Algorithmic self-assembly of DNA Sierpinski triangles

A biomimetic branching signal-passing tile assembly model with dynamic growth and disassembly

Natural biological branching processes can form tree-like structures at all scales and, moreover, can perform various functions to achieve specific goals; these include receiving stimuli, performing two-way communication along their branches, and dynamically reforming (extending or retracting branches). They underlie many biological systems with considerable diversity, frequency, and geometric complexity; these include networks of neurons, organ tissue, mycorrhizal fungal networks, plant growth, foraging networks, etc. This paper presents a biomimetic DNA tile assembly model (Y-STAM) to implement dynamic branching processes. The Y-STAM is a relatively compact mathematical model providing a design space where complex, biomimetic branch-like growth and behaviour can emerge from the appropriate parametrization of the model. We also introduce a class of augmented models (Y-STAM+) that provide time- and space-dependent modulations of tile glue strengths, which enable further diverse behaviours that are not possible in the Y-STAM; these additional behaviours include refinement of network assemblies, obstacle avoidance, and programmable growth patterns. We perform and discuss extensive simulations of the Y-STAM and the Y-STAM+. We envision that these models could be applied at the mesoscale and the molecular scale to dynamically assemble branching DNA nanostructures and offer insights into complex biological self-assembly processes.

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.

Dynamic control of DNA condensation

Artificial biomolecular condensates are emerging as a versatile approach to organize molecular targets and reactions without the need for lipid membranes. Here we ask whether the temporal response of artificial condensates can be controlled via designed chemical reactions. We address this general question by considering a model problem in which a phase separating component participates in reactions that dynamically activate or deactivate its ability to self-attract. Through a theoretical model we illustrate the transient and equilibrium effects of reactions, linking condensate response and reaction parameters. We experimentally realize our model problem using star-shaped DNA motifs known as nanostars to generate condensates, and we take advantage of strand invasion and displacement reactions to kinetically control the capacity of nanostars to interact. We demonstrate reversible dissolution and growth of DNA condensates in the presence of specific DNA inputs, and we characterize the role of toehold domains, nanostar size, and nanostar valency. Our results will support the development of artificial biomolecular condensates that can adapt to environmental changes with prescribed temporal dynamics.

Designing 3D multicomponent self-assembling systems with signal-passing building blocks

We introduce an allostery-mimetic building block model for the self-assembly of 3D structures. We represent the building blocks as patchy particles, where each binding site (patch) can be irreversibly activated or deactivated by binding of the particle's other controlling patches to another particle. We show that these allostery-mimetic systems can be designed to increase yields of target structures by disallowing misassembled states and can further decrease the smallest number of distinct species needed to assemble a target structure. Next, we show applications to design a programmable nanoparticle swarm for multifarious assembly: a system of particles that stores multiple possible target structures and a particular structure is recalled by presenting an external trigger signal. Finally, we outline a possible pathway for realization of such structures at nanoscale using DNA nanotechnology devices.

DNA Logic Gates for Small Molecule Activation Circuits in Cells

DNA-based devices such as DNA logic gates self-assemble into supramolecular structures, as dictated by the sequences of the constituent oligonucleotides and their predictable Watson-Crick base pairing interactions. The programmable nature of DNA-based devices permits the design and implementation of DNA circuits that interact in a dynamic and sequential manner capable of spatially arranging disparate DNA species. Here, we report the application of an activatable fluorescence reporter based on a proximity-driven inverse electron demand Diels-Alder (IEDDA) reaction and its robust integration with DNA strand displacement circuits. In response to specific DNA input patterns, sequential strand displacement reactions are initiated and culminate in the hybridization of two modified DNA strands carrying probes capable of undergoing an IEDDA reaction between a vinyl-ether-caged fluorophore and its reactive partner tetrazine, leading to the activation of fluorescence. This approach provides a major advantage for DNA computing in mammalian cells since circuit degradation does not induce fluorescence, in contrast to traditional fluorophore-quencher designs. We demonstrate the robustness and sensitivity of the reporter by testing its ability to serve as a readout for DNA logic circuits of varying complexity inside cells.

DNA Nanostructures as Catalysts: Double Crossover Tile-Assisted 5' to 5' and 3' to 3' Chemical Ligation of Oligonucleotides

Accessibility of synthetic oligonucleotides and the success of DNA nanotechnology open a possibility to use DNA nanostructures for building sophisticated enzyme-like catalytic centers. Here we used a double DNA crossover (DX) tile nanostructure to enhance the rate, the yield, and the specificity of 5'-5' ligation of two oligonucleotides with arbitrary sequences. The ligation product was isolated via a simple procedure. The same strategy was applied for the synthesis of 3'-3' linked oligonucleotides, thus introducing a synthetic route to DNA and RNA with a switched orientation that is affordable by a low-resource laboratory. To emphasize the utility of the ligation products, we synthesized a circular structure formed from intramolecular complementarity that we named "an impossible DNA wheel" since it cannot be built from regular DNA strands by enzymatic reactions. Therefore, DX-tile nanostructures can open a route to producing useful chemical products that are unattainable via enzymatic synthesis. This is the first example of the use of DNA nanostructures as a catalyst. This study advocates for further exploration of DNA nanotechnology for building enzyme-like reactive systems.

Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly

Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles1-3. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks4-7. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems.

Supercluster states and phase transitions in aggregation-fragmentation processes

We study the evolution of aggregates triggered by collisions with monomers that either lead to the attachment of monomers or the break-up of aggregates into constituting monomers. Depending on parameters quantifying addition and break-up rates, the system falls into a jammed or a steady state. Supercluster states (SCSs) are very peculiar nonextensive jammed states that also arise in some models. Fluctuations underlie the formation of the SCSs. Conventional tools, such as the van Kampen expansion, apply to small fluctuations. We go beyond the van Kampen expansion and determine a set of critical exponents quantifying SCSs. We observe continuous and discontinuous phase transitions between the states. Our theoretical predictions are in good agreement with numerical results.

Molecular system for an exponentially fast growing programmable synthetic polymer

In this paper, we demonstrate a molecular system for the first active self-assembly linear DNA polymer that exhibits programmable molecular exponential growth in real time, also the first to implement "internal" parallel insertion that does not rely on adding successive layers to "external" edges for growth. Approaches like this can produce enhanced exponential growth behavior that is less limited by volume and external surface interference, for an early step toward efficiently building two and three dimensional shapes in logarithmic time. We experimentally demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism and results in the exponential growth of a population of polymers per unit time. In the supplementary material, we note that an "extension" beyond conventional Turing machine theory is needed to theoretically analyze exponential growth itself in programmable physical systems. Sequential physical Turing Machines that run a roughly constant number of Turing steps per unit time cannot achieve an exponential growth of structure per time. In contrast, the "active" self-assembly model in this paper, computationally equivalent to a Push-Down Automaton, is exponentially fast when implemented in molecules, but is taxonomically less powerful than a Turing machine. In this sense, a physical Push-Down Automaton can be more powerful than a sequential physical Turing Machine, even though the Turing Machine can compute any computable function. A need for an "extended" computational/physical theory arises, described in the supplementary material section S1.

Photonic elementary cellular automata for simulation of complex phenomena

Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the level of software. This can be taken one step further by simplifying the underlying physical hardware. Here, we propose and implement a simple photonic hardware platform for simulating complex phenomena based on cellular automata. Using this special-purpose computer, we experimentally demonstrate complex phenomena, including fractals, chaos, and solitons, which are typically associated with much more complex physical systems. The flexibility and programmability of our photonic computer present new opportunities to simulate and harness complexity for efficient, robust, and decentralized information processing using light.

Modular reconfiguration of DNA origami assemblies using tile displacement

The power of natural evolution lies in the adaptability of biological organisms but is constrained by the time scale of genetics and reproduction. Engineeringartificial molecular machines should not only include adaptability as a core feature but also apply it within a larger design space and at a faster time scale. A lesson from engineering electromechanical robots is that modular robots can perform diverse functions through self-reconfiguration, a large-scale form of adaptation. Molecular machines made of modular, reconfigurable components may form the basis for dynamic self-reprogramming in future synthetic cells. To achieve modular reconfiguration in DNA origami assemblies, we previously developed a tile displacement mechanism in which an invader tile replaces another tile in an array with controlled kinetics. Here, we establish design principles for simultaneous reconfigurations in tile assemblies using complex invaders with distinct shapes. We present toehold and branch migration domain configurations that expand the design space of tile displacement reactions by two orders of magnitude. We demonstrate the construction of multitile invaders with fixed and variable sizes and controlled size distributions. We investigate the growth of three-dimensional (3D) barrel structures with variable cross sections and introduce a mechanism for reconfiguring them into 2D structures. Last, we show an example of a sword-shaped assembly transforming into a snake-shaped assembly, illustrating two independent tile displacement reactions occurring concurrently with minimum cross-talk. This work serves as a proof of concept that tile displacement could be a fundamental mechanism for modular reconfiguration robust to temperature and tile concentration.

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.

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.

Prime factorization via localized tile assembly in a DNA origami framework

Modern cybersecurity built on public-key cryptosystems like Rivest-Shamir-Adleman is compromised upon finding solutions to the prime factorization. Nevertheless, solving the prime factorization problem, given a large N, remains computationally challenging. Here, we design DNA origami frameworks (DOFs) to direct localized assembly of double-crossover (DX) tiles for solving prime factorization with a model consisting of the computing, decision-making, and reporting motifs. The model implementation is based on the sequential assembly of different DX tiles in the DOF cavity that carries overhangs encoding the prime and composite integers. The primes are multiplied and then verified with the composite, and the result is visualized under atomic force microscopy via the presence (success) or absence (failure) of biotin-streptavidin labels on the reporting DX tile. The factorization of semiprimes 6 and 15 is realized with this DOF-based demonstration. Given the potential of massively parallel processing ability of DNA, this strategy opens an avenue to solve complex mathematical puzzles like prime factoring with molecular computing.

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.

Multi-micron crisscross structures grown from DNA-origami slats

Living systems achieve robust self-assembly across a wide range of length scales. In the synthetic realm, nanofabrication strategies such as DNA origami have enabled robust self-assembly of submicron-scale shapes from a multitude of single-stranded components. To achieve greater complexity, subsequent hierarchical joining of origami can be pursued. However, erroneous and missing linkages restrict the number of unique origami that can be practically combined into a single design. Here we extend crisscross polymerization, a strategy previously demonstrated with single-stranded components, to DNA-origami 'slats' for fabrication of custom multi-micron shapes with user-defined nanoscale surface patterning. Using a library of ~2,000 strands that are combinatorially arranged to create unique DNA-origami slats, we realize finite structures composed of >1,000 uniquely addressable slats, with a mass exceeding 5 GDa, lateral dimensions of roughly 2 µm and a multitude of periodic structures. Robust production of target crisscross structures is enabled through strict control over initiation, rapid growth and minimal premature termination, and highly orthogonal binding specificities. Thus crisscross growth provides a route for prototyping and scalable production of structures integrating thousands of unique components (that is, origami slats) that each is sophisticated and molecularly precise.

DNA Droplets: Intelligent, Dynamic Fluid

Breathtaking advances in DNA nanotechnology have established DNA as a promising biomaterial for the fabrication of programmable higher-order nano/microstructures. In the context of developing artificial cells and tissues, DNA droplets have emerged as a powerful platform for creating intelligent, dynamic cell-like machinery. DNA droplets are a microscale membrane-free coacervate of DNA formed through phase separation. This new type of DNA system couples dynamic fluid-like property with long-established DNA programmability. This hybrid nature offers an advantageous route to facile and robust control over the structures, functions, and behaviors of DNA droplets. This review begins by describing programmable DNA condensation, commenting on the physical properties and fabrication strategies of DNA hydrogels and droplets. By presenting an overview of the development pathways leading to DNA droplets, it is shown that DNA technology has evolved from static, rigid systems to soft, dynamic systems. Next, the basic characteristics of DNA droplets are described as intelligent, dynamic fluid by showcasing the latest examples highlighting their distinctive features related to sequence-specific interactions and programmable mechanical properties. Finally, this review discusses the potential and challenges of numerical modeling able to connect a robust link between individual sequences and macroscopic mechanical properties of DNA droplets.

Multiscale Biofabrication: Integrating Additive Manufacturing with DNA-Programmable Self-Assembly

Structure and hierarchical organization are crucial elements of biological systems and are likely required when engineering synthetic biomaterials with life-like behavior. In this context, additive manufacturing techniques like bioprinting have become increasingly popular. However, 3D bioprinting, as well as other additive manufacturing techniques, show limited resolution, making it difficult to yield structures on the sub-cellular level. To be able to form macroscopic synthetic biological objects with structuring on this level, manufacturing techniques have to be used in conjunction with biomolecular nanotechnology. Here, a short overview of both topics and a survey of recent advances to combine additive manufacturing with microfabrication techniques and bottom-up self-assembly involving DNA, are given.

DNA strand displacement based computational systems and their applications

DNA computing has become the focus of computing research due to its excellent parallel processing capability, data storage capacity, and low energy consumption characteristics. DNA computational units can be precisely programmed through the sequence specificity and base pair principle. Then, computational units can be cascaded and integrated to form large DNA computing systems. Among them, DNA strand displacement (DSD) is the simplest but most efficient method for constructing DNA computing systems. The inputs and outputs of DSD are signal strands that can be transferred to the next unit. DSD has been used to construct logic gates, integrated circuits, artificial neural networks, etc. This review introduced the recent development of DSD-based computational systems and their applications. Some DSD-related tools and issues are also discussed.

RNA origami: design, simulation and application

Design strategies for DNA and RNA nanostructures have developed along parallel lines for the past 30 years, from small structural motifs derived from biology to large 'origami' structures with thousands to tens of thousands of bases. With the recent publication of numerous RNA origami structures and improved design methods-even permitting co-transcriptional folding of kilobase-sized structures - the RNA nanotechnolgy field is at an inflection point. Here, we review the key achievements which inspired and enabled RNA origami design and draw comparisons with the development and applications of DNA origami structures. We further present the available computational tools for the design and the simulation, which will be key to the growth of the RNA origami community. Finally, we portray the transition from RNA origami structure to function. Several functional RNA origami structures exist already, their expression in cells has been demonstrated and first applications in cell biology have already been realized. Overall, we foresee that the fast-paced RNA origami field will provide new molecular hardware for biophysics, synthetic biology and biomedicine, complementing the DNA origami toolbox.

The wending rhombus: Self-assembling 3D DNA crystals

In this perspective, we provide a summary of recent developments in self-assembling three-dimensional (3D) DNA crystals. Starting from the inception of this subfield, we describe the various advancements in structure that have led to an increase in the diversity of macromolecular crystal motifs formed through self-assembly, and we further comment on the future directions of the field, which exploit noncanonical base pairing interactions beyond Watson-Crick. We then survey the current applications of self-assembling 3D DNA crystals in reversibly active nanodevices and materials engineering and provide an outlook on the direction researchers are taking these structures. Finally, we compare 3D DNA crystals with DNA origami and suggest how these distinct subfields might work together to enhance biomolecule structure solution, nanotechnological motifs, and their applications.

Tomography of DNA tiles influences the kinetics of surface-mediated DNA self-assembly

This manuscript studies the impact of extruding hairpins on two-dimensional self-assembly of DNA tiles on solid surface. Hairpins are commonly used as tomographic markers in DNA nanostructures for atomic force microscopy imaging. In this study, we have discovered that hairpins play a more active role. They modulate the adsorption of the DNA tiles onto the solid surface, thus changing the tile assembly kinetics on the solid surface. Based on this discovery, we were able to promote or slow down DNA self-assembly on the surface by changing the hairpin locations on the DNA tiles. This knowledge gained will be helpful for the future design of DNA self-assembly on surface.

Emerging Approaches to DNA Data Storage: Challenges and Prospects

With the total amount of worldwide data skyrocketing, the global data storage demand is predicted to grow to 1.75 × 10¹⁴ GB by 2025. Traditional storage methods have difficulties keeping pace given that current storage media have a maximum density of 10³ GB/mm³. As such, data production will far exceed the capacity of currently available storage methods. The costs of maintaining and transferring data, as well as the limited lifespans and significant data losses associated with current technologies also demand advanced solutions for information storage. Nature offers a powerful alternative through the storage of information that defines living organisms in unique orders of four bases (A, T, C, G) located in molecules called deoxyribonucleic acid (DNA). DNA molecules as information carriers have many advantages over traditional storage media. Their high storage density, potentially low maintenance cost, ease of synthesis, and chemical modification make them an ideal alternative for information storage. To this end, rapid progress has been made over the past decade by exploiting user-defined DNA materials to encode information. In this review, we discuss the most recent advances of DNA-based data storage with a major focus on the challenges that remain in this promising field, including the current intrinsic low speed in data writing and reading and the high cost per byte stored. Alternatively, data storage relying on DNA nanostructures (as opposed to DNA sequence) as well as on other combinations of nanomaterials and biomolecules are proposed with promising technological and economic advantages. In summarizing the advances that have been made and underlining the challenges that remain, we provide a roadmap for the ongoing research in this rapidly growing field, which will enable the development of technological solutions to the global demand for superior storage methodologies.

Derivable genetic programming for two-dimensional colloidal materials

We describe a method for deriving surface functionalization patterns for colloidal systems that can induce self-assembly into any chosen periodic symmetry at a planar interface. The result is a sequence of letters, s ∈ {A,T,C,G}, or a gene, that describes the perimeter of the colloidal object and programs its self-assembly. This represents a genome that is finite and can be exhaustively enumerated. These genes derive from symmetry, which may be topologically represented by two-dimensional parabolic orbifolds; since these orbifolds are surfaces that may be derived from first principles, this represents an ab initio route to colloid functionality. The genes are human readable and can be employed to easily design colloidal units. We employ a biological (genetic) analogy to demonstrate this and illustrate their connection to the designs of Maurits Cornelis (M. C.) Escher.

4-bit adhesion logic enables universal multicellular interface patterning

Multicellular systems, from bacterial biofilms to human organs, form interfaces (or boundaries) between different cell collectives to spatially organize versatile functions^1,2. The evolution of sufficiently descriptive genetic toolkits probably triggered the explosion of complex multicellular life and patterning^3,4. Synthetic biology aims to engineer multicellular systems for practical applications and to serve as a build-to-understand methodology for natural systems^5–8. However, our ability to engineer multicellular interface patterns^2,9 is still very limited, as synthetic cell–cell adhesion toolkits and suitable patterning algorithms are underdeveloped^5,7,10–13. Here we introduce a synthetic cell–cell adhesin logic with swarming bacteria and establish the precise engineering, predictive modelling and algorithmic programming of multicellular interface patterns. We demonstrate interface generation through a swarming adhesion mechanism, quantitative control over interface geometry and adhesion-mediated analogues of developmental organizers and morphogen fields. Using tiling and four-colour-mapping concepts, we identify algorithms for creating universal target patterns. This synthetic 4-bit adhesion logic advances practical applications such as human-readable molecular diagnostics, spatial fluid control on biological surfaces and programmable self-growing materials^5–8,14. Notably, a minimal set of just four adhesins represents 4 bits of information that suffice to program universal tessellation patterns, implying a low critical threshold for the evolution and engineering of complex multicellular systems^3,5.

A synthetic cell-cell adhesion logic using swarming E. coli with 4 bits of information is introduced, enabling the programming of interfaces that combine to form universal tessellation patterns over a large scale.

Assembly of Two-Dimensional DNA Arrays Could Influence the Formation of Their Component Tiles

Tile-based DNA self-assembly is a powerful approach for nano-constructions. In this approach, individual DNA single strands first assemble into well-defined structural tiles, which, then, further associate with each other into final nanostructures. It is a general assumption that the lower-level structures (tiles) determines the higher-level, final structures. In this study, we present concrete experimental data to show that higher-level structures could, at least in the current example, also impact on the formation of lower-level structures. This study prompts questions such as: how general does this phenomenon exist in programmed DNA self-assembly and can we turn it into a useful tool for fine tuning DNA self-assembly?

Characterizing the Asymmetry in Hardness between Synthesis and Destruction of Heteropolymers

We present a simple model describing the assembly and disassembly of heteropolymers consisting of two types of monomers A and B. We prove that no matter how we manipulate the concentrations of A and B, it takes longer than the exponential function of d to synthesize a fixed amount of the desired heteropolymer, where d is the number of A-B connections. We also prove the decomposition time is linear for chain length n. When d is proportional to n, synthesis and destruction have an exponential asymmetry. Our findings may facilitate research on the more general asymmetry of operational hardness.

Graph Computation Using Algorithmic Self-Assembly of DNA Molecules

DNA molecules have been used as novel computing tools, by which Synthetic DNA was designed to execute computing processes with a programmable sequence. Here, we proposed a parallel computing method using DNA origamis as agents to solve the three-color problem, an example of the graph problem. Each agent was fabricated with a DNA origami of ∼50 nm diameter and contained DNA probes with programmable sticky ends that execute preset computing processes. With the interaction of different nanoagents, DNA molecules self-assemble into spatial nanostructures, which embody the computation results of the three-color problem with polynomial numbers of computing nanoagents in a one-pot annealing step. The computing results were confirmed by atomic force microscopy. Our method is completely different from existing DNA computing methods in its computing algorithm, and it has an advantage in terms of computational complexity and results detection for solving graph problems.

Gold-Nanoparticle-Mediated Assembly of High-Order DNA Nano-Architectures

Constructing high-order DNA nano-architectures in large sizes is of critical significance for the application of DNA nanotechnology. Robust and flexible design strategies together with easy protocols to construct high-order large-size DNA nano-architectures remain highly desirable. In this work, the authors report a simple and versatile one-pot strategy to fabricate DNA architectures with the assistance of spherical gold nanoparticles modified with thiolated oligonucleotide strands (SH-DNA-AuNPs), which serve as "power strips" to connect various DNA nanostructures carrying complementary ssDNA strands as "plugs". By modulating the plug numbers and positions on each DNA nanostructure and the ratios between DNA nanostructures and AuNPs, the desired architectures are formed via the stochastic co-assembly of different modules. This SH-DNA-AuNP-mediated plug-in assembly (SAMPA) strategy offers new opportunities to drive macroscopic self-assembly to meet the demand of the fabrication of well-defined nanomaterials and nanodevices.

Developmental Self-Assembly of a DNA Ring with Stimulus-Responsive Size and Growth Direction

Developmental self-assembly of DNA nanostructures provides an ideal platform for studying the power and programmability of kinetically controlled structural growth in engineered molecular systems. Triggered initiation and designated sequencing of assembly and disassembly steps have been demonstrated in structures with branches and loops. Here we introduce a new strategy for selectively activating distinct subroutines in a developmental self-assembly program, allowing structures with distinct properties to be created in response to various molecular signals. We demonstrate this strategy in triggered self-assembly of a DNA ring, the size and growth direction of which are responsive to a key molecule. We articulate that reversible assembly steps with slow kinetics at appropriate locations in a reaction pathway could enable multiple populations of structures with stimulus-responsive properties to be simultaneously created in one developmental program. These results open up a broad design space for the self-assembly of molecules with adaptive behaviors toward advanced control in synthetic materials and molecular motors.

Suppressing high-dimensional crystallographic defects for ultra-scaled DNA arrays

While DNA-directed nano-fabrication enables the high-resolution patterning for conventional electronic materials and devices, the intrinsic self-assembly defects of DNA structures present challenges for further scaling into sub-1 nm technology nodes. The high-dimensional crystallographic defects, including line dislocations and grain boundaries, typically lead to the pattern defects of the DNA lattices. Using periodic line arrays as model systems, we discover that the sequence periodicity mainly determines the formation of line defects, and the defect rate reaches 74% at 8.2-nm line pitch. To suppress high-dimensional defects rate, we develop an effective approach by assigning the orthogonal sequence sets into neighboring unit cells, reducing line defect rate by two orders of magnitude at 7.5-nm line pitch. We further demonstrate densely aligned metal nano-line arrays by depositing metal layers onto the assembled DNA templates. The ultra-scaled critical pitches in the defect-free DNA arrays may further promote the dimension-dependent properties of DNA-templated materials.

Programming DNA Self-Assembly by Geometry†

This manuscript introduces geometry as a means to program the tile-based DNA self-assembly in two and three dimensions. This strategy complements the sequence-focused programmable assembly. DNA crystal assembly critically relies on intermotif, sticky-end cohesion, which requires complementarity not only in sequence but also in geometry. For DNA motifs to assemble into crystals, they must be associated with each other in the proper geometry and orientation to ensure that geometric hindrance does not prevent sticky ends from associating. For DNA motifs with exactly the same pair of sticky-end sequences, by adjusting the length (thus, helical twisting phase) of the motif branches, it is possible to program the assembly of these distinct motifs to either mix with one another, to self-sort and consequently separate from one another, or to be alternatingly arranged. We demonstrate the ability to program homogeneous crystals, DNA "alloy" crystals, and definable grain boundaries through self-assembly. We believe that the integration of this strategy and conventional sequence-focused assembly strategy could further expand the programming versatility of DNA self-assembly.

Construction and Configuration Analysis of Zelkova Serrata Lenticel-Like Patterns Generated through DNA Algorithmic Self-Assembly

Multiple models and simulations have been proposed and performed to understand the mechanism of the various pattern formations existing in nature. However, the logical implementation of those patterns through efficient building blocks such as nanomaterials and biological molecules is rarely discussed. This study adopts a cellular automata model to generate simulation patterns (SPs) and experimental patterns (EPs) obtained from DNA lattices similar to the discrete horizontal brown-color line-like patterns on the bark of the Zelkova serrata tree, known as lenticels [observation patterns (OPs)]. SPs and EPs are generated through the implementation of six representative rules (i.e., R004, R105, R108, R110, R126, and R218) in three-input/one-output algorithmic logic gates. The EPs obtained through DNA algorithmic self-assembly are visualized by atomic force microscopy. Three different modules (A, B, and C) are introduced to analyze the similarities between the SPs, EPs, and OPs of Zelkova serrata lenticels. Each module has unique configurations with specific orientations allowing the calculation of the deviation of the SPs and the EPs with respect to the OPs within each module. The findings show that both the SP and the EP generated under R105 and R126 and analyzed with module B provide a higher similarity of Zelkova serrata lenticel-like patterns than the other four rules. This study provides a perspective regarding the use of DNA algorithmic self-assembly for the construction of various complex natural patterns.

Tumor-targeting [2]catenane-based grid-patterned periodic DNA monolayer array for in vivo theranostic application

DNA nanotechnology is often used to build various nano-structures for signaling and/or drug delivery, but it essentially suffers from several major limitations, such as a large number of DNA strands and limited targeting ligands. Moreover, there is no report on in vivo two-dimensional DNA arrays because of various technical challenges. By cross-catenating two palindromic DNA rings, herein, we demonstrate a catenane-based grid-patterned periodic DNA monolayer array ([2]GDA) capable of preferentially accumulating in tumor tissues without any targeting ligands, with a thickness equal to the double-helical DNA monolayer (nearly 2 nm). The structural flexibility of [2]GDA enabled it to fold into a spherical object in solution, favoring cellular uptake. Thus, its cellular internalization activity was comparable with that of the commercial lipofectamine 3000. Moreover, [2]GDA retained the structural integrity over 24 h incubation in biological solutions, achieving a 360-fold improvement in in vivo stability. Significantly, anticancer drug-loaded [2]GDA exhibits desirable therapeutic efficacy in tumor-bearing animals without detectable side effects.

An RNA-Based Theory of Natural Universal Computation

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.

Nonextensive Supercluster States in Aggregation with Fragmentation

Systems evolving through aggregation and fragmentation may possess an intriguing supercluster state (SCS). Clusters constituting this state are mostly very large, so the SCS resembles a gelling state, but the formation of the SCS is controlled by fluctuations and in this aspect, it is similar to a critical state. The SCS is nonextensive, that is, the number of clusters varies sublinearly with the system size. In the parameter space, the SCS separates equilibrium and jamming (extensive) states. The conventional methods, such as, e.g., the van Kampen expansion, fail to describe the SCS. To characterize the SCS we propose a scaling approach with a set of critical exponents. Our theoretical findings are in good agreement with numerical results.

Concepts and Application of DNA Origami and DNA Self-Assembly: A Systematic Review

With the arrival of the post-Moore Era, the development of traditional silicon-based computers has reached the limit, and it is urgent to develop new computing technology to meet the needs of science and life. DNA computing has become an essential branch and research hotspot of new computer technology because of its powerful parallel computing capability and excellent data storage capability. Due to good biocompatibility and programmability properties, DNA molecules have been widely used to construct novel self-assembled structures. In this review, DNA origami is briefly introduced firstly. Then, the applications of DNA self-assembly in material physics, biogenetics, medicine, and other fields are described in detail, which will aid the development of DNA computational model in the future.

DNA nanotechnology-facilitated ligand manipulation for targeted therapeutics and diagnostics

Ligands, mostly binding to proteins to form complexes and catalyze chemical reactions, can serve as drug and probe molecules, as well as sensing elements. DNA nanotechnology can integrate the high editability of DNA nanostructures and the biological activity of ligands into functionalized DNA nanostructures in a manner of controlled ligand stoichiometry, type, and arrangement, which provides significant advantages for targeted therapeutics and diagnostics. As therapeutic agents, multiple- and multivalent-ligands functionalized DNA nanostructures increase ligand-receptor affinity and activate multivalent ligand-receptor interactions, enabling improved regulation of cell signaling and enhanced control of cell behavior. As diagnostic agents, multiple ligands interaction via DNA nanostructures endows DNA nanosensors with high sensitivity and excellent signal transduction capability. Herein, we review the principles and advantages of using DNA nanostructures to manipulate ligands for targeted therapeutics and diagnostics and provide future perspectives.

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.

DNA dynamics and computation based on toehold-free strand displacement

We present a simple and effective scheme of a dynamic switch for DNA nanostructures. Under such a framework of toehold-free strand displacement, blocking strands at an excess amount are applied to displace the complementation of specific segments of paired duplexes. The functional mechanism of the scheme is illustrated by modelling the base pairing kinetics of competing strands on a target strand. Simulation reveals the unique properties of toehold-free strand displacement in equilibrium control, which can be leveraged for information processing. Based on the controllable dynamics in the binding of preformed DNA nanostructures, a multi-input-multi-output (MIMO) Boolean function is controlled by the presence of the blockers. In conclusion, we implement two MIMO Boolean functions (one with 4-bit input and 2-bit output, and the other with 16-bit input and 8-bit output) to showcase the controllable dynamics.

Synthetic DNA constructs can to used to recognise and respond to input signals. Here the authors present complex DNA nanostructures with toehold-free strand displacement for generation of ON/OFF switches and Boolean gates.

Molecular-level similarity search brings computing to DNA data storage

As global demand for digital storage capacity grows, storage technologies based on synthetic DNA have emerged as a dense and durable alternative to traditional media. Existing approaches leverage robust error correcting codes and precise molecular mechanisms to reliably retrieve specific files from large databases. Typically, files are retrieved using a pre-specified key, analogous to a filename. However, these approaches lack the ability to perform more complex computations over the stored data, such as similarity search: e.g., finding images that look similar to an image of interest without prior knowledge of their file names. Here we demonstrate a technique for executing similarity search over a DNA-based database of 1.6 million images. Queries are implemented as hybridization probes, and a key step in our approach was to learn an image-to-sequence encoding ensuring that queries preferentially bind to targets representing visually similar images. Experimental results show that our molecular implementation performs comparably to state-of-the-art in silico algorithms for similarity search.

Storage technology based on DNA is emerging as an information dense and durable medium. Here the authors use machine learning-based encoding and hybridization probes to execute similarity searches in a DNA database.

A Primer on the oxDNA Model of DNA: When to Use it, How to Simulate it and How to Interpret the Results

The oxDNA model of Deoxyribonucleic acid has been applied widely to systems in biology, biophysics and nanotechnology. It is currently available via two independent open source packages. Here we present a set of clearly documented exemplar simulations that simultaneously provide both an introduction to simulating the model, and a review of the model's fundamental properties. We outline how simulation results can be interpreted in terms of-and feed into our understanding of-less detailed models that operate at larger length scales, and provide guidance on whether simulating a system with oxDNA is worthwhile.

Sierpiński Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Deposition of Bi on InSb(111)B reveals a striking Sierpiński-triangle (ST)-like structure in Bi thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic topology in a thin film. Relaxation of a huge misfit strain of about 30% to 40% between Bi adlayer and substrate is revealed to drive the ST-like island formation. A Frenkel-Kontrova model is developed to illustrate the enhanced strain relief in the ST islands offsetting the additional step energy cost. Besides a sufficiently large tensile strain, forming ST-like structures also requires larger adlayer-substrate and intra-adlayer elastic stiffnesses, and weaker intra-adlayer interatomic interactions.

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

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

Regulating DNA Self-Assembly Dynamics with Controlled Nucleation

Controlling the nucleation step of a self-assembly system is essential for engineering structural complexity and dynamic behaviors. Here, we design a "frame-filling" model system that comprises one type of self-complementary DNA tile and a hosting DNA origami frame to investigate the inherent dynamics of three general nucleation modes in nucleated self-assembly: unseeded, facet, and seeded nucleation. Guided by kinetic simulation, which suggested an optimal temperature range to differentiate the individual nucleation modes, and complemented by single-molecule observations, the transition of tiles from a metastable, monomeric state to a stable, polymerized state through the three nucleation pathways was monitored by Mg²⁺-triggered kinetic measurements. The temperature-dependent kinetics for all three nucleation modes were correlated by a "nucleation-growth" model, which quantified the tendency of nucleation using an empirical nucleation number. Moreover, taking advantage of the temperature dependence of nucleation, tile assembly can be regulated externally by the hosting frame. An ultraviolet (UV)-responsive trigger was integrated into the frame to simultaneously control "when" and "where" nucleation started. Our results reveal the dynamic mechanisms of the distinct nucleation modes in DNA tile-based self-assembly and provide a general strategy for controlling the self-assembly process.

Robust nucleation control via crisscross polymerization of highly coordinated DNA slats

Natural biomolecular assemblies such as actin filaments or microtubules can exhibit all-or-nothing polymerization in a kinetically controlled fashion. The kinetic barrier to spontaneous nucleation arises in part from positive cooperativity deriving from joint-neighbor capture, where stable capture of incoming monomers requires straddling multiple subunits on a filament end. For programmable DNA self-assembly, it is likewise desirable to suppress spontaneous nucleation to enable powerful capabilities such as all-or-nothing assembly of nanostructures larger than a single DNA origami, ultrasensitive detection, and more robust algorithmic assembly. However, existing DNA assemblies use monomers with low coordination numbers that present an effective kinetic barrier only for slow, near-reversible growth conditions. Here we introduce crisscross polymerization of elongated slat monomers that engage beyond nearest neighbors which sustains the kinetic barrier under conditions that promote fast, irreversible growth. By implementing crisscross slats as single-stranded DNA, we attain strictly seed-initiated nucleation of crisscross ribbons with distinct widths and twists.

3D DNA Nanostructures: The Nanoscale Architect

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