OPERATIONAL RULES OF THE DIGITAL CODING OF DNA SEQUENCESIN HIGH DIMENSION SPACE
DNA序列高维空间数字编码的运算法则

Digital coding of DNA sequence has great advantages of mathematical and logical operations. (1). According to the parity of DNA digital sequences, the last nucleotide bases can be determined. When the digital value of DNA sequence X(s)=4n, 4n+1, 4n+2, 4n+3, (n=0, 1, 2,…), the last nucleotide base is C, T, A, G respectively. (2). The difference between the visual dimension Nv and the digital dimension Nx is called the difference dimension Nd of DNA sequence. When Nd=0, the initial nucleotide is A or G, and when Nd=2n or 2n+1,(n=1, 2,…), then the initial nucleotide bases are (C)n or (C)nT. (3). Operation rules for three kinds of point mutation of DNA sequences (transition, transversion and transformation) are derived. (4). The digital coding for a tandem repeat (Sp)n is, X(Sp)n=X(Sp)(2np-1)/(2p-1).(5). DNA sequence Sk with m subsequences, X(Sk)=X(Si)Qi. X(Si) and Qi are the digital value and location value of the DNA subsequence Si repectively. (6). The formulae of truncation operation, the elongation operation, the deletion operation, the insertion operation, the translocation operation, the transformation operation and the substitution operation of DNA subsequences are also deduced. (7). The Hamming value of even bits Vh′ in DNA sequence represents the number of purine base and the Hamming value of odd bits Vh″ is the number of keto base. (8). The relationship of the Hamming distance dh, the base distance db, the functional group distance df and the conjugate distance dG between two DNA sequences are also discussed.