DNA Tiles Research Articles

Solving Vertex Cover Problem Using DNA Tile Assembly Model

DNA tile assembly models are a class of mathematically distributed and parallel biocomputing models in DNA tiles. In previous works, tile assembly models have been proved be Turing-universal; that is, the system can do what Turing machine can do. In this paper, we use tile systems to solve computational hard problem. Mathematically, we construct three tile subsystems, which can be combined together to solve vertex cover problem. As a result, each of the proposed tile subsystems consists ofΘ(1) types of tiles, and the assembly process is executed in a parallel way (like DNA’s biological function in cells); thus the systems can generate the solution of the problem in linear time with respect to the size of the graph.

Precise Normal Mode Analysis and Frequency Prediction of DNA Nanostructure through Mass-Weighted Chemical Elastic Network Model

In our previous study on self-assembly mechanism of DNA nanostructures, using elastic network model (ENM) based normal mode analysis (NMA), we successfully explained the reason why planar DNA tiles were self-assembled as a helical nanotube, which was totally contrast to our preconception such that they could form a planar lattice nanostructure. Although this traditional ENM based NMA is very useful to catch collective motions of biomolecules in a timely fashion, it is impossible to predict vibration frequency due to its dimensionless uniform mass and spring constants.We propose a mass-weighted chemical elastic network model (MWCENM) which takes inertia effect and chemical bond information into account. For example, lumped masses are assigned to the representative atoms and different spring constants are given to bonded and non-bonded interactions including covalent bond, hydrogen bond, and van der Waals interaction.Several comparison studies convince us that MWCENM is able to catch DNA dynamics more precisely and more effectively. It is also expected that one can use MWCENM based NMA results, which include both predicted frequencies and corresponding mode shapes, as a fingerprint to characterize molecular dynamics by a comparison with vibration spectrum data.

Three-Dimensional Structures Self-Assembled from DNA Bricks

We describe a simple and robust method to construct complex three-dimensional (3D) structures by using short synthetic DNA strands that we call "DNA bricks." In one-step annealing reactions, bricks with hundreds of distinct sequences self-assemble into prescribed 3D shapes. Each 32-nucleotide brick is a modular component; it binds to four local neighbors and can be removed or added independently. Each 8-base pair interaction between bricks defines a voxel with dimensions of 2.5 by 2.5 by 2.7 nanometers, and a master brick collection defines a "molecular canvas" with dimensions of 10 by 10 by 10 voxels. By selecting subsets of bricks from this canvas, we constructed a panel of 102 distinct shapes exhibiting sophisticated surface features, as well as intricate interior cavities and tunnels.

Extended DNA Tile Actuators

AbstractA dynamic linear DNA tile actuator is expanded to three new structures of higher complexity. The original DNA actuator was constructed from a central roller strand which hybridizes with two piston strands by forming two half‐crossover junctions. A linear expansion of the actuator is obtained by fusing two actuators of different sequence designs with a third central roller strand. This structure spans 35 nm and its integrity was verified by PAGE analysis. Owing to sequence homology around the crossovers the actuator can obtain 12 different states. The states of the actuator are controlled by a lock strand inserted at one end of the actuator and monitored by Förster resonance energy transfer (FRET) spectroscopy between a fluorophore pair which is located at the other end of the actuator. Two other designs were made where the linear actuator monomer is expanded into two dimensions by forming triangular and quadrilateral actuators. This could be attained by extending the central roller to three or four repeated 32 nucleotide regions that are complementary to the same piston. The triangular and quadrilateral actuators were characterized by PAGE analysis and it was shown that they could be locked in states 0, 5, and 10 and furthermore that they could be switched between the different states by strand displacement reactions.

Direct Atomic Force Microscopy Observation of DNA Tile Crystal Growth at the Single-Molecule Level

While the theoretical implications of models of DNA tile self-assembly have been extensively researched and such models have been used to design DNA tile systems for use in experiments, there has been little research testing the fundamental assumptions of those models. In this paper, we use direct observation of individual tile attachments and detachments of two DNA tile systems on a mica surface imaged with an atomic force microscope (AFM) to compile statistics of tile attachments and detachments. We show that these statistics fit the widely used kinetic Tile Assembly Model and demonstrate AFM movies as a viable technique for directly investigating DNA tile systems during growth rather than after assembly.

Steric Crowding and the Kinetics of DNA Hybridization within a DNA Nanostructure System

The ability to generate precisely designed molecular networks and modulate the surrounding environment is vital for fundamental studies of chemical reactions. DNA nanotechnology simultaneously affords versatility and modularity for the construction of tailored molecular environments. We systematically studied the effects of steric crowding on the hybridization of a 20 nucleotide (nt) single-stranded DNA (ssDNA) target to a complementary probe strand extended from a rectangular six-helix tile, where the number and character of the surrounding strands influence the molecular environment of the hybridization site. The hybridization events were monitored through an increase in the quantum yield of a single reporter fluorophore (5-carboxyfluorescein) upon hybridization of the 20-nt ssDNA, an effect previously undocumented in similar systems. We observed that as the hybridization site moved from outer to inner positions along the DNA tile, the hybridization rate constant decreased. A similar rate decrease was observed when noncomplementary single- and double-stranded DNA flanked the hybridization site. However, base-pairing interactions between the hybridization site of the probe and the surrounding DNA resulted in a reduction in the reaction kinetics. The decreases in the hybridization rate constants can be explained by the reduced probability of successful nucleation of the invading ssDNA target to the complementary probe.

Complex shapes self-assembled from single-stranded DNA tiles

Programmed self-assembly of strands of nucleic acid has proved highly effective for creating a wide range of structures with desired shapes. A particularly successful implementation is DNA origami, in which a long scaffold strand is folded by hundreds of short auxiliary strands into a complex shape. Modular strategies are in principle simpler and more versatile and have been used to assemble DNA or RNA tiles into periodic and algorithmic two-dimensional lattices, extended ribbons and tubes, three-dimensional crystals, polyhedra and simple finite two-dimensional shapes. But creating finite yet complex shapes from a large number of uniquely addressable tiles remains challenging. Here we solve this problem with the simplest tile form, a 'single-stranded tile' (SST) that consists of a 42-base strand of DNA composed entirely of concatenated sticky ends and that binds to four local neighbours during self-assembly. Although ribbons and tubes with controlled circumferences have been created using the SST approach, we extend it to assemble complex two-dimensional shapes and tubes from hundreds (in some cases more than one thousand) distinct tiles. Our main design feature is a self-assembled rectangle that serves as a molecular canvas, with each of its constituent SST strands--folded into a 3 nm-by-7 nm tile and attached to four neighbouring tiles--acting as a pixel. A desired shape, drawn on the canvas, is then produced by one-pot annealing of all those strands that correspond to pixels covered by the target shape; the remaining strands are excluded. We implement the strategy with a master strand collection that corresponds to a 310-pixel canvas, and then use appropriate strand subsets to construct 107 distinct and complex two-dimensional shapes, thereby establishing SST assembly as a simple, modular and robust framework for constructing nanostructures with prescribed shapes from short synthetic DNA strands.

Robust self-replication of combinatorial information via crystal growth and scission

Understanding how a simple chemical system can accurately replicate combinatorial information, such as a sequence, is an important question for both the study of life in the universe and for the development of evolutionary molecular design techniques. During biological sequence replication, a nucleic acid polymer serves as a template for the enzyme-catalyzed assembly of a complementary sequence. Enzymes then separate the template and complement before the next round of replication. Attempts to understand how replication could occur more simply, such as without enzymes, have largely focused on developing minimal versions of this replication process. Here we describe how a different mechanism, crystal growth and scission, can accurately replicate chemical sequences without enzymes. Crystal growth propagates a sequence of bits while mechanically-induced scission creates new growth fronts. Together, these processes exponentially increase the number of crystal sequences. In the system we describe, sequences are arrangements of DNA tile monomers within ribbon-shaped crystals. 99.98% of bits are copied correctly and 78% of 4-bit sequences are correct after two generations; roughly 40 sequence copies are made per growth front per generation. In principle, this process is accurate enough for 1,000-fold replication of 4-bit sequences with 50% yield, replication of longer sequences, and darwinian evolution. We thus demonstrate that neither enzymes nor covalent bond formation are required for robust chemical sequence replication. The form of the replicated information is also compatible with the replication and evolution of a wide class of materials with precise nanoscale geometry such as plasmonic nanostructures or heterogeneous protein assemblies.

NMR Studies of Artificial Double-Crossover DNA Tiles

This report documents the design and characterization of DNA molecular nanoarchitectures consisting of artificial double crossover DNA tiles with different geometry and chemistry. The Structural characterization of the unit tiles, including normal, biotinylated and hairpin loop structures, are morphologically studied by atomic force microscopy. The specific proton resonance of the individual tiles and their intra/inter nucleotide relationships are verified by proton nuclear magnetic resonance spectroscopy and 2-dimensional correlation spectral studies, respectively. Significant up-field and down-field shifts in the resonance signals of the individual residues at various temperatures are discussed. The results suggest that with artificially designed DNA tiles it is feasible to obtain structural information of the relative base sequences. These tiles were later fabricated into 2D DNA lattice structures for specific applications such as protein arrangement by biotinylated bulged loops or pattern generation using a hairpin structure.

Computation of Multiplicative Inversion and Division in GF(2<SUP><I>n</I></SUP>) by Self-Assembly of DNA Tiles

Computation of Multiplicative Inversion and Division in GF(2<SUP><I>n</I></SUP>) by Self-Assembly of DNA Tiles

Simple evolution of complex crystal species

Cairns-Smith has proposed that life began as structural patterns in clays that self-replicated during cycles of crystal growth and fragmentation. Complex, evolved crystal forms could then have catalyzed the formation of a more advanced genetic material. A crucial weakness of this theory is that it is unclear how complex crystals might arise through Darwinian evolution and selection. Here we investigate whether complex crystal patterns could evolve using a model system for crystal growth, DNA tile crystals, that is amenable to both theoretical and experimental inquiry. It was previously shown that in principle, the evolution of crystals assembled from a set of thousands of DNA tile types under very specific environmental conditions could produce arbitrarily complex patterns. Here we show that evolution driven only by the dearth of one monomer type could produce complex crystals from just 12 monomer types. When a monomer type is rare, crystals that use few of this monomer type are selected for. We use explicit enumeration to show that there are situations in which crystal species that use a particular monomer type less frequently will grow faster, yet to do so requires that the information contained in the crystal become more complex. We show that this feature of crystal organization could allow more complex crystal morphologies to be selected for in the right environment, using both analysis in a simple model of self-assembly and stochastic kinetic simulations of crystal growth. The proposed mechanism of evolution is simple enough to test experimentally and is sufficiently general that it may apply to other DNA tile crystals or even to natural crystals, suggesting that complex crystals could evolve from simple starting materials because of relative differences in concentrations of the materials needed for growth.

2D Gold Nanoparticle Structures Engineered Through DNA Tiles for Delivery and Therapy

Self-assembly of 13 nm gold nanoparticles (AuNPs) engineered into 2D structures in solution using DNA tiles for their possible use for gene delivery and photothermal therapy is reported. The two different DNA tiles were constructed and the AuNPs coated with oligonucleotides possessing complementary sequence from the free ends were hybridized with the sticky ends of the tiles. The DNA tiles were bind to each other by mixing the tile structures without a heating and cooling step. The constructed nanostructures were 5 to 7 DNA tiles long since heat was not used to elongate them. When the DNA tiles were bound to the AuNPs, it was observed that AuNPs tend to stay in close proximity by filling the gaps between tiles. The stability of the constructed structures was tested against DNase, a DNA cleaving enzyme, for possible applications for gene delivery and photothermal therapy. It was found that the AuNP bound DNA tile structures resist the DNase cleavage up to eighty percent. Due to the presence of the AuNPs in the structure, the enzyme cannot bind to DNA sequences and this increases the DNA tile structures’ stability.

The world's smallest assembly line

Two separate studies show how DNA tiles can be used in automated assembly processes: one system self-replicates, the second assembles the output of a molecular computation.

Logical NAND and NOR Operations Using Algorithmic Self-assembly of DNA Molecules

Abstract DNA self-assembly is the most advanced and versatile system that has been experimentally demonstrated for programmable construction of patterned systems on the molecular scale. It has been demonstrated that the simple binary arithmetic and logical operations can be computed by the process of self assembly of DNA tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules that can be used to execute five steps of a logical NAND and NOR operations on a string of binary bits. To achieve this, abstract tiles were translated into DNA tiles based on triple-crossover motifs. Serving as input for the computation, long single stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. Our method shows that engineered DNA self-assembly can be treated as a bottom-up design techniques, and can be capable of designing DNA computer organization and architecture.

A Programmable Transducer Self-Assembled from DNA.

A transducer consists of an input/output alphabet, a finite set of states, and a transition function. From an input symbol applied to a given state, the transition function determines the next state, and an output symbol. Using DNA, we have constructed a transducer that divides a number by 3. The input consists of a series of individually addressable 2-state DNA nanomechanical devices that control the orientations of a group of flat 6-helix DNA motifs; these motifs have edge domains tailed in sticky ends corresponding to the numbers 0 and 1. Three-domain DNA molecules (TX tiles) act as computational tiles that correspond to the transitions that the transducer can undergo. The output domain of these TX tiles contains sticky ends that also correspond to 0 or 1. Two different DNA tiles can chelate these output domains: A 5 nm gold nanoparticle is attached to the chelating tile that binds to 0-domains and a 10 nm gold nanoparticle is attached to the chelating tile that binds to 1-domains. The answer to the division is represented by the series of gold nanoparticles, which can be interpreted as a binary number. The answers of the computation are read out by examination of the transducer complexes under a transmission electron microscope. The start or end points of the output sequence can be indicated by the presence of a 15 nm gold nanoparticle. This work demonstrates two previously unreported features integrated in a single framework: [1] a system that combines DNA algorithmic self-assembly with DNA nanomechanical devices that control that input, and [2] the arrangement of non-DNA species, here metallic nanoparticles, through DNA algorithmic self-assembly. The nanomechanical devices are controlled by single-stranded DNA strands, allowing multiple input sequences to be applied to the rest of the system, thus guiding the algorithmic self-assembly to a variety of outputs.

3PT110 A Growth mechanism of DNA tile array(The 50th Annual Meeting of the Biophysical Society of Japan)

3PT110 A Growth mechanism of DNA tile array(The 50th Annual Meeting of the Biophysical Society of Japan)

The Application of DNA Self-Assembly Model for Bin Packing Problem

Bin Packing Problem (BPP) is a classical combinatorial optimization problem of graph theory, which has been proved to be NP-complete, and has high computational complexity. DNA self-assembly, a formal model of crystal growth, has been proposed as a mechanism for the bottom-up fabrication of autonomous DNA computing. In this paper, the authors propose a DNA self-assembly model for solving the BPP, this model consists of two units: grouping based on binary method and subtraction system. The great advantage of the model is that the number of DNA tile types used in the model is constant and it can solve any BPP within linear time. This work demonstrates the ability of DNA tiles to solve other NP-complete problems in the future.

Atomic force microscopy of arrays of asymmetrical DNA motifs

DNA can easily be assembled into wide and relatively flat nanostructures that lend themselves to study viaAtomic Force Microscopy (AFM). It is often important to know which side of an assembly the AFM is imaging. This is particularly crucial for characterizing nanomachines, where the movement must be measured relative to fiducial features visible to the AFM. We have developed a cheap and simple technique for building DNA arrays with distinguishable sides, a technique requiring 10 or fewer strands – dozens or hundreds of strands fewer than used for these purposes previously. Our approach involves constructing arrays out of DNA tiles that have low apparent symmetry when imaged viaAFM. We have surveyed the effects of varying degrees of motif asymmetry in AFM micrographs. Even at resolutions where the individual tiles cannot be resolved (either because of sub-optimal tip quality, or very gentle tapping by the AFM tip) the larger scale features of the arrays have predictable structures that allow the determination of which side of the array is facing up. We have used this information to verify that DNA hairpins attached to either the up- or down-facing side of an array on mica can be detected in AFM height scans. We have also characterized differences in appearance between hairpins attached to different sides of the arrays.

Self-replication of information-bearing nanoscale patterns

DNA molecules provide what is probably the most iconic example of self-replication—the ability of a system to replicate, or make copies of, itself. In living cells the process is mediated by enzymes and occurs autonomously, with the number of replicas increasing exponentially over time without the need for external manipulation. Self-replication has also been implemented with synthetic systems, including RNA enzymes designed to undergo self-sustained exponential amplification1-5. An exciting next step would be to use self-replication in materials fabrication, which requires robust and general systems capable of copying and amplifying functional materials or structures. Here we report a first development in this direction, using DNA tile motifs that can recognize and bind complementary tiles in a pre-programmed fashion. We first design tile motifs so they form a seven-tile seed sequence, then use the seeds to instruct the formation of a first generation of complementary seven-tile daughter sequences, and finally use the daughters to instruct the formation of seven-tile granddaughter sequences that are identical to the initial seed sequences. Considering that DNA is a functional material that can organize itself and other molecules into useful structures6-13, our findings raise the tantalizing prospect that we may one day be able to realize self-replicating materials with various patterns or useful functions.

Covalent Tethering of Protruding Arms for Addressable DNA Nanostructures

Functionalization of self-assembled DNA nanostructures is of fundamental importance for the realization of their application in nanotechnology and biosensing. Approaches reported so far suffer from lack of general applicability and usually require careful system design to avoid poor yields in the assembly of target structures. A novel approach well suited for fabrication of addressable DNA superstructures is reported here to generate DNA tile motifs. The method is based on the covalent linkage of a single-stranded protruding arm (covPA) to one of the oligomers forming the tile. Subsequent to assembly of tile motifs and superlattices, the covPA can be addressed by hybridization with complementary oligonucleotides or DNA-protein conjugates. The covPA can be located at arbitrary positions in a given tile motif without changing the general design and without compromising the structural integrity of the tile. The covPA strategy can also be readily extended to different PA sequences and multiple covPA arms can be linked to a tile. Superlattices obtained by self-assembly of covPA tiles reveal partial folding into double layers which possess an intrinsic order at the ultrastructural level. This phenomenon is likely associated with the increased flexibility of the covPA and might open up novel ways for DNA-based functionalization of solid surfaces and other applications of structural DNA nanotechnology.