RNAmute: RNA secondary structure mutation analysis tool

Background  

RNAMute is an interactive Java application that calculates the secondary structure of all single point mutations, given an RNA sequence, and organizes them into categories according to their similarity with respect to the wild type predicted structure. The secondary structure predictions are performed using the Vienna RNA package. Several alternatives are used for the categorization of single point mutations: Vienna's RNAdistance based on dot-bracket representation, as well as tree edit distance and second eigenvalue of the Laplacian matrix based on Shapiro's coarse grain tree graph representation.     

Computing the partition function for kinetically trapped RNA secondary structures

An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in O(n3) time and O(n2) space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1) the number of locally optimal structures is far fewer than the total number of structures--indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2) the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3) the (modified) maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model) can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected accuracy. Web server and source code available at http://bioinformatics.bc.edu/clotelab/RNAlocopt/.     

图论在RNA二级结构中的应用

图论是以图为研究对象的数学分支,是一门研究事物对象在图表示法中的特征与性质的学科。鉴于RNA二级结构在功能基因组研究中的重要地位,已发展了用二维图解表示法描述RNA二级结构。文章介绍了用于RNA二级结构图解表示法的两种图,即树图和对偶图的构造规则。并在树图表示基础上产生Laplacian矩阵和相应本征值谱。以有害突变预测和类RNA模体设计的例子,说明图论在RNA二级结构中的应用,同时对可能存在的一些问题做了讨论。     

Predicting a set of minimal free energy RNA secondary structures common to two sequences

MOTIVATION: Function derives from structure, therefore, there is need for methods to predict functional RNA structures. RESULTS: The Dynalign algorithm, which predicts the lowest free energy secondary structure common to two unaligned RNA sequences, is extended to the prediction of a set of low-energy structures. Dot plots can be drawn to show all base pairs in structures within an energy increment. Dynalign predicts more well-defined structures than structure prediction using a single sequence; in 5S rRNA sequences, the average number of base pairs in structures with energy within 20% of the lowest energy structure is 317 using Dynalign, but 569 using a single sequence. Structure prediction with Dynalign can also be constrained according to experiment or comparative analysis. The accuracy, measured as sensitivity and positive predictive value, of Dynalign is greater than predictions with a single sequence. AVAILABILITY: Dynalign can be downloaded at http://rna.urmc.rochester.edu     

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.     

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.     

Abstract shapes of RNA

The function of a non-protein-coding RNA is often determined by its structure. Since experimental determination of RNA structure is time-consuming and expensive, its computational prediction is of great interest, and efficient solutions based on thermodynamic parameters are known. Frequently, however, the predicted minimum free energy structures are not the native ones, leading to the necessity of generating suboptimal solutions. While this can be accomplished by a number of programs, the user is often confronted with large outputs of similar structures, although he or she is interested in structures with more fundamental differences, or, in other words, with different abstract shapes. Here, we formalize the concept of abstract shapes and introduce their efficient computation. Each shape of an RNA molecule comprises a class of similar structures and has a representative structure of minimal free energy within the class. Shape analysis is implemented in the program RNAshapes. We applied RNAshapes to the prediction of optimal and suboptimal abstract shapes of several RNAs. For a given energy range, the number of shapes is considerably smaller than the number of structures, and in all cases, the native structures were among the top shape representatives. This demonstrates that the researcher can quickly focus on the structures of interest, without processing up to thousands of near-optimal solutions. We complement this study with a large-scale analysis of the growth behaviour of structure and shape spaces. RNAshapes is available for download and as an online version on the Bielefeld Bioinformatics Server.     

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      

A kinetic approach to the prediction of RNA secondary structures

A new approach to the prediction of secondary RNA structures based on the analysis of the kinetics of molecular self-organisation is proposed herein. The Markov process is used to describe structural reconstructions during secondary structure formation. This process is modelled by a Monte-Carlo method. Examples of the calculation by this method of the secondary structures kinetic ensemble are given. Distribution of time-dependent probabilities within the ensembles is obtained. An effective method for search for the equilibrium ensemble is also suggested. This method is based on the construction of a tree of all possible secondary structures of RNA. By ascribing a probability for each structure (according to its free energy) the Boltzmann equilibrium ensemble can be obtained.     

Computational approaches for RNA energy parameter estimation

Methods for efficient and accurate prediction of RNA structure are increasingly valuable, given the current rapid advances in understanding the diverse functions of RNA molecules in the cell. To enhance the accuracy of secondary structure predictions, we developed and refined optimization techniques for the estimation of energy parameters. We build on two previous approaches to RNA free-energy parameter estimation: (1) the Constraint Generation (CG) method, which iteratively generates constraints that enforce known structures to have energies lower than other structures for the same molecule; and (2) the Boltzmann Likelihood (BL) method, which infers a set of RNA free-energy parameters that maximize the conditional likelihood of a set of reference RNA structures. Here, we extend these approaches in two main ways: We propose (1) a max-margin extension of CG, and (2) a novel linear Gaussian Bayesian network that models feature relationships, which effectively makes use of sparse data by sharing statistical strength between parameters. We obtain significant improvements in the accuracy of RNA minimum free-energy pseudoknot-free secondary structure prediction when measured on a comprehensive set of 2518 RNA molecules with reference structures. Our parameters can be used in conjunction with software that predicts RNA secondary structures, RNA hybridization, or ensembles of structures. Our data, software, results, and parameter sets in various formats are freely available at http://www.cs.ubc.ca/labs/beta/Projects/RNA-Params.     

Second eigenvalue of the Laplacian matrix for predicting RNA conformational switch by mutation

MOTIVATION: Conformational switching in RNAs is thought to be of fundamental importance in several biological processes, including translational regulation, regulation of self-cleavage in viruses, protein biosynthesis and mRNA splicing. Current methods for detecting bi-stable RNAs that can lead to structural switching when triggered by an outside event rely on kinetics, energetics and properties of the combinatorial structure space of RNAs. Based on these properties, tools have been developed to predict whether a given sequence folds to a structure characterized by a bi-stable conformation, or to design multi-stable RNAs by an iterative algorithm. A useful addition is in developing a local procedure to prescribe, given an initial sequence, the least amount of mutations needed to drive the system into an optimal bi-stable conformation. RESULTS: We introduce a local procedure for predicting mutations, by generating and analyzing eigenvalue tables, that are capable of transforming the wild-type sequence into a bi-stable conformation. The method is independent of the folding algorithms but relies on their success. It can be used in conjunction with existing tools, as well as being incorporated into more general RNA prediction packages. We apply this procedure on three well-studied structures. First, the method is validated on the mutation leading to a conformational switch in the spliced leader RNA from Leptomonas collosoma, a mutation that has already been confirmed by an experiment. Second, the method is used to predict a mutation that can lead to a novel conformational switch in the P5abc subdomain of the group I intron ribozyme in Tetrahymena thermophila. Third, the method is applied on Hepatitis delta virus to predict mutations that transform the wild-type into a bi-stable conformation, a configuration assessed by calculating the free energies using folding prediction algorithms. The predictions in the final examples need to be verified experimentally, whereas the mutation predicted in the first example complies with the experiment. This supports the use of our proposed method on other known structures, as well as genetically engineered ones. AVAILABILITY: An eigenvalue application will be available in the near future attached to one of the existing tools.     

Improvement of RNA secondary structure prediction using RNase H cleavage and randomized oligonucleotides

RNA secondary structure prediction using free energy minimization is one method to gain an approximation of structure. Constraints generated by enzymatic mapping or chemical modification can improve the accuracy of secondary structure prediction. We report a facile method that identifies single-stranded regions in RNA using short, randomized DNA oligonucleotides and RNase H cleavage. These regions are then used as constraints in secondary structure prediction. This method was used to improve the secondary structure prediction of Escherichia coli 5S rRNA. The lowest free energy structure without constraints has only 27% of the base pairs present in the phylogenetic structure. The addition of constraints from RNase H cleavage improves the prediction to 100% of base pairs. The same method was used to generate secondary structure constraints for yeast tRNA^Phe, which is accurately predicted in the absence of constraints (95%). Although RNase H mapping does not improve secondary structure prediction, it does eliminate all other suboptimal structures predicted within 10% of the lowest free energy structure. The method is advantageous over other single-stranded nucleases since RNase H is functional in physiological conditions. Moreover, it can be used for any RNA to identify accessible binding sites for oligonucleotides or small molecules.     

Incorporating global features of RNA motifs in predictions for an ensemble of secondary structures for encapsidated MS2 bacteriophage RNA

The secondary structure of encapsidated MS2 genomic RNA poses an interesting RNA folding challenge. Cryoelectron microscopy has demonstrated that encapsidated MS2 RNA is well-ordered. Models of MS2 assembly suggest that the RNA hairpin-protein interactions and the appropriate placement of hairpins in the MS2 RNA secondary structure can guide the formation of the correct icosahedral particle. The RNA hairpin motif that is recognized by the MS2 capsid protein dimers, however, is energetically unfavorable, and thus free energy predictions are biased against this motif. Computer programs called Crumple, Sliding Windows, and Assembly provide useful tools for prediction of viral RNA secondary structures when the traditional assumptions of RNA structure prediction by free energy minimization may not apply. These methods allow incorporation of global features of the RNA fold and motifs that are difficult to include directly in minimum free energy predictions. For example, with MS2 RNA the experimental data from SELEX experiments, crystallography, and theoretical calculations of the path for the series of hairpins can be incorporated in the RNA structure prediction, and thus the influence of free energy considerations can be modulated. This approach thoroughly explores conformational space and generates an ensemble of secondary structures. The predictions from this new approach can test hypotheses and models of viral assembly and guide construction of complete three-dimensional models of virus particles.     

Mutational analysis in RNAs: comparing programs for RNA deleterious mutation prediction

Programs for RNA mutational analysis that are structure-based and rely on secondary structure prediction have been developed and expanded in the past several years. They can be used for a variety of purposes, such as in suggesting point mutations that will alter RNA virus replication or translation initiation, investigating the effect of deleterious and compensatory mutations in allosteric ribozymes and riboswitches, computing an optimal path of mutations to get from one ribozyme fold to another, or analyzing regulatory RNA sequences by their mutational profile. This review describes three different freeware programs (RNAMute, RDMAS and RNAmutants) that have been developed for such purposes. RNAMute and RDMAS in principle perform energy minimization prediction by available software such as RNAfold from the Vienna RNA package or Zuker's Mfold, while RNAmutants provides an efficient method using essential ingredients from energy minimization prediction. Both RNAMute in its extended version that uses RNAsubopt from the Vienna RNA package and the RNAmutants software are able to predict multiple-point mutations using developed methodologies, while RDMAS is currently restricted to single-point mutations. The strength of RNAMute in its extended version is the ability to predict a small number of point mutations in an accurate manner. RNAmutants is well fit for large scale simulations involving the calculation of all k-mutants, where k can be a large integer number, of a given RNA sequence.     

A Kinetic Approach to the Prediction of RNA Secondary Structures

Abstract

A new approach to the prediction of secondary RNA structures based on the analysis of the kinetics of molecular self-organisation is proposed herein. The Markov process is used to describe structural reconstructions during secondary structure formation. This process is modelled by a Monte-Carlo method. Examples of the calculation by this method of the secondary structures kinetic ensemble are given. Distribution of time-dependent probabilities within the ensembles is obtained.

An effective method for search for the equilibrium ensemble is also suggested. This method is based on the construction of a tree of all possible secondary structures of RNA. By ascribing a probability for each structure (according to its free energy) the Boltzmann equilibrium ensemble can be obtained.     

Novel and efficient RNA secondary structure prediction using hierarchical folding.

Algorithms for prediction of RNA secondary structure-the set of base pairs that form when an RNA molecule folds-are valuable to biologists who aim to understand RNA structure and function. Improving the accuracy and efficiency of prediction methods is an ongoing challenge, particularly for pseudoknotted secondary structures, in which base pairs overlap. This challenge is biologically important, since pseudoknotted structures play essential roles in functions of many RNA molecules, such as splicing and ribosomal frameshifting. State-of-the-art methods, which are based on free energy minimization, have high run-time complexity (typically Theta(n(5)) or worse), and can handle (minimize over) only limited types of pseudoknotted structures. We propose a new approach for prediction of pseudoknotted structures, motivated by the hypothesis that RNA structures fold hierarchically, with pseudoknot-free (non-overlapping) base pairs forming first, and pseudoknots forming later so as to minimize energy relative to the folded pseudoknot-free structure. Our HFold algorithm uses two-phase energy minimization to predict hierarchically formed secondary structures in O(n(3)) time, matching the complexity of the best algorithms for pseudoknot-free secondary structure prediction via energy minimization. Our algorithm can handle a wide range of biological structures, including kissing hairpins and nested kissing hairpins, which have previously required Theta(n(6)) time.     

Combinatorics of saturated secondary structures of RNA.

Following Zuker (1986), a saturated secondary structure for a given RNA sequence is a secondary structure such that no base pair can be added without violating the definition of secondary structure, e.g., without introducing a pseudoknot. In the Nussinov-Jacobson energy model (Nussinov and Jacobson, 1980), where the energy of a secondary structure is -1 times the number of base pairs, saturated secondary structures are local minima in the energy landscape, hence form kinetic traps during the folding process. Here we present recurrence relations and closed form asymptotic limits for combinatorial problems related to the number of saturated secondary structures. In addition, Python source code to compute the number of saturated secondary structures having k base pairs can be found at the web servers link of bioinformatics.bc.edu/clotelab/.     

R-CHIE: a web server and R package for visualizing RNA secondary structures

Visually examining RNA structures can greatly aid in understanding their potential functional roles and in evaluating the performance of structure prediction algorithms. As many functional roles of RNA structures can already be studied given the secondary structure of the RNA, various methods have been devised for visualizing RNA secondary structures. Most of these methods depict a given RNA secondary structure as a planar graph consisting of base-paired stems interconnected by roundish loops. In this article, we present an alternative method of depicting RNA secondary structure as arc diagrams. This is well suited for structures that are difficult or impossible to represent as planar stem-loop diagrams. Arc diagrams can intuitively display pseudo-knotted structures, as well as transient and alternative structural features. In addition, they facilitate the comparison of known and predicted RNA secondary structures. An added benefit is that structure information can be displayed in conjunction with a corresponding multiple sequence alignments, thereby highlighting structure and primary sequence conservation and variation. We have implemented the visualization algorithm as a web server R-chie as well as a corresponding R package called R4RNA, which allows users to run the software locally and across a range of common operating systems.