Predicting RNA Structure Using Mutual Information

BACKGROUND: With the ever-increasing number of sequenced RNAs and the establishment of new RNA databases, such as the Comparative RNA Web Site and Rfam, there is a growing need for accurately and automatically predicting RNA structures from multiple alignments. Since RNA secondary structure is often conserved in evolution, the well known, but underused, mutual information measure for identifying covarying sites in an alignment can be useful for identifying structural elements. This article presents MIfold, a MATLAB toolbox that employs mutual information, or a related covariation measure, to display and predict conserved RNA secondary structure (including pseudoknots) from an alignment. RESULTS: We show that MIfold can be used to predict simple pseudoknots, and that the performance can be adjusted to make it either more sensitive or more selective. We also demonstrate that the overall performance of MIfold improves with the number of aligned sequences for certain types of RNA sequences. In addition, we show that, for these sequences, MIfold is more sensitive but less selective than the related RNAalifold structure prediction program and is comparable with the COVE structure prediction package. CONCLUSION: MIfold provides a useful supplementary tool to programs such as RNA Structure Logo, RNAalifold and COVE, and should be useful for automatically generating structural predictions for databases such as Rfam.     

An information measure of the quality of protein secondary structure prediction.

We describe an information-theory-based measure of the quality of secondary structure prediction (RELINFO). RELINFO has a simple yet intuitive interpretation: it represents the factor by which secondary structure choice at a residue has been restricted by a prediction scheme. As an alternative interpretation of secondary structure prediction, RELINFO complements currently used methods by providing an information-based view as to why a prediction succeeds and fails. To demonstrate this score's capabilities, we applied RELINFO to an analysis of a large set of secondary structure predictions obtained from the first five rounds of the Critical Assessment of Structure Prediction (CASP) experiment. RELINFO is compared with two other common measures: percent correct (Q3) and secondary structure overlap (SOV). While the correlation between Q3 and RELINFO is approximately 0.85, RELINFO avoids certain disadvantages of Q3, including overestimating the quality of a prediction. The correlation between SOV and RELINFO is approximately 0.75. The valuable SOV measure unfortunately suffers from a saturation problem, and perhaps has unfairly given the general impression that secondary structure prediction has reached its limit since SOV hasn't improved much over the recent rounds of CASP. Although not a replacement for SOV, RELINFO has greater dispersion. Over the five rounds of CASP assessed here, RELINFO shows that predictions targets have been more difficult in successive CASP experiments, yet the predictions quality has continued to improve measurably over each round. In terms of information, the secondary structure prediction quality has almost doubled from CASP1 to CASP5. Therefore, as a different perspective of accuracy, RELINFO can help to improve prediction of protein secondary structure by providing a measure of difficulty as well as final quality of a prediction.     

Measures for the assessment of fuzzy predictions of protein secondary structure

Many of the recent secondary structure prediction methods incorporate the idea of fuzzy set theory, where instead of assigning a definite secondary structure to a query residue, probability for the residue being in each of the conformational states is estimated. Moreover, continuous assignment of conformational states to the experimentally observed protein structures can be performed in order to reflect inherent flexibility. Although various measures have been developed for evaluating performances of secondary structure prediction methods, they depend only on the most probable secondary structures. They do not assess the accuracy of the probabilities produced by fuzzy prediction methods, and they cannot incorporate information contained in continuous assignments of conformational states to observed structures. Three important measures for evaluating performance of a secondary structure prediction algorithm, Q score, Segment OVerlap (SOV) measure, and the k-state correlation coefficient (Corr), are deformed into fuzzy measures F score, Fuzzy OVerlap (FOV) measure, and the fuzzy correlation coefficient (Forr), so that the new measures not only assess probabilistic outputs of fuzzy prediction methods, but also incorporate information from continuous assignments of secondary structure. As an example of application, prediction results of four fuzzy secondary structure prediction methods, PSIPRED, PROFking, SABLE, and PREDICT, are assessed using the new fuzzy measures.     

Information theory provides a comprehensive framework for the evaluation of protein structure predictions

Protein structure prediction has a number of important ad hoc similarity measures for evaluating predictions, but would benefit from a measure that is able to provide a common framework for a broad range of comparisons. Here we show that a mutual information-like measure can provide a comprehensive framework for evaluating protein structure prediction of all types. We discuss the concept of information, its application to secondary structure, and the obstacle to applying it to 3D structure. On the basis of the insights from the secondary structure case, we present an approach to work around the 3D difficulties, and develop a method to measure the mutual information provided by a 3D structure prediction. We integrate the evaluation of all types of protein structure prediction into a single framework, and compare the amount of information provided by various prediction methods, including secondary structure prediction. Within this broadened framework, the idea that structure is better preserved than sequence during evolution is evaluated quantitatively for the globin family. A nearly perfect sequence match in the globin family corresponds to about 300 bits of information, whereas a nearly perfect structural match for the same two proteins corresponds to about 2500 bits of information, where bits of information describes the probability of obtaining a match of similar closeness by chance. Mutual information provides both a theoretical basis for evaluating structure similarity and an explanatory surround for existing similarity measures.     

Structural constraints identified with covariation analysis in ribosomal RNA

Covariation analysis is used to identify those positions with similar patterns of sequence variation in an alignment of RNA sequences. These constraints on the evolution of two positions are usually associated with a base pair in a helix. While mutual information (MI) has been used to accurately predict an RNA secondary structure and a few of its tertiary interactions, early studies revealed that phylogenetic event counting methods are more sensitive and provide extra confidence in the prediction of base pairs. We developed a novel and powerful phylogenetic events counting method (PEC) for quantifying positional covariation with the Gutell lab's new RNA Comparative Analysis Database (rCAD). The PEC and MI-based methods each identify unique base pairs, and jointly identify many other base pairs. In total, both methods in combination with an N-best and helix-extension strategy identify the maximal number of base pairs. While covariation methods have effectively and accurately predicted RNAs secondary structure, only a few tertiary structure base pairs have been identified. Analysis presented herein and at the Gutell lab's Comparative RNA Web (CRW) Site reveal that the majority of these latter base pairs do not covary with one another. However, covariation analysis does reveal a weaker although significant covariation between sets of nucleotides that are in proximity in the three-dimensional RNA structure. This reveals that covariation analysis identifies other types of structural constraints beyond the two nucleotides that form a base pair.     

RNA secondary structure prediction based on free energy and phylogenetic analysis.

We describe a computational method for the prediction of RNA secondary structure that uses a combination of free energy and comparative sequence analysis strategies. Using a homology-based sequence alignment as a starting point, all favorable pairings with respect to the Turner energy function are identified. Each potentially paired region within a multiple sequence alignment is scored using a function that combines both predicted free energy and sequence covariation with optimized weightings. High scoring regions are ranked and sequentially incorporated to define a growing secondary structure. Using a single set of optimized parameters, it is possible to accurately predict the foldings of several test RNAs defined previously by extensive phylogenetic and experimental data (including tRNA, 5 S rRNA, SRP RNA, tmRNA, and 16 S rRNA). The algorithm correctly predicts approximately 80% of the secondary structure. A range of parameters have been tested to define the minimal sequence information content required to accurately predict secondary structure and to assess the importance of individual terms in the prediction scheme. This analysis indicates that prediction accuracy most strongly depends upon covariational information and only weakly on the energetic terms. However, relatively few sequences prove sufficient to provide the covariational information required for an accurate prediction. Secondary structures can be accurately defined by alignments with as few as five sequences and predictions improve only moderately with the inclusion of additional sequences.     

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.     

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.     

Detecting compensatory covariation signals in protein evolution using reconstructed ancestral sequences

When protein sequences divergently evolve under functional constraints, some individual amino acid replacements that reverse the charge (e.g. Lys to Asp) may be compensated by a replacement at a second position that reverses the charge in the opposite direction (e.g. Glu to Arg). When these side-chains are near in space (proximal), such double replacements might be driven by natural selection, if either is selectively disadvantageous, but both together restore fully the ability of the protein to contribute to fitness (are together "neutral"). Accordingly, many have sought to identify pairs of positions in a protein sequence that suffer compensatory replacements, often as a way to identify positions near in space in the folded structure. A "charge compensatory signal" might manifest itself in two ways. First, proximal charge compensatory replacements may occur more frequently than predicted from the product of the probabilities of individual positions suffering charge reversing replacements independently. Conversely, charge compensatory pairs of changes may be observed to occur more frequently in proximal pairs of sites than in the average pair. Normally, charge compensatory covariation is detected by comparing the sequences of extant proteins at the "leaves" of phylogenetic trees. We show here that the charge compensatory signal is more evident when it is sought by examining individual branches in the tree between reconstructed ancestral sequences at nodes in the tree. Here, we find that the signal is especially strong when the positions pairs are in a single secondary structural unit (e.g. alpha helix or beta strand) that brings the side-chains suffering charge compensatory covariation near in space, and may be useful in secondary structure prediction. Also, "node-node" and "node-leaf" compensatory covariation may be useful to identify the better of two equally parsimonious trees, in a way that is independent of the mathematical formalism used to construct the tree itself. Further, compensatory covariation may provide a signal that indicates whether an episode of sequence evolution contains more or less divergence in functional behavior. Compensatory covariation analysis on reconstructed evolutionary trees may become a valuable tool to analyze genome sequences, and use these analyses to extract biomedically useful information from proteome databases.     

Analysis of covariation in an SH3 domain sequence alignment: applications in tertiary contact prediction and the design of compensating hydrophobic core substitutions

We have analyzed sequence covariation in an alignment of 266 non-redundant SH3 domain sequences using chi-squared statistical methods. Artifactual covariations arising from close evolutionary relationships among certain sequence subgroups were eliminated using empirically derived sequence diversity thresholds. This covariation detection method was able to predict residue-residue contacts (side-chain centres of mass within 8 A) in the structure of the SH3 domain with an accuracy of 85 %, which is greater than that achieved in many previous covariation studies. In examining the positions involved most frequently in covariations, we discovered a dramatic over-representation of a subset of five hydrophobic core positions. This covariation information was used to design second and third site substitutions that could compensate for highly destabilizing hydrophobic core substitutions in the Fyn SH3 domain, thus providing experimental data to validate the covariation analysis. The testing of our covariation detection method on 15 other alignments showed that the accuracy of contact prediction is highly variable depending on which sequence alignment is used, and useful levels of prediction accuracy were obtained with only approximately one-third of alignments. The results presented here provide insight into the difficulties inherent in covariation analysis, and suggest that it may have limited usefulness in tertiary structure prediction. On the other hand, our ability to use covariation analysis to design stabilizing combinations of hydrophobic core substitutions attests to its potential utility for gaining deeper insight into the stability determinants and functional mechanisms of proteins with known three-dimensional structures.     

Fast evaluation of internal loops in RNA secondary structure prediction.

MOTIVATION: Though not as abundant in known biological processes as proteins, RNA molecules serve as more than mere intermediaries between DNA and proteins. Research in the last 15 years demonstrates that RNA molecules serve in many roles, including catalysis. Furthermore, RNA secondary structure prediction based on free energy rules for stacking and loop formation remains one of the few major breakthroughs in the field of structure prediction, as minimum free energy structures and related quantities can be computed with full mathematical rigor. However, with the current energy parameters, the algorithms used hitherto suffer the disadvantage of either employing heuristics that risk (though highly unlikely) missing the optimal structure or becoming prohibitively time consuming for moderate to large sequences. RESULTS: We present a new method to evaluate internal loops utilizing currently used energy rules. This method reduces the time complexity of this part of the structure prediction from O(n4) to O(n3), thus reducing the overall complexity to O(n3). Even when the size of evaluated internal loops is bounded by k (a commonly used heuristic), the method presented has a competitive edge by reducing the time complexity of internal loop evaluation from O(k2n2) to O(kn2). The method also applies to the calculation of the equilibrium partition function. AVAILABILITY: Source code for an RNA secondary structure prediction program implementing this method is available at ftp://www.ibc.wustl.edu/pub/zuker/zuker .tar.Z     

Murlet: a practical multiple alignment tool for structural RNA sequences

MOTIVATION: Structural RNA genes exhibit unique evolutionary patterns that are designed to conserve their secondary structures; these patterns should be taken into account while constructing accurate multiple alignments of RNA genes. The Sankoff algorithm is a natural alignment algorithm that includes the effect of base-pair covariation in the alignment model. However, the extremely high computational cost of the Sankoff algorithm precludes its application to most RNA sequences. RESULTS: We propose an efficient algorithm for the multiple alignment of structural RNA sequences. Our algorithm is a variant of the Sankoff algorithm, and it uses an efficient scoring system that reduces the time and space requirements considerably without compromising on the alignment quality. First, our algorithm computes the match probability matrix that measures the alignability of each position pair between sequences as well as the base pairing probability matrix for each sequence. These probabilities are then combined to score the alignment using the Sankoff algorithm. By itself, our algorithm does not predict the consensus secondary structure of the alignment but uses external programs for the prediction. We demonstrate that both the alignment quality and the accuracy of the consensus secondary structure prediction from our alignment are the highest among the other programs examined. We also demonstrate that our algorithm can align relatively long RNA sequences such as the eukaryotic-type signal recognition particle RNA that is approximately 300 nt in length; multiple alignment of such sequences has not been possible by using other Sankoff-based algorithms. The algorithm is implemented in the software named 'Murlet'. AVAILABILITY: The C++ source code of the Murlet software and the test dataset used in this study are available at http://www.ncrna.org/papers/Murlet/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

HYPROSP: a hybrid protein secondary structure prediction algorithm--a knowledge-based approach

We develop a knowledge-based approach (called PROSP) for protein secondary structure prediction. The knowledge base contains small peptide fragments together with their secondary structural information. A quantitative measure M, called match rate, is defined to measure the amount of structural information that a target protein can extract from the knowledge base. Our experimental results show that proteins with a higher match rate will likely be predicted more accurately based on PROSP. That is, there is roughly a monotone correlation between the prediction accuracy and the amount of structure matching with the knowledge base. To fully utilize the strength of our knowledge base, a hybrid prediction method is proposed as follows: if the match rate of a target protein is at least 80%, we use the extracted information to make the prediction; otherwise, we adopt a popular machine-learning approach. This comprises our hybrid protein structure prediction (HYPROSP) approach. We use the DSSP and EVA data as our datasets and PSIPRED as our underlying machine-learning algorithm. For target proteins with match rate at least 80%, the average Q₃ of PROSP is 3.96 and 7.2 better than that of PSIPRED on DSSP and EVA data, respectively.     

A simple and fast secondary structure prediction method using hidden neural networks

MOTIVATION: In this paper, we present a secondary structure prediction method YASPIN that unlike the current state-of-the-art methods utilizes a single neural network for predicting the secondary structure elements in a 7-state local structure scheme and then optimizes the output using a hidden Markov model, which results in providing more information for the prediction. RESULTS: YASPIN was compared with the current top-performing secondary structure prediction methods, such as PHDpsi, PROFsec, SSPro2, JNET and PSIPRED. The overall prediction accuracy on the independent EVA5 sequence set is comparable with that of the top performers, according to the Q3, SOV and Matthew's correlations accuracy measures. YASPIN shows the highest accuracy in terms of Q3 and SOV scores for strand prediction. AVAILABILITY: YASPIN is available on-line at the Centre for Integrative Bioinformatics website (http://ibivu.cs.vu.nl/programs/yaspinwww/) at the Vrije University in Amsterdam and will soon be mirrored on the Mathematical Biology website (http://www.mathbio.nimr.mrc.ac.uk) at the NIMR in London. CONTACT: kxlin@nimr.mrc.ac.uk     

Decision tree-based formation of consensus protein secondary structure prediction

MOTIVATION: Prediction of protein secondary structure provides information that is useful for other prediction methods like fold recognition and ab initio 3D prediction. A consensus prediction constructed from the output of several methods should yield more reliable results than each of the individual methods. METHOD: We present an approach that reveals subtle but systematic differences in the output of different secondary structure prediction methods allowing the derivation of coherent consensus predictions. The method uses a machine learning technique that builds decision trees from existing data. RESULTS: The first results of our analysis show that consensus prediction of protein secondary structure may be improved both quantitatively and qualitatively.     

Identification and application of the concepts important for accurate and reliable protein secondary structure prediction.

A protein secondary structure prediction method from multiply aligned homologous sequences is presented with an overall per residue three-state accuracy of 70.1%. There are two aims: to obtain high accuracy by identification of a set of concepts important for prediction followed by use of linear statistics; and to provide insight into the folding process. The important concepts in secondary structure prediction are identified as: residue conformational propensities, sequence edge effects, moments of hydrophobicity, position of insertions and deletions in aligned homologous sequence, moments of conservation, auto-correlation, residue ratios, secondary structure feedback effects, and filtering. Explicit use of edge effects, moments of conservation, and auto-correlation are new to this paper. The relative importance of the concepts used in prediction was analyzed by stepwise addition of information and examination of weights in the discrimination function. The simple and explicit structure of the prediction allows the method to be reimplemented easily. The accuracy of a prediction is predictable a priori. This permits evaluation of the utility of the prediction: 10% of the chains predicted were identified correctly as having a mean accuracy of > 80%. Existing high-accuracy prediction methods are "black-box" predictors based on complex nonlinear statistics (e.g., neural networks in PHD: Rost & Sander, 1993a). For medium- to short-length chains (> or = 90 residues and < 170 residues), the prediction method is significantly more accurate (P < 0.01) than the PHD algorithm (probably the most commonly used algorithm). In combination with the PHD, an algorithm is formed that is significantly more accurate than either method, with an estimated overall three-state accuracy of 72.4%, the highest accuracy reported for any prediction method.     

Prediction of Beta-Turn in Protein Using E-SSpred and Support Vector Machine

β-Turn is a secondary protein structure type that plays an important role in protein configuration and function. Here, we introduced an approach of β-turn prediction that used the support vector machine (SVM) algorithm combined with predicted secondary structure information. The secondary structure information was obtained by using E-SSpred, a new secondary protein structure prediction method. A 7-fold cross validation based on the benchmark dataset of 426 non-homologous protein chains was used to evaluate the performance of our method. The prediction results broke the 80% Q _total barrier and achieved Q _total = 80.9%, MCC = 0.44, and Q _predicted higher 0.9% when compared with the best method. The results in our research are coincident with the conclusion that β-turn prediction accuracy can be improved by inclusion of secondary structure information.     

Protein secondary structure: entropy, correlations and prediction

MOTIVATION: Is protein secondary structure primarily determined by local interactions between residues closely spaced along the amino acid backbone or by non-local tertiary interactions? To answer this question, we measure the entropy densities of primary and secondary structure sequences, and the local inter-sequence mutual information density. RESULTS: We find that the important inter-sequence interactions are short ranged, that correlations between neighboring amino acids are essentially uninformative and that only one-fourth of the total information needed to determine the secondary structure is available from local inter-sequence correlations. These observations support the view that the majority of most proteins fold via a cooperative process where secondary and tertiary structure form concurrently. Moreover, existing single-sequence secondary structure prediction algorithms are almost optimal, and we should not expect a dramatic improvement in prediction accuracy. AVAILABILITY: Both the data sets and analysis code are freely available from our Web site at http://compbio.berkeley.edu/     

Structural constraints on the covariance matrix derived from multiple aligned protein sequences

Residue contact predictions were calculated based on the mutual information observed between pairs of positions in large multiple protein sequence alignments. Where previously only the statistical properties of these data have been considered important, we introduce new measures to impose constraints that make the contact map more consistent with a three dimensional structure. These included global (bulk) properties and local secondary structure properties. The latter allowed the contact constraints to be employed at the level of filtering pairs of secondary structure contacts which led to a more efficient (lower-level) implementation in the PLATO structure prediction server. Where previously the measure of success with this method had been whether the correct fold was predicted in the top 10 ranked models, with the current implementation, our summary statistic is the number of correct folds included in the top 10 models--which is on average over 50 percent.     

Identifying and Seeing beyond Multiple Sequence Alignment Errors Using Intra-Molecular Protein Covariation

Background

There is currently no way to verify the quality of a multiple sequence alignment that is independent of the assumptions used to build it. Sequence alignments are typically evaluated by a number of established criteria: sequence conservation, the number of aligned residues, the frequency of gaps, and the probable correct gap placement. Covariation analysis is used to find putatively important residue pairs in a sequence alignment. Different alignments of the same protein family give different results demonstrating that covariation depends on the quality of the sequence alignment. We thus hypothesized that current criteria are insufficient to build alignments for use with covariation analyses.

Methodology/Principal Findings

We show that current criteria are insufficient to build alignments for use with covariation analyses as systematic sequence alignment errors are present even in hand-curated structure-based alignment datasets like those from the Conserved Domain Database. We show that current non-parametric covariation statistics are sensitive to sequence misalignments and that this sensitivity can be used to identify systematic alignment errors. We demonstrate that removing alignment errors due to 1) improper structure alignment, 2) the presence of paralogous sequences, and 3) partial or otherwise erroneous sequences, improves contact prediction by covariation analysis. Finally we describe two non-parametric covariation statistics that are less sensitive to sequence alignment errors than those described previously in the literature.

Conclusions/Significance

Protein alignments with errors lead to false positive and false negative conclusions (incorrect assignment of covariation and conservation, respectively). Covariation analysis can provide a verification step, independent of traditional criteria, to identify systematic misalignments in protein alignments. Two non-parametric statistics are shown to be somewhat insensitive to misalignment errors, providing increased confidence in contact prediction when analyzing alignments with erroneous regions because of an emphasis on they emphasize pairwise covariation over group covariation.