CAJ | 학술논문

在文献中,DNA序列曾被描述为一维游动和三维游动.对前者,一个游动对应于多个DNA序列;对后者,游动和DNA序列一一对应.我们发现在三维游动(xn,yn,zn)中,由xn,yn和zn中任意有序的两个给出的二维游动已经与DNA序列一一对应,且余下的一维游动由该二维游动完全决定.因此,二维游动似乎是描述DNA序列最合适的模型.4个碱基A,C,G和T共有4 !=24个排序.每一个排序都给出DNA序列用二维游动的一种描述.两个游动(x'n,y'n)和(x"n,y"n)被看作是等价的,如果(x'n,y'n)=(εx"n,δy"n)或(εy"n,δx"n),这里ε=±1,且δ=±1.于是这24个类型的游动被分成三个等价类;它们的代表分别是(xn,yn),(yn,zn),和(xn,zn),这里(xn,yn,zn)正好是张和张的三维游动.
재문헌중,DNA서렬증피묘술위일유유동화삼유유동.대전자,일개유동대응우다개DNA서렬;대후자,유동화DNA서렬일일대응.아문발현재삼유유동(xn,yn,zn)중,유xn,yn화zn중임의유서적량개급출적이유유동이경여DNA서렬일일대응,차여하적일유유동유해이유유동완전결정.인차,이유유동사호시묘술DNA서렬최합괄적모형.4개감기A,C,G화T공유4 !=24개배서.매일개배서도급출DNA서렬용이유유동적일충묘술.량개유동(x'n,y'n)화(x"n,y"n)피간작시등개적,여과(x'n,y'n)=(εx"n,δy"n)혹(εy"n,δx"n),저리ε=±1,차δ=±1.우시저24개류형적유동피분성삼개등개류;타문적대표분별시(xn,yn),(yn,zn),화(xn,zn),저리(xn,yn,zn)정호시장화장적삼유유동.
In the literature, DNA sequences were described as 1-dimensional walks and 3-dimensional walks. In the former case, one walk corresponds to many DNA sequences; and in the latter case, the walks and the DNA sequences are in one-to-one correspondence. We find that in the3-dimensional walks (xn, yn, zn), the 2-dimensional walks given by any ordered two of xn, yn and zn,are already in one-to-one correpondence with the DNA sequences, and the remained 1-dimensional walks are determined completely by the 2-dimensional walks. Therefore, it seems that, 2-dimensional walks are the most suitable model for describing DNA sequences. There are 4! = 24orderings of the four bases A ,C,G and T. Any such ordering gives a description of DNA sequences by 2-dimensional walks. Two walks (x'n, y'n) and (x″n, y″n) are regarded to be equivalent if (x'n, y'n) =(εx″n, δy″n) or (εy″n, δx″n), where ε =± 1, and δ =± 1. Then the 24 types of walks are divided into 3 equivalence classes with representives (xn, yn), (yn, zn) and (xn, zn) respecitively, where (xn, yn,zn) are exact the 3-dimensional walks of Zhang and Zhang.