Suboptimal Secondary Structures Research Articles

AliFreeFold: an alignment-free approach to predict secondary structure from homologous RNA sequences.

MotivationPredicting the conserved secondary structure of homologous ribonucleic acid (RNA) sequences is crucial for understanding RNA functions. However, fast and accurate RNA structure prediction is challenging, especially when the number and the divergence of homologous RNA increases. To address this challenge, we propose aliFreeFold, based on a novel alignment-free approach which computes a representative structure from a set of homologous RNA sequences using sub-optimal secondary structures generated for each sequence. It is based on a vector representation of sub-optimal structures capturing structure conservation signals by weighting structural motifs according to their conservation across the sub-optimal structures.ResultsWe demonstrate that aliFreeFold provides a good balance between speed and accuracy regarding predictions of representative structures for sets of homologous RNA compared to traditional methods based on sequence and structure alignment. We show that aliFreeFold is capable of uncovering conserved structural features fastly and effectively thanks to its weighting scheme that gives more (resp. less) importance to common (resp. uncommon) structural motifs. The weighting scheme is also shown to be capable of capturing conservation signal as the number of homologous RNA increases. These results demonstrate the ability of aliFreefold to efficiently and accurately provide interesting structural representatives of RNA families.Availability and implementationaliFreeFold was implemented in C++. Source code and Linux binary are freely available at https://github.com/UdeS-CoBIUS/aliFreeFold.Supplementary information Supplementary data are available at Bioinformatics online.

Exploiting Co-Transcriptional Folding and Processing of Nascent Messenger RNA for Modulating Specific Exon Splicing

RNA splicing, which involves intron removal and exon ligation, is a key step that transforms eukaryotic nascent messenger RNA (pre-mRNA) into mature mRNA. The ability to modulate inclusion or exclusion of specific exons to elicit switching between alternatively spliced variants, restoration or disruption codon-reading frame, and correcting aberrant splicing has applications for both biomedical research and therapy. However, the identification of potent pre-mRNA sites, that when targeted or masked via therapeutics efficiently induce specific exon splicing, remains a challenge. As the transcription elongation of a pre-mRNA, exon recognition and exon splicing occur simultaneously, we hypothesized that the dynamics of co-transcriptional pre-mRNA folding could be a key factor in determining the accessibility of target sites. By analyzing all possible optimal and sub-optimal local secondary structures of the pre-mRNA at each step of transcriptional analysis, we predicted the co-transcriptional accessibility profile and identified possible target sites that have the highest probability of being accessible throughout transcription process. To test the hypothesis, we used glycine decarboxylase (GLDC), an ‘oncogenic protein’ overexpressed in metastatic lung cancer cells, as a test case. Ten target sites each to induce specific exclusion of one of the two targeted exons of the GLDC gene, were identified to disrupt the codon reading frame to induce nonsense-mediated decay. In our wet experiments on NSCLC (non-small cell lung carcinoma) cell lines, specific exon exclusion were observed when each of the ten sites was masked; of these, three sites induced exon exclusion in more than 80% of total pre-mRNA. Notably, two sites predicted to be ineffective were validated to be so. Our results suggest that co-transcriptional binding accessibility can be used to aid the rational identification of potent target sites for modulating specific exon splicing.

Predictions of RNA secondary structure by combining homologous sequence information

Motivation: Secondary structure prediction of RNA sequences is an important problem. There have been progresses in this area, but the accuracy of prediction from an RNA sequence is still limited. In many cases, however, homologous RNA sequences are available with the target RNA sequence whose secondary structure is to be predicted.Results: In this article, we propose a new method for secondary structure predictions of individual RNA sequences by taking the information of their homologous sequences into account without assuming the common secondary structure of the entire sequences. The proposed method is based on posterior decoding techniques, which consider all the suboptimal secondary structures of the target and homologous sequences and all the suboptimal alignments between the target sequence and each of the homologous sequences. In our computational experiments, the proposed method provides better predictions than those performed only on the basis of the formation of individual RNA sequences and those performed by using methods for predicting the common secondary structure of the homologous sequences. Remarkably, we found that the common secondary predictions sometimes give worse predictions for the secondary structure of a target sequence than the predictions from the individual target sequence, while the proposed method always gives good predictions for the secondary structure of target sequences in all tested cases.Availability: Supporting information and software are available online at: http://www.ncrna.org/software/centroidfold/ismb2009/.Contact: hamada-michiaki@aist.go.jpSupplementary information:Supplementary data are available at Bioinformatics online.

ConStruct: Improved construction of RNA consensus structures

BackgroundAligning homologous non-coding RNAs (ncRNAs) correctly in terms of sequence and structure is an unresolved problem, due to both mathematical complexity and imperfect scoring functions. High quality alignments, however, are a prerequisite for most consensus structure prediction approaches, homology searches, and tools for phylogeny inference. Automatically created ncRNA alignments often need manual corrections, yet this manual refinement is tedious and error-prone.ResultsWe present an extended version of CONSTRUCT, a semi-automatic, graphical tool suitable for creating RNA alignments correct in terms of both consensus sequence and consensus structure. To this purpose CONSTRUCT combines sequence alignment, thermodynamic data and various measures of covariation.One important feature is that the user is guided during the alignment correction step by a consensus dotplot, which displays all thermodynamically optimal base pairs and the corresponding covariation. Once the initial alignment is corrected, optimal and suboptimal secondary structures as well as tertiary interaction can be predicted. We demonstrate CONSTRUCT's ability to guide the user in correcting an initial alignment, and show an example for optimal secondary consensus structure prediction on very hard to align SECIS elements. Moreover we use CONSTRUCT to predict tertiary interactions from sequences of the internal ribosome entry site of CrP-like viruses. In addition we show that alignments specifically designed for benchmarking can be easily be optimized using CONSTRUCT, although they share very little sequence identity.ConclusionCONSTRUCT's graphical interface allows for an easy alignment correction based on and guided by predicted and known structural constraints. It combines several algorithms for prediction of secondary consensus structure and even tertiary interactions. The CONSTRUCT package can be downloaded from the URL listed in the Availability and requirements section of this article.

A fuzzy model of predicting RNA secondary structure

We propose a novel model to predict RNA secondary structure based on the fuzzy sets theory. Through the fuzzy partition of state spaces and the incorporation of fuzzy goals, we can find the optimal fuzzy policy of the model using fuzzy dynamic programming algorithm effectively, and then determine optimal and suboptimal RNA secondary structures. Compared to the existing sophisticated prediction models, such as Zuker’s method and the SCFG model, our fuzzy model based approach has many advantages: 1) computational complexity can be reduced by the fuzzy partition; 2) the optimal secondary structure and several suboptimal ones can be generated simultaneously; and 3) subjective prior knowledge can readily be incorporated. This paper presents a complete description of our fuzzy model and gives the implementation of the proposed method. We also apply the BJK fuzzy model structure to secondary structure predictions based on datasets of tRNA and tmRNA sequences. By the comparison of our fuzzy method with both the minimum free energy based mfold tool and the BJK grammar model of SCFG, our experimental results validate the effectiveness of the proposed method and the prediction accuracy is shown to be further improved.

Prediction of RNA structures containing pseudoknots

This paper describes a genetic algorithm for predicting RNA structures that contain various types of pseudoknots. Pseudoknotted RNA structures are much more difficult to predict by computational methods than RNA secondary structures, as they are more complex and the analysis is time-consuming. We developed an efficient genetic algorithm to predict RNA folding structures containing any type of pseudoknot, as well as a novel initial population method to decrease computational complexity and increase the accuracy of the results. We also used an interaction filter to decrease the size of the possible stem lists for long RNA sequences. We predicted RNA structures using a number of different termination conditions and compared the validity of the results and the times required for the analyses. The algorithm proved able to predict efficiently RNA structures containing various types of pseudoknots. Corresponding Author: Kyungsook Han (Email: khan@inha.ac.kr) This work was supported by the Korea Science and Engineering Foundation (KOSEF) under grant R01-2003000-10461-0. Introduction The prediction of an RNA structure with a pseudoknot using computational methods requires much computation. Predicting the most stable structure with minimal free energy from an RNA sequence is an optimization problem (Lee and Han, 2002; Lee and Han, 2003; Deiman and Pleij, 1997). Computational methods for predicting RNA structure generally make use of two algorithms, one combinatorial the other recursive. The combinatorial algorithm first creates an inventory of all possible stem lists that can be formed by a given RNA sequence, and then determines the combination with the lowest free energy. This algorithm has the advantage that it can include pseudoknot structures, but the number of possible structures increases immensely with sequence length (Rivas and Eddy, 1999; Akutsu, 2000). The recursive algorithm finds the lowest free energy structure from the sub-fragments of a sequence. It makes a systematic search of all sub-fragments for the lowest free energy structure containing at least one base pair. The first sub-fragments considered are those capable of forming a hairpin loop closed by a single base pair. So in a first pass it will find the lowest free energy structures for all pentanucleotides in the sequence. This method always finds the structure with least free energy, but it does not identify structures such as pseudoknots because of their computational complexity. A genetic algorithm (GA) is an optimization procedure that implements the mechanism of biological evolution. It begins with a set of solutions called populations. Solutions are then taken and used to form a new population in the hope that the new population will be superior to the old one. They are selected to generate new solutions according to their fitness; the fitter they are, the more opportunities they have to reproduce. This procedure is repeated until some specified condition is satisfied. Genetic algorithms have been theoretically and empirically proven to provide robust searches in highly complex and uncertain spaces, and they are finding widespread application in commerce, science and engineering. They are computationally simple and powerful search methods, and many workers have used them to predict RNA structures and sequence alignments; they have been used to seek optimal and sub-optimal secondary RNA structures (Benedetti and Morosetti, 1995; Shapiro and Navetta, 1994) and to simulate RNA folding pathways (Gultyaev et al., 1995; Shapiro et al., 2001). Massively parallel genetic algorithms have been employed to predict RNA structures that include pseudoknots (Shapiro and Wu, 1996; Shapiro and Wu, 1997). However the structures predicted contained only H (Hairpin)-type pseudoknots and the computations were extremely complex as they used randomly generated initial populations. Dynamic programming algorithms also used to predict RNA structures including pseudoknots (Rivas and Eddy, 1999) again could only predict structures with H type pseudoknots, and only from short RNA sequences. We have developed a GA that is able to predict efficiently

Secondary Structure Prediction of Interacting RNA Molecules

Computational tools for prediction of the secondary structure of two or more interacting nucleic acid molecules are useful for understanding mechanisms for ribozyme function, determining the affinity of an oligonucleotide primer to its target, and designing good antisense oligonucleotides, novel ribozymes, DNA code words, or nanostructures. Here, we introduce new algorithms for prediction of the minimum free energy pseudoknot-free secondary structure of two or more nucleic acid molecules, and for prediction of alternative low-energy (sub-optimal) secondary structures for two nucleic acid molecules. We provide a comprehensive analysis of our predictions against secondary structures of interacting RNA molecules drawn from the literature. Analysis of our tools on 17 sequences of up to 200 nucleotides that do not form pseudoknots shows that they have 79% accuracy, on average, for the minimum free energy predictions. When the best of 100 sub-optimal foldings is taken, the average accuracy increases to 91%. The accuracy decreases as the sequences increase in length and as the number of pseudoknots and tertiary interactions increases. Our algorithms extend the free energy minimization algorithm of Zuker and Stiegler for secondary structure prediction, and the sub-optimal folding algorithm by Wuchty et al. Implementations of our algorithms are freely available in the package MultiRNAFold.

DNA sequence analysis of the ribosomal DNA ITS2 region for the Anopheles punctulatus group of mosquitoes.

The internal transcribed spacer 2 (ITS2) from the ribosomal DNA was sequenced and characterized for ten cryptic species in the Anopheles punctulatus group, the members of which are major vectors of malaria and filariasis in the south-west Pacific. The length of the ITS2 ranged from 549 bp to 565 bp and displayed levels of sequence variation ranging from 2.3% to 24.3% due mainly to indels of simple sequences. The GC content varied from 61.3% to 70.9%. These values were higher than those found in other cryptic species of mosquitoes and comparable only to members of the An. dirus complex suggesting a possible link between this group of Asian mosquitoes and the An. punctulatus group. Optimal and suboptimal secondary structures were investigated and revealed structures where the 5' region folded independently of the 3' region. Due to the large level of sequence variation between species, the ITS2 region proved unsuitable for phylogenetic analysis.

Complete suboptimal folding of RNA and the stability of secondary structures.

An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm is particularly fast in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities, such as the partition function or measures for structural diversity. The density of states at low energies and its associated structures are crucial in assessing from a thermodynamic point of view how well-defined the ground state is. We demonstrate this by exploring the role of base modification in tRNA secondary structures, both at the level of individual sequences from Escherichia coli and by comparing artificially generated ensembles of modified and unmodified sequences with the same tRNA structure. The two major conclusions are that (1) base modification considerably sharpens the definition of the ground state structure by constraining energetically adjacent structures to be similar to the ground state, and (2) sequences whose ground state structure is thermodynamically well defined show a significant tendency to buffer single point mutations. This can have evolutionary implications, since selection pressure to improve the definition of ground states with biological function may result in increased neutrality.

Complete suboptimal folding of RNA and the stability of secondary structures

An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm performs particularly well in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities, such as the partition function or measures for structural diversity. The density of states at low energies and its associated structures are crucial in assessing from a thermodynamic point of view how well defined the ground state is. We demonstrate this by exploring the role of base modification in tRNA secondary structures, both at the level of individual sequences from E. coli and by comparing artificially generated ensembles of modified and unmodified sequences with the same tRNA structure. The two major conclusions are that (1) base modification considerably sharpens the definition of the ground state structure by constraining energetically adjacent structures to be similar to the ground state, and (2) sequences whose ground state structure is thermodynamically well defined show a significant tendency to buffer single point mutations. This can have evolutionary implications, since selection pressure to improve the definition of ground states with biological function may result in increased neutrality.

Classification of RNA Secondary Structures Using the Techniques of Cluster Analysis

An RNA molecule has a lot of suboptimal secondary structures. Some of these suboptimal structures are very similar and some are entirely different. In some cases, the free energy of these suboptimal structures does not differ much from that of the optimal structure. In order to characterize this relationship more clearly, we defined a metric among the secondary structures by the unweighted pair group method, using the arithmetic average and extended this metric to the sets of secondary structures. We report two applications of this metric. First, we developed a method for the classification of these suboptimal secondary structures of a given RNA sequence. Results of classification are presented with the secondary structures of cadang-cadang coconut viroid, potato spindle tuber viroid and polio virus as examples. Second, we applied this metric to the classification of the secondary structures derived from a set of mutant RNA sequences. We discuss that the mutation of a given RNA sequence changes not only the optimal secondary structure, but also the population of the cluster of the secondary structures.

Thermodynamic Prediction of Conserved Secondary Structure: Application to the RRE Element of HIV, the tRNA-like Element of CMV and the mRNA of Prion Protein

An algorithm for prediction of conserved secondary structure of single-stranded RNA is presented. For each RNA of a set of homologous RNAs optimal and suboptimal secondary structures are calculated and stored in a base-pair probability matrix. A multiple sequence alignment is performed for the set of RNAs. The resulting gaps are introduced into the individual probability matrices. These homologous probability matrices are summed to give a consensus probability matrix emphasizing the conserved secondary structure elements of the RNA set. Thus the algorithm combines the advantages of thermodynamic structure prediction by energy minimization with the information obtained from phylogenetic alignment of sequences. The algorithm is applied to three examples. The REV-responsive element of HIV, the structure of which is well known from the literature, was chosen to test the algorithm. The second example is the 3′ terminal segment of genomic single-stranded RNAs of cucumber mosaic viruses; a structure similar to that of the related brome mosaic virus was expected and was confirmed. The third example is the prion-protein mRNA from different organisms; the structure of this mRNA is not known. By application of the algorithm highly conserved hairpins were found in the prion-protein mRNA.

An Interactive Framework for RNA Secondary Structure Prediction with a Dynamical Treatment of Constraints

A novel approach aiding in the prediction of RNA secondary structures is presented. Although phylogenetic methods are the most successful at deriving RNA secondary structures, the are not applicable when the number of sequences or the sequence variability is too low. Methods based on energy minimization are therefore of great interest. However, some of the suboptimal RNA secondary structures computed with classic methods are unsaturated structures, i.e. some structures are included into others. Thus, the incorporation of constraints during the process of folding is not possible, while the incorporation of constraints before the process of folding often introduces a bias into the energy function. This paper describes a new procedure which allows for the incorporation of constraints before and during the process of RNA folding. SAPSSARN is an interactive program which offers a framework, both to specify a secondary structure through a set of folding constraints and to compute all the supoptimal saturated RNA secondary structures which satisfy all the folding constraints. At the start, it relies on the computation of the probabilities of pairing of each base with all others according to McCaskill's algorithm. The constraint satisfaction formulation of the problem deals dynamically with a chosen set of folding constraints and, finally, a search algorithm computes all the suboptimal saturated secondary structures which satisfy those folding constraints. Within such a framework, it is possible to test new ideas about RNA folding and secondary structures, including pseudoknots, can be computed. The program is illustrated with RNA sequences on which we obtained results in agreement with known structures by using a protocol which mimics the hierarchical folding of RNA molecules.

A genetic algorithm to search for optimal and suboptimal RNA secondary structures

Genetic algorithms are a search method used in solving problems by selection, recombination and mutation of tentative solutions, until the better ones are achieved. They are very efficient when the ‘building block’ hypothesis is effective for the solutions, which means that a better solution can be obtained by assembling short ‘motifs’ or ‘schemata’ that can be retrieved in some other worse solutions. The additive nature of the secondary structure free energy rules suggests the validity of this hypothesis, and therefore the likely power of a genetic algorithm approach to search for RNA secondary structures. We describe in detail an original genetic algorithm specific for this problem. The sharing function used to obtain differentiated solutions is also described. It results in a greater effectiveness of the algorithm in retrieving a large number of suboptimal RNA foldings besides the optimal one. RNA sequences of different length are used to test the method. The PSTV viroid sequence has been studied.

Optimization and Performance Analysis of a Massively Parallel Dynamic Programming Algorithm for Rna Secondary Structure Prediction

An optimized and parallelized form of a dynamic pro gramming algorithm capable of generating optimal and suboptimal RNA secondary structures is pre sented. Implementation of this algorithm on a MasPar MP-2 with 16K processors is shown to perform ex tremely well for very large nucleic acid sequences such as HIV (AIDS) and Rhinovirus (common cold). These sequences are, respectively, 9,128 and 7,208 nu cleotides in length. By taking advantage of the parallel nature of MasPar and also optimizing the communica tion requirements the implementation essentially re duced the algorithm from order O(n3) to 0(n2). This reduction in complexity enables us to fold large RNA sequences in reasonable amounts of time. This capa bility has proven to be a valuable tool in studying the molecular structure and biological function of mole cules this large.

Learning to fold RNA with parallel processors

We implement a parallel processed simulation of sequential folding pathways occuring concurrently as a growing RNA chain explores the space of available secondary structures. An appropriate learning or updating strategy is introduced to systematically trim the branching of sequential folding pathways. By applying our algorithm to specific RNA sequences with known native structure, we provide evidence that this learning strategy determines the expeditious convergence to the actual ensemble of optimal and suboptimal secondary structures. The robustness of our results to uncertainties in the thermodynamic parameters is shown to result from the very nature of the parallel process. Our final goal is to examine the dependence of the learning efficiency on the information content of the primary sequence. This is done by contrasting the folding process of specific RNA species whose native structures are known with the folding of random sequences.

A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by phylogenetic comparison

This article describes the latest version of an RNA folding algorithm that predicts both optimal and suboptimal solutions based on free energy minimization. A number of RNA's with known structures deduced from comparative sequence analysis are folded to test program performance. The group of solutions obtained for each molecule is analysed to determine how many of the known helixes occur in the optimal solution and in the best suboptimal solution. In most cases, a structure about 80% correct is found with a free energy within 2% of the predicted lowest free energy structure.

Predicting Common Foldings of Homologous RNAs

A new approach is proposed for determining common RNA secondary structures within a set of homologous RNAs. The approach is a combination of phylogenetic and thermodynamic methods which is based on the prediction of optimal and suboptimal secondary structures, topological similarity searches and phylogenetic comparative analysis. The optimal and suboptimal RNA secondary structures are predicted by energy minimization. Structural comparison of the predicted RNA secondary structures is used to find conserved structures that are topologically similar in all these homologous RNAs. The validity of the conserved structural elements found is then checked by phylogenetic comparison of the sequences. This procedure is used to predict common structures of ribonuclease P (RNAase P) RNAs.

Higher-order structure of the 5.8 S rRNA sequence within the yeast 35 S precursor ribosomal RNA synthesized in vitro

Dimethylsulfate, 1-cyclohexyl-3-(2-morpholinoethyl)-carbodiimide metho- p-toluene-sulfonate, RNase T 1 and RNase V 1 have been used as structure-sensitive probes to examine the higher-order structure of the 5.8 S rRNA sequence within the yeast 35 S precursor ribosomal RNA molecule. Data produced have been used to evaluate several theoretical structure models for the 5.8 S rRNA sequence within the precursor rRNA. These models are generated by minimum free energy calculations. A model is proposed that accommodates 83% of the residues experimentally shown to be in either base-paired or single-stranded structure in the correct configuration. Several alternative suboptimal secondary structures have been evaluated. Moreover, the chemical reactivities of several residues within the 5.8 S rRNA sequence in the precursor rRNA molecule differ from those of the corresponding residues in the mature rRNA molecule. This finding provides experimental evidence to support the notion that the 5.8 S rRNA sequence within the precursor rRNA undergoes structural reorganization following rRNA processing.

Common structures of the 5′ non-coding RNA in enteroviruses and rhinoviruses: Thermodynamical stability and statistical significance

A total of 4051 suboptimal secondary structures are predicted by folding the 5′ non-coding region of ten polioviruses, five human rhinoviruses and three coxsackieviruses using our new suboptimal folding algorithm for the prediction of both optimal and suboptimal RNA secondary structures. A comparative analysis of these RNA secondary structures reveals the conservation of common secondary structure that can be supported by phylogenetic data. The thermodynamic stability and statistical significance of these predicted, conserved helical elements are assessed and significant structure motifs in the 5′ non-coding region are proposed. The possible roles of these structure motifs in the virus life cycle are discussed.