Memory Efficient Folding Algorithms for Circular RNA Secondary Structures

BACKGROUND A small class of RNA molecules, in particular the tiny genomes of viroids, are circular. Yet most structure prediction algorithms handle only linear RNAs. The most straightforward approach is to compute circular structures from 'internal' and 'external' substructures separated by a base pair. This is incompatible, however, with the memory-saving approach of the Vienna RNA Package which builds a linear RNA structure from shorter (internal) structures only. RESULT Here we describe how circular secondary structures can be obtained without additional memory requirements as a kind of 'post-processing' of the linear structures. AVAILABILITY The circular folding algorithm is implemented in the current version of the of RNAfold program of the Vienna RNA Package, which can be downloaded from http://www.tbi.univie.ac.at/RNA/

[1]  Sanjay K. Singh,et al.  Two reactions of Haloferax volcanii RNA splicing enzymes: joining of exons and circularization of introns. , 2003, RNA.

[2]  Martin Tabler,et al.  Viroids: petite RNA pathogens with distinguished talents. , 2004, Trends in plant science.

[3]  H. Puchta,et al.  Primary and secondary structure of citrus viroid IV (CVd IV), a new chimeric viroid present in dwarfed grapefruit in Israel. , 1991, Nucleic acids research.

[4]  M. Huynen,et al.  Automatic detection of conserved RNA structure elements in complete RNA virus genomes. , 1998, Nucleic acids research.

[5]  Ivo L. Hofacker,et al.  Vienna RNA secondary structure server , 2003, Nucleic Acids Res..

[6]  M. Zuker.  On finding all suboptimal foldings of an RNA molecule. , 1989, Science.

[7]  Ricardo Flores,et al.  Viroids: the minimal non‐coding RNAs with autonomous replication , 2004, FEBS letters.

[8]  D. Turner,et al.  Incorporating chemical modification constraints into a dynamic programming algorithm for prediction of RNA secondary structure. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[9]  G. Steger,et al.  Conformational transitions in viroids and virusoids: comparison of results from energy minimization algorithm and from experimental data. , 1984, Journal of biomolecular structure & dynamics.

[10]  T. S. Wadkins,et al.  Ribozyme activity in the genomic and antigenomic RNA strands of hepatitis delta virus , 2002, Cellular and Molecular Life Sciences CMLS.

[11]  Xiang-duo Kong,et al.  A circular RNA-DNA enzyme obtained by in vitro selection. , 2002, Biochemical and biophysical research communications.

[12]  P. Schuster,et al.  Complete suboptimal folding of RNA and the stability of secondary structures. , 1999, Biopolymers.

[13]  M. Maes,et al.  On a Cyclic String-To-String Correction Problem , 1990, Inf. Process. Lett..

[14]  Jerrold R. Griggs,et al.  Algorithms for Loop Matchings , 1978 .

[15]  Jens Gregor,et al.  Dynamic Programming Alignment of Sequences Representing Cyclic Patterns , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Henrik Nielsen,et al.  The ability to form full-length intron RNA circles is a general property of nuclear group I introns. , 2003, RNA.

[17]  Michael Zuker,et al.  Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information , 1981, Nucleic Acids Res..

[18]  Peter F. Stadler,et al.  Automatic Detection of Conserved Base Pairing Patterns in RNA Virus Genomes , 1998, Comput. Chem..

[19]  D Repsilber,et al.  Formation of metastable RNA structures by sequential folding during transcription: time-resolved structural analysis of potato spindle tuber viroid (-)-stranded RNA by temperature-gradient gel electrophoresis. , 1999, RNA.

[20]  Jinhong Chang,et al.  Features Affecting the Ability of Hepatitis Delta Virus RNAs To Initiate RNA-Directed RNA Synthesis , 2004, Journal of Virology.

[21]  Sean R Eddy,et al.  Circular box C/D RNAs in Pyrococcus furiosus. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[22]  J. McCaskill.  The equilibrium partition function and base pair binding probabilities for RNA secondary structure , 1990, Biopolymers.

[23]  P. Stadler,et al.  Secondary structure prediction for aligned RNA sequences. , 2002, Journal of molecular biology.

[24]  J. Sabina,et al.  Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. , 1999, Journal of molecular biology.

[25]  Walter Fontana,et al.  Fast folding and comparison of RNA secondary structures , 1994 .

[26]  Michael Zuker,et al.  Mfold web server for nucleic acid folding and hybridization prediction , 2003, Nucleic Acids Res..

[27]  D. Sankoff,et al.  RNA secondary structures and their prediction , 1984 .

[28]  Peter F. Stadler,et al.  Minimal Cycle Bases of Outerplanar Graphs , 1998, Electron. J. Comb..