Self‐Assembly of Complex DNA Tessellations by Using Low‐Symmetry Multi‐arm DNA Tiles

Three-Point-Star Deoxyribonucleic Acid Tiles with the Core Arm Length at Three Half-Turns for Two-Dimensional Archimedean Tilings and Beyond

2D Archimedean tiling and complex tessellation patterns assembled from soft materials including modular DNA tiles have attracted great interest because of their specific structures and potential applications in nanofabrication, nanoelectronics, nanophotonics, biomedical sensing, drug delivery, therapeutics, etc. Traditional three- and four-point-star DNA tiles with the core arm length at two half-turns (specified as three- and four-point-star-E previously and abbreviated as 3PSE and 4PSE tiles here) have been applied to assemble intricate tessellations through tuning the size of inserted nT (n = 1-7, T is thymine) loops on helper strands at the tile center. Following our recent findings using a new type of four-point-star tiles with the core arm length at three half-turns (specified as four-point-star-O previously and abbreviated as 4PSO tiles here) to assemble DNA tubes and flat 2D arrays, we report here the cross-hybridization weaving architectures at the tile center to construct three new 3PSO tiles with circular DNA oligonucleotides of 96-nt (nucleotides) serving as the scaffolds, further the monotonous and combinatory E- and O-tilings on one type of 3PSO tiles to create 2D Archimedean tiling patterns (6.6.6) and (4.8.8), and finally, the combination of 3PSO with 4PSO as well as 2PSO tiles to tile into complex tessellation patterns. The easy realization of regular and intricate DNA tessellations with 2-4PSO tiles not only richens the fundamental DNA modules and complex DNA nanostructures in types but also broadens the potential application scopes of DNA nanostructures in nanofabrication, DNA computing, biomedicine, etc.

Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T = 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.

DNA T-shaped crossover tiles for 2D tessellation and nanoring reconfiguration

DNA tiles serve as the fundamental building blocks for DNA self-assembled nanostructures such as DNA arrays, origami, and designer crystals. Introducing additional binding arms to DNA crossover tiles holds the promise of unlocking diverse nano-assemblies and potential applications. Here, we present one-, two-, and three-layer T-shaped crossover tiles, by integrating T junction with antiparallel crossover tiles. These tiles carry over the orthogonal binding directions from T junction and retain the rigidity from antiparallel crossover tiles, enabling the assembly of various 2D tessellations. To demonstrate the versatility of the design rules, we create 2-state reconfigurable nanorings from both single-stranded tiles and single-unit assemblies. Moreover, four sets of 4-state reconfiguration systems are constructed, showing effective transformations between ladders and/or rings with pore sizes spanning ~20 nm to ~168 nm. These DNA tiles enrich the design tools in nucleic acid nanotechnology, offering exciting opportunities for the creation of artificial dynamic DNA nanopores.

Kinetics-accelerated one-step detection of MicroRNA through spatially localized reactions based on DNA tile self-assembly

The localization of isothermal amplification systems has elicited extensive attention due to the enhanced reaction kinetics when detecting ultra-trace small-molecule nucleic acids. Therefore, the seek for an appropriate localization cargo of spatially confined reactions is urgent. Herein, we have developed a novel approach to localize the catalytic hairpin assembly (CHA) system into the DNA tile self-assembly nanostructure. Thanks to the precise programming and robust probe loading capacity, this strategy achieved a 2.3 × 10⁵-fold higher local reaction concentration than a classical CHA system with enhanced reaction kinetics in theory. From the experimental results, this strategy could reach the reaction plateau faster and get access to a magnified effect of 1.57-6.99 times higher in the linear range of microRNA (miRNA) than the simple CHA system. Meanwhile, this strategy satisfied the demand for the one-step detection of miRNA in cell lysates at room temperature with good sensitivity and specificity. These features indicated its excellent potential for ultra-trace molecule detection in clinical diagnosis and provided new insights into the field of bioassays based on DNA tile self-assembly nanotechnology.

Two-Dimensional Excitonic Networks Directed by DNA Templates as an Efficient Model Light-Harvesting and Energy Transfer System

Photosynthetic organisms organize discrete light-harvesting complexes into large-scale networks to facilitate efficient light collection and utilization. Inspired by nature, herein, synthetic DNA templates were used to direct the formation of dye aggregates with a cyanine dye, K21, into discrete branched photonic complexes, and two-dimensional (2D) excitonic networks. The DNA templates ranged from four-arm DNA tiles, ≈10 nm in each arm, to 2D wireframe DNA origami nanostructures with different geometries and varying dimensions up to 100×100 nm. These DNA-templated dye aggregates presented strongly coupled spectral features and delocalized exciton characteristics, enabling efficient photon collection and energy transfer. Compared to the discrete branched photonic systems templated on individual DNA tiles, the interconnected excitonic networks showed approximately a 2-fold increase in energy transfer efficiency. This bottom-up assembly strategy paves the way to create 2D excitonic systems with complex geometries and engineered energy pathways.

Finite Assembly of Three-Dimensional DNA Hierarchical Nanoarchitectures through Orthogonal and Directional Bonding

Reliable orthogonal bonding with precise and flexible orientation control would be ideal for building finite complex nanostructures via self-assembly. Employing a three-dimensional (3D) DNA origami, hexagonal prism DNA origami (HDO), as building block, we demonstrate it is practical to construct finite hierarchical nanoarchitectures with complicated conformations through orthogonal and directional bonding. The as-designed HDO building block has twelve prescribed directional valences in 3D space and each of them supports two opposite orientations, yielding the capability to generate abundant directional bonding. Meanwhile, we minimize the thorny non-specific interactions among HDOs and enable the orthogonal bonding between any two valences based on self-similar designing. Consequently, various hierarchical nanostructures are prepared at will simply by the combination of HDOs with appropriate valences. We believe this route towards hierarchically assembly is inspiring and hope it will facilitate the fabrication of functional superstructures.

Supramolecular tessellations by the exo-wall interactions of pagoda[4]arene

Supramolecular tessellation has gained increasing interest in supramolecular chemistry for its structural aesthetics and potential applications in optics, magnetics and catalysis. In this work, a new kind of supramolecular tessellations (STs) have been fabricated by the exo-wall interactions of pagoda[4]arene (P4). ST with rhombic tiling pattern was first constructed by P4 itself through favorable π···π interactions between anthracene units of adjacent P4. Notably, various highly ordered STs with different tiling patterns have been fabricated based on exo-wall charge transfer interactions between electron-rich P4 and electron-deficient guests including 1,4-dinitrobenzene, terephthalonitrile and tetrafluoroterephthalonitrile. Interestingly, solvent modulation and guest selection played a crucial role in controlling the molecular arrangements in the co-crystal superstructures. This work not only proves that P4 is an excellent macrocyclic building block for the fabrication of various STs, but also provides a new perspective and opportunity for the design and construction of supramolecular two-dimensional organic materials.

Supramolecular tessellation has gained increasing interest in supramolecular chemistry for its structural aesthetics and potential applications in optics, magnetics and catalysis. Here, the authors expand the examples of molecular building blocks for supramolecular tessellation and fabricate supramolecular tessellations using the exo-wall interactions of pagoda[4]arene.

Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.

Constructing and Transferring Two-Dimensional Tessellation Kagome Lattices via Chemical Reactions on Cu(111) Surface

Two-dimensional (2D) tessellation of organic species acquired increased interests recently because of their potential applications in physics, biology, and chemistry. 2D tessellations have been successfully constructed on surfaces via various intermolecular interactions. However, the transformation between 2D tessellation lattices has been rarely reported. Herein, we successfully fabricated two types of Kagome lattices on Cu(111). The former phase exhibits (3,6,3,6) Kagome lattices, which are stabilized via the intermolecular hydrogen bond interactions. The latter phase is formed through direct chemical transferring from the former one maintaining almost the same Kagome lattices, except for that the unit cell rotates for 4°. Detailed scanning tunneling microscopy and density functional calculation studies reveal that the chemical transformation is achieved by the formation of the N-Cu-N metal-organic bonds via dehydrogenation reactions of the amines.

Stretching DNA origami: effect of nicks and Holliday junctions on the axial stiffness

The axial stiffness of DNA origami is determined as a function of key nanostructural characteristics. Different constructs of two-helix nanobeams with specified densities of nicks and Holliday junctions are synthesized and stretched by fluid flow. Implementing single particle tracking to extract force–displacement curves enables the measurement of DNA origami stiffness values at the enthalpic elasticity regime, i.e. for forces larger than 15 pN. Comparisons between ligated and nicked helices show that the latter exhibit nearly a two-fold decrease in axial stiffness. Numerical models that treat the DNA helices as elastic rods are used to evaluate the local loss of stiffness at the locations of nicks and Holliday junctions. It is shown that the models reproduce the experimental data accurately, indicating that both of these design characteristics yield a local stiffness two orders of magnitude smaller than the corresponding value of the intact double-helix. This local degradation in turn leads to a macroscopic loss of stiffness that is evaluated numerically for multi-helix DNA bundles.

Insights into the Structure and Energy of DNA Nanoassemblies

Since the pioneering work of Ned Seeman in the early 1980s, the use of the DNA molecule as a construction material experienced a rapid growth and led to the establishment of a new field of science, nowadays called structural DNA nanotechnology. Here, the self-recognition properties of DNA are employed to build micrometer-large molecular objects with nanometer-sized features, thus bridging the nano- to the microscopic world in a programmable fashion. Distinct design strategies and experimental procedures have been developed over the years, enabling the realization of extremely sophisticated structures with a level of control that approaches that of natural macromolecular assemblies. Nevertheless, our understanding of the building process, i.e., what defines the route that goes from the initial mixture of DNA strands to the final intertwined superstructure, is, in some cases, still limited. In this review, we describe the main structural and energetic features of DNA nanoconstructs, from the simple Holliday junction to more complicated DNA architectures, and present the theoretical frameworks that have been formulated until now to explain their self-assembly. Deeper insights into the underlying principles of DNA self-assembly may certainly help us to overcome current experimental challenges and foster the development of original strategies inspired to dissipative and evolutive assembly processes occurring in nature.

Complex k-uniform tilings by a simple bitopic precursor self-assembled on Ag(001) surface

The realization of complex long-range ordered structures in a Euclidean plane presents a significant challenge en route to the utilization of their unique physical and chemical properties. Recent progress in on-surface supramolecular chemistry has enabled the engineering of regular and semi-regular tilings, expressing translation symmetric, quasicrystalline, and fractal geometries. However, the k-uniform tilings possessing several distinct vertices remain largely unexplored. Here, we show that these complex geometries can be prepared from a simple bitopic molecular precursor - 4,4'-biphenyl dicarboxylic acid (BDA) - by its controlled chemical transformation on the Ag(001) surface. The realization of 2- and 3-uniform tilings is enabled by partially carboxylated BDA mediating the seamless connection of two distinct binding motifs in a single long-range ordered molecular phase. These results define the basic self-assembly criteria, opening way to the utilization of complex supramolecular tilings.

Engineering Lipid Membranes with Programmable DNA Nanostructures

Lipid and DNA are abundant biomolecules with critical functions in cells. The water-insoluble, amphipathic lipid molecules are best known for their roles in energy storage (e.g. as triglyceride), signaling (e.g. as sphingolipid), and compartmentalization (e.g. by forming membrane-enclosed bodies). The soluble, highly negatively charged DNA, which stores cells' genetic information, has proven to be an excellent material for constructing programmable nanostructures in vitro thanks to its self-assembling capabilities. These two seemingly distant molecules make contact within cell nuclei, often via lipidated proteins, with proposed functions of modulating chromatin structures. Carefully formulated lipid/DNA complexes are promising reagents for gene therapy. The past few years saw an emerging research field of interfacing DNA nanostructures with lipid membranes, with an overarching goal of generating DNA/lipid hybrid materials that possess novel and controllable structure, dynamics, and function. An arsenal of DNA-based tools has been created to coat, mold, deform, and penetrate lipid bilayers, affording us the ability to manipulate membranes with nanoscopic precision. These membrane engineering methods not only enable quantitative biophysical studies, but also open new opportunities in synthetic biology (e.g. artificial cells) and therapeutics (e.g. drug delivery).

Patterning Porous Networks through Self-Assembly of Programmed Biomacromolecules

Two-dimensional (2D) porous networks are of great interest for the fabrication of complex organized functional materials for potential applications in nanotechnologies and nanoelectronics. This review aims at providing an overview of bottom-up approaches towards the engineering of 2D porous networks by using biomacromolecules, with a particular focus on nucleic acids and proteins. The first part illustrates how the advancements in DNA nanotechnology allowed for the attainment of complex ordered porous two-dimensional DNA nanostructures, thanks to a biomimetic approach based on DNA molecules self-assembly through specific hydrogen-bond base pairing. The second part focuses the attention on how polypeptides and proteins structural properties could be used to engineer organized networks templating the formation of multifunctional materials. The structural organization of all examples is discussed as revealed by scanning probe microscopy or transmission electron microscopy imaging techniques.

Supramolecular Tessellations at Surfaces by Vertex Design

Assembly and tessellation of organic species at surfaces are important for the design of advanced materials, particularly for the development of spontaneous self-assemblies of supramolecular systems of increasing complexity. However, there are few examples where the ability to steer the system between supramolecular tessellations has been achieved. Here, we demonstrate a series of steps to reduce and then restore molecular symmetry; those variations impact vertex symmetry and thus generate a series of tessellations that reflect the molecular symmetry. We deposit 4,4'-dihydroxybiphenyl on the Ag(111) surface, then anneal at specific temperatures to achieve stepwise dehydrogenation of the terminal hydroxyls. The symmetry of tessellation vertices in the self-assembled structure also changes, as characterized by scanning tunneling microscopy and synchrotron radiation photoemission spectroscopy. This control over vertex geometry and spontaneous tessellation structure extends our understanding of supramolecular design control and advances architectural complexity for the development of functional surfaces.

Exotic Vortex Lattices in Binary Repulsive Superfluids

We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m_{1}≠m_{2}. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m_{2}/m_{1}=2 and list a number of geometries that are found for higher integer mass ratios.

Mineralization of magnetic nano-tape in self-organized nanospace composed of nucleopeptides and peptides

Self-organization based on specific interactions has been actively studied for the formation of highly ordered and hierarchical structures on the molecular scale.

Designing Molecular Building Blocks for the Self-assembly of Complex Porous Networks

The creation of molecular or colloidal building blocks which can self-assemble into complex, ordered porous structures has been long sought-after, and so are the guiding principles behind this creation. The pursuit of this goal has led to the creation of novel classes of materials like metal organic frameworks (MOFs) and covalent organic frameworks (COFs). In theory, a tremendous number of structures can be formed by these materials due to the variety of geometries available to their building blocks. However, most realized crystal structures tend to be simple or homoporous and typically assemble from building blocks with high degrees of symmetry. Building blocks with low degrees of symmetry suitable for assembly into the more complex structures tend to assemble into polymorphous or disordered structures instead. In this work, we use Monte Carlo simulations of patchy vertex-like building blocks to show how the addition of chemical specificity via orthogonally reacting functional sites can allow vertex-like building blocks with even asymmetric geometries to self-assemble into ordered crystallites of various complex structures. In addition to demonstrating the utility of such a strategy in creating ordered, heteroporous structures, we also demonstrate that it can be used as a means for tuning specific features of the crystal structure, accomplishing such aims as the control of relative pore sizes. We also discuss heuristics for properly designing molecules so that they can assemble into target structures.

Evolution of Structural DNA Nanotechnology

The research field entitled structural DNA nanotechnology emerged in the beginning of the 1980s as the first immobile synthetic nucleic acid junctions were postulated and demonstrated. Since then, the field has taken huge leaps toward advanced applications, especially during the past decade. This Progress Report summarizes how the controllable, custom, and accurate nanostructures have recently evolved together with powerful design and simulation software. Simultaneously they have provided a significant expansion of the shape space of the nanostructures. Today, researchers can select the most suitable fabrication methods, and design paradigms and software from a variety of options when creating unique DNA nanoobjects and shapes for a plethora of implementations in materials science, optics, plasmonics, molecular patterning, and nanomedicine.

Optical Properties of Vibronically Coupled Cy3 Dimers on DNA Scaffolds

We examine the effect of electronic coupling on the optical properties of Cy3 dimers attached to DNA duplexes as a function of base pair (bp) separation using steady-state and time-resolved spectroscopy. For close Cy3-Cy3 separations, 0 and 1 bp between dyes, intermediate to strong electronic coupling is revealed by modulation of the absorption and fluorescence properties including spectral band shape, peak wavelength, and excited-state lifetime. Using a vibronic exciton model, we estimate coupling strengths of 150 and 266 cm^-1 for the 1 and 0 bp separations, respectively, which are comparable to those found in natural light-harvesting complexes. For the strongest electronic coupling (0 bp separation), we observe that the absorption band shape is strongly affected by the base pairs that surround the dyes, where more strongly hydrogen-bonded G-C pairs produce a red-shifted absorption spectrum consistent with a J-type dimer. This effect is studied theoretically using molecular dynamics simulation, which predicts an in-line dye configuration that is consistent with the experimental J-type spectrum. When the Cy3 dimers are in a standard aqueous buffer, the presence of relatively strong electronic coupling is accompanied by decreased fluorescence lifetime, suggesting that it promotes nonradiative relaxation in cyanine dyes. However, we show that the use of a viscous solvent can suppress this nonradiative recombination and thereby restore the dimer fluorescent emission. Ultrafast transient absorption measurements of Cy3 dimers in both standard aqueous buffer and viscous glycerol buffer suggest that sufficiently strong electronic coupling increases the probability of excited-state relaxation through a dark state that is related to Cy3 torsional motion.

Structural DNA Nanotechnology: Artificial Nanostructures for Biomedical Research

Structural DNA nanotechnology utilizes synthetic or biologic DNA as designer molecules for the self-assembly of artificial nanostructures. The field is founded upon the specific interactions between DNA molecules, known as Watson-Crick base pairing. After decades of active pursuit, DNA has demonstrated unprecedented versatility in constructing artificial nanostructures with significant complexity and programmability. The nanostructures could be either static, with well-controlled physicochemical properties, or dynamic, with the ability to reconfigure upon external stimuli. Researchers have devoted considerable effort to exploring the usability of DNA nanostructures in biomedical research. We review the basic design methods for fabricating both static and dynamic DNA nanostructures, along with their biomedical applications in fields such as biosensing, bioimaging, and drug delivery.

Complex supramolecular interfacial tessellation through convergent multi-step reaction of a dissymmetric simple organic precursor

Interfacial supramolecular self-assembly represents a powerful tool for constructing regular and quasicrystalline materials. In particular, complex two-dimensional molecular tessellations, such as semi-regular Archimedean tilings with regular polygons, promise unique properties related to their nontrivial structures. However, their formation is challenging, because current methods are largely limited to the direct assembly of precursors, that is, where structure formation relies on molecular interactions without using chemical transformations. Here, we have chosen ethynyl-iodophenanthrene (which features dissymmetry in both geometry and reactivity) as a single starting precursor to generate the rare semi-regular (3.4.6.4) Archimedean tiling with long-range order on an atomically flat substrate through a multi-step reaction. Intriguingly, the individual chemical transformations converge to form a symmetric alkynyl-Ag-alkynyl complex as the new tecton in high yields. Using a combination of microscopy and X-ray spectroscopy tools, as well as computational modelling, we show that in situ generated catalytic Ag complexes mediate the tecton conversion.

Irregular model DNA particles self-assemble into a regular structure

DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling. Both networks are built from a single type of vertex. Here we use analytic theory and equilibrium and dynamic simulation to show that a model particle, whose rotational properties lie between those of the vertices of the 6.6.6 and 4.8.8 networks, can self-assemble into a network built from three types of vertex. Important in forming this network is the ability of the particle to rotate when bound, thereby allowing the formation of more than one type of binding motif. The network in question is equivalent to a false tiling, a periodic structure built from irregular polygons, and possesses 40 particles in its unit cell. The emergence of this complex structure, whose symmetry properties are not obviously related to those of its constituent particles, highlights the potential for creating new structures from simple variants of existing nanoparticles.

DNA nanotubes assembled from tensegrity triangle tiles with circular DNA scaffolds

Using small circular DNA molecules of different lengths as scaffolds, we successfully synthesised DNA nanotubes consisting of Mao's DNA tensegrity triangle tiles with four-arm junctions (Holliday junctions) at all vertices. Due to the intrinsic curvature of the triangle tile and the consecutive tile alignment, the 2D arrays are organised in the form of nanotubes. Two sized triangle tiles with equilateral side lengths of 1.5 and 2.5 full helical turns are connected by the sticky ended cohesion of a duplex with a length of 2.5 helical turns respectively, and their parallel lozenge tiling lattices were demonstrated by high resolution AFM images, where the former lozenge unit cell has a lattice constant of 13.6 nm, and the latter has a larger lattice constant of 17.0 nm. Modification of the triangle tile with infinitesimal disturbance on side lengths and insertion of one thymine single stranded loop at every vertex resulted in comparably similar nanotubes.

Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.

Self-assembly of two-dimensional binary quasicrystals: a possible route to a DNA quasicrystal

We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm 'star' motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA.