TY - JOUR

T1 - An algebraic representation of rna secondary structures

AU - Magarshak, Yuri

AU - Benham, Craig J.

N1 - Funding Information:
The authors gratefully acknowledge discussions with Dr. A. Kister, who first suggested the possibility of movable loops to us. We also thank Dr. V. Ivanov for fruitful discussions. This work was supported in part by grant DMB 88-96284 from the National Science Foundation.

PY - 1992/12

Y1 - 1992/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027081236&partnerID=8YFLogxK

U2 - 10.1080/07391102.1992.10508663

DO - 10.1080/07391102.1992.10508663

M3 - Article

C2 - 1283516

AN - SCOPUS:0027081236

VL - 10

SP - 465

EP - 488

JO - Journal of Biomolecular Structure and Dynamics

JF - Journal of Biomolecular Structure and Dynamics

SN - 0739-1102

IS - 3

ER -