Pair hidden Markov models on tree structures

MOTIVATION: Computationally identifying non-coding RNA regions on the genome has much scope for investigation and is essentially harder than gene-finding problems for protein-coding regions. Since comparative sequence analysis is effective for non-coding RNA detection, efficient computational methods are expected for structural alignments of RNA sequences. On the other hand, Hidden Markov Models (HMMs) have played important roles for modeling and analysing biological sequences. Especially, the concept of Pair HMMs (PHMMs) have been examined extensively as mathematical models for alignments and gene finding. RESULTS: We propose the pair HMMs on tree structures (PHMMTSs), which is an extension of PHMMs defined on alignments of trees and provides a unifying framework and an automata-theoretic model for alignments of trees, structural alignments and pair stochastic context-free grammars. By structural alignment, we mean a pairwise alignment to align an unfolded RNA sequence into an RNA sequence of known secondary structure. First, we extend the notion of PHMMs defined on alignments of 'linear' sequences to pair stochastic tree automata, called PHMMTSs, defined on alignments of 'trees'. The PHMMTSs provide various types of alignments of trees such as affine-gap alignments of trees and an automata-theoretic model for alignment of trees. Second, based on the observation that a secondary structure of RNA can be represented by a tree, we apply PHMMTSs to the problem of structural alignments of RNAs. We modify PHMMTSs so that it takes as input a pair of a 'linear' sequence and a 'tree' representing a secondary structure of RNA to produce a structural alignment. Further, the PHMMTSs with input of a pair of two linear sequences is mathematically equal to the pair stochastic context-free grammars. We demonstrate some computational experiments to show the effectiveness of our method for structural alignments, and discuss a complexity issue of PHMMTSs.     

Multiple protein sequence alignment from tertiary structure comparison: assignment of global and residue confidence levels.

An algorithm is presented for the accurate and rapid generation of multiple protein sequence alignments from tertiary structure comparisons. A preliminary multiple sequence alignment is performed using sequence information, which then determines an initial superposition of the structures. A structure comparison algorithm is applied to all pairs of proteins in the superimposed set and a similarity tree calculated. Multiple sequence alignments are then generated by following the tree from the branches to the root. At each branchpoint of the tree, a structure-based sequence alignment and coordinate transformations are output, with the multiple alignment of all structures output at the root. The algorithm encoded in STAMP (STructural Alignment of Multiple Proteins) is shown to give alignments in good agreement with published structural accounts within the dehydrogenase fold domains, globins, and serine proteinases. In order to reduce the need for visual verification, two similarity indices are introduced to determine the quality of each generated structural alignment. Sc quantifies the global structural similarity between pairs or groups of proteins, whereas Pij' provides a normalized measure of the confidence in the alignment of each residue. STAMP alignments have the quality of each alignment characterized by Sc and Pij' values and thus provide a reproducible resource for studies of residue conservation within structural motifs.     

PROMALS3D: a tool for multiple protein sequence and structure alignments

Although multiple sequence alignments (MSAs) are essential for a wide range of applications from structure modeling to prediction of functional sites, construction of accurate MSAs for distantly related proteins remains a largely unsolved problem. The rapidly increasing database of spatial structures is a valuable source to improve alignment quality. We explore the use of 3D structural information to guide sequence alignments constructed by our MSA program PROMALS. The resulting tool, PROMALS3D, automatically identifies homologs with known 3D structures for the input sequences, derives structural constraints through structure-based alignments and combines them with sequence constraints to construct consistency-based multiple sequence alignments. The output is a consensus alignment that brings together sequence and structural information about input proteins and their homologs. PROMALS3D can also align sequences of multiple input structures, with the output representing a multiple structure-based alignment refined in combination with sequence constraints. The advantage of PROMALS3D is that it gives researchers an easy way to produce high-quality alignments consistent with both sequences and structures of proteins. PROMALS3D outperforms a number of existing methods for constructing multiple sequence or structural alignments using both reference-dependent and reference-independent evaluation methods.     

Alignment of RNA base pairing probability matrices

MOTIVATION: Many classes of functional RNA molecules are characterized by highly conserved secondary structures but little detectable sequence similarity. Reliable multiple alignments can therefore be constructed only when the shared structural features are taken into account. Since multiple alignments are used as input for many subsequent methods of data analysis, structure-based alignments are an indispensable necessity in RNA bioinformatics. RESULTS: We present here a method to compute pairwise and progressive multiple alignments from the direct comparison of base pairing probability matrices. Instead of attempting to solve the folding and the alignment problem simultaneously as in the classical Sankoff's algorithm, we use McCaskill's approach to compute base pairing probability matrices which effectively incorporate the information on the energetics of each sequences. A novel, simplified variant of Sankoff's algorithms can then be employed to extract the maximum-weight common secondary structure and an associated alignment. AVAILABILITY: The programs pmcomp and pmmulti described in this contribution are implemented in Perl and can be downloaded together with the example datasets from http://www.tbi.univie.ac.at/RNA/PMcomp/. A web server is available at http://rna.tbi.univie.ac.at/cgi-bin/pmcgi.pl     

Biological insights from topology independent comparison of protein 3D structures

Comparing and classifying the three-dimensional (3D) structures of proteins is of crucial importance to molecular biology, from helping to determine the function of a protein to determining its evolutionary relationships. Traditionally, 3D structures are classified into groups of families that closely resemble the grouping according to their primary sequence. However, significant structural similarities exist at multiple levels between proteins that belong to these different structural families. In this study, we propose a new algorithm, CLICK, to capture such similarities. The method optimally superimposes a pair of protein structures independent of topology. Amino acid residues are represented by the Cartesian coordinates of a representative point (usually the C(α) atom), side chain solvent accessibility, and secondary structure. Structural comparison is effected by matching cliques of points. CLICK was extensively benchmarked for alignment accuracy on four different sets: (i) 9537 pair-wise alignments between two structures with the same topology; (ii) 64 alignments from set (i) that were considered to constitute difficult alignment cases; (iii) 199 pair-wise alignments between proteins with similar structure but different topology; and (iv) 1275 pair-wise alignments of RNA structures. The accuracy of CLICK alignments was measured by the average structure overlap score and compared with other alignment methods, including HOMSTRAD, MUSTANG, Geometric Hashing, SALIGN, DALI, GANGSTA(+), FATCAT, ARTS and SARA. On average, CLICK produces pair-wise alignments that are either comparable or statistically significantly more accurate than all of these other methods. We have used CLICK to uncover relationships between (previously) unrelated proteins. These new biological insights include: (i) detecting hinge regions in proteins where domain or sub-domains show flexibility; (ii) discovering similar small molecule binding sites from proteins of different folds and (iii) discovering topological variants of known structural/sequence motifs. Our method can generally be applied to compare any pair of molecular structures represented in Cartesian coordinates as exemplified by the RNA structure superimposition benchmark.     

Progressive structure-based alignment of homologous proteins: Adopting sequence comparison strategies

Comparison of multiple protein structures has a broad range of applications in the analysis of protein structure, function and evolution. Multiple structure alignment tools (MSTAs) are necessary to obtain a simultaneous comparison of a family of related folds. In this study, we have developed a method for multiple structure comparison largely based on sequence alignment techniques. A widely used Structural Alphabet named Protein Blocks (PBs) was used to transform the information on 3D protein backbone conformation as a 1D sequence string. A progressive alignment strategy similar to CLUSTALW was adopted for multiple PB sequence alignment (mulPBA). Highly similar stretches identified by the pairwise alignments are given higher weights during the alignment. The residue equivalences from PB based alignments are used to obtain a three dimensional fit of the structures followed by an iterative refinement of the structural superposition. Systematic comparisons using benchmark datasets of MSTAs underlines that the alignment quality is better than MULTIPROT, MUSTANG and the alignments in HOMSTRAD, in more than 85% of the cases. Comparison with other rigid-body and flexible MSTAs also indicate that mulPBA alignments are superior to most of the rigid-body MSTAs and highly comparable to the flexible alignment methods.     

基于结构信息的RNA多序列比对

多序列比对是生物信息学中重要的基础研究内容,对各种RNA序列分析方法而言,这也是非常重要的一步。不像DNA和蛋白质,许多功能RNA分子的序列保守性要远差于其结构的保守性,因此,对RNA的分析研究要求其多序列比对不仅要考虑序列信息,而且要充分考虑到其结构信息。本文提出了一种考虑了结构信息的同源RNA多序列比对算法,它先利用热力学方法计算出每条序列的配对概率矩阵,得到结构信息,由此构造各条序列的结构信息矢量,结合传统序列比对方法,提出优化目标函数,采用动态规划算法和渐进比对得到最后的多序列比对。试验证实该方法的有效性。     

On comparing two structured RNA multiple alignments

We present a method, called BlockMatch, for aligning two blocks, where a block is an RNA multiple sequence alignment with the consensus secondary structure of the alignment in Stockholm format. The method employs a quadratic-time dynamic programming algorithm for aligning columns and column pairs of the multiple alignments in the blocks. Unlike many other tools that can perform pairwise alignment of either single sequences or structures only, BlockMatch takes into account the characteristics of all the sequences in the blocks along with their consensus structures during the alignment process, thus being able to achieve a high-quality alignment result. We apply BlockMatch to phylogeny reconstruction on a set of 5S rRNA sequences taken from fifteen bacteria species. Experimental results showed that the phylogenetic tree generated by our method is more accurate than the tree constructed based on the widely used ClustalW tool. The BlockMatch algorithm is implemented into a web server, accessible at http://bioinformatics.njit.edu/blockmatch. A jar file of the program is also available for download from the web server.     

Automated multiple structure alignment and detection of a common substructural motif

While a number of approaches have been geared toward multiple sequence alignments, to date there have been very few approaches to multiple structure alignment and detection of a recurring substructural motif. Among these, none performs both multiple structure comparison and motif detection simultaneously. Further, none considers all structures at the same time, rather than initiating from pairwise molecular comparisons. We present such a multiple structural alignment algorithm. Given an ensemble of protein structures, the algorithm automatically finds the largest common substructure (core) of C(alpha) atoms that appears in all the molecules in the ensemble. The detection of the core and the structural alignment are done simultaneously. Additional structural alignments also are obtained and are ranked by the sizes of the substructural motifs, which are present in the entire ensemble. The method is based on the geometric hashing paradigm. As in our previous structural comparison algorithms, it compares the structures in an amino acid sequence order-independent way, and hence the resulting alignment is unaffected by insertions, deletions and protein chain directionality. As such, it can be applied to protein surfaces, protein-protein interfaces and protein cores to find the optimally, and suboptimally spatially recurring substructural motifs. There is no predefinition of the motif. We describe the algorithm, demonstrating its efficiency. In particular, we present a range of results for several protein ensembles, with different folds and belonging to the same, or to different, families. Since the algorithm treats molecules as collections of points in three-dimensional space, it can also be applied to other molecules, such as RNA, or drugs.     

RNA global alignment in the joint sequence–structure space using elastic shape analysis

The functions of RNAs, like proteins, are determined by their structures, which, in turn, are determined by their sequences. Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships. For RNA sequence alignment, most methods developed for protein and DNA sequence alignment can be directly applied. RNA 3-dimensional structure alignment, on the other hand, tends to be more difficult than protein structure alignment due to the lack of regular secondary structures as observed in proteins. Most of the existing RNA 3D structure alignment methods use only the backbone geometry and ignore the sequence information. Using both the sequence and backbone geometry information in RNA alignment may not only produce more accurate classification, but also deepen our understanding of the sequence–structure–function relationship of RNA molecules. In this study, we developed a new RNA alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves with sequence information encoded on additional dimensions so that the alignment can be performed in the joint sequence–structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. Based on ESA, a rigorous mathematical framework can be built for RNA structure comparison. Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs. Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets. The programs are available at http://stat.fsu.edu/ ∼jinfeng/ESA.html.     

The RNA structure alignment ontology

Multiple sequence alignments are powerful tools for understanding the structures, functions, and evolutionary histories of linear biological macromolecules (DNA, RNA, and proteins), and for finding homologs in sequence databases. We address several ontological issues related to RNA sequence alignments that are informed by structure. Multiple sequence alignments are usually shown as two-dimensional (2D) matrices, with rows representing individual sequences, and columns identifying nucleotides from different sequences that correspond structurally, functionally, and/or evolutionarily. However, the requirement that sequences and structures correspond nucleotide-by-nucleotide is unrealistic and hinders representation of important biological relationships. High-throughput sequencing efforts are also rapidly making 2D alignments unmanageable because of vertical and horizontal expansion as more sequences are added. Solving the shortcomings of traditional RNA sequence alignments requires explicit annotation of the meaning of each relationship within the alignment. We introduce the notion of “correspondence,” which is an equivalence relation between RNA elements in sets of sequences as the basis of an RNA alignment ontology. The purpose of this ontology is twofold: first, to enable the development of new representations of RNA data and of software tools that resolve the expansion problems with current RNA sequence alignments, and second, to facilitate the integration of sequence data with secondary and three-dimensional structural information, as well as other experimental information, to create simultaneously more accurate and more exploitable RNA alignments.     

4SALE – A tool for synchronous RNA sequence and secondary structure alignment and editing

Background  

In sequence analysis the multiple alignment builds the fundament of all proceeding analyses. Errors in an alignment could strongly influence all succeeding analyses and therefore could lead to wrong predictions. Hand-crafted and hand-improved alignments are necessary and meanwhile good common practice. For RNA sequences often the primary sequence as well as a secondary structure consensus is well known, e.g., the cloverleaf structure of the t-RNA. Recently, some alignment editors are proposed that are able to include and model both kinds of information. However, with the advent of a large amount of reliable RNA sequences together with their solved secondary structures (available from e.g. the ITS2 Database), we are faced with the problem to handle sequences and their associated secondary structures synchronously.     

Two accurate sequence,structure, and phylogenetic template-based RNA alignment systems

Background

The analysis of RNA sequences, once a small niche field for a small collection of scientists whose primary emphasis was the structure and function of a few RNA molecules, has grown most significantly with the realizations that 1) RNA is implicated in many more functions within the cell, and 2) the analysis of ribosomal RNA sequences is revealing more about the microbial ecology within all biological and environmental systems. The accurate and rapid alignment of these RNA sequences is essential to decipher the maximum amount of information from this data.

Methods

Two computer systems that utilize the Gutell lab's RNA Comparative Analysis Database (rCAD) were developed to align sequences to an existing template alignment available at the Gutell lab's Comparative RNA Web (CRW) Site. Multiple dimensions of cross-indexed information are contained within the relational database - rCAD, including sequence alignments, the NCBI phylogenetic tree, and comparative secondary structure information for each aligned sequence. The first program, CRWAlign-1 creates a phylogenetic-based sequence profile for each column in the alignment. The second program, CRWAlign-2 creates a profile based on phylogenetic, secondary structure, and sequence information. Both programs utilize their profiles to align new sequences into the template alignment.

Results

The accuracies of the two CRWAlign programs were compared with the best template-based rRNA alignment programs and the best de-novo alignment programs. We have compared our programs with a total of eight alternative alignment methods on different sets of 16S rRNA alignments with sequence percent identities ranging from 50% to 100%. Both CRWAlign programs were superior to these other programs in accuracy and speed.

Conclusions

Both CRWAlign programs can be used to align the very extensive amount of RNA sequencing that is generated due to the rapid next-generation sequencing technology. This latter technology is augmenting the new paradigm that RNA is intimately implicated in a significant number of functions within the cell. In addition, the use of bacterial 16S rRNA sequencing in the identification of the microbiome in many different environmental systems creates a need for rapid and highly accurate alignment of bacterial 16S rRNA sequences.

     

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.     

3DCoffee: combining protein sequences and structures within multiple sequence alignments

Most bioinformatics analyses require the assembly of a multiple sequence alignment. It has long been suspected that structural information can help to improve the quality of these alignments, yet the effect of combining sequences and structures has not been evaluated systematically. We developed 3DCoffee, a novel method for combining protein sequences and structures in order to generate high-quality multiple sequence alignments. 3DCoffee is based on TCoffee version 2.00, and uses a mixture of pairwise sequence alignments and pairwise structure comparison methods to generate multiple sequence alignments. We benchmarked 3DCoffee using a subset of HOMSTRAD, the collection of reference structural alignments. We found that combining TCoffee with the threading program Fugue makes it possible to improve the accuracy of our HOMSTRAD dataset by four percentage points when using one structure only per dataset. Using two structures yields an improvement of ten percentage points. The measures carried out on HOM39, a HOMSTRAD subset composed of distantly related sequences, show a linear correlation between multiple sequence alignment accuracy and the ratio of number of provided structure to total number of sequences. Our results suggest that in the case of distantly related sequences, a single structure may not be enough for computing an accurate multiple sequence alignment.     

Scoring profile-to-profile sequence alignments

Sequence alignment profiles have been shown to be very powerful in creating accurate sequence alignments. Profiles are often used to search a sequence database with a local alignment algorithm. More accurate and longer alignments have been obtained with profile-to-profile comparison. There are several steps that must be performed in creating profile-profile alignments, and each involves choices in parameters and algorithms. These steps include (1) what sequences to include in a multiple alignment used to build each profile, (2) how to weight similar sequences in the multiple alignment and how to determine amino acid frequencies from the weighted alignment, (3) how to score a column from one profile aligned to a column of the other profile, (4) how to score gaps in the profile-profile alignment, and (5) how to include structural information. Large-scale benchmarks consisting of pairs of homologous proteins with structurally determined sequence alignments are necessary for evaluating the efficacy of each scoring scheme. With such a benchmark, we have investigated the properties of profile-profile alignments and found that (1) with optimized gap penalties, most column-column scoring functions behave similarly to one another in alignment accuracy; (2) some functions, however, have much higher search sensitivity and specificity; (3) position-specific weighting schemes in determining amino acid counts in columns of multiple sequence alignments are better than sequence-specific schemes; (4) removing positions in the profile with gaps in the query sequence results in better alignments; and (5) adding predicted and known secondary structure information improves alignments.     

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/.     

Refinement by shifting secondary structure elements improves sequence alignments

Constructing a model of a query protein based on its alignment to a homolog with experimentally determined spatial structure (the template) is still the most reliable approach to structure prediction. Alignment errors are the main bottleneck for homology modeling when the query is distantly related to the template. Alignment methods often misalign secondary structural elements by a few residues. Therefore, better alignment solutions can be found within a limited set of local shifts of secondary structures. We present a refinement method to improve pairwise sequence alignments by evaluating alignment variants generated by local shifts of template‐defined secondary structures. Our method SFESA is based on a novel scoring function that combines the profile‐based sequence score and the structure score derived from residue contacts in a template. Such a combined score frequently selects a better alignment variant among a set of candidate alignments generated by local shifts and leads to overall increase in alignment accuracy. Evaluation of several benchmarks shows that our refinement method significantly improves alignments made by automatic methods such as PROMALS, HHpred and CNFpred. The web server is available at http://prodata.swmed.edu/sfesa . Proteins 2015; 83:411–427. © 2014 Wiley Periodicals, Inc.