Magarshak Y, Benham C J
Biomathematical Sciences Department, Mount Sinai School of Medicine, New York, NY 10029.
J Biomol Struct Dyn. 1992 Dec;10(3):465-88. doi: 10.1080/07391102.1992.10508663.
This paper develops mathematical methods for describing and analyzing RNA secondary structures. It was motivated by the need to develop rigorous yet efficient methods to treat transitions from one secondary structure to another, which we propose here may occur as motions of loops within RNAs having appropriate sequences. In this approach a molecular sequence is described as a vector of the appropriate length. The concept of symmetries between nucleic acid sequences is developed, and the 48 possible different types of symmetries are described. Each secondary structure possible for a particular nucleotide sequence determines a symmetric, signed permutation matrix. The collection of all possible secondary structures is comprised of all matrices of this type whose left multiplication with the sequence vector leaves that vector unchanged. A transition between two secondary structures is given by the product of the two corresponding structure matrices. This formalism provides an efficient method for describing nucleic acid sequences that allows questions relating to secondary structures and transitions to be addressed using the powerful methods of abstract algebra. In particular, it facilitates the determination of possible secondary structures, including those containing pseudoknots. Although this paper concentrates on RNA structure, this formalism also can be applied to DNA.
本文开发了用于描述和分析RNA二级结构的数学方法。其动机源于需要开发严谨且高效的方法来处理从一种二级结构到另一种二级结构的转变，我们在此提出这种转变可能作为具有适当序列的RNA内环状结构的运动而发生。在这种方法中，分子序列被描述为具有适当长度的向量。开发了核酸序列之间对称性的概念，并描述了48种可能的不同类型的对称性。特定核苷酸序列可能的每种二级结构都确定一个对称的、带符号的置换矩阵。所有可能二级结构的集合由所有这种类型的矩阵组成，这些矩阵与序列向量的左乘使该向量保持不变。两种二级结构之间的转变由两个相应结构矩阵的乘积给出。这种形式体系提供了一种描述核酸序列的有效方法，使得与二级结构和转变相关的问题能够使用抽象代数的强大方法来解决。特别是，它有助于确定可能的二级结构，包括那些含有假结的结构。虽然本文主要关注RNA结构，但这种形式体系也可应用于DNA。
