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.

RNA Pseudoknot Prediction in Energy-Based Models

Motivation: Since the whole genome sequences of many species have been determined, computational prediction of RNA secondary structures and computational identification of those non-coding RNA regions by comparative genomics become important. Therefore, more advanced alignment methods are required. Recently, an approach of structural alignment for RNA sequences has been introduced to solve these problems. Pair hidden Markov models on tree structures (PHMMTSs) proposed by Sakakibara are efficient automata-theoretic models for structural alignment of RNA secondary structures, although PHMMTSs are incapable of handling pseudoknots. On the other hand, tree adjoining grammars (TAGs), a subclass of context-sensitive grammars, are suitable for modeling pseudoknots. Our goal is to extend PHMMTSs by incorporating TAGs to be able to handle pseudoknots.

Results: We propose pair stochastic TAGs (PSTAGs) for aligning and predicting RNA secondary structures including a simple type of pseudoknot which can represent most known pseudoknot structures. First, we extend PHMMTSs defined on alignment of 'trees' to PSTAGs defined on alignment of 'TAG trees' which represent derivation processes of TAGs and are functionally equivalent to derived trees of TAGs. Then, we develop an efficient dynamic programming algorithm of PSTAGs for obtaining an optimal structural alignment including pseudoknots. We implement the PSTAG algorithm and demonstrate the properties of the algorithm by using it to align and predict several small pseudoknot structures. We believe that our implemented program based on PSTAGs is the first grammar-based and practically executable software for comparative analyses of RNA pseudoknot structures, and, further, non-coding RNAs.

Availability: The source code of PSTAG and its web application are available at http://phmmts.dna.bio.keio.ac.jp/pstag/

Contact: yasu@bio.keio.ac.jp

/pdf/pair-stochastic-tree-adjoining-grammars-for-aligning-and-14rtzuyvmo.pdf

Pair stochastic tree adjoining grammars for aligning and predicting pseudoknot RNA structures

π-Stacked complexes formed by two, three, and four thiophene rings have been investigated using abinitio quantum mechanical calculations. The relative orientation between the rings was investigated for each complex by exploring the corresponding potential energy surface at the MP2/6-31+G(d,p) level, the inter-ring distance, and the degree of tilting being examined in each case. Interaction energies were calculated at the MP2, MP3, MP4, and CCSD, levels of theory. Negligible or even slightly positive n-body effects have been predicted for the stacked thiophene arrangements studied in this work. This is consequence of the cancellation of favorable induction contribution by the destabilizing dispersion component. On the other hand analysis of the optimized geometries obtained for the trimer and tetramer revealed that the orientation of the rings presents a preferred degree of periodicity. Finally, we found that the lowest transition energy decreases when the size of the complex increases, this feature being attributed to desestabilization of the HOMO and stabilization of the LUMO that occur simultaneously. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

Ab initio calculations on pi-stacked thiophene dimer, trimer, and tetramer: structure, interaction energy, cooperative effects, and intermolecular electronic parameters.

Motivation: RNA H-type pseudoknots are ubiquitous pseudoknots that are found in almost all classes of RNA and thought to play very important roles in a variety of biological processes. Detection of these RNA H-type pseudoknots can improve our understanding of RNA structures and their associated functions. However, the currently existing programs for detecting such RNA H-type pseudoknots are still time consuming and sometimes even ineffective. Therefore, efficient and effective tools for detecting the RNA H-type pseudoknots are needed.

Results: In this paper, we have adopted a heuristic approach to develop a novel tool, called HPknotter, for efficiently and accurately detecting H-type pseudoknots in an RNA sequence. In addition, we have demonstrated the applicability and effectiveness of HPknotter by testing on some sequences with known H-type pseudoknots. Our approach can be easily extended and applied to other classes of more general pseudoknots.

Availability: The web server of our HPknotter is available for online analysis at http://bioalgorithm.life.nctu.edu.tw/HPKNOTTER/

Contact:cllu@mail.nctu.edu.tw, chiu@cc.nctu.edu.tw

https://ir.nctu.edu.tw:443/bitstream/11536/13331/1/000231472500007.pdf

A heuristic approach for detecting RNA H-type pseudoknots

Efficient exact algorithms for finding optimal secondary structures of RNA sequences have been known for a quarter of a century. However, these algorithms are restricted to structures without overlapping base pairs, or pseudoknots. The ability to include pseudoknots has gained increased attention over the last five years, but three recent publications indicate that this might leave the problem intractable. In this paper we further investigate the complexity of the pseudoknot prediction problem in two simple models based on base pair stacking. We confirm the intractability of pseudoknot prediction by proving it NP hard for binary strings in one model, and for strings over an unbounded alphabet in the other model. Conversely, we are also able to present a polynomial time algorithm for pseudoknot prediction for strings over a fixed size alphabet in the second model and a polynomial time approximation scheme for pseudoknot prediction for strings over a fixed size alphabet in the first model.

Complexity of Pseudoknot Prediction in Simple Models

In this paper we investigate the computational problem of predicting RNA secondary structures that allow any kinds of pseudoknots. The general belief is that allowing pseudoknots makes the problem very difficult. Existing polynomial-time algorithms, which aim at structures that optimize some energy functions, can only handle a certain types of pseudoknots. In this paper we initiate the study of approximation algorithms for handling all kinds of pseudoknots. We focus on predicting RNA secondary structures with a maximum number of stacking pairs and obtain two approximation algorithms with worst-case approximation ratios of 1/2 and 1/3 for planar and general secondary structures, respectively. Furthermore, we prove that allowing pseudoknots would make the problem of maximizing the number of stacking pairs on planar secondary structure to be NP-hard. This result should be contrasted with the recent NP-hard results on psuedoknots which are based on optimizing some peculiar energy functions.

Predicting RNA secondary structures with arbitrary pseudoknots by maximizing the number of stacking pairs

The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no performance guarantee and can only handle limited types of pseudoknots. In this paper we initiate the study of predicting RNA secondary structures with a maximum number of stacking pairs while allowing arbitrary pseudoknots. We obtain two approximation algorithms with worst-case approximation ratios of 1/2 and 1/3 for planar and general secondary structures,respectively. For an RNA sequence of $n$ bases, the approximation algorithm for planar secondary structures runs in $O(n^3)$ time while that for the general case runs in linear time. Furthermore, we prove that allowing pseudoknots makes it NP-hard to maximize the number of stacking pairs in a planar secondary structure. This result is in contrast with the recent NP-hard results on psuedoknots which are based on optimizing some general and complicated energy functions.

Samuel Ieong

Papers

Predicting RNA secondary structures with arbitrary pseudoknots by maximizing the number of stacking pairs

Predicting RNA Secondary Structures with Arbitrary Pseudoknots by Maximizing the Number of Stacking Pairs