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.

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

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 [Formula: see text] 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.

The observation of resistive switching characteristics using transparent and biocompatible Cu2+-doped salmon DNA composite thin film.

For the potential switching bio-memory device application using DNA composite thin film, we fabricated and characterized the transparent and biocompatible resistive switching random access memory (RRAM) device within the structure stacking of Pt/Cu2+ doped salmon DNA/FTO, where Cu2+ doping into salmon DNA was solution-processed. The device shows good bipolar switching characteristics with SET and RESET processes at negative and positive sweeps, respectively, with switching memory window greater than 103 ratios. The device was observed to be in low resistance state as its pristine state and an initial RESET state was necessary to achieve programmable SET and RESET cycles. Based on the electrical characteristics of the Cu2+-doped salmon DNA-based RRAM device we propose a switching mechanism with the formation and rupture of conductive filaments due to the migration of Cu2+ during the electrical stress. Our understanding could contribute to the engineering of biomaterial memory switching medium for the environmentally benign, biocompatible and biodegradable memory storage devices.

M-State and N-Color (M-N = 1-1, 2-1, and 1-2) Turing Algorithms Demonstrated via DNA Self-Assembly.

The fast and extensive generation of patterns using specific algorithms is a major challenge in the field of DNA algorithmic self-assembly. Turing machines (TMs) are simple computable machines that execute certain algorithms using carefully designed logic gates. We investigate Turing algorithms for the generation of patterns on algorithmic lattices using specific logic gates. Logic gates can be implemented into Turing building blocks. We discuss comprehensive methods for designing Turing building blocks to demonstrate an M-state and N-color Turing machine (M-N TM). The M-state and N-color (M-N = 1-1, 2-1, and 1-2) TMs generate Turing patterns that can be fabricated via DNA algorithmic self-assembly. The M-N TMs require two-input and three-output logic gates. We designed the head, tape, and transition rule tiles to demonstrate TMs for the 1-1, 2-1, and 1-2 Turing algorithms. By analyzing the characteristics of the Turing patterns, we classified them into two classes (DL and DR for states grown diagonally to the left and right, respectively) for the 1-1 TM, three for the 2-1 TM, and nine for the 1-2 TM. Among these, six representative Turing patterns generated using rules R11-0 and R11-1 for 1-1 TM, R21-01 and R21-09 for 2-1 TM, and R12-02 and R12-08 for 1-2 TM were constructed with DNA building blocks. Turing patterns on the DNA lattices were visualized by atomic force microscopy. The Turing patterns on the DNA lattices were similar to those simulated patterns. Implementing the Turing algorithms into DNA building blocks, as demonstrated via DNA algorithmic self-assembly, can be extended to a higher order of state and color to generate more complicated patterns, compute arithmetic operations, and solve mathematical functions.

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.

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

Using sequence programmability and the characteristics of self-assembly, DNA has been utilized in the construction of various nanostructures and the placement of specific patterns on lattices. Even though many complex structures and patterns formed by DNA assembly have been reported, the fabrication of multi-domain patterns in a single lattice has rarely been discussed. Multi-domains possessing specifically designed patterns in a single lattice provide the possibility to generate multiple patterns that enhance the pattern density in a given single lattice. Here, we introduce boundaries to construct double- and quadruple-domains with specific patterns in a single lattice and verify them with atomic force microscopy. ON, OFF, and ST (stripe) patterns on a lattice are made of DNA tiles with hairpins (ON), without hairpins (OFF), and alternating DNA tiles without and with hairpins (formed as a stripe, ST). For double- and quadruple-domain lattices, linear and cross boundaries were designed to fabricate two (e.g., ON and OFF, ON and ST, and OFF and ST) and four (OFF, ST, OFF, and ON) different types of patterns in single lattices, respectively. In double-domain lattices, each linear boundary is placed between two different domains. Similarly, four linear boundaries connected with a seed tile (i.e., a cross boundary) can separate four domains in a single lattice in quadruple-domain lattices. Due to the presence of boundaries, the pattern growth directions are different in each domain. The experimentally obtained multi-domain patterns agree well with our design. Lastly, we propose the possibility of the construction of a hexadomain lattice through the mapping from hexagonal to square grids converted by using an axial coordinate system. By proposing a hexadomain lattice design, we anticipate the possibility to extend to higher numbers of multi-domains in a single lattice, thereby further increasing the information density in a given lattice.

Configuration Analysis of a Lizard Skin-like Pattern Formed by DNA Self-Assembly.

Nature manifests diverse and complicated patterns through efficient physical, chemical, and biological processes. One of the approaches to generate complex patterns, as well as simple patterns, is the use of the cellular automata algorithm. However, there are certain limitations to produce such patterns experimentally due to the difficulty of finding candidate programmable building blocks. Here, we demonstrated the feasibility of generating an ocellated lizard skin-like pattern by simulation considering the probabilistic occurrence of cells and constructed the simulation results on DNA lattices via bottom-up self-assembly. To understand the similarity between the simulated pattern (SP) and the observed pattern (OP) of lizard skin, a unique configuration scheme (unit configuration was composed of 7 cells) was conceived. SPs were generated through a computer with a controlling population of gray and black cells in a given pattern. Experimental patterns (EPs) on DNA lattices, consisting of double-crossover (DX) tiles without and with protruding hairpins, were fabricated and verified through atomic force microscopy (AFM). For analyzing the similarity of the patterns, we introduced deviation of the average configuration occurrence for SP and EP with respect to OP, i.e., σα(SO) and σα(EO). The configuration and deviation provide characteristic information of patterns. We recognized that the minimum values of <σα(SO)> and <σα(EO)> occurred when 50% (55%) of black cells in given SPs (DX tiles with hairpins in given EPs) appeared to be most similar to the OP. Our study provides a novel platform for the applicability of DNA molecules to systematically demonstrate other naturally existing complex patterns or processes with ease.

Demonstration of elementary functions via DNA algorithmic self-assembly.

Target-oriented cellular automata with computation are the primary challenge in the field of DNA algorithmic self-assembly in connection with specific rules. We investigate the feasibility of using the principle of cellular automata for mathematical subjects by using specific logic gates that can be implemented into DNA building blocks. Here, we connect the following five representative elementary functions: (i) enumeration of multiples of 2, 3, and 4 (demonstrated via R094, R062, and R190 in 3-input/1-output logic rules); (ii) the remainder of 0 and 1 (R132); (iii) powers of 2 (R129); (iv) ceiling function for n/2 and n/4 (R152 and R144); and (v) analogous pattern of annihilation (R184) to DNA algorithmic patterns formed by specific rules. After designing the abstract building blocks and simulating the generation of algorithmic lattices, we conducted an experiment as follows: designing of DNA tiles with specific sticky ends, construction of DNA lattices via a two-step annealing method, and verification of expected algorithmic patterns on a given DNA lattice using an atomic force microscope (AFM). We observed representative patterns, such as horizontal and diagonal stripes and embedded triangles, on the given algorithmic lattices. The average error rates of individual rules are in the range of 8.8% (R184) to 11.9% (R062), and the average error rate for all the rules was 10.6%. Interpretation of elementary functions demonstrated through DNA algorithmic patterns could be extended to more complicated functions, which may lead to new insights for achieving the final answers of functions with experimentally obtained patterns.

Demonstration of Arithmetic Calculations by DNA Tile-Based Algorithmic Self-Assembly.

Owing to its high information density, energy efficiency, and massive parallelism, DNA computing has undergone several advances and made significant contributions to nanotechnology. Notably, arithmetic calculations implemented by multiple logic gates such as adders and subtractors have received much attention because of their well-established logic algorithms and feasibility of experimental implementation. Although small molecules have been used to implement these computations, a DNA tile-based calculator has been rarely addressed owing to complexity of rule design and experimental challenges for direct verification. Here, we construct a DNA-based calculator with three types of building blocks (propagator, connector, and solution tiles) to perform addition and subtraction operations through algorithmic self-assembly. An atomic force microscope is used to verify the solutions. Our method provides a potential platform for the construction of various types of DNA algorithmic crystals (such as flip-flops, encoders, and multiplexers) by embedding multiple logic gate operations in the DNA base sequences.