Secondary structure prediction for aligned RNA sequences

Most functional RNA molecules have characteristic secondary structures that are highly conserved in evolution. Here we present a method for computing the consensus structure of a set aligned RNA sequences taking into account both thermodynamic stability and sequence covariation. Comparison with phylogenetic structures of rRNAs shows that a reliability of prediction of more than 80% is achieved for only five related sequences. As an application we show that the Early Noduline mRNA contains significant secondary structure that is supported by sequence covariation.     

Revolutions in RNA secondary structure prediction

RNA structure formation is hierarchical and, therefore, secondary structure, the sum of canonical base-pairs, can generally be predicted without knowledge of the three-dimensional structure. Secondary structure prediction algorithms evolved from predicting a single, lowest free energy structure to their current state where statistics can be determined from the thermodynamic ensemble. This article reviews the free energy minimization technique and the salient revolutions in the dynamic programming algorithm methods for secondary structure prediction. Emphasis is placed on highlighting the recently developed method, which statistically samples structures from the complete Boltzmann ensemble.     

基于PDB数据库的三个RNA二级结构预测软件评估

随着21世纪分子生物学研究的蓬勃发展,RNA二级结构预测成为其中一项重要内容。由于RNA二级结构预测的准确性最为关键,因此寻找高精度且易操作的二级结构预测工具显得非常重要。本文选取三种简单且易操作的二级结构预测软件,先基于PDB数据库收录的318个RNA发夹序列进行二级结构预测,进而通过比较预测结果与实验测定结果进行软件预测性能评估。比较结果显示,RNAstructure为三个软件中性能最优的RNA二级结构预测软件。     

Combinatorial analysis of interacting RNA molecules

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no “zigzag” configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.     

RNA二级结构预测系统构建

运用下列RNA二级结构预测算法:碱基最大配对方法、Zuker极小化自由能方法、螺旋区最优堆积、螺旋区随机堆积和所有可能组合方法与基于一级螺旋区的RNA二级结构绘图技术, 构建了RNA二级结构预测系统Rnafold. 另外, 通过随机选取20个tRNA序列, 从自由能和三叶草结构两个方面比较了前4种二级结构预测算法, 并运用t检验方法分析了自由能的统计学差别. 从三叶草结构来看, 以随机堆积方法最好, 其次是螺旋区最优堆积方法和Zuker算法, 以碱基最大配对方法最差. 最后, 分析了两种极小化自由能方法之间的差别.     

Improved free energy parameters for RNA pseudoknotted secondary structure prediction

Accurate prediction of RNA pseudoknotted secondary structures from the base sequence is a challenging computational problem. Since prediction algorithms rely on thermodynamic energy models to identify low-energy structures, prediction accuracy relies in large part on the quality of free energy change parameters. In this work, we use our earlier constraint generation and Boltzmann likelihood parameter estimation methods to obtain new energy parameters for two energy models for secondary structures with pseudoknots, namely, the Dirks–Pierce (DP) and the Cao–Chen (CC) models. To train our parameters, and also to test their accuracy, we create a large data set of both pseudoknotted and pseudoknot-free secondary structures. In addition to structural data our training data set also includes thermodynamic data, for which experimentally determined free energy changes are available for sequences and their reference structures. When incorporated into the HotKnots prediction algorithm, our new parameters result in significantly improved secondary structure prediction on our test data set. Specifically, the prediction accuracy when using our new parameters improves from 68% to 79% for the DP model, and from 70% to 77% for the CC model.     

基于启发式算法预测含假结RNA二级结构的研究进展

RNA二级结构的预测算法研究已有近40年的发展历程,研究假结也将近30年的历史。在此期间,RNA二级结构的预测算法取得了很大进步,但假结预测的正确率依然偏低。其中启发式算法能较好地处理复杂假结,使其成为率先解决假结预测难题可能性最大的算法。迄今为止,未见系统地专门总结预测假结的各种启发式算法及其优点与缺点的报道。本文详细介绍了近年来国际上流行的贪婪算法、遗传算法、ILM算法、HotKnots算法以及FlexStem算法等五种算法,并总结分析了每种算法的优点与不足,最后提出在未来一段时期内,利用启发式算法提高假结预测准确度应从建立更完善的假结模型、加入更多影响因素、借鉴不同算法的优势等方面入手。为含假结RNA二级结构预测的研究提供参考。     

Secondary structure prediction and unrefined tertiary structure prediction for cyclin A,B, and D

We present heuristic-based predictions of the secondary and tertiary structures of the cyclins A, B, and D, representatives of the cyclin superfamily. The list of suggested constraints for tertiary structure assembly was left unrefined in order to submit this report before an announced crystal structure for cyclin A becomes available. To predict these constraints, a master sequence alignment over 270 positions of cyclin types A, B, and D was adjusted based on individual secondary structure predictions for each type. We used new heuristics for predicting aromatic residues at protein-protein interfaces and to identify sequentially distinct regions in the protein chain that cluster in the folded structure. The boundaries of two conjectured domains in the cyclin fold were predicted based on experimental data in the literature. The domain that is important for interaction of the cyclins with cyclin-dependent kinases (CDKs) is predicted to contain six helices; the second domain in the consensus model contains both helices and a β-sheet that is formed by sequentially distant regions in the protein chain. A plausible phosphorylation site is identified. This work represents a blinded test of the method for prediction of secondary and, to a lesser extent, tertiary structure from a set of homologous protein sequences. Evaluation of our predictions will become possible with the publication of the announced crystal structure.     

Search for Conserved Secondary Structures of RNA

We suggest a new algorithm to search a given set of the RNA sequences for conserved secondary structures. The algorithm is based on alignment of the sequences for potential helical strands. This procedure can be used to search for new structured RNAs and new regulatory elements. It is efficient for the genome-scale analysis. The results of various tests run with this algorithm are shown.     

ProbKnot: Fast prediction of RNA secondary structure including pseudoknots

It is a significant challenge to predict RNA secondary structures including pseudoknots. Here, a new algorithm capable of predicting pseudoknots of any topology, ProbKnot, is reported. ProbKnot assembles maximum expected accuracy structures from computed base-pairing probabilities in O(N²) time, where N is the length of the sequence. The performance of ProbKnot was measured by comparing predicted structures with known structures for a large database of RNA sequences with fewer than 700 nucleotides. The percentage of known pairs correctly predicted was 69.3%. Additionally, the percentage of predicted pairs in the known structure was 61.3%. This performance is the highest of four tested algorithms that are capable of pseudoknot prediction. The program is available for download at: http://rna.urmc.rochester.edu/RNAstructure.html.     

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.     

A critique of the utility of the prediction of protein secondary structure

The Chou-Fasman predictive algorithm for determining the secondary structure of proteins from the primary sequence is reviewed. Many examples of its use are presented which illustrate its wide applicability, such as predicting (a) regions with the potential for conformational change, (b) sequences which are capable of assuming several conformations in different environments, (c) effects of single amino acid mutations, (d) amino acid replacements in synthesis of peptides to bring about a change in conformation, (e) guide to the synthesis of polypeptides with definitive secondary structure,e.g. signal sequences, (f) conformational homologues from varying sequences and (g) the amino acid requirements for amphiphilicα-helical peptides.     

RNA-SSPT: RNA Secondary Structure Prediction Tools

The prediction of RNA structure is useful for understanding evolution for both in silico and in vitro studies. Physical methods like NMR studies to predict RNA secondary structure are expensive and difficult. Computational RNA secondary structure prediction is easier. Comparative sequence analysis provides the best solution. But secondary structure prediction of a single RNA sequence is challenging. RNA-SSPT is a tool that computationally predicts secondary structure of a single RNA sequence. Most of the RNA secondary structure prediction tools do not allow pseudoknots in the structure or are unable to locate them. Nussinov dynamic programming algorithm has been implemented in RNA-SSPT. The current studies shows only energetically most favorable secondary structure is required and the algorithm modification is also available that produces base pairs to lower the total free energy of the secondary structure. For visualization of RNA secondary structure, NAVIEW in C language is used and modified in C# for tool requirement. RNA-SSPT is built in C# using Dot Net 2.0 in Microsoft Visual Studio 2005 Professional edition. The accuracy of RNA-SSPT is tested in terms of Sensitivity and Positive Predicted Value. It is a tool which serves both secondary structure prediction and secondary structure visualization purposes.     

Algorithm independent properties of RNA secondary structure predictions

Algorithms predicting RNA secondary structures based on different folding criteria – minimum free energies (mfe), kinetic folding (kin), maximum matching (mm) – and different parameter sets are studied systematically. Two base pairing alphabets were used: the binary GC and the natural four-letter AUGC alphabet. Computed structures and free energies depend strongly on both the algorithm and the parameter set. Statistical properties, such as mean number of base pairs, mean numbers of stacks, mean loop sizes, etc., are much less sensitive to the choice of parameter set and even of algorithm. Some features of RNA secondary structures, such as structure correlation functions, shape space covering and neutral networks, seem to depend only on the base pairing logic (GC or AUGC alphabet). Received: 16 May 1996 / Accepted: 10 July 1996     

Protein secondary structure prediction using dynamic programming

In the present paper, we describe how a directed graph was constructed and then searched for the optimum path using a dynamic programming approach, based on the secondary structure propensity of the protein short sequence derived from a training data set. The protein secondary structure was thus predicted in this way. The average three-state accuracy of the algorithm used was 76.70%.     

RNA二级结构数据库

RNA分子众多、结构复杂、功能重要,已经成为当前重要的研究热点之一。RNA的功能与结构密切相关,伴随RNA分子及功能的发现,建立了有关RNA二级结构的数据库,一方面有助于理解RNA功能的结构基础,一方面有助于开发各种有关RNA结构的预测模型。本文对近年常见的RNA二级结构数据库作一概述,希望有助于相关工作者更好地了解与应用相关数据。     

RNA二级子结构的计数

多核苷酸的二级结构可视为一类顶点标号平面图,通常通过枚举每类RNA二级结构图的各种子图来计算其递推公式．本文给出了若干限制端环长度的RNA二级子结构的递推公式及渐近值。     

Improved RNA secondary structure prediction by maximizing expected pair accuracy

Free energy minimization has been the most popular method for RNA secondary structure prediction for decades. It is based on a set of empirical free energy change parameters derived from experiments using a nearest-neighbor model. In this study, a program, MaxExpect, that predicts RNA secondary structure by maximizing the expected base-pair accuracy, is reported. This approach was first pioneered in the program CONTRAfold, using pair probabilities predicted with a statistical learning method. Here, a partition function calculation that utilizes the free energy change nearest-neighbor parameters is used to predict base-pair probabilities as well as probabilities of nucleotides being single-stranded. MaxExpect predicts both the optimal structure (having highest expected pair accuracy) and suboptimal structures to serve as alternative hypotheses for the structure. Tested on a large database of different types of RNA, the maximum expected accuracy structures are, on average, of higher accuracy than minimum free energy structures. Accuracy is measured by sensitivity, the percentage of known base pairs correctly predicted, and positive predictive value (PPV), the percentage of predicted pairs that are in the known structure. By favoring double-strandedness or single-strandedness, a higher sensitivity or PPV of prediction can be favored, respectively. Using MaxExpect, the average PPV of optimal structure is improved from 66% to 68% at the same sensitivity level (73%) compared with free energy minimization.     

A range of complex probabilistic models for RNA secondary structure prediction that includes the nearest-neighbor model and more

The standard approach for single-sequence RNA secondary structure prediction uses a nearest-neighbor thermodynamic model with several thousand experimentally determined energy parameters. An attractive alternative is to use statistical approaches with parameters estimated from growing databases of structural RNAs. Good results have been reported for discriminative statistical methods using complex nearest-neighbor models, including CONTRAfold, Simfold, and ContextFold. Little work has been reported on generative probabilistic models (stochastic context-free grammars [SCFGs]) of comparable complexity, although probabilistic models are generally easier to train and to use. To explore a range of probabilistic models of increasing complexity, and to directly compare probabilistic, thermodynamic, and discriminative approaches, we created TORNADO, a computational tool that can parse a wide spectrum of RNA grammar architectures (including the standard nearest-neighbor model and more) using a generalized super-grammar that can be parameterized with probabilities, energies, or arbitrary scores. By using TORNADO, we find that probabilistic nearest-neighbor models perform comparably to (but not significantly better than) discriminative methods. We find that complex statistical models are prone to overfitting RNA structure and that evaluations should use structurally nonhomologous training and test data sets. Overfitting has affected at least one published method (ContextFold). The most important barrier to improving statistical approaches for RNA secondary structure prediction is the lack of diversity of well-curated single-sequence RNA secondary structures in current RNA databases.