Shapes of RNA Pseudoknot Structures

Abstract

Abstract

In this article, we study abstract shapes of k-noncrossing, σ-canonical RNA pseudoknot structures. We consider \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$ { \bf lv}_{ \bf k}^{ \bf 1} $$ \end{document} - and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$ { \bf lv}_{ \bf k}^{ \bf 5} $$ \end{document} -shapes, which represent a generalization of the abstract π′- and π-shapes of RNA secondary structures introduced by Giegerich et al. Using a novel approach, we compute the generating functions of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$ { \bf lv}_{ \bf k}^{ \bf 1} $$ \end{document} - and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$ { \bf lv}_{ \bf k}^{ \bf 5} $$ \end{document} -shapes as well as the generating functions of all \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$ { \bf lv}_{ \bf k}^{ \bf 1} $$ \end{document} - and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} $$ { \bf lv}_{ \bf k}^{ \bf 5} $$ \end{document} -shapes induced by all k-noncrossing, σ-canonical RNA structures for fixed n. By means of singularity analysis of the generating functions, we derive explicit asymptotic expressions For online Supplementary Material , see www.liebertonline.com.