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.     

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.     

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.     

Dynalign: an algorithm for finding the secondary structure common to two RNA sequences

With the rapid increase in the size of the genome sequence database, computational analysis of RNA will become increasingly important in revealing structure-function relationships and potential drug targets. RNA secondary structure prediction for a single sequence is 73 % accurate on average for a large database of known secondary structures. This level of accuracy provides a good starting point for determining a secondary structure either by comparative sequence analysis or by the interpretation of experimental studies. Dynalign is a new computer algorithm that improves the accuracy of structure prediction by combining free energy minimization and comparative sequence analysis to find a low free energy structure common to two sequences without requiring any sequence identity. It uses a dynamic programming construct suggested by Sankoff. Dynalign, however, restricts the maximum distance, M, allowed between aligned nucleotides in the two sequences. This makes the calculation tractable because the complexity is simplified to O(M(3)N(3)), where N is the length of the shorter sequence.The accuracy of Dynalign was tested with sets of 13 tRNAs, seven 5 S rRNAs, and two R2 3' UTR sequences. On average, Dynalign predicted 86.1 % of known base-pairs in the tRNAs, as compared to 59.7 % for free energy minimization alone. For the 5 S rRNAs, the average accuracy improves from 47.8 % to 86.4 %. The secondary structure of the R2 3' UTR from Drosophila takahashii is poorly predicted by standard free energy minimization. With Dynalign, however, the structure predicted in tandem with the sequence from Drosophila melanogaster nearly matches the structure determined by comparative sequence analysis.     

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.     

A new algorithm for RNA secondary structure design

The function of many RNAs depends crucially on their structure. Therefore, the design of RNA molecules with specific structural properties has many potential applications, e.g. in the context of investigating the function of biological RNAs, of creating new ribozymes, or of designing artificial RNA nanostructures. Here, we present a new algorithm for solving the following RNA secondary structure design problem: given a secondary structure, find an RNA sequence (if any) that is predicted to fold to that structure. Unlike the (pseudoknot-free) secondary structure prediction problem, this problem appears to be hard computationally. Our new algorithm, "RNA Secondary Structure Designer (RNA-SSD)", is based on stochastic local search, a prominent general approach for solving hard combinatorial problems. A thorough empirical evaluation on computationally predicted structures of biological sequences and artificially generated RNA structures as well as on empirically modelled structures from the biological literature shows that RNA-SSD substantially out-performs the best known algorithm for this problem, RNAinverse from the Vienna RNA Package. In particular, the new algorithm is able to solve structures, consistently, for which RNAinverse is unable to find solutions. The RNA-SSD software is publically available under the name of RNA Designer at the RNASoft website (www.rnasoft.ca).     

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。     

General combinatorics of RNA secondary structure

The total number of RNA secondary structures of a given length with minimal hairpin loop length m(m>0) and with minimal stack length l(l>0) is computed, under the assumption that all base pairs can occur. Asymptotics are derived from the determination of recurrence relations of decomposition properties.     

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.     

Statistics of RNA melting kinetics

We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that. assigns structure dependent overall rate constants of melting (or refolding) to a sequence. This induces a landscape of reaction rates, or activation energies, over the space of sequences with fixed length. We study the distribution and the correlation structure of these activation energies. Correspondence to: P. Schuster     

RNA二级结构的最小自由能算法

RNA(即tRNA,rRNA,mRNA和SnRNA)有两大主要功能：一是某些病毒的遗传物质;二是参与蛋白质的合成,这些与细胞分化、代谢、记忆的储存等有重要关系,这些功能与RNA二级结构的稳定性。自由能密切相关．常用的计算自由能的方法有热力学微扰法及热力学微积分法等．本文以寻找最小自由能二级结构为目的,给出了RNA二级结构的最小自由能算法,该算法的时间复杂性不超过O(n^4)。     

Selection for fitness versus selection for robustness in RNA secondary structure folding

I investigate the competition between two quasispecies residing on two disparate neutral networks. Under the assumption that the two neutral networks have different topologies and fitness levels, it is the mutation rate that determines which quasispecies will eventually be driven to extinction. For small mutation rates, I find that the quasispecies residing on the neutral network with the lower replication rate will disappear. For higher mutation rates, however, the faster replicating sequences may be outcompeted by the slower replicating ones if the connection density on the second neutral network is sufficiently high. The analytical results are in excellent agreement with flow-reactor simulations of replicating RNA sequences.     

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。     

Measuring the thermodynamics of RNA secondary structure formation

The thermodynamics of RNA secondary structure formation in small model systems provides a database for predicting RNA structure from sequence. Methods for making these measurements are reviewed with emphasis on optical methods and treatment of experimental errors. Analysis of experimental results in terms of simple nearest-neighbor models is presented. Some measured sequence dependences of non-Watson-Crick motifs are discussed. © 1998 John Wiley & Sons, Inc. Biopoly 44: 309–319, 1997     

RNA secondary structure and in vitro translation efficiency

Cell-free protein synthesis is a promising technology featuring many advantages compared to in vivo expression techniques. However, most proteins are still synthesized in vivo due to relatively low protein yields commonly achieved in vitro, especially in the batch mode of reaction. In Escherichia coli S30 extract-based cell-free systems protein yields are supposed to be partially limited by a secondary structure formation of the mRNA. In this study we checked promising members of various classes of RNA chaperones and several different RNA helicases on their ability to enhance in vitro translation. The data clearly show that the addition of none of these factors provides a general solution to the problem. However, protein yields can be increased in presence of a microRNA hybridizing with the 5′ untranslated region of mRNAs, possibly by inducing structural changes improving accessibility of the Shine Dalgarno sequence for the ribosomes.     

Statistical correlation between protein secondary structure and messenger RNA stem-loop structure

A new integrated sequence-structure database, called IADE (Integrated ASTRAL-DSSP-EMBL), incorporating matching mRNA sequence, amino acid sequence, and protein secondary structural data, is constructed. It includes 648 protein domains. Based on the IADE database, we studied the relation between RNA stem-loop frequencies and protein secondary structure. It was found that the alpha-helices and beta-strands on proteins tend to be preferably "coded" by mRNA stem region, while the coils on proteins tend to be preferably "coded" by mRNA loop region. These tendencies are more obvious if we observe the structural words (SWs). An SW is defined by a four-amino-acid-fragment that shows the pronounced secondary structural (alpha-helix or beta-strand) propensity. It is demonstrated that the deduced correlation between protein and mRNA structure can hardly be explained as the stochastic fluctuation effect.     

Simulating the Folding Pathway of RNA Secondary Structure Using the Modified Ant Colony Algorithm

<正> A new method for simulating the folding pathway of RNA secondary structure using the modified ant colony algorithmis proposed.For a given RNA sequence,the set of all possible stems is obtained and the energy of each stem iscalculated and stored at the initial stage.Furthermore,a more realistic formula is used to compute the energy ofmulti-branch loop in the following iteration.Then a folding pathway is simulated,including such processes as constructionof the heuristic information,the rule of initializing the pheromone,the mechanism of choosing the initial andnext stem and the strategy of updating the pheromone between two different stems.Finally by testing RNA sequences withknown secondary structures from the public databases,we analyze the experimental data to select appropriate values forparameters.The measure indexes show that our procedure is more consistent with phylogenetically proven structures thansoftware RNAstructure sometimes and more effective than the standard Genetic Algorithm.     

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.