Design and Characterization of Programmable DNA Nanotubes

DNA as a promising biomaterial for bone regeneration and potential mechanisms of action

DNA nanotechnology has created new possibilities for the use of DNA in tissue regeneration - an important advance for DNA use beyond its paradigmatic role as the hereditary biomacromolecule. Biomaterials containing synthetic or natural DNA have been proposed for several applications including drug and gene delivery, and more recently, as osteoconductive biomaterials. This review provides an in-depth discussion of studies that have used DNA-based materials for biomineralization and/or bone repair, with expansion on the topic of DNA hydrogels specifically, and the advantages they offer for advancing the field of bone regeneration. Four mechanisms of action for the osteoconductive capabilities of DNA-based materials are discussed, and a proposed model for degradation of these materials and its link to their osteoconductive properties is later presented. Finally, the review considers current limitations of DNA-based materials and summarizes important aspects that need to be addressed for future application of DNA nanotechnology in tissue repair. STATEMENT OF SIGNIFICANCE: Herein we summarize the developing field of DNA-based materials for biomineralization and bone repair, with a focus on DNA hydrogels. We first provide a comprehensive review of different forms of DNA-based materials described thus far which have been shown to enhance bone repair and mineralization (namely DNA coatings, DNA-containing pastes, DNA nanostructures and DNA hydrogels). Next, we describe four different mechanisms by which DNA-based materials could be exerting their osteogenic effect. Then, we propose a novel model that links DNA degradation and osteoconductivity. Lastly, we suggest possible research directions to enhance DNA-based materials for future clinical application. The suggested mechanisms and the proposed model can guide future research to better understand how DNA functions as a mineral- and bone-promoting molecule.

Vertical DNA Nanostructure Arrays: Facilitating Functionalization on Macro-Scale Surfaces

The capability for varied functionalization and precise control at the nanoscale are significant advantages of DNA nanostructures. In the assembly of DNA nanostructure, the surface-assisted growth method utilizing double-crossover (DX) tile structures facilitates nucleation at relatively low concentrations on the surface based on electrostatic interactions, thereby enabling crystal growth over large areas. However, in surface-assisted growth, the geometrical hindrance of vertical structures on the DX tile structure surface makes it challenging to conjugate DNA nanostructures into fabricated surfaces. Here, the surface-assisted growth method was employed to extend the DX tile growth for forming vertical structure arrays on the substrate, providing attachment sites for functionalization on uniformly covered substrates at the macroscopic scale. Additionally, the spacing of the vertical structure arrays was demonstrated to be controllable through the strategic design of the repeating unit tiles that construct the DX crystals.

Light-Modulated Self-Assembly of Synthetic Nanotubes

Artificial biomolecular polymers with the capacity to respond to stimuli are emerging as a key component to the development of living materials and synthetic cells. Here, we demonstrate artificial DNA tubular nanostructures that form in response to light in a dose-dependent manner. These nanotubes assemble from programmable DNA tile motifs that are engineered to include a UV-responsive domain so that UV irradiation activates nanotube self-assembly. We demonstrate that the nanotube formation speed can be tuned by adjusting the UV dose. We then couple the light-dependent activation of tiles with RNA transcription, making it possible to control nanotube formation via concurrent physical and biochemical stimuli. Finally, we illustrate how UV activation effectively controls nanotube assembly in confinement as a rudimentary stimulus-responsive cytoskeletal system that can achieve various conformations in a minimal synthetic cell. This study contributes new tile designs that are immediately useful to building biomolecular scaffolds with controllable dynamics in response to multiple stimuli.

Covalent Dynamic DNA Networks to Translate Multiple Inputs into Programmable Outputs

Inspired by naturally occurring protein dimerization networks, in which a set of proteins interact with each other to achieve highly complex input-output behaviors, we demonstrate here a fully synthetic DNA-based dimerization network that enables highly programmable input-output computations. Our DNA-based dimerization network consists of DNA oligonucleotide monomers modified with reactive moieties that can covalently bond with each other to form dimer outputs in an all-to-all or many-to-many fashion. By designing DNA-based input strands that can specifically sequester DNA monomers, we can control the size of the reaction network and thus fine-tune the yield of each DNA dimer output in a predictable manner. Thanks to the programmability and specificity of DNA-DNA interactions, we show that this approach can be used to control the yield of different dimer outputs using different inputs. The approach is also versatile and we demonstrate dimerization networks based on two distinct covalent reactions: thiol-disulfide and strain-promoted azide-alkyne cycloaddition (SPAAC) reactions. Finally, we show here that the DNA-based dimerization network can be used to control the yield of a functional dimer output, ultimately controlling the assembly and disassembly of DNA nanostructures. The covalent dynamic DNA networks shown here provide a way to convert multiple inputs into programmable outputs that can control a broader range of functions, including ones that mimic those of living cells.

Engineering Dynein Motors to Move on DNA Nanotube Tracks

The recent development of the DNA-binding domain (DBD)-dynein chimera motors with a dynein motor core and a DNA-binding domain has made it possible to move on DNA nanostructure tracks. In contrast to naturally occurring cytoskeletal filaments such as microtubules and actin filaments, DNA tracks can be programmed with structural properties such as length, stiffness, and circumference. There might be many advantages to using DNA as a track, for example, for applications in nanotechnology. However, care must be taken in design and motility assay conditions to ensure the successful operation of such novel motors; the novel motor system functions under conditions different from those commonly used in the field of natural biomolecular motors. Here, we describe the methods for designing DNA nanostructures and the conditions for motility assays in which the DBD-dynein motors translocate DNA nanotube tracks or move on them.

miR-21 Responsive Nanocarrier Targeting Ovarian Cancer Cells

In recent years, DNA origami-based nanocarriers have been extensively utilized for efficient cancer therapy. However, developing a nanocarrier capable of effectively protecting cargos such as RNA remains a challenge. In this study, we designed a compact and controllable DNA tubular origami (DTO) measuring 120 nm in length and 18 nm in width. The DTO exhibited appropriate structural characteristics for encapsulating and safeguarding cargo. Inside the DTO, we incorporated 20 connecting points to facilitate the delivery of cargoes to various ovarian and normal epithelial cell lines. Specifically, fluorescent-labeled DNA strands were attached to these sites as cargoes. The DTO was engineered to open upon encountering miR-21 through RNA/DNA strand displacement. Significantly, for the first time, we inhibited fluorescence using the compact DNA nanotube and observed dynamic fluorescent signals, indicating the controllable opening of DTO through live-cell imaging. Our results demonstrated that the DTO remained properly closed, exhibited effective internalization in ovarian cancer cells in vitro, showcasing marked differential expression of miR-21, and efficiently opened with short-term exposure to miR-21. Leveraging its autonomous behavior and compact design, the DTO emerges as a promising nanocarrier for various clinically relevant materials. It holds significant application prospects in anti-cancer therapy and the development of flexible biosensors.

A bioswitchable siRNA delivery system: RNAi therapy based on tetrahedral framework nucleic acids for bone defect repair

Craniofacial bone defects, caused by trauma, congenital abnormalities, or various diseases, present a significant challenge in regenerative medicine. One approach to addressing this problem is the use of RNA interference (RNAi) technology with small interfering RNA (siRNA). CKIP-1 is a negative regulatory molecule for bone formation. However, direct applications of CKIP-1 siRNA for bone defects are still limited. The instability and poor cellular uptake ability of CKIP-1 siRNA restrict its clinical applications. A new drug delivery system is critically needed to enhance the effectiveness and potential applications of CKIP-1 siRNA. Tetrahedral framework nucleic acid (tFNA) is a promising drug delivery system due to its stability and transport abilities. In this study, we developed a bioswitchable siRNA delivery system (BiRDS) based on tFNA to carry CKIP-1 siRNA and examined its effect on bone defect repair. siRNA was successfully loaded into the tFNA core, forming BiRDS, which improved siRNA stability and cellular uptake. After entering cells, BiRDS exposed siRNA, enhancing CKIP-1 silencing efficiency. This system significantly promoted osteogenic differentiation and bone regeneration in rat mandibular bone defects, offering a new strategy for bone regeneration therapy.

Exploring Framework Nucleic Acids: A Perspective on Their Cellular Applications

Cells are fundamental units of life. The coordination of cellular functions and behaviors relies on a cascade of molecular networks. Technologies that enable exploration and manipulation of specific molecular events in living cells with high spatiotemporal precision would be critical for pathological study, disease diagnosis, and treatment. Framework nucleic acids (FNAs) represent a novel class of nucleic acid materials characterized by their monodisperse and rigid nanostructure. Leveraging their exceptional programmability, convenient modification property, and predictable atomic-level architecture, FNAs have attracted significant attention in diverse cellular applications such as cell recognition, imaging, manipulation, and therapeutic interventions. In this perspective, we will discuss the utilization of FNAs in living cell systems while critically assessing the opportunities and challenges presented in this burgeoning field.

Developmental assembly of multi-component polymer systems through interconnected synthetic gene networks in vitro

Living cells regulate the dynamics of developmental events through interconnected signaling systems that activate and deactivate inert precursors. This suggests that similarly, synthetic biomaterials could be designed to develop over time by using chemical reaction networks to regulate the availability of assembling components. Here we demonstrate how the sequential activation or deactivation of distinct DNA building blocks can be modularly coordinated to form distinct populations of self-assembling polymers using a transcriptional signaling cascade of synthetic genes. Our building blocks are DNA tiles that polymerize into nanotubes, and whose assembly can be controlled by RNA molecules produced by synthetic genes that target the tile interaction domains. To achieve different RNA production rates, we use a strategy based on promoter "nicking" and strand displacement. By changing the way the genes are cascaded and the RNA levels, we demonstrate that we can obtain spatially and temporally different outcomes in nanotube assembly, including random DNA polymers, block polymers, and as well as distinct autonomous formation and dissolution of distinct polymer populations. Our work demonstrates a way to construct autonomous supramolecular materials whose properties depend on the timing of molecular instructions for self-assembly, and can be immediately extended to a variety of other nucleic acid circuits and assemblies.

Supramolecular materials constructed from synthetic glycopeptides via aqueous self-assembly and their bioapplications in immunotherapy

Synthetic glycopeptides capable of self-assembly in aqueous environments form a range of supramolecular nanostructures, such as nanoparticles and nanofibers, owing to their amphiphilic nature and the diverse structures of the saccharides introduced. These glycopeptide-based supramolecular materials are promising for immunotherapy applications because of their biocompatibility and multivalent saccharide display, which enhances lectin-saccharide interactions. This review highlights recent advances in the molecular design of synthetic glycopeptide-based supramolecular materials and their use as immunomodulatory agents.

Symmetry-Guided Inverse Design of Self-Assembling Multiscale DNA Origami Tilings

Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions between multiple particle species to target a user-specified complex structure or pattern. In this article, we develop a symmetry-based method to generate the interaction matrices that specify the assembly of two-dimensional tilings, which we illustrate using equilateral triangles. By exploiting the allowed 2D symmetries, we develop an algorithmic approach by which any periodic 2D tiling can be generated from an arbitrarily large number of subunit species, notably addressing an unmet challenge of engineering 2D crystals with periodicities that can be arbitrarily larger than the subunit size. To demonstrate the utility of our design approach, we encode specific interactions between triangular subunits synthesized by DNA origami and show that we can guide their self-assembly into tilings with a wide variety of symmetries, using up to 12 unique species of triangles. By conjugating specific triangles with gold nanoparticles, we fabricate gold-nanoparticle supracrystals whose lattice parameter spans up to 300 nm. Finally, to generate economical design rules, we compare the design economy of various tilings. In particular, we show that (1) higher symmetries allow assembly of larger unit cells with fewer subunits and (2) linear supracrystals can be designed more economically using linear primitive unit cells. This work provides a simple algorithmic approach to designing periodic assemblies, aiding in the multiscale assembly of supracrystals of nanostructured "meta-atoms" with engineered plasmonic functions.

Strategies to Reduce Promoter-Independent Transcription of DNA Nanostructures and Strand Displacement Complexes

Bacteriophage RNA polymerases, in particular T7 RNA polymerase (RNAP), are well-characterized and popular enzymes for many RNA applications in biotechnology both in vitro and in cellular settings. These monomeric polymerases are relatively inexpensive and have high transcription rates and processivity to quickly produce large quantities of RNA. T7 RNAP also has high promoter-specificity on double-stranded DNA (dsDNA) such that it only initiates transcription downstream of its 17-base promoter site on dsDNA templates. However, there are many promoter-independent T7 RNAP transcription reactions involving transcription initiation in regions of single-stranded DNA (ssDNA) that have been reported and characterized. These promoter-independent transcription reactions are important to consider when using T7 RNAP transcriptional systems for DNA nanotechnology and DNA computing applications, in which ssDNA domains often stabilize, organize, and functionalize DNA nanostructures and facilitate strand displacement reactions. Here we review the existing literature on promoter-independent transcription by bacteriophage RNA polymerases with a specific focus on T7 RNAP, and provide examples of how promoter-independent reactions can disrupt the functionality of DNA strand displacement circuit components and alter the stability and functionality of DNA-based materials. We then highlight design strategies for DNA nanotechnology applications that can mitigate the effects of promoter-independent T7 RNAP transcription. The design strategies we present should have an immediate impact by increasing the rate of success of using T7 RNAP for applications in DNA nanotechnology and DNA computing.

Economical routes to size-specific assembly of self-closing structures

Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target "self-limiting" assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity.

Cascadable-Controllable Self-Assembly DNA Tiles for Large-Scale DNA Logic Circuits

In the last few decades, DNA-based self-assembly tiles has become a hot field in research due to its special applications and advantages. The regularity and strong design methods comprise other DNA-based digital circuit design methods. In addition to the obvious advantages of this method, there are challenges in performing computations based on self-assembly tiles, which have hindered the development and construction of large computing circuits with this method. The first challenge is the creation of crystals from DNA molecules in the output, which has led to the impossibility of cascading. The second challenge of this method is the uncontrollability of the reactions of the tiles, which increases the percentage of computing errors. In this article, these two challenges have been solved by changing the structure of leading tiles so that without the activator strand, tiles remain inactive and cannot be connected to other tiles. Also, when the tiles are activated, single-strand DNA will be released after connecting to other tiles, which will be used as the output of the circuit. This output gives the possibility of cascading to self-assembly designed circuits. The method introduced in this article can be a beginning for the re-development of DNA-based circuit design with the self-assembly tile method.

Harnessing DNA origami's therapeutic potential for revolutionizing cardiovascular disease treatment: A comprehensive review

DNA origami is a cutting-edge nanotechnology approach that creates precise and detailed 2D and 3D nanostructures. The crucial feature of DNA origami is how it is created, which enables precise control over its size and shape. Biocompatibility, targetability, programmability, and stability are further advantages that make it a potentially beneficial technique for a variety of applications. The preclinical studies of sophisticated programmable nanomedicines and nanodevices that can precisely respond to particular disease-associated triggers and microenvironments have been made possible by recent developments in DNA origami. These stimuli, which are endogenous to the targeted disorders, include protein upregulation, pH, redox status, and small chemicals. Oncology has traditionally been the focus of the majority of past and current research on this subject. Therefore, in this comprehensive review, we delve into the intricate world of DNA origami, exploring its defining features and capabilities. This review covers the fundamental characteristics of DNA origami, targeting DNA origami to cells, cellular uptake, and subcellular localization. Throughout the review, we emphasised on elucidating the imperative for such a therapeutic platform, especially in addressing the complexities of cardiovascular disease (CVD). Moreover, we explore the vast potential inherent in DNA origami technology, envisioning its promising role in the realm of CVD treatment and beyond.

Synthetic DNA-based Swimmers Driven by Enzyme Catalysis

Here, we report DNA-based synthetic nanostructures decorated with enzymes (hereafter referred to as DNA-enzyme swimmers) that self-propel by converting the enzymatic substrate to the product in solution. The DNA-enzyme swimmers are obtained from tubular DNA structures that self-assemble spontaneously by the hybridization of DNA tiles. We functionalize these DNA structures with two different enzymes, urease and catalase, and show that they exhibit concentration-dependent movement and enhanced diffusion upon addition of the enzymatic substrate (i.e., urea and H2O2). To demonstrate the programmability of such DNA-based swimmers, we also engineer DNA strands that displace the enzyme from the DNA scaffold, thus acting as molecular "brakes" on the DNA swimmers. These results serve as a first proof of principle for the development of synthetic DNA-based enzyme-powered swimmers that can self-propel in fluids.

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Triggered contraction of self-assembled micron-scale DNA nanotube rings

Contractile rings are formed from cytoskeletal filaments during cell division. Ring formation is induced by specific crosslinkers, while contraction is typically associated with motor protein activity. Here, we engineer DNA nanotubes and peptide-functionalized starPEG constructs as synthetic crosslinkers to mimic this process. The crosslinker induces bundling of ten to hundred DNA nanotubes into closed micron-scale rings in a one-pot self-assembly process yielding several thousand rings per microliter. Molecular dynamics simulations reproduce the detailed architectural properties of the DNA rings observed in electron microscopy. Theory and simulations predict DNA ring contraction - without motor proteins - providing mechanistic insights into the parameter space relevant for efficient nanotube sliding. In agreement between simulation and experiment, we obtain ring contraction to less than half of the initial ring diameter. DNA-based contractile rings hold promise for an artificial division machinery or contractile muscle-like materials.

Engineering ssRNA tile filaments for (dis)assembly and membrane binding

Cytoskeletal protein filaments such as actin and microtubules confer mechanical support to cells and facilitate many cellular functions such as motility and division. Recent years have witnessed the development of a variety of molecular scaffolds that mimic such filaments. Indeed, filaments that are programmable and compatible with biological systems may prove useful in studying or substituting such proteins. Here, we explore the use of ssRNA tiles to build and modify filaments in vitro. We engineer a number of functionalities that are crucial to the function of natural proteins filaments into the ssRNA tiles, including the abilities to assemble or disassemble filaments, to tune the filament stiffness, to induce membrane binding, and to bind proteins. This work paves the way for building dynamic cytoskeleton-mimicking systems made out of rationally designed ssRNA tiles that can be transcribed in natural or synthetic cells.

Transient physics in the compression and mixing dynamics of two nanochannel-confined polymer chains

We use molecular dynamics (MD) simulation and nanofluidic experiments to probe the non-equilibrium transient physics of two nanochannel-confined polymers driven against a permeable barrier in a flow field. For chains with a persistence length P smaller than the channel diameter D, both simulation and experiment with dsDNA reveal nonuniform mixing of the two chains, with one chain dominating locally in what we term "aggregates." Aggregates undergo stochastic dynamics, persisting for a limited time, then disappearing and reforming. Whereas aggregate-prone mixing occurs immediately at sufficiently high flow speeds, chains stay segregated at intermediate flow for some time, often attempting to mix multiple times, before suddenly successfully mixing. Observation of successful mixing nucleation events in nanofluidic experiments reveal that they arise through a peculiar "back-propagation" mechanism whereby the upstream chain, closest to the barrier, penetrates and passes through the downstream chain (farthest from the barrier) moving against the flow direction. Simulations suggest that the observed back-propagation nucleation mechanism is favored at intermediate flow speeds and arises from a special configuration where the upstream chain exhibits one or more folds facing the downstream chain, while the downstream chain has an unfolded chain end facing upstream.

Light-Activated Assembly of DNA Origami into Dissipative Fibrils

Hierarchical DNA nanostructures offer programmable functions at scale, but making these structures dynamic, while keeping individual components intact, is challenging. Here we show that the DNA A-motif-protonated, self-complementary poly(adenine) sequences-can propagate DNA origami into one-dimensional, micron-length fibrils. When coupled to a small molecule pH regulator, visible light can activate the hierarchical assembly of our DNA origami into dissipative fibrils. This system is recyclable and does not require DNA modification. By employing a modular and waste-free strategy to assemble and disassemble hierarchical structures built from DNA origami, we offer a facile and accessible route to developing well-defined, dynamic, and large DNA assemblies with temporal control. As a general tool, we envision that coupling the A-motif to cycles of dissipative protonation will allow the transient construction of diverse DNA nanostructures, finding broad applications in dynamic and non-equilibrium nanotechnology.

Structural Description of Chiral E-Tiling DNA Nanotubes with the Chiral Indices (n,m) and Handedness Defined by Microscopic Imaging

In structural DNA nanotechnology, E-tiling DNA nanotubes are evidenced to be homogeneous in diameter and thus have great potential in biomedical applications such as cellular transport and communication, transmembrane ion/molecule channeling, and drug delivery. However, a precise structural description of chiral DNA nanotubes with chiral parameters was lacking, thus greatly hindering their application breadth and depth, until we recently raised and partly solved this problem. In this perspective, we summarize recent progress in defining the chiral indices and handedness of E-tiling DNA nanotubes by microscopic imaging, especially atomic force microscopy (AFM) imaging. Such a detailed understanding of the chiral structures of E-tiling DNA nanotubes will be very helpful in the future, on the one hand for engineering DNA nanostructures precisely, and, on the other, for realizing specific physicochemical properties and biological functions successfully.

Minimalist Design of Wireframe DNA Nanotubes: Tunable Geometry, Size, Chirality, and Dynamics

DNA nanotubes (NTs) have attracted extensive interest as artificial cytoskeletons for biomedical, synthetic biology, and materials applications. Here, we report the modular design and assembly of a minimalist yet robust DNA wireframe nanotube with tunable cross-sectional geometry, cavity size, chirality, and length, while using only four DNA strands. We introduce an h-motif structure incorporating double-crossover (DX) tile-like DNA edges to achieve structural rigidity and provide efficient self-assembly of h-motif-based DNA nanotube (H-NT) units, thus producing programmable, micrometer-long nanotubes. We demonstrate control of the H-NT nanotube length via short DNA modulators. Finally, we use an enzyme, RNase H, to take these structures out of equilibrium and trigger nanotube assembly at a physiologically relevant temperature, underlining future cellular applications. The minimalist H-NTs can assemble at near-physiological salt conditions and will serve as an easily synthesized, DNA-economical modular template for biosensors, plasmonics, or other functional materials and as cost-efficient drug-delivery vehicles for biomedical applications.

Motility of Synthetic Cells from Engineered Lipids

Synthetic cells are artificial systems that resemble natural cells. Significant efforts have been made over the years to construct synthetic protocells that can mimic biological mechanisms and perform various complex processes. These include compartmentalization, metabolism, energy supply, communication, and gene reproduction. Cell motility is also of great importance, as nature uses elegant mechanisms for intracellular trafficking, immune response, and embryogenesis. In this review, we discuss the motility of synthetic cells made from lipid vesicles and relevant molecular mechanisms. Synthetic cell motion may be classified into surface-based or solution-based depending on whether it involves interactions with surfaces or movement in fluids. Collective migration behaviors have also been demonstrated. The swarm motion requires additional mechanisms for intercellular signaling and directional motility that enable communication and coordination among the synthetic vesicles. In addition, intracellular trafficking for molecular transport has been reconstituted in minimal cells with the help of DNA nanotechnology. These efforts demonstrate synthetic cells that can move, detect, respond, and interact. We envision that new developments in protocell motility will enhance our understanding of biological processes and be instrumental in bioengineering and therapeutic applications.

Engineering DNA-based cytoskeletons for synthetic cells

The development and bottom-up assembly of synthetic cells with a functional cytoskeleton sets a major milestone to understand cell mechanics and to develop man-made machines on the nano- and microscale. However, natural cytoskeletal components can be difficult to purify, deliberately engineer and reconstitute within synthetic cells which therefore limits the realization of multifaceted functions of modern cytoskeletons in synthetic cells. Here, we review recent progress in the development of synthetic cytoskeletons made from deoxyribonucleic acid (DNA) as a complementary strategy. In particular, we explore the capabilities and limitations of DNA cytoskeletons to mimic functions of natural cystoskeletons like reversible assembly, cargo transport, force generation, mechanical support and guided polymerization. With recent examples, we showcase the power of rationally designed DNA cytoskeletons for bottom-up assembled synthetic cells as fully engineerable entities. Nevertheless, the realization of dynamic instability, self-replication and genetic encoding as well as contractile force generating motors remains a fruitful challenge for the complete integration of multifunctional DNA-based cytoskeletons into synthetic cells.

Timed Pulses in DNA Strand Displacement Reactions

Inspired by naturally occurring regulatory mechanisms that allow complex temporal pulse features with programmable delays, we demonstrate here a strategy to achieve temporally programmed pulse output signals in DNA-based strand displacement reactions (SDRs). To achieve this, we rationally designed input strands that, once bound to their target duplex, can be gradually degraded, resulting in a pulse output signal. We also designed blocker strands that suppress strand displacement and determine the time at which the pulse reaction is generated. We show that by controlling the degradation rate of blocker and input strands, we can finely control the delayed pulse output over a range of 10 h. We also prove that it is possible to orthogonally delay two different pulse reactions in the same solution by taking advantage of the specificity of the degradation reactions for the input and blocker strands. Finally, we show here two possible applications of such delayed pulse SDRs: the time-programmed pulse decoration of DNA nanostructures and the sequentially appearing and self-erasing formation of DNA-based patterns.

The Current Progress of Tetrahedral DNA Nanostructure for Antibacterial Application and Bone Tissue Regeneration

Recently, programmable assembly technologies have enabled the application of DNA in the creation of new nanomaterials with unprecedented functionality. One of the most common DNA nanostructures is the tetrahedral DNA nanostructure (TDN), which has attracted great interest worldwide due to its high stability, simple assembly procedure, high predictability, perfect programmability, and excellent biocompatibility. The unique spatial structure of TDN allows it to penetrate cell membranes in abundance and regulate cellular biological properties as a natural genetic material. Previous studies have demonstrated that TDNs can regulate various cellular biological properties, including promoting cells proliferation, migration and differentiation, inhibiting cells apoptosis, as well as possessing anti-inflammation and immunomodulatory capabilities. Furthermore, functional molecules can be easily modified at the vertices of DNA tetrahedron, DNA double helix structure, DNA tetrahedral arms or DNA tetrahedral cage structure, enabling TDN to be used as a nanocarrier for a variety of biological applications, including targeted therapies, molecular diagnosis, biosensing, antibacterial treatment, antitumor strategies, and tissue regeneration. In this review, we mainly focus on the current progress of TDN-based nanomaterials for antimicrobial applications, bone and cartilage tissue repair and regeneration. The synthesis and characterization of TDN, as well as the biological merits are introduced. In addition, the challenges and prospects of TDN-based nanomaterials are also discussed.

Flexibility Analysis of DNA Nanotubes with Prescribed Circumferences and Their Pearl-Necklace Assemblies with Gold Nanoclusters

DNA has been demonstrated as a powerful platform for the construction of inorganic nanoparticles (NPs) into complex three-dimensional assemblies. Despite extensive research, the physical fundamental details of DNA nanostructures and their assemblies with NPs remain obscure. Here, we report the identification and quantification of the assembly details of programmable DNA nanotubes with monodisperse circumferences of a 4, 5, 6, 7, 8, or 10 DNA helix and their pearl-necklace-like assemblies with ultrasmall gold nanoparticles, Au₂₅ nanoclusters (AuNCs), liganded by -S(CH₂)_nNH₃⁺ (n = 3, 6, 11). The flexibilities of DNA nanotubes, analyzed via statistical polymer physics analysis through atomic force microscopy (AFM), demonstrate that ∼2.8 power exponentially increased with the DNA helix number. Moreover, the short-length liganded AuS(CH₂)₃NH₃⁺ NCs were observed to be able to form pearl-necklace-like DNA-AuNC assemblies stiffened than neat DNA nanotubes, while long-length liganded AuS(CH₂)₆NH₃⁺ and AuS(CH₂)₁₁NH₃⁺ NCs could fragment DNA nanotubular structures, indicating that DNA-AuNC assembling can be precisely manipulated by customizing the hydrophobic domains of the AuNC nanointerfaces. We prove the advantages of polymer science concepts in unraveling useful intrinsic information on physical fundamental details of DNA-AuNC assembling, which facilitates DNA-metal nanocomposite construction.

Conformational dynamics and mechanical properties of biomimetic RNA, DNA, and RNA-DNA hybrid nanotubes: an atomistic molecular dynamics study

With the nanotechnology boom, artificially designed nucleic acid nanotubes have aroused interest due to their practical applications in nanorobotics, vaccine design, membrane channels, drug delivery, and force sensing. In this paper, computational study was performed to investigate the structural dynamics and mechanical properties of RNA nanotubes (RNTs), DNA nanotubes (DNTs), and RNA-DNA hybrid nanotubes (RDHNTs). So far, the structural and mechanical properties of RDHNTs have not been examined in experiments or theoretical calculations, and there is limited knowledge regarding these properties for RNTs. Here, the simulations were carried out using the equilibrium molecular dynamics (MD) and steered molecular dynamics (SMD) approaches. Using in-house scripting, we modeled hexagonal nanotubes composed of six double-stranded molecules connected by four-way Holliday junctions. Classical MD analyses were performed on the collected trajectory data to investigate structural properties. Analyses of the microscopic structural parameters of RDHNT indicated a structural transition from the A-form to a conformation between the A- and B-forms, which may be attributable to the increased rigidity of RNA scaffolds compared to DNA staples. Comprehensive research on the elastic mechanical properties was also conducted based on spontaneous thermal fluctuations of nanotubes and employing the equipartition theorem. The Young's modulus of RDHNT (E = 165 MPa) and RNT (E = 144 MPa) was found to be almost the same and nearly half of that found for DNT (E = 325 MPa). Furthermore, the results showed that RNT was more resistant to bending, torsional, and volumetric deformations than DNT and RDHNT. We also used non-equilibrium SMD simulations to acquire comprehensive knowledge of the mechanical response of nanotubes to tensile stress.

Building Large DNA Bundles via Controlled Hierarchical Assembly of DNA Tubes

Structural DNA nanotechnology is capable of fabricating designer nanoscale artificial architectures. Developing simple and yet versatile assembly methods to construct large DNA structures of defined spatial features and dynamic capabilities has remained challenging. Herein, we designed a molecular assembly system where DNA tiles can assemble into tubes and then into large one-dimensional DNA bundles following a hierarchical pathway. A cohesive link was incorporated into the tile to induce intertube binding for the formation of DNA bundles. DNA bundles with length of dozens of micrometers and width of hundreds of nanometers were produced, whose assembly was revealed to be collectively determined by cationic strength and linker designs (binding strength, spacer length, linker position, etc.). Furthermore, multicomponent DNA bundles with programmable spatial features and compositions were realized by using various distinct tile designs. Lastly, we implemented dynamic capability into large DNA bundles to realize reversible reconfigurations among tile, tube, and bundles following specific molecular stimulations. We envision this assembly strategy can enrich the toolbox of DNA nanotechnology for rational design of large-size DNA materials of defined features and properties that may be applied to a variety of fields in materials science, synthetic biology, biomedical science, and beyond.

Elasticity of a Grafted Rod-like Filament with Fluctuating Bending Stiffness

Quite often polymers exhibit different elastic behavior depending on the statistical ensemble (Gibbs vs. Helmholtz). This is an effect of strong fluctuations. In particular, two-state polymers, which locally or globally fluctuate between two classes of microstates, can exhibit strong ensemble inequivalence with negative elastic moduli (extensibility or compressibility) in the Helmholtz ensemble. Two-state polymers consisting of flexible beads and springs have been studied extensively. Recently, similar behavior was predicted in a strongly stretched wormlike chain consisting of a sequence of reversible blocks, fluctuating between two values of the bending stiffness (the so called reversible wormlike chain, rWLC). In this article, we theoretically analyse the elasticity of a grafted rod-like semiflexible filament which fluctuates between two states of bending stiffness. We consider the response to a point force at the fluctuating tip in both the Gibbs and the Helmholtz ensemble. We also calculate the entropic force exerted by the filament on a confining wall. This is done in the Helmholtz ensemble and, under certain conditions, it yields negative compressibility. We consider a two-state homopolymer and a two-block copolymer with two-state blocks. Possible physical realizations of such a system would be grafted DNA or carbon nanorods undergoing hybridization, or grafted F-actin bundles undergoing collective reversible unbinding.

Dynamic and Reversible Decoration of DNA-Based Scaffolds

An approach to achieving dynamic and reversible decoration of DNA-based scaffolds is demonstrated here. To do this, rationally engineered DNA tiles containing enzyme-responsive strands covalently conjugated to different molecular labels are employed. These strands are designed to be recognized and degraded by specific enzymes (i.e., Ribonuclease H, RNase H, or Uracil DNA Glycosylase, UDG) inducing their spontaneous de-hybridization from the assembled tile and replacement by a new strand conjugated to a different label. Multiple enzyme-responsive strands that specifically respond to different enzymes allow for dynamic, orthogonal, and reversible decoration of the DNA structures. As a proof-of-principle of the strategy, the possibility to orthogonally control the distribution of different labels (i.e., fluorophores and small molecules) on the same scaffold without crosstalk is demonstrated. By doing so, DNA scaffolds that display different antibody recognition patterns are obtained. The approach offers the possibility to control the decoration of higher-order supramolecular assemblies (including origami) with several functional moieties to achieve functional biomaterials with improved adaptability, precision, and sensing capabilities.

Systematic altering of semiflexible DNA-based polymer networks via tunable crosslinking

In order to understand and predict the mechanical behaviours of complex, soft biomaterials such as cells or stimuli-responsive hydrogels, it is important to connect how the nanoscale properties of their constituent components impact those of the bulk material. Crosslinked networks of semiflexible polymers are particularly ubiquitous, being underlying mechanical components of biological systems such as cells or ECM, as well as many synthetic or biomimetic materials. Cell-derived components such as filamentous biopolymers or protein crosslinkers are readily available and well-studied model systems. However, as evolutionarily derived materials, they are constrained to a fixed set of structural parameters such as the rigidity and size of the filaments, or the valency and strength of binding of crosslinkers forming inter-filament connections. By implementing a synthetic model system based on the self-assembly of DNA oligonucleotides into nanometer-scale tubes and simple crosslinking constructs, we used the thermodynamic programmability of DNA hybridization to explore the impact of binding affinity on bulk mechanical response. Stepwise tuning the crosslinking affinity over a range from transient to thermodynamically stable shows an according change in viscoelastic behaviour from loosely entangled to elastic, consistent with models accounting for generalized inter-filament interactions. While characteristic signatures of concentration-dependent changes in network morphology found in some other natural and synthetic filament-crosslinker systems were not apparent, the presence of a distinct elasticity increase within a narrow range of conditions points towards potential subtle alterations of crosslink-filament architecture. Here, we demonstrate a new synthetic approach for gaining a deeper understanding of both biological as well as engineered hydrogel systems.

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.

A Dynamic Control Center Based on a DNA Reaction Network for Programmable Building of DNA Nanostructures

DNA-based nanostructures allow for complex self-assembly with nanometer precision through the specificity of Watson-Crick base pairing, but network behavior-directed control of the kinetic process is less studied. Here we show how the DNA reaction network (DRN), which has emerged as a reliable and programmable way to implement artificial network dynamics, can be built as the control center of programmable nanostructures, allowing spatiotemporal control over the dynamic behavior of DNA nanotubes. We chose a common network motif in biological control systems, the feed-forward loop, as the model network and demonstrated that dynamic behaviors, such as self-tuning control and multilayer hierarchical assembly, could be programmed by constructing an inhibition network and an excitation network, separately, in buffer solution and inside protocells.

DNA lattice growth with single, double, and triple double-crossover boundaries by stepwise self-assembly

Construction of various nanostructures with nanometre-scale precision through various DNA building blocks depends upon self-assembly, base-pair complementarity and sequence programmability. During annealing, unit tiles are formed by the complementarity of base pairs in each strand. Enhancement of growth of target lattices is expected if seed lattices (i.e. boundaries for growth of target lattices) are initially present in a test tube during annealing. Although most processes for annealing DNA nanostructures adopt a one-step high temperature method, multi-step annealing provides certain advantages such as reusability of unit tiles and tuneability of lattice formation. We can construct target lattices effectively (through multi-step annealing) and efficiently (via boundaries) by multi-step annealing and combining boundaries. Here, we construct efficient boundaries made of single, double, and triple double-crossover DNA tiles for growth of DNA lattices. Two unit double-crossover DNA tile-based lattices and copy-logic implemented algorithmic lattices were introduced to test the growth of target lattices on boundaries. We used multi-step annealing to tune the formation of DNA crystals during fabrication of DNA crystals comprised of boundaries and target lattices. The formation of target DNA lattices was visualized using atomic force microscopy (AFM). The borders between boundaries and lattices in a single crystal were clearly differentiable from AFM images. Our method provides way to construct various types of lattices in a single crystal, which might generate various patterns and enhance the information capacity in a given crystal.

Programming rigidity into size-defined wireframe DNA nanotubes

Nanotubes built from DNA hold promise for several biological and materials applications, due to their high aspect ratio and encapsulation potential. A particularly appealing goal is to control the size, shape, and dynamic behaviour of DNA nanotubes with minimal design alteration, as nanostructures of varying morphologies and lengths have been shown to exhibit distinct cellular uptake, encapsulation behaviour, and in vivo biodistribution. Herein, we report a systematic investigation, combining experimental and computational design, to modulate the length, flexibility, and longitudinal patterns of wireframe DNA nanotubes. Subtle design changes govern the structure and properties of our nanotubes, which are built from a custom-made, long, and size-defined template strand to which DNA rungs and linkers are attached. Unlike DNA origami, these custom-made strands possess regions with repeating sequences at strategic locations, thereby reducing the number of strands necessary for assembly. Through strand displacement, the nanotubes can be reversibly altered between extended and collapsed morphologies. These design concepts enable fine-tuning of the nanotube stiffness and may pave the way for the development of designer nanotubes for a variety of applications, including the study of cellular internalization, biodistribution, and uptake mechanisms for structures of varied shapes and sizes.

Creating complex protocells and prototissues using simple DNA building blocks

Building synthetic protocells and prototissues hinges on the formation of biomimetic skeletal frameworks. Recreating the complexity of cytoskeletal and exoskeletal fibers, with their widely varying dimensions, cellular locations and functions, represents a major material hurdle and intellectual challenge which is compounded by the additional demand of using simple building blocks to ease fabrication and control. Here we harness simplicity to create complexity by assembling structural frameworks from subunits that can support membrane-based protocells and prototissues. We show that five oligonucleotides can anneal into nanotubes or fibers whose tunable thicknesses and lengths spans four orders of magnitude. We demonstrate that the assemblies' location inside protocells is controllable to enhance their mechanical, functional and osmolar stability. Furthermore, the macrostructures can coat the outside of protocells to mimic exoskeletons and support the formation of millimeter-scale prototissues. Our strategy could be exploited in the bottom-up design of synthetic cells and tissues, to the generation of smart material devices in medicine.

Multidimensional Honeycomb-like DNA Nanostructures Made of C-Motifs

Thanks to its remarkable properties of self-assembly and molecular recognition, DNA can be used in the construction of various dimensional nanostructures to serve as templates for decorating nanomaterials with nanometer-scale precision. Accordingly, this study discusses a design strategy for fabricating such multidimensional DNA nanostructures made of simple C-motifs. One-dimensional (1D) honeycomb-like tubes (1HTs) and two-dimensional (2D) honeycomb-like lattices (2HLs) were constructed using a C-motif with an arm length of 14 nucleotides (nt) at an angle of 240° along the counterclockwise direction. We designed and fabricated four different types of 1HTs and three different 2HLs. The study used atomic force microscopy to characterize the distinct topologies of the 1D and 2D DNA nanostructures (i.e., 1HTs and 2HLs, respectively). The width deviation of the 1HTs and height suppression percentage of the 2HLs were calculated and discussed. Our study can be provided to construct various dimensional DNA nanostructures easily with high efficiency.

Photocontrolled DNA nanotubes as stiffness tunable matrices for controlling cellular behavior

Cell behavior is determined by a variety of properties of the extracellular environment like ligand spacing, nanotopography, and matrix stiffness. Matrix stiffness changes occur during many biological processes like wound healing, tumorigenesis, and development. These spatio-temporal dynamic changes in stiffness can cause significant changes in cell morphology, cell signaling, migration, cytoskeleton etc. In this paper, we have created photocontrolled stiffness-tunable DNA nanotubes which can undergo reversible changes in their conformation upon UV and VIS irradiation. When used as a substrate for cell culture, the photocontrolled DNA nanotubes can tune the cell morphology of HeLa cells from a long spindle-shaped morphology with long filopodia protrusions to a round morphology with short filopodia-like extrusions. Such a photocontrolled nanosystem can give us deep insights into the cell-matrix interactions in the native extracellular matrix caused by nanoscopic changes in stiffness.

Design of supramolecular hybrid nanomaterials comprising peptide-based supramolecular nanofibers and in situ generated DNA nanoflowers through rolling circle amplification

The artificial construction of multicomponent supramolecular materials comprising plural supramolecular architectures that are assembled orthogonally from their constituent molecules has attracted growing attention. Here, we describe the design and development of multicomponent supramolecular materials by combining peptide-based self-assembled fibrous nanostructures with globular DNA nanoflowers constructed by the rolling circle amplification reaction. The orthogonally constructed architectures were dissected by fluorescence imaging using the selective fluorescence staining procedures adapted to this study. The present, unique hybrid materials developed by taking advantage of each supramolecular architecture based on their peptide and DNA functions may offer distinct opportunities to explore their bioapplications as a soft matrix.

Tuning the Roundabout of Four-Point-Star Tiles with the Core Arm Length of Three Half-Turns for 2D DNA Arrays

By rationally adjusting the weaving modes of point-star tiles, the curvature inherent in the tiles can be changed, and various DNA nanostructures can be assembled, such as planar wireframe meshes, perforated wireframe tubes, and curved wireframe polyhedra. Based on the weaving and tiling architectures for traditional point-star tiles with the core arm length at two DNA half-turns, we improved the weaving modes of our newly reported four-point-star tiles with the core arm length at three half-turns to adjust their curvature and rigidity for assembling 2D arrays of DNA grids and tubes. Following our previous terms and methods to analyze the structural details of E-tiling tubes, we used the chiral indices (n,m) to describe the most abundant tube of typical assemblies; especially, we applied both one-locus and/or dual-locus biotin/streptavidin (SA) labelling strategies to define the configurations of two specific tubes, along with the absolute conformations of their component tiles. Such structural details of the DNA tubes composed of tiles with addressable concave and convex faces and packing directions should help us understand their physio-chemical and biological properties, and therefore promote their applications in drug delivery, biocatalysis, biomedicine, etc.

Elasticity of Semiflexible ZigZag Nanosprings with a Point Magnetic Moment

Kinks can appear along the contour of semiflexible polymers (biopolymers or synthetic ones), and they affect their elasticity and function. A regular sequence of alternating kink defects can form a semiflexible nanospring. In this article, we theoretically analyze the elastic behavior of such a nanospring with a point magnetic dipole attached to one end while the other end is assumed to be grafted to a rigid substrate. The rod-like segments of the nanospring are treated as weakly bending wormlike chains, and the propagator (Green's function) method is used in order to calculate the conformational and elastic properties of this system. We analytically calculate the distribution of orientational and positional fluctuations of the free end, the force-extension relation, as well as the compressional force that such a spring can exert on a planar wall. Our results show how the magnetic interaction affects the elasticity of the semiflexible nanospring. This sensitivity, which is based on the interplay of positional and orientational degrees of freedom, may prove useful in magnetometry or other applications.

Chiral DNA Nanotubes Self-Assembled from Building Blocks with Tailorable Curvature and Twist

DNA nanotubes with prescribed geometry could allow for nanomaterial organization with designed optical or electrical function. As one of the dominating driving forces for DNA nanotube assembly, intrinsic curvature and twist of building blocks can be induced by bending deformation and twisting deformation. However, it is still unknown that how bending and twisting design on nanoscale building blocks affects the geometry of DNA tubes with micrometer length. Here, through targeted base pair deletion or insertion, the amount of bending deformation in building blocks is modulated by length gradient and the amount of twisting deformation is modulated by average twist density. This work systematically explores the independent effect and synergistic effect of two types of deformation on tube geometry, including diameter, chirality, and helical angles, via a streptavidin-labeling technique. The design rules enable the construction of DNA nanotubes with prescribed chirality and tailored diameters.

Growth Rate and Thermal Properties of DNA Origami Filaments

Synthetic DNA filaments exploit the programmability of the individual units and their predictable self-association to mimic the structural and dynamic features of natural protein filaments. Among them, DNA origami filamentous structures are of particular interest, due to the versatility of morphologies, mechanical properties, and functionalities attainable. We here explore the thermodynamic and kinetic properties of linear structures grown from a ditopic DNA origami unit, i.e., a monomer with two distinct interfaces, and employ either base-hybridization or base-stacking interactions to trigger the dimerization and polymerization process. By observing the temporal evolution of the system toward equilibrium, we reveal kinetic aspects of filament growth that cannot be easily captured by postassembly studies. Our work thus provides insights into the thermodynamics and kinetics of hierarchical DNA origami assembly and shows how it can be mastered by the anisotropy of the building unit and its self-association mode.

Fueling DNA Self-Assembly via Gel-Released Regulators

The development of responsive, multicomponent molecular materials requires means to physically separate yet easily couple distinct processes. Here we demonstrate methods to use molecules and reactions loaded into microliter-sized polyacrylamide hydrogels (mini-gels) to control the dynamic self-assembly of DNA nanotubes. We first characterize the UV-mediated release of DNA molecules from mini-gels, changing diffusion rates and minimizing spontaneous leakage of DNA. We then demonstrate that mini-gels can be used as compartments for storage and release of DNA that mediates the assembly or disassembly of DNA nanotubes in a one-pot process and that the speed of DNA release is controlled by the mini-gel porosity. With this approach, we achieve control of assembly and disassembly of nanotubes with distinct kinetics, including a finite delay that is obtained by loading distinct DNA regulators into distinct mini-gels. We finally show that mini-gels can also host and localize enzymatic reactions, by transcribing RNA regulators from synthetic genes loaded in the mini-gels, with diffusion of RNA to the aqueous phase resulting in the activation of self-assembly. Our experimental data are recapitulated by a mathematical model that describes the diffusion of DNA molecules from the gel phase to the aqueous phase in which they control self-assembly of nanotubes. Looking forward, DNA-loaded mini-gels may be further miniaturized and patterned to build more sophisticated storage compartments for use within multicomponent, complex biomolecular materials relevant for biomedical applications and artificial life.

Geometrically programmed self-limited assembly of tubules using DNA origami colloids

Nature is replete with self-assembled materials that have one or more self-limited dimensions, including shells, tubules, and fibers. Despite significant advances in making nanometer- and micrometer-scale subunits, the programmable assembly of similar self-limiting architectures from synthetic components has remained largely out of reach. In this article, we create geometrically programmed subunits using DNA origami and study their assembly into tubules with a self-limited width. We show that the average self-limited dimension can be tuned by changing the local curvature encoded in a single subunit. Exploiting the programmability of our system, we further test the tradeoffs between fidelity and complexity embodied by two paradigms for self-limited assembly: self-closure through programmed curvature and addressable assembly through programmed specific interactions.

Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are needed. To address this challenge, we explore the tradeoffs between addressable assembly and self-closing assembly of a specific class of self-limiting structures: cylindrical tubules. We make triangular subunits using DNA origami that have specific, valence-limited interactions and designed binding angles, and we study their assembly into tubules that have a self-limited width that is much larger than the size of an individual subunit. In the simplest case, the tubules are assembled from a single component by geometrically programming the dihedral angles between neighboring subunits. We show that the tubules can reach many micrometers in length and that their average width can be prescribed through the dihedral angles. We find that there is a distribution in the width and the chirality of the tubules, which we rationalize by developing a model that considers the finite bending rigidity of the assembled structure as well as the mechanism of self-closure. Finally, we demonstrate that the distributions of tubules can be further sculpted by increasing the number of subunit species, thereby increasing the assembly complexity, and demonstrate that using two subunit species successfully reduces the number of available end states by half. These results help to shed light on the roles of assembly complexity and geometry in self-limited assembly and could be extended to other self-limiting architectures, such as shells, toroids, or triply periodic frameworks.

Ray Optics for Gliders

Control of self-propelled particles is central to the development of many microrobotic technologies, from dynamically reconfigurable materials to advanced lab-on-a-chip systems. However, there are few physical principles by which particle trajectories can be specified and can be used to generate a wide range of behaviors. Within the field of ray optics, a single principle for controlling the trajectory of light─Snell's law─yields an intuitive framework for engineering a broad range of devices, from microscopes to cameras and telescopes. Here we show that the motion of self-propelled particles gliding across a resistance discontinuity is governed by a variant of Snell's law, and develop a corresponding ray optics for gliders. Just as the ratio of refractive indexes sets the path of a light ray, the ratio of resistance coefficients is shown to determine the trajectories of gliders. The magnitude of refraction depends on the glider's shape, in particular its aspect ratio, which serves as an analogue to the wavelength of light. This enables the demixing of a polymorphic, many-shaped, beam of gliders into distinct monomorphic, single-shaped, beams through a friction prism. In turn, beams of monomorphic gliders can be focused by spherical and gradient friction lenses. Alternatively, the critical angle for total internal reflection can be used to create shape-selective glider traps. Overall our work suggests that furthering the analogy between light and microscopic gliders may be used for sorting, concentrating, and analyzing self-propelled particles.