on length scales beyond those associated with the spacings between the interhelix crossovers do the bending fluctuations behave like those of a wormlike chain. The obtained bending persistence lengths are much larger than that for double-stranded DNA and increase nonlinearly with the number of helices, whereas the twist moduli increase approximately linearly. To within the numerical error in our data, the twist-bend coupling constants are of order zero. That the bending persistence lengths that we obtain are generally somewhat higher than in experiment probably reflects both that the simulated origamis have no assembly defects and that the oxDNA extensional modulus for double-stranded DNA is too large.