DNA Encoding Methods in the Field of DNA Computing

Summary

Bioinformatics studies the acquisition, process, store, distribution, analysis, etc of biological information so as to understand the meanings of biological data by means of mathematics, computer science and biological techniques. Some researches on Bioinformatics, such as the properties of DNA and the Watson-Crick’s law, provide a probability of computing with DNA molecules. DNA computing is a new computational paradigm that executes parallel computation with DNA molecules based on the Watson-Crick’s law. The procedure of DNA computing can be divided into three stages: encoding information, computation (molecular operations) and extraction of solution. The stage of encoding information is the first and most important step, which directly affects the formation of optimal solution. The methods of encoding information can be divided into two classes: the methods of encoding information in graphs without weights and the methods of encoding information in graphs with weights. The previous researches, which belong to the first class, such as Adleman’s encoding method [1] for the directed Hamiltonian path problem, Lipton’s encoding method [2] for the SAT problem, and Ouyang’s encoding method [3] for the maximal clique problem, do not require the consideration of weight representation in DNA strands. However, there are many practical applications related to weights. Therefore, weight representation in DNA strand is an important issue toward expanding the capability of DNA computing to solve optimization problems. Narayanan et al [6] presented a method of encoding weights by the lengths of DNA strands. Shin et al [6] proposed a method of encoding weights by the number of hydrogen bonds in fixed-length DNA strand. Yamamoto et al [7] proposed a method of encoding weights by the concentrations of DNA strands. Lee et al [9] proposed a method of encoding weights by the melting temperatures of fixed-length DNA strands. Han et al [10, 11] proposed a method of encoding weights by means of the general line graph. They also gave a method of encoding weights [12] by means of the relative length graph and several improved DNA encoding methods [13–16] for the maximal weight clique problem, the traveling salesman problem, the minimum spanning tree problem and the 0/1 knapsack problem. In this chapter, I collect and classify the present methods of encoding information in DNA strands, which will benefit the further research on DNA computing.