On the algebraic representation of RNA secondary structures with G x U pairs.

Magarshak et al. represented an RNA molecule as a complex vector x and an RNA secondary structure gamma as a complex matrix Sgamma in such a way that the molecule represented by x was compatible with the secondary structure gamma if and only if Sgamma o x=x. They only considered Watson-Crick base pairs and their representation cannot be extended to allow for G x U pairs. In this paper we study a generalization of Magarshak's representation that allows for these pairs, and in particular we provide a family of algebraic structures where that generalization can be carried out. We also show that this representation can be used to compare secondary structures, through transfer matrices which transform the representation of one secondary structure into the representation of the other.