3D DNA Self-Assembly Algorithmic Model to Solve the Hamiltonian Path Problem

Self-assembly reveals the innate character of DNA computing, DNA self-assembly is regarded as the best way to make DNA computing transform into computer chip. This paper introduces a strategy of DNA 3D self-assembly algorithm to solve the Hamiltonian Path Problem. Firstly, I introduced a non-deterministic algorithm. Then, according to the algorithm I designed the types of DNA tiles which the computing process needs. Lastly, I demonstrated the self-assembly process and the experimental methods which can get the final result. The computing time is linear, and the number of the different tile types is constant.

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Application of DNA Nanoparticle Conjugation on the Hamiltonian Path Problem

Journal of Nanoelectronics and Optoelectronics ◽

10.1166/jno.2021.2930 ◽

2021 ◽

Vol 16 (3) ◽

pp. 501-505

Author(s):

Jingjing Ma

Keyword(s):

Graph Theory ◽

Self Assembly ◽

Dna Computing ◽

Hamiltonian Path ◽

Au Nanoparticle ◽

Assembly Model ◽

Hamiltonian Path Problem ◽

Complete Problem ◽

Np Complete ◽

Nanoparticle Conjugation

A DNA computing algorithm is proposed in this paper. The algorithm uses the assembly of DNA/Au nanoparticle conjugation to solve an NP-complete problem in the Graph theory, the Hamiltonian Path problem. According to the algorithm, I designed the special DNA/Au nanoparticle conjugations which assembled based on a specific graph, then, a series of experimental techniques are utilized to get the final result. This biochemical algorithm can reduce the complexity of the Hamiltonian Path problem greatly, which will provide a practical way to the best use of DNA self-assembly model.

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The Design and Application of Exclusive OR Logical Computation Based on DNA 3-Arm Sub-Tile Self-Assembly

Journal of Nanoelectronics and Optoelectronics ◽

10.1166/jno.2020.2853 ◽

2020 ◽

Vol 15 (11) ◽

pp. 1327-1334

Author(s):

Chun Huang ◽

Ying-Jie Han ◽

Jun-Wei Sun ◽

Wei-Jun Zhu ◽

Yan-Feng Wang ◽

...

Keyword(s):

Integrated Circuits ◽

Self Assembly ◽

Dna Computing ◽

Vital Role ◽

Model Design ◽

Dna Encoding ◽

Computing Model ◽

Dna Tiles ◽

Half Adder ◽

Exclusive Or

DNA algorithmic self-assembly plays a vital role in DNA computing, which is applied to create new DNA tiles and then guides these tiles into an algorithmic lattice. However, the larger the logical calculation scale is, the more tile sets will be needed, so that computing model design and experiment will be increasingly difficult. This paper presents a new DNA ‘3-arm sub-tile strategy’ that constructs XOR and half-adder logical circuits. The types of DNA tile corresponding to the logical values is unified in DNA XOR and half-adder logical circuits, which have only three kinds of DNA tiles: logic ‘0’, logic ‘1’ and fixation tile. Compared with the previous references, the amount of DNA tile types has been greatly reduced. Moreover, the half-adder molecular circuit has a distinctive feature, which is an application of the expansion of the XOR logic circuit. Meanwhile, a set of DNA 3-arm sub-tiles suitable for half-adder logical computation is designed on the NUPACK online server. The simulated experiments show that the correct rate of base pairing of the designed DNA encoding is high and the structures are stable. The DNA 3-arm sub-tile self-assembly methods provide a new way to form DNA logical circuits, and has a great potential in the expansion of the integrated circuits.

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Hamiltonian path problem solution using DNA computing

Cybernetics and Physics ◽

10.35470/2226-4116-2020-9-1-69-74 ◽

2020 ◽

pp. 69-74

Author(s):

Anna Sergeenko ◽

Maria Yakunina ◽

Oleg Granichin

Keyword(s):

Branch And Bound ◽

Dna Computing ◽

Hamiltonian Path ◽

Combinatorial Problem ◽

Problem Solution ◽

Branch And Bound Method ◽

Popular Method ◽

Time Consumption ◽

Hamiltonian Path Problem ◽

Classical Algorithm

In this article we study DNA computing, a method which is based on working with DNA molecules in a laboratory. That approach is implemented in solving one of the most popular combinatorial problem — the Hamiltonian path problem. Related to recent improvements in the biophysics methods, which are needed for DNA computing, we propose to change some steps in the classical algorithm to increase accuracy of this method. The branch-and-bound method, the most popular method which is realized on a computer, is also shown in this paper to compare its performance with the time consumption of DNA computing. The results of that comparison prove that it becomes inefficient to use the branch-and-bound method from the counted number of vertices because of its exponentially growing complexity, while DNA computing works parallel and has linearly growing time consumption.

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Nanopore Decoding for a Hamiltonian Path Problem

Nanoscale ◽

10.1039/d0nr09031j ◽

2021 ◽

Author(s):

Sotaro Takiguchi ◽

Ryuji Kawano

Keyword(s):

Energy Consumption ◽

Dna Computing ◽

Hamiltonian Path ◽

Low Energy ◽

Massive Parallelism ◽

Hamiltonian Path Problem ◽

Low Energy Consumption ◽

Mathematical Problems ◽

Output Information

DNA computing has attracted attention as a tool for solving mathematical problems due to the potential for massive parallelism with low energy consumption. However, decoding the output information to a...

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Operation of Queue and Stack by DNA Tiles

E3S Web of Conferences ◽

10.1051/e3sconf/202021803051 ◽

2020 ◽

Vol 218 ◽

pp. 03051

Author(s):

Xinxin Zhang ◽

Nan Zhao ◽

Jing Yang

Keyword(s):

Self Assembly ◽

Dna Computing ◽

Active Material ◽

Software Systems ◽

Experimental Conditions ◽

Free System ◽

Insertion And Deletion ◽

Dna Tiles ◽

Dna Strands ◽

First In First Out

DNA is used as self-nanomaterials to assemble into specific structures. DNA tile provides a new idea for the application of DNA tile in the field of computing. Recent years, Queue and Stack are important linear data structures which are used in various software systems widely. The implementation of DNA based queue and stack has been studied continuously for many years. In the traditional DNA computing, queue and stack are mostly realized by DNA strands displacement, restriction endonuclease and ligase were used. However, as an active material, it has a high requirement for enzyme experimental conditions. The purpose of this paper is to implement queue and stack structures using non-enzyme systems. The rule of Queue is characterized by FIFO (first in first out), which allows for insertion at one end of the list and deletion at the other. The rule of Stack is characterized by FILO(first in last out), which allows for insertion and deletion at one end of the list. We are aimed to implement Queue and Stack using self-assembly and disassembly via DNA Tiles. No enzymes are needed for the whole experiment. As an enzyme-free system, it provides a new method to implement stack and queue.

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Constructing Large 2D Lattices Out of DNA-Tiles

Molecules ◽

10.3390/molecules26061502 ◽

2021 ◽

Vol 26 (6) ◽

pp. 1502

Author(s):

Johannes M. Parikka ◽

Karolina Sokołowska ◽

Nemanja Markešević ◽

J. Jussi Toppari

Keyword(s):

Self Assembly ◽

Dna Nanotechnology ◽

Building Blocks ◽

High Yield ◽

Dna Nanostructures ◽

Liquid Interfaces ◽

Basic Principles ◽

Dna Tiles ◽

One Step ◽

Solid Liquid

The predictable nature of deoxyribonucleic acid (DNA) interactions enables assembly of DNA into almost any arbitrary shape with programmable features of nanometer precision. The recent progress of DNA nanotechnology has allowed production of an even wider gamut of possible shapes with high-yield and error-free assembly processes. Most of these structures are, however, limited in size to a nanometer scale. To overcome this limitation, a plethora of studies has been carried out to form larger structures using DNA assemblies as building blocks or tiles. Therefore, DNA tiles have become one of the most widely used building blocks for engineering large, intricate structures with nanometer precision. To create even larger assemblies with highly organized patterns, scientists have developed a variety of structural design principles and assembly methods. This review first summarizes currently available DNA tile toolboxes and the basic principles of lattice formation and hierarchical self-assembly using DNA tiles. Special emphasis is given to the forces involved in the assembly process in liquid-liquid and at solid-liquid interfaces, and how to master them to reach the optimum balance between the involved interactions for successful self-assembly. In addition, we focus on the recent approaches that have shown great potential for the controlled immobilization and positioning of DNA nanostructures on different surfaces. The ability to position DNA objects in a controllable manner on technologically relevant surfaces is one step forward towards the integration of DNA-based materials into nanoelectronic and sensor devices.

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