Combinatorics of RNA–RNA interaction

RNA–RNA binding is an important phenomenon observed for many classes of non-coding RNAs and plays a crucial role in a number of regulatory processes. Recently several MFE folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Here joint structure means that in a diagram representation the intramolecular bonds of each partner are pseudoknot-free, that the intermolecular binding pairs are noncrossing, and that there is no so-called “zigzag” configuration. This paper presents the combinatorics of RNA interaction structures including their generating function, singularity analysis as well as explicit recurrence relations. In particular, our results imply simple asymptotic formulas for the number of joint structures.     

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.     

Consensus folding of unaligned RNA sequences revisited.

As one of the earliest problems in computational biology, RNA secondary structure prediction (sometimes referred to as "RNA folding") problem has attracted attention again, thanks to the recent discoveries of many novel non-coding RNA molecules. The two common approaches to this problem are de novo prediction of RNA secondary structure based on energy minimization and the consensus folding approach (computing the common secondary structure for a set of unaligned RNA sequences). Consensus folding algorithms work well when the correct seed alignment is part of the input to the problem. However, seed alignment itself is a challenging problem for diverged RNA families. In this paper, we propose a novel framework to predict the common secondary structure for unaligned RNA sequences. By matching putative stacks in RNA sequences, we make use of both primary sequence information and thermodynamic stability for prediction at the same time. We show that our method can predict the correct common RNA secondary structures even when we are given only a limited number of unaligned RNA sequences, and it outperforms current algorithms in sensitivity and accuracy.     

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 handle only 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.     

Small RNAs with 5′-Polyphosphate Termini Associate with a Piwi-Related Protein and Regulate Gene Expression in the Single-Celled Eukaryote Entamoeba histolytica

Small interfering RNAs regulate gene expression in diverse biological processes, including heterochromatin formation and DNA elimination, developmental regulation, and cell differentiation. In the single-celled eukaryote Entamoeba histolytica, we have identified a population of small RNAs of 27 nt size that (i) have 5′-polyphosphate termini, (ii) map antisense to genes, and (iii) associate with an E. histolytica Piwi-related protein. Whole genome microarray expression analysis revealed that essentially all genes to which antisense small RNAs map were not expressed under trophozoite conditions, the parasite stage from which the small RNAs were cloned. However, a number of these genes were expressed in other E. histolytica strains with an inverse correlation between small RNA and gene expression level, suggesting that these small RNAs mediate silencing of the cognate gene. Overall, our results demonstrate that E. histolytica has an abundant 27 nt small RNA population, with features similar to secondary siRNAs from C. elegans, and which appear to regulate gene expression. These data indicate that a silencing pathway mediated by 5′-polyphosphate siRNAs extends to single-celled eukaryotic organisms.     

Using binding profiles to predict binding sites of target RNAs

Prediction of RNA-RNA interaction is a key to elucidating possible functions of small non-coding RNAs, and a number of computational methods have been proposed to analyze interacting RNA secondary structures. In this article, we focus on predicting binding sites of target RNAs that are expected to interact with regulatory antisense RNAs in a general form of interaction. For this purpose, we propose bistaRNA, a novel method for predicting multiple binding sites of target RNAs. bistaRNA employs binding profiles that represent scores for hybridized structures, leading to reducing the computational cost for interaction prediction. bistaRNA considers an ensemble of equilibrium interacting structures and seeks to maximize expected accuracy using dynamic programming. Experimental results on real interaction data validate good accuracy and fast computation time of bistaRNA as compared with several competitive methods. Moreover, we aim to find new targets given specific antisense RNAs, which provides interesting insights into antisense RNA regulation. bistaRNA is implemented in C++. The program and Supplementary Material are available at http://rna.naist.jp/program/bistarna/.     

Prediction of RNA secondary structure, including pseudoknotting, by computer simulation.

A computer program is presented which determines the secondary structure of linear RNA molecules by simulating a hypothetical process of folding. This process implies the concept of 'nucleation centres', regions in RNA which locally trigger the folding. During the simulation, the RNA is allowed to fold into pseudoknotted structures, unlike all other programs predicting RNA secondary structure. The simulation uses published, experimentally determined free energy values for nearest neighbour base pair stackings and loop regions, except for new extrapolated values for loops larger than seven nucleotides. The free energy value for a loop arising from pseudoknot formation is set to a single, estimated value of 4.2 kcal/mole. Especially in the case of long RNA sequences, our program appears superior to other secondary structure predicting programs described so far, as tests on tRNAs, the LSU intron of Tetrahymena thermophila and a number of plant viral RNAs show. In addition, pseudoknotted structures are often predicted successfully. The program is written in mainframe APL and is adapted to run on IBM compatible PCs, Atari ST and Macintosh personal computers. On an 8 MHz 8088 standard PC without coprocessor, using STSC APL, it folds a sequence of 700 nucleotides in one and a half hour.     

Improving the accuracy of predicting secondary structure for aligned RNA sequences

Considerable attention has been focused on predicting the secondary structure for aligned RNA sequences since it is useful not only for improving the limiting accuracy of conventional secondary structure prediction but also for finding non-coding RNAs in genomic sequences. Although there exist many algorithms of predicting secondary structure for aligned RNA sequences, further improvement of the accuracy is still awaited. In this article, toward improving the accuracy, a theoretical classification of state-of-the-art algorithms of predicting secondary structure for aligned RNA sequences is presented. The classification is based on the viewpoint of maximum expected accuracy (MEA), which has been successfully applied in various problems in bioinformatics. The classification reveals several disadvantages of the current algorithms but we propose an improvement of a previously introduced algorithm (CentroidAlifold). Finally, computational experiments strongly support the theoretical classification and indicate that the improved CentroidAlifold substantially outperforms other algorithms.     

Genome-Wide Double-Stranded RNA Sequencing Reveals the Functional Significance of Base-Paired RNAs in Arabidopsis

The functional structure of all biologically active molecules is dependent on intra- and inter-molecular interactions. This is especially evident for RNA molecules whose functionality, maturation, and regulation require formation of correct secondary structure through encoded base-pairing interactions. Unfortunately, intra- and inter-molecular base-pairing information is lacking for most RNAs. Here, we marry classical nuclease-based structure mapping techniques with high-throughput sequencing technology to interrogate all base-paired RNA in Arabidopsis thaliana and identify ∼200 new small (sm)RNA–producing substrates of RNA–DEPENDENT RNA POLYMERASE6. Our comprehensive analysis of paired RNAs reveals conserved functionality within introns and both 5′ and 3′ untranslated regions (UTRs) of mRNAs, as well as a novel population of functional RNAs, many of which are the precursors of smRNAs. Finally, we identify intra-molecular base-pairing interactions to produce a genome-wide collection of RNA secondary structure models. Although our methodology reveals the pairing status of RNA molecules in the absence of cellular proteins, previous studies have demonstrated that structural information obtained for RNAs in solution accurately reflects their structure in ribonucleoprotein complexes. Furthermore, our identification of RNA–DEPENDENT RNA POLYMERASE6 substrates and conserved functional RNA domains within introns and both 5′ and 3′ untranslated regions (UTRs) of mRNAs using this approach strongly suggests that RNA molecules are correctly folded into their secondary structure in solution. Overall, our findings highlight the importance of base-paired RNAs in eukaryotes and present an approach that should be widely applicable for the analysis of this key structural feature of RNA.     

Stimulatory effect of an indirectly attached RNA helicase-recruiting sequence on the suppression of gene expression by antisense oligonucleotides

Antisense oligonucleotides (ODNs) are powerful tools with which to determine the consequences of the reduced expression of a selected target gene, and they may have important therapeutic applications. Methods for predicting optimum antisense sites are not always effective because various factors, such as RNA-binding proteins, influence the secondary and tertiary structures of RNAs in vivo. To overcome this obstacle, we have attempted to engineer an antisense system that can unravel secondary and tertiary RNA structures. To create such an antisense system, we connected the constitutive transport element (CTE), an RNA motif that has the ability to interact with intracellular RNA helicases, to an antisense sequence so that helicase-binding hybrid antisense ODN would be produced in cells. We postulated that this modification would enhance antisense activity in vivo, with more frequent hybridization of the antisense ODN with its targeting site. Western blotting analysis demonstrated that a hybrid antisense ODN targeted to the bcl-2 gene suppressed the expression of this gene more effectively than did the antisense ODN alone. Our results suggest that the effects of antisense ODNs can be enhanced when their actions are combined with those of RNA helicases.     

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

Accurate free energy estimation is essential for RNA structure prediction. The widely used Turner''s energy model works well for nested structures. For pseudoknotted RNAs, however, there is no effective rule for estimation of loop entropy and free energy. In this work we present a new free energy estimation method, termed the pseudoknot predictor in three-dimensional space (pk3D), which goes beyond Turner''s model. Our approach treats nested and pseudoknotted structures alike in one unifying physical framework, regardless of how complex the RNA structures are. We first test the ability of pk3D in selecting native structures from a large number of decoys for a set of 43 pseudoknotted RNA molecules, with lengths ranging from 23 to 113. We find that pk3D performs slightly better than the Dirks and Pierce extension of Turner''s rule. We then test pk3D for blind secondary structure prediction, and find that pk3D gives the best sensitivity and comparable positive predictive value (related to specificity) in predicting pseudoknotted RNA secondary structures, when compared with other methods. A unique strength of pk3D is that it also generates spatial arrangement of structural elements of the RNA molecule. Comparison of three-dimensional structures predicted by pk3D with the native structure measured by nuclear magnetic resonance or X-ray experiments shows that the predicted spatial arrangement of stems and loops is often similar to that found in the native structure. These close-to-native structures can be used as starting points for further refinement to derive accurate three-dimensional structures of RNA molecules, including those with pseudoknots.     

GPRM: A genetic programming approach to finding common RNA secondary structure elements

RNA molecules play an important role in many biological activities. Knowing its secondary structure can help us better understand the molecule's ability to function. The methods for RNA structure determination have traditionally been implemented through biochemical, biophysical and phylogenetic analyses. As the advance of computer technology, an increasing number of computational approaches have recently been developed. They have different goals and apply various algorithms. For example, some focus on secondary structure prediction for a single sequence; some aim at finding a global alignment of multiple sequences. Some predict the structure based on free energy minimization; some make comparative sequence analyses to determine the structure. In this paper, we describe how to correctly use GPRM, a genetic programming approach to finding common secondary structure elements in a set of unaligned coregulated or homologous RNA sequences. GPRM can be accessed at http://bioinfo.cis.nctu.edu.tw/service/gprm/.     

Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design

Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for finding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a two-dimensional graphical representation approach for describing and estimating the size of RNA’s secondary structural repertoire, including naturally occurring and other possible RNA motifs. We employ tree graphs to describe RNA tree motifs and more general (dual) graphs to describe both RNA tree and pseudoknot motifs. Our estimates of RNA’s structural space are vastly smaller than the nucleotide sequence space, suggesting a new avenue for finding novel RNAs. Specifically our survey shows that known RNA trees and pseudoknots represent only a small subset of all possible motifs, implying that some of the ‘missing’ motifs may represent novel RNAs. To help pinpoint RNA-like motifs, we show that the motifs of existing functional RNAs are clustered in a narrow range of topological characteristics. We also illustrate the applications of our approach to the design of novel RNAs and automated comparison of RNA structures; we report several occurrences of RNA motifs within larger RNAs. Thus, our graph theory approach to RNA structures has implications for RNA genomics, structure analysis and design.     

Efficient and specific knockdown of small non-coding RNAs in mammalian cells and in mice

Hundreds of small nuclear non-coding RNAs, including small nucleolar RNAs (snoRNAs), have been identified in different organisms, with important implications in regulating gene expression and in human diseases. However, functionalizing these nuclear RNAs in mammalian cells remains challenging, due to methodological difficulties in depleting these RNAs, especially snoRNAs. Here we report a convenient and efficient approach to deplete snoRNA, small Cajal body RNA (scaRNA) and small nuclear RNA in human and mouse cells by conventional transfection of chemically modified antisense oligonucleotides (ASOs) that promote RNaseH-mediated cleavage of target RNAs. The levels of all seven tested snoRNA/scaRNAs and four snRNAs were reduced by 80-95%, accompanied by impaired endogenous functions of the target RNAs. ASO-targeting is highly specific, without affecting expression of the host genes where snoRNAs are embedded in the introns, nor affecting the levels of snoRNA isoforms with high sequence similarities. At least five snoRNAs could be depleted simultaneously. Importantly, snoRNAs could be dramatically depleted in mice by systematic administration of the ASOs. Together, our findings provide a convenient and efficient approach to characterize nuclear non-coding RNAs in mammalian cells, and to develop antisense drugs against disease-causing non-coding RNAs.     

Enrichment and analysis of RNA centered on ion pair reverse phase methodology

Here we describe a procedure for the rapid enrichment of RNA from cell extracts and the subsequent fractionation and analysis of the "small RNA" population by ion pair reverse phase chromatography. Solid phase extraction procedures have been developed utilizing nonporous alkylated poly(styrene-divinylbenzene) particles in conjunction with ion pair reagents to enrich total RNA. This approach facilitates the selective enrichment and separation of the relatively lower abundance small RNAs, from the more abundant higher molecular weight rRNA species. We also describe the application of monolithic capillaries in conjunction with ion pair reverse phase chromatography to bring increased sensitivity in the analysis of very low abundance RNAs. These approaches will simplify the biochemical analysis of this class of molecules, which are emerging as important regulators of global gene expression in higher organisms.     

RNANetMotif: Identifying sequence-structure RNA network motifs in RNA-protein binding sites

RNA molecules can adopt stable secondary and tertiary structures, which are essential in mediating physical interactions with other partners such as RNA binding proteins (RBPs) and in carrying out their cellular functions. In vivo and in vitro experiments such as RNAcompete and eCLIP have revealed in vitro binding preferences of RBPs to RNA oligomers and in vivo binding sites in cells. Analysis of these binding data showed that the structure properties of the RNAs in these binding sites are important determinants of the binding events; however, it has been a challenge to incorporate the structure information into an interpretable model. Here we describe a new approach, RNANetMotif, which takes predicted secondary structure of thousands of RNA sequences bound by an RBP as input and uses a graph theory approach to recognize enriched subgraphs. These enriched subgraphs are in essence shared sequence-structure elements that are important in RBP-RNA binding. To validate our approach, we performed RNA structure modeling via coarse-grained molecular dynamics folding simulations for selected 4 RBPs, and RNA-protein docking for LIN28B. The simulation results, e.g., solvent accessibility and energetics, further support the biological relevance of the discovered network subgraphs.     

A new Motzkin class for joint RNA secondary structures

In general RNA prediction problem includes genetic mapping, physical mapping and structure prediction. The ultimate goal of structure prediction is to obtain the three dimensional structure of bimolecules through computation. The key concept for solving the above mentioned problem is the appropriate representation of the biological structures. Even though, the problems that concern representations of certain biological structures like secondary structures either are characterized as NP-complete or with high complexity, few approximation algorithms and techniques had been constructed, mainly with polynomial complexity, concerning the prediction of RNA secondary structures. In this paper, a new class of Motzkin paths is introduced, the so-called semi-elevated inverse Motzkin peakless paths for the representation of two interacting RNA molecules. The basic combinatorial interpretations on single RNA secondary structures are extended via these new Motzkin paths on two RNA molecules and can be applied to the prediction methods of joint structures formed by interacting RNAs.