DNA序列高维空间数字编码的运算法则

DNA序列的高维空间二进制数字编码，除可以对DNA序列的碱基结构、功能基团、碱基互补、氢键强弱等性质进行编码之外，还可以方便地进行 数学运算和逻辑运算。DNA序列高维空间数字编码的运算法则是：（1）根据DNA序列数码的奇偶性质，可以推导出其与末位碱基的对应关系。当DNA序列S的数值X（S）＝4n,4n 1,4n 2,4n 3时，其末位碱基依次为C，T，A，G（n=0,1,2,…）。（2）提出DNA序列高维空间的表观维数Nv，数值维数Nx及差异维数Nd的概念。当Nd=0时，首位碱基为A或G，当Nd=2n或2n 1(n=1,2,…）时，首痊碱基为（C）^n或（C）^nT。（3）推导出DNA序列点突变（单核苷酸多态性SNP）的运算法则。（4）推导出DNA重复序列（Tandem repeat)的运算法则。（5）提出DNA子序列（subsequence)的概念并定义DNA子序列的定值部Xi(digital value)和定位部Qi(location value)及其计算公式。（6）推导出DNA序列的延长运算、删除运算、缺失运算、插入运算、转位运算、换位运算和置换运算等的运算法则。（7）通过按位加运算求得DNA序列的汉明距离dh，碱基距离dh‘，基团距离dh″和共轭距离dG以及这些距离的意义与联系。（8）分析结果表明DNA序列的数字编码比常规的字符编码在数学运算上具有明显的优越性。

OPERATIONAL RULES OF THE DIGITAL CODING OF DNA SEQUENCESIN HIGH DIMENSION SPACE

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.