RNA Pseudoknot Prediction in Energy-Based Models

RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g., as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactorily in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots introduces modeling and computational problems. In this paper we consider the problem of predicting RNA secondary structures with pseudoknots based on free energy minimization. We first give a brief comparison of energy-based methods for predicting RNA secondary structures with pseudoknots. We then prove that the general problem of predicting RNA secondary structures containing pseudoknots is NP complete for a large class of reasonable models of pseudoknots.

[1]  Manolo Gouy,et al.  An energy model that predicts the correct folding of both the tRNA and the 5S RNA molecules , 1984, Nucleic Acids Res..

[2]  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.

[3]  Christian N. S. Pedersen,et al.  Pseudoknots in RNA Secondary Structures , 2000 .

[4]  D. Turner,et al.  RNA structure prediction. , 1988, Annual review of biophysics and biophysical chemistry.

[5]  M Brown,et al.  RNA pseudoknot modeling using intersections of stochastic context free grammars with applications to database search. , 1996, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[6]  Kaizhong Zhang,et al.  Simple Fast Algorithms for the Editing Distance Between Trees and Related Problems , 1989, SIAM J. Comput..

[7]  Satoshi Kobayashi,et al.  Tree Adjoining Grammars for RNA Structure Prediction , 1999, Theor. Comput. Sci..

[8]  Luc Jaeger,et al.  RNA pseudoknots , 1992, Current Biology.

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

[10]  D. Sankoff.  Simultaneous Solution of the RNA Folding, Alignment and Protosequence Problems , 1985 .

[11]  Tatsuya Akutsu,et al.  Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots , 2000, Discret. Appl. Math..

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

[13]  R. C. Underwood,et al.  Stochastic context-free grammars for tRNA modeling. , 1994, Nucleic acids research.

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

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

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

[17]  Gary D. Stormo,et al.  An RNA folding method capable of identifying pseudoknots and base triples , 1998, Bioinform..

[18]  David B. Searls,et al.  The Linguistics of DNA , 1992 .

[19]  C. Pleij,et al.  An APL-programmed genetic algorithm for the prediction of RNA secondary structure. , 1995, Journal of theoretical biology.

[20]  Gary D. Stormo,et al.  Finding Common Sequence and Structure Motifs in a Set of RNA Sequences , 1997, ISMB.

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

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

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

[24]  B. Ganem.  RNA world , 1987, Nature.

[25]  T. Pollard,et al.  Annual review of biophysics and biophysical chemistry , 1985 .

[26]  Bjarne Knudsen,et al.  RNA secondary structure prediction using stochastic context-free grammars and evolutionary history , 1999, Bioinform..

[27]  R. Durbin,et al.  RNA sequence analysis using covariance models. , 1994, Nucleic acids research.

[28]  Gordon Reynolds,et al.  G T-B , 1980 .

[29]  E Rivas,et al.  A dynamic programming algorithm for RNA structure prediction including pseudoknots. , 1998, Journal of molecular biology.