Analysis of internal loops within the RNA secondary structure in almost quadratic time

MOTIVATION Evaluating all possible internal loops is one of the key steps in predicting the optimal secondary structure of an RNA molecule. The best algorithm available runs in time O(L(3)), L is the length of the RNA. RESULTS We propose a new algorithm for evaluating internal loops, its run-time is O(M(*)log(2)L), M < L(2) is a number of possible nucleotide pairings. We created a software tool Afold which predicts the optimal secondary structure of RNA molecules of lengths up to 28 000 nt, using a computer with 2 Gb RAM. We also propose algorithms constructing sets of conditionally optimal multi-branch loop free (MLF) structures, e.g. the set that for every possible pairing (x, y) contains an optimal MLF structure in which nucleotides x and y form a pair. All the algorithms have run-time O(M(*)log(2)L).

[1]  Christian N. S. Pedersen,et al.  Fast evaluation of internal loops in RNA secondary structure prediction , 1999, Bioinform..

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

[3]  I. Tinoco,et al.  Estimation of Secondary Structure in Ribonucleic Acids , 1971, Nature.

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

[5]  Georg Sczakiel,et al.  The activity of siRNA in mammalian cells is related to structural target accessibility: a comparison with antisense oligonucleotides. , 2003, Nucleic acids research.

[6]  Temple F. Smith,et al.  Rapid dynamic programming algorithms for RNA secondary structure , 1986 .

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

[8]  W. Issel,et al.  Aho, A. V. / Hopcroft, J. E. / Ullman, J. D., The Design and Analysis of Computer Algorithms. London‐Amsterdam‐Don Mills‐Sydney. Addison‐Wesley Publ. Comp. 1974 X, 470 S., $ 24,– , 1979 .

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

[10]  D. Turner,et al.  Improved predictions of secondary structures for RNA. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[11]  D. Crothers,et al.  Improved estimation of secondary structure in ribonucleic acids. , 1973, Nature: New biology.

[12]  Daniel S. Hirschberg,et al.  A linear space algorithm for computing maximal common subsequences , 1975, Commun. ACM.

[13]  David Eppstein,et al.  Sparse dynamic programming II: convex and concave cost functions , 1992, JACM.

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

[15]  Ali Ehsani,et al.  Expression of small interfering RNAs targeted against HIV-1 rev transcripts in human cells , 2002, Nature Biotechnology.

[16]  E. Southern,et al.  The Efficacy of Small Interfering RNAs Targeted to the Type 1 Insulin-like Growth Factor Receptor (IGF1R) Is Influenced by Secondary Structure in the IGF1R Transcript* , 2003, The Journal of Biological Chemistry.

[17]  Aleksey Y. Ogurtsov,et al.  A hierarchical approach to aligning collinear regions of genomes , 2002, Bioinform..

[18]  Peter F. Stadler,et al.  Conserved RNA secondary structures in viral genomes: A survey , 2004, German Conference on Bioinformatics.

[19]  R. Nussinov,et al.  Fast algorithm for predicting the secondary structure of single-stranded RNA. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Michael Zuker,et al.  Algorithms and Thermodynamics for RNA Secondary Structure Prediction: A Practical Guide , 1999 .

[21]  C. F. Bennett,et al.  Efficient Reduction of Target RNAs by Small Interfering RNA and RNase H-dependent Antisense Agents , 2003, The Journal of Biological Chemistry.

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

[23]  D. Chang,et al.  Using a hydrogen-bond index to predict the gene-silencing efficiency of siRNA based on the local structure of mRNA , 2017, 1710.07413.

[24]  A V Finkelstein,et al.  Computation of biopolymers: a general approach to different problems. , 1993, Bio Systems.

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

[26]  Baruch Schieber,et al.  On-line dynamic programming with applications to the prediction of RNA secondary structure , 1991, SODA '90.

[27]  D. Turner,et al.  Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs. , 1998, Biochemistry.

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