INFO-RNA--a fast approach to inverse RNA folding

MOTIVATION: The structure of RNA molecules is often crucial for their function. Therefore, secondary structure prediction has gained much interest. Here, we consider the inverse RNA folding problem, which means designing RNA sequences that fold into a given structure. RESULTS: We introduce a new algorithm for the inverse folding problem (INFO-RNA) that consists of two parts; a dynamic programming method for good initial sequences and a following improved stochastic local search that uses an effective neighbor selection method. During the initialization, we design a sequence that among all sequences adopts the given structure with the lowest possible energy. For the selection of neighbors during the search, we use a kind of look-ahead of one selection step applying an additional energy-based criterion. Afterwards, the pre-ordered neighbors are tested using the actual optimization criterion of minimizing the structure distance between the target structure and the mfe structure of the considered neighbor. We compared our algorithm to RNAinverse and RNA-SSD for artificial and biological test sets. Using INFO-RNA, we performed better than RNAinverse and in most cases, we gained better results than RNA-SSD, the probably best inverse RNA folding tool on the market. AVAILABILITY: www.bioinf.uni-freiburg.de?Subpages/software.html.     

Inverse folding of RNA pseudoknot structures

Background  

RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and G-U-base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse folding algorithms, RNAinverse, RNA-SSD as well as INFO-RNA are limited to RNA secondary structures, we present in this paper the inverse folding algorithm Inv which can deal with 3-noncrossing, canonical pseudoknot structures.     

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.     

Reconstruction of natural RNA sequences from RNA shape, thermodynamic stability, mutational robustness, and linguistic complexity by evolutionary computation

The process of designing novel RNA sequences by inverse RNA folding, available in tools such as RNAinverse and InfoRNA, can be thought of as a reconstruction of RNAs from secondary structure. In this reconstruction problem, no physical measures are considered as additional constraints that are independent of structure, aside of the goal to reach the same secondary structure as the input using energy minimization methods. An extension of the reconstruction problem can be formulated since in many cases of natural RNAs, it is desired to analyze the sequence and structure of RNA molecules using various physical quantifiable measures. In prior works that used secondary structure predictions, it has been shown that natural RNAs differ significantly from random RNAs in some of these measures. Thus, we relax the problem of reconstructing RNAs from secondary structure into reconstructing RNAs from shapes, and in turn incorporate physical quantities as constraints. This allows for the design of novel RNA sequences by inverse folding while considering various physical quantities of interest such as thermodynamic stability, mutational robustness, and linguistic complexity. At the expense of altering the number of nucleotides in stems and loops, for example, physical measures can be taken into account. We use evolutionary computation for the new reconstruction problem and illustrate the procedure on various natural RNAs.     

Conserved secondary structures in Aspergillus

Background

Recent evidence suggests that the number and variety of functional RNAs (ncRNAs as well as cis-acting RNA elements within mRNAs ) is much higher than previously thought; thus, the ability to computationally predict and analyze RNAs has taken on new importance. We have computationally studied the secondary structures in an alignment of six Aspergillus genomes. Little is known about the RNAs present in this set of fungi, and this diverse set of genomes has an optimal level of sequence conservation for observing the correlated evolution of base-pairs seen in RNAs.

Methodology/Principal Findings

We report the results of a whole-genome search for evolutionarily conserved secondary structures, as well as the results of clustering these predicted secondary structures by structural similarity. We find a total of 7450 predicted secondary structures, including a new predicted ∼60 bp long hairpin motif found primarily inside introns. We find no evidence for microRNAs. Different types of genomic regions are over-represented in different classes of predicted secondary structures. Exons contain the longest motifs (primarily long, branched hairpins), 5′ UTRs primarily contain groupings of short hairpins located near the start codon, and 3′ UTRs contain very little secondary structure compared to other regions. There is a large concentration of short hairpins just inside the boundaries of exons. The density of predicted intronic RNAs increases with the length of introns, and the density of predicted secondary structures within mRNA coding regions increases with the number of introns in a gene.

Conclusions/Sigificance

There are many conserved, high-confidence RNAs of unknown function in these Aspergillus genomes, as well as interesting spatial distributions of predicted secondary structures. This study increases our knowledge of secondary structure in these aspergillus organisms.     

Computational RNA secondary structure design: empirical complexity and improved methods

Background  

We investigate the empirical complexity of the RNA secondary structure design problem, that is, the scaling of the typical difficulty of the design task for various classes of RNA structures as the size of the target structure is increased. The purpose of this work is to understand better the factors that make RNA structures hard to design for existing, high-performance algorithms. Such understanding provides the basis for improving the performance of one of the best algorithms for this problem, RNA-SSD, and for characterising its limitations.     

Reconstruction of Natural RNA Sequences from RNA Shape,Thermodynamic Stability,Mutational Robustness,and Linguistic Complexity by Evolutionary Computation

Abstract

The process of designing novel RNA sequences by inverse RNA folding, available in tools such as RNAinverse and InfoRNA, can be thought of as a reconstruction of RNAs from secondary structure. In this reconstruction problem, no physical measures are considered as additional constraints that are independent of structure, aside of the goal to reach the same secondary structure as the input using energy minimization methods. An extension of the reconstruction problem can be formulated since in many cases of natural RNAs, it is desired to analyze the sequence and structure of RNA molecules using various physical quantifiable measures. In prior works that used secondary structure predictions, it has been shown that natural RNAs differ significantly from random RNAs in some of these measures. Thus, we relax the problem of reconstructing RNAs from secondary structure into reconstructing RNAs from shapes, and in turn incorporate physical quantities as constraints. This allows for the design of novel RNA sequences by inverse folding while considering various physical quantities of interest such as thermodynamic stability, mutational robustness, and linguistic complexity. At the expense of altering the number of nucleotides in stems and loops, for example, physical measures can be taken into account. We use evolutionary computation for the new reconstruction problem and illustrate the procedure on various natural RNAs.     

Sampled ensemble neutrality as a feature to classify potential structured RNAs

Background

Structured RNAs have many biological functions ranging from catalysis of chemical reactions to gene regulation. Yet, many homologous structured RNAs display most of their conservation at the secondary or tertiary structure level. As a result, strategies for structured RNA discovery rely heavily on identification of sequences sharing a common stable secondary structure. However, correctly distinguishing structured RNAs from surrounding genomic sequence remains challenging, especially during de novo discovery. RNA also has a long history as a computational model for evolution due to the direct link between genotype (sequence) and phenotype (structure). From these studies it is clear that evolved RNA structures, like protein structures, can be considered robust to point mutations. In this context, an RNA sequence is considered robust if its neutrality (extent to which single mutant neighbors maintain the same secondary structure) is greater than that expected for an artificial sequence with the same minimum free energy structure.

Results

In this work, we bring concepts from evolutionary biology to bear on the structured RNA de novo discovery process. We hypothesize that alignments corresponding to structured RNAs should consist of neutral sequences. We evaluate several measures of neutrality for their ability to distinguish between alignments of structured RNA sequences drawn from Rfam and various decoy alignments. We also introduce a new measure of RNA structural neutrality, the structure ensemble neutrality (SEN). SEN seeks to increase the biological relevance of existing neutrality measures in two ways. First, it uses information from an alignment of homologous sequences to identify a conserved biologically relevant structure for comparison. Second, it only counts base-pairs of the original structure that are absent in the comparison structure and does not penalize the formation of additional base-pairs.

Conclusion

We find that several measures of neutrality are effective at separating structured RNAs from decoy sequences, including both shuffled alignments and flanking genomic sequence. Furthermore, as an independent feature classifier to identify structured RNAs, SEN yields comparable performance to current approaches that consider a variety of features including stability and sequence identity. Finally, SEN outperforms other measures of neutrality at detecting mutational robustness in bacterial regulatory RNA structures.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-014-1203-8) contains supplementary material, which is available to authorized users.     

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.     

An algorithm for searching RNA motifs in genomic sequences

RNA molecules, which are found in all living cells, fold into characteristic structures that account for their diverse functional activities. Many of these RNA structures consist of a collection of fundamental RNA motifs. The various combinations of RNA basic components form different RNA classes and define their unique structural and functional properties. The availability of many genome sequences makes it possible to search computationally for functional RNAs. Biological experiments indicate that functional RNAs have characteristic RNA structural motifs represented by specific combinations of base pairings and conserved nucleotides in the loop regions. The searching for those well-ordered RNA structures and their homologues in genomic sequences is very helpful for the understanding of RNA-based gene regulation. In this paper, we consider the following problem: given an RNA sequence with a known secondary structure, efficiently determine candidate segments in genomic sequences that can potentially form RNA secondary structures similar to the given RNA secondary structure. Our new bottom-up approach searches all potential stem-loops similar to ones of the given RNA secondary structure first, and then based on located stem-loops, detects potential homologous structural RNAs in genomic sequences.     

Prediction of RNA secondary structure based on helical regions distribution

MOTIVATION: RNAs play an important role in many biological processes and knowing their structure is important in understanding their function. Due to difficulties in the experimental determination of RNA secondary structure, the methods of theoretical prediction for known sequences are often used. Although many different algorithms for such predictions have been developed, this problem has not yet been solved. It is thus necessary to develop new methods for predicting RNA secondary structure. The most-used at present is Zuker's algorithm which can be used to determine the minimum free energy secondary structure. However many RNA secondary structures verified by experiments are not consistent with the minimum free energy secondary structures. In order to solve this problem, a method used to search a group of secondary structures whose free energy is close to the global minimum free energy was developed by Zuker in 1989. When considering a group of secondary structures, if there is no experimental data, we cannot tell which one is better than the others. This case also occurs in combinatorial and heuristic methods. These two kinds of methods have several weaknesses. Here we show how the central limit theorem can be used to solve these problems. RESULTS: An algorithm for predicting RNA secondary structure based on helical regions distribution is presented, which can be used to find the most probable secondary structure for a given RNA sequence. It consists of three steps. First, list all possible helical regions. Second, according to central limit theorem, estimate the occurrence probability of every helical region based on the Monte Carlo simulation. Third, add the helical region with the biggest probability to the current structure and eliminate the helical regions incompatible with the current structure. The above processes can be repeated until no more helical regions can be added. Take the current structure as the final RNA secondary structure. In order to demonstrate the confidence of the program, a test on three RNA sequences: tRNAPhe, Pre-tRNATyr, and Tetrahymena ribosomal RNA intervening sequence, is performed. AVAILABILITY: The program is written in Turbo Pascal 7.0. The source code is available upon request. CONTACT: Wujj@nic.bmi.ac.cn or Liwj@mail.bmi.ac.cn      

RGRNA: prediction of RNA secondary structure based on replacement and growth of stems

Owing to their structural diversity, RNAs perform many diverse biological functions in the cell. RNA secondary structure is thus important for predicting RNA function. Here, we propose a new combinatorial optimization algorithm, named RGRNA, to improve the accuracy of predicting RNA secondary structure. Following the establishment of a stempool, the stems are sorted by length, and chosen from largest to smallest. If the stem selected is the true stem, the secondary structure of this stem when combined with another stem selected at random will have low free energy, and the free energy will tend to gradually diminish. The free energy is considered as a parameter and the structure is converted into binary numbers to determine stem compatibility, for step-by-step prediction of the secondary structure for all combinations of stems. The RNA secondary structure can be predicted by the RGRNA method. Our experimental results show that the proposed algorithm outperforms RNAfold in terms of sensitivity, specificity, and Matthews correlation coefficient value.     

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.     

SCARNA: fast and accurate structural alignment of RNA sequences by matching fixed-length stem fragments

MOTIVATION: The functions of non-coding RNAs are strongly related to their secondary structures, but it is known that a secondary structure prediction of a single sequence is not reliable. Therefore, we have to collect similar RNA sequences with a common secondary structure for the analyses of a new non-coding RNA without knowing the exact secondary structure itself. Therefore, the sequence comparison in searching similar RNAs should consider not only their sequence similarities but also their potential secondary structures. Sankoff's algorithm predicts the common secondary structures of the sequences, but it is computationally too expensive to apply to large-scale analyses. Because we often want to compare a large number of cDNA sequences or to search similar RNAs in the whole genome sequences, much faster algorithms are required. RESULTS: We propose a new method of comparing RNA sequences based on the structural alignments of the fixed-length fragments of the stem candidates. The implemented software, SCARNA (Stem Candidate Aligner for RNAs), is fast enough to apply to the long sequences in the large-scale analyses. The accuracy of the alignments is better or comparable with the much slower existing algorithms. AVAILABILITY: The web server of SCARNA with graphical structural alignment viewer is available at http://www.scarna.org/.     

RBPBind: Quantitative Prediction of Protein-RNA Interactions

There are hundreds of RNA binding proteins in the human genome alone and their interactions with messenger and other RNAs in a cell regulate every step in an RNA's life cycle. To understand this interplay of proteins and RNA it is important to be able to know which protein binds which RNA how strongly and where. Here, we introduce RBPBind, a web-based tool for the quantitative prediction of the interaction of single-stranded RNA binding proteins with target RNAs that fully takes into account the effect of RNA secondary structure on binding affinity. Given a user-specified RNA and a protein selected from a set of several RNA-binding proteins, RBPBind computes their binding curve and effective binding constant. The server also computes the probability that, at a given protein concentration, a protein molecule will bind to any particular nucleotide along the RNA. The sequence specificity of the protein-RNA interaction is parameterized from public RNAcompete experiments and integrated into the recursions of the Vienna RNA package to simultaneously take into account protein binding and RNA secondary structure. We validate our approach by comparison to experimentally determined binding affinities of the HuR protein for several RNAs of different sequence contexts from the literature, showing that integration of raw sequence affinities into RNA secondary structure prediction significantly improves the agreement between computationally predicted and experimentally measured binding affinities. Our resource thus provides a quick and easy way to obtain reliable predicted binding affinities and locations for single-stranded RNA binding proteins based on RNA sequence alone.     

基于最小自由能和协变信息预测带伪结RNA二级结构的迭代化方法

多数RNA分子的结构在进化中是高度保守的, 其中很多包含伪结。而RNA伪结的预测一直是一个棘手问题, 很多RNA 二级结构预测算法都不能预测伪结。文章提出一种基于迭代法预测带伪结RNA 二级结构的新方法。该方法在给潜在碱基对打分时综合了热力学和协变信息, 通过基于最小自由能RNA折叠算法的多次迭代选出所有的碱基对。测试结果表明: 此方法几乎能预测到所有的伪结。与其他方法相比, 敏感度接近最优, 而特异性达到最优。     

Cardioviral RNA structure logo analysis: entropy, correlations, and prediction

In recent years, there has been an increased number of sequenced RNAs leading to the development of new RNA databases. Thus, predicting RNA structure from multiple alignments is an important issue to understand its function. Since RNA secondary structures are often conserved in evolution, developing methods to identify covariate sites in an alignment can be essential for discovering structural elements. Structure Logo is a technique established on the basis of entropy and mutual information measured to analyze RNA sequences from an alignment. We proposed an efficient Structure Logo approach to analyze conservations and correlations in a set of Cardioviral RNA sequences. The entropy and mutual information content were measured to examine the conservations and correlations, respectively. The conserved secondary structure motifs were predicted on the basis of the conservation and correlation analyses. Our predictive motifs were similar to the ones observed in the viral RNA structure database, and the correlations between bases also corresponded to the secondary structure in the database.     

Specificity of mRNA Folding and Its Association with Evolutionarily Adaptive mRNA Secondary Structures

The secondary structure is a fundamental feature of both non-coding RNAs (ncRNAs) and messenger RNAs (mRNAs). However, our understanding of the secondary structures of mRNAs, especially those of the coding regions, remains elusive, likely due to translation and the lack of RNA-binding proteins that sustain the consensus structure like those binding to ncRNAs. Indeed, mRNAs have recently been found to adopt diverse alternative structures, but the overall functional significance remains untested. We hereby approach this problem by estimating the folding specificity, i.e., the probability that a fragment of an mRNA folds back to the same partner once refolded. We show that the folding specificity of mRNAs is lower than that of ncRNAs and exhibits moderate evolutionary conservation. Notably, we find that specific rather than alternative folding is likely evolutionarily adaptive since specific folding is frequently associated with functionally important genes or sites within a gene. Additional analysis in combination with ribosome density suggests the ability to modulate ribosome movement as one potential functional advantage provided by specific folding. Our findings reveal a novel facet of the RNA structurome with important functional and evolutionary implications and indicate a potential method for distinguishing the mRNA secondary structures maintained by natural selection from molecular noise.     

RNA secondary structure modeling at consistent high accuracy using differential SHAPE

RNA secondary structure modeling is a challenging problem, and recent successes have raised the standards for accuracy, consistency, and tractability. Large increases in accuracy have been achieved by including data on reactivity toward chemical probes: Incorporation of 1M7 SHAPE reactivity data into an mfold-class algorithm results in median accuracies for base pair prediction that exceed 90%. However, a few RNA structures are modeled with significantly lower accuracy. Here, we show that incorporating differential reactivities from the NMIA and 1M6 reagents—which detect noncanonical and tertiary interactions—into prediction algorithms results in highly accurate secondary structure models for RNAs that were previously shown to be difficult to model. For these RNAs, 93% of accepted canonical base pairs were recovered in SHAPE-directed models. Discrepancies between accepted and modeled structures were small and appear to reflect genuine structural differences. Three-reagent SHAPE-directed modeling scales concisely to structurally complex RNAs to resolve the in-solution secondary structure analysis problem for many classes of RNA.