DNA序列全对称群和多义密码子的对称性(Ⅰ)(英文)

A Complete Symmetrical Group of DNA Sequences and Symmetry of Poly-Codon Sequences (Ⅰ)

为了完善ＤＮＡ序列对称理论，本文将１２阶ＤＮＡ群（Ｄ群）推广为２４阶ＤＮＡ全对称群（Ｄｄ群）．ＤＮＡ全对称群被定义为特殊的交换群（Ｓ４），其交换元素是ＤＮＡ序列的４个碱基．ＤＮＡ群与四面体群（Ｔ群）同构， ＤＮＡ全对称群与正四面体全对称群（Ｔｄ群）同构， Ｄ群是 Ｄｄ群的一个子群．本文还推导出了 Ｄｄ群１２个新元素的矩阵表， Ｄｄ 群的乘法表，得到了在 Ｄｄ群操作下四碱基 Ａ，Ｃ，Ｇ和 Ｔ的变换表等．

In order to perfect the unified symmetrical theory of DNA sequences (Zhang, 1997), we expand the DNA group of the order being 12 to a complete symmetrical group of DNA of the order being 24 based on the complete symmetrical group of a regular tetrahedron (Td). The complete symmetrical group of DNA (Dd) is defined as a particular permulation group (S4) in which the permuted objects are the four bases of a DNA molecule. The DNA group which is isomorphic to the tetrahedron group (T-group) is a subgroup of the complete symmetrical group of DNA which is isomorphic to the complete symmetrical group of a regular tetrahedron (Td group). The matrix representation of the 12 new elements of the complete symmetrical group of DNA has been obtained.