Ternary representation of N (N = 1 or 2)-input and 1-output algorithmic self-assembly demonstrated by DNA

Abstract

Deoxyribonucleic acid (DNA) is effective for molecular computation because of its high energy efficiency, high information density, and parallel-computing capability. Although logic implementation using DNA molecules is well established in binary systems (base value of 2) via decoration of hairpin structures on DNA duplexes, systems with base values of >2 (e.g. 3, corresponding to a ternary system) are rarely discussed owing to the complexity of the design and the experimental difficulties with DNA. In this study, DNA rule tiles that participate to form algorithmic DNA crystals exhibiting the ternary representation of an N (N = 1 or 2)-input and 1-output algorithmic assembly are conceived. The number of possible algorithmic patterns is in the ternary N-input and 1-output logic gate. Thus, the number of possible rules is 27 (=33) for a 1-input and 1-output algorithmic logic gate and 19 638 (=39) for a 2-input and 1-output algorithmic logic gate. Ternary bit information (i.e. 0-, 1-, and 2-bit) is encoded on rule tiles without hairpins and with short and long hairpins. We construct converged, line-like, alternating, and commutative patterns by implementing specific rules (TR00, TR05, TR07, and TR15, respectively) for the 1-input and 1-output gate and an ascending line-like pattern (with the rule of TR3785) for the 2-input and 1-output gate. Specific patterns generated on ternary-representing rule-embedded algorithmic DNA crystals are visualized via atomic force microscopy, and the errors during the growth of the crystals are analyzed (average error rates obtained for all experimental data are <4%). Our method can easily be extended to a system having base values of >3.

Multi-Domains in a Single Lattice Formed by DNA Self-Assembly

“…Figure a–c shows the sticky end design of a unit of DNA double-crossover (DX) tiles in each quadrant for the fabrication of DNA lattices with OFF, ON, and ST patterns. , A rectangular shaped DX tile (with length and width of 12.6 and 6 nm, respectively) comprises four DNA strands and is used in the construction of 1D and 2D lattices. − Each domain is represented by Roman numerals (I, II, III, and IV). In domains II and IV, we have specified R and S types of DX tiles that indicate 5′ → 3′ and 3′ → 5′ directionalities in their strands, respectively. − In the case of domains I and III, a single unit DX tile used in an OFF [D­(I,0) is identical to D­(III,0)] or ON [D­(I,1) is identical to D­(III,1)] lattice is required and serves as both R and S types due to the specific sticky end design. Here, non-prime (input) and prime (output) sticky ends with the same name and color are complementary (e.g., b and b′).…”

“…DNA nanotechnology encompasses the fabrication of DNA nanostructures, the demonstration of DNA algorithms, the construction of devices and sensors made of DNA, and data storage in DNA . Diverse nanostructures made of DNA tiles and DNA strands without and with long scaffold virus genomes have been reported. − DNA logic gates can also be constructed by using the implementation of bit information into DNA sequences. − By embedding functional nanomaterials into DNA molecules, it is feasible to construct a variety of physical devices and biological/chemical sensors. − One of the promising practical DNA applications in physical engineering is to construct a data storage apparatus that might enhance the capability of data storage in the near future. − …”

Multidimensional Honeycomb-like DNA Nanostructures Made of C-Motifs

“…The molecular recognition ability, molecular stability among biomaterials, and structural rigidity of DNA molecules make them appropriate for use in the design and construction of various nanometer-scale structures and arrays, which are central to the growing field of structural DNA nanotechnology. Consequently, DNA nanostructures with diverse, well-defined geometries, including one-dimensional (1D) nanotubes, periodic two-dimensional (2D) nanolattices, − finite-size 2D rings, , 2D/three-dimensional (3D) molecular canvases, − and 3D polyhedral structures, − have been proposed for use in multiple applications, e.g., structural scaffolds for aligning nanomaterials, computations implemented with logic algorithms, drug delivery via DNA containers, and physical devices/biochemical sensors constructed using nanomaterial-embedded DNA molecules. − The demands of increasing interdisciplinary research and specific applications require the development of multidimensional nanostructures made of simple but versatile DNA building blocks.…”

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

“…During annealing, unit tiles are formed by the complementarity of base pairs in each strand. Moving from tiles to lattices, seed lattices consisting of a few unit tiles must form to allow for further formation of lattices during gradual cooling of a test tube [19][20][21]. We expect enhancement of growth of target lattices (such as two-dimernsional lattices and logic gate-embedded algorithmic lattices) if seed lattices (i.e.…”