Local sequence-structure motifs in RNA

Ribonuclic acid (RNA) enjoys increasing interest in molecular biology; despite this interest fundamental algorithms are lacking, e.g. for identifying local motifs. As proteins, RNA molecules have a distinctive structure. Therefore, in addition to sequence information, structure plays an important part in assessing the similarity of RNAs. Furthermore, common sequence-structure features in two or several RNA molecules are often only spatially local, where possibly large parts of the molecules are dissimilar. Consequently, we address the problem of comparing RNA molecules by computing an optimal local alignment with respect to sequence and structure information. While local alignment is superior to global alignment for identifying local similarities, no general local sequence-structure alignment algorithms are currently known. We suggest a new general definition of locality for sequence-structure alignments that is biologically motivated and efficiently tractable. To show the former, we discuss locality of RNA and prove that the defined locality means connectivity by atomic and non-atomic bonds. To show the latter, we present an efficient algorithm for the newly defined pairwise local sequence-structure alignment (lssa) problem for RNA. For molecules of lengthes n and m, the algorithm has worst-case time complexity of O(n2 x m2 x max(n,m)) and a space complexity of only O(n x m). An implementation of our algorithm is available at http://www.bio.inf.uni-jena.de. Its runtime is competitive with global sequence-structure alignment.     

MUSTA--a general, efficient, automated method for multiple structure alignment and detection of common motifs: application to proteins.

Here we present an algorithm designed to carry out multiple structure alignment and to detect recurring substructural motifs. So far we have implemented it for comparison of protein structures. However, this general method is applicable to comparisons of RNA structures and to detection of a pharmacophore in a series of drug molecules. Further, its sequence order independence permits its application to detection of motifs on protein surfaces, interfaces, and binding/active sites. While there are many methods designed to carry out pairwise structure comparisons, there are only a handful geared toward the multiple structure alignment task. Most of these tackle multiple structure comparison as a collection of pairwise structure comparison tasks. The multiple structural alignment algorithm presented here automatically finds the largest common substructure (core) of atoms that appears in all the molecules in the ensemble. The detection of the core and the structural alignment are done simultaneously. The algorithm begins by finding small substructures that are common to all the proteins in the ensemble. One of the molecules is considered the reference; the others are the source molecules. The small substructures are stored in special arrays termed combinatorial buckets, which define sets of multistructural alignments from the source molecules that coincide with the same small set of reference atoms (C(alpha)-atoms here). These substructures are initial small fragments that have congruent copies in each of the proteins. The substructures are extended, through the processing of the combinatorial buckets, by clustering the superpositions (transformations). The method is very efficient.     

A method for discovering common patterns from two RNA secondary structures and its application to structural repeat detection

We propose an ab initio method, named DiscoverR, for finding common patterns from two RNA secondary structures. The method works by representing RNA secondary structures as ordered labeled trees and performs tree pattern discovery using an efficient dynamic programming algorithm. DiscoverR is able to identify and extract the largest common substructures from two RNA molecules having different sizes without prior knowledge of the locations and topologies of these substructures. We also extend DiscoverR to find repeated regions in an RNA secondary structure, and apply this extended method to detect structural repeats in the 3'-untranslated region of a protein kinase gene. We describe the biological significance of a repeated hairpin found by our method, demonstrating the usefulness of the method. DiscoverR is implemented in Java; a jar file including the source code of the program is available for download at http://bioinformatics.njit.edu/DiscoverR.     

Mining frequent stem patterns from unaligned RNA sequences

MOTIVATION: In detection of non-coding RNAs, it is often necessary to identify the secondary structure motifs from a set of putative RNA sequences. Most of the existing algorithms aim to provide the best motif or few good motifs, but biologists often need to inspect all the possible motifs thoroughly. RESULTS: Our method RNAmine employs a graph theoretic representation of RNA sequences and detects all the possible motifs exhaustively using a graph mining algorithm. The motif detection problem boils down to finding frequently appearing patterns in a set of directed and labeled graphs. In the tasks of common secondary structure prediction and local motif detection from long sequences, our method performed favorably both in accuracy and in efficiency with the state-of-the-art methods such as CMFinder. AVAILABILITY: The software is available upon request.     

Accelerated Profile HMM Searches

Profile hidden Markov models (profile HMMs) and probabilistic inference methods have made important contributions to the theory of sequence database homology search. However, practical use of profile HMM methods has been hindered by the computational expense of existing software implementations. Here I describe an acceleration heuristic for profile HMMs, the "multiple segment Viterbi" (MSV) algorithm. The MSV algorithm computes an optimal sum of multiple ungapped local alignment segments using a striped vector-parallel approach previously described for fast Smith/Waterman alignment. MSV scores follow the same statistical distribution as gapped optimal local alignment scores, allowing rapid evaluation of significance of an MSV score and thus facilitating its use as a heuristic filter. I also describe a 20-fold acceleration of the standard profile HMM Forward/Backward algorithms using a method I call "sparse rescaling". These methods are assembled in a pipeline in which high-scoring MSV hits are passed on for reanalysis with the full HMM Forward/Backward algorithm. This accelerated pipeline is implemented in the freely available HMMER3 software package. Performance benchmarks show that the use of the heuristic MSV filter sacrifices negligible sensitivity compared to unaccelerated profile HMM searches. HMMER3 is substantially more sensitive and 100- to 1000-fold faster than HMMER2. HMMER3 is now about as fast as BLAST for protein searches.     

FAMCS： Finding All Maximal Common Substructures in Proteins

Finding the common substructures shared by two proteins is considered as one of the central issues in computational biology because of its usefulness in understanding the structure-function relationship and application in drug and vaccine design. In this paper, we propose a novel algorithm called FAMCS （Finding All Maximal Common Substructures） for the common substructure identification problem. Our method works initially at the protein secondary structural element （SSE） level and starts with the identification of all structurally similar SSE pairs. These SSE pairs are then merged into sets using a modified Apriori algorithm, which will test the similarity of various sets of SSE pairs incrementally until all the maximal sets of SSE pairs that deemed to be similar are found. The maximal common substructures of the two proteins will be formed from these maximal sets. A refinement algorithm is also proposed to fine tune the alignment from the SSE level to the residue level. Comparison of FAMCS with other methods on various proteins shows that FAMCS can address all four requirements and infer interesting biological discoveries.     

Improved gapped alignment in BLAST

Homology search is a key tool for understanding the role, structure, and biochemical function of genomic sequences. The most popular technique for rapid homology search is BLAST, which has been in widespread use within universities, research centers, and commercial enterprises since the early 1990s. We propose a new step in the BLAST algorithm to reduce the computational cost of searching with negligible effect on accuracy. This new step - semigapped alignment - compromises between the efficiency of ungapped alignment and the accuracy of gapped alignment, allowing BLAST to accurately filter sequences with lower computational cost. In addition, we propose a heuristic - restricted insertion alignment - that avoids unlikely evolutionary paths with the aim of reducing gapped alignment cost with negligible effect on accuracy. Together, after including an optimization of the local alignment recursion, our two techniques more than double the speed of the gapped alignment stages in blast. We conclude that our techniques are an important improvement to the BLAST algorithm. Source code for the alignment algorithms is available for download at http://www.bsg.rmit.edu.au/iga/.     

Rapid significance estimation in local sequence alignment with gaps.

In order to assess the significance of sequence alignments, it is crucial to know the distribution of alignment scores of pairs of random sequences. For gapped local alignment, it is empirically known that the shape of this distribution is of the Gumbel form. However, the determination of the parameters of this distribution is a computationally very expensive task. We present a new algorithmic approach which allows estimation of the more important of the Gumbel parameters at least five times faster than the traditional methods. Actual runtimes of our algorithm between less than a second and a few minutes on a workstation bring significance estimation into the realm of interactive applications.     

The identification of novel RNA structural motifs using COMPADRES: an automated approach to structural discovery

Recurring RNA structural motifs are important sites of tertiary interaction and as such, are integral to RNA macromolecular structure. Although numerous RNA motifs have been classified and characterized, the identification of new motifs is of great interest. In this study, we discovered four new conformationally recurring motifs: the pi-turn, the Omega-turn, the alpha-loop and the C2'-endo mediated flipped adenosine motif. Not only do they have complex and interesting structures, but they participate in contacts of high biological significance. In a first for the RNA field, new motifs were discovered by a fully automated algorithm. This algorithm, COMPADRES, utilized a reduced representation of the RNA backbone and was highly successful at discerning unique structural relationships. This study also shows that recurring RNA substructures are not necessarily accompanied by consistent primary or secondary structure.     

BetaSearch: a new method for querying beta-residue motifs

ABSTRACT: BACKGROUND: Searching for structural motifs across known protein structures can be useful for identifying unrelated proteins with similar function and characterising secondary structures such as beta-sheets. This is infeasible using conventional sequence alignment because linear protein sequences do not contain spatial information. beta-residue motifs are beta-sheet substructures that can be represented as graphs and queried using existing graph indexing methods, however, these approaches are designed for general graphs that do not incorporate the inherent structural constraints of beta-sheets and require computationally-expensive filtering and verification procedures. 3D substructure search methods, on the other hand, allow beta-residue motifs to be queried in a three-dimensional context but at significant computational costs. RESULTS: We developed a new method for querying beta-residue motifs, called BetaSearch, which leverages the natural planar constraints of beta-sheets by indexing them as 2D matrices, thus avoiding much of the computational complexities involved with structural and graph querying. BetaSearch demonstrates faster filtering, verification, and overall query time than existing graph indexing approaches whilst producing comparable index sizes. Compared to 3D substructure search methods, BetaSearch achieves 33 and 240 times speedups over index-based and pairwise alignment-based approaches, respectively. Furthermore, we have presented case-studies to demonstrate its capability of motif matching in sequentially dissimilar proteins and described a method for using BetaSearch to predict beta-strand pairing. CONCLUSIONS: We have demonstrated that BetaSearch is a fast method for querying substructure motifs. The improvements in speed over existing approaches make it useful for efficiently performing high-volume exploratory querying of possible protein substructural motifs or conformations. BetaSearch was used to identify a nearly identical beta-residue motif between an entirely synthetic (Top7) and a naturally-occurring protein (Charcot-Leyden crystal protein), as well as identifying structural similarities between biotin-binding domains of avidin, streptavidin and the lipocalin gamma subunit of human C8. AVAILABILITY: The web-interface, source code, and datasets for BetaSearch can be accessed from http://www.csse.unimelb.edu.au/~hohkhkh1/betasearch.     

SEGA: semiglobal graph alignment for structure-based protein comparison

Comparative analysis is a topic of utmost importance in structural bioinformatics. Recently, a structural counterpart to sequence alignment, called multiple graph alignment, was introduced as a tool for the comparison of protein structures in general and protein binding sites in particular. Using approximate graph matching techniques, this method enables the identification of approximately conserved patterns in functionally related structures. In this paper, we introduce a new method for computing graph alignments motivated by two problems of the original approach, a conceptual and a computational one. First, the existing approach is of limited usefulness for structures that only share common substructures. Second, the goal to find a globally optimal alignment leads to an optimization problem that is computationally intractable. To overcome these disadvantages, we propose a semiglobal approach to graph alignment in analogy to semiglobal sequence alignment that combines the advantages of local and global graph matching.     

ParAlign: a parallel sequence alignment algorithm for rapid and sensitive database searches

There is a need for faster and more sensitive algorithms for sequence similarity searching in view of the rapidly increasing amounts of genomic sequence data available. Parallel processing capabilities in the form of the single instruction, multiple data (SIMD) technology are now available in common microprocessors and enable a single microprocessor to perform many operations in parallel. The ParAlign algorithm has been specifically designed to take advantage of this technology. The new algorithm initially exploits parallelism to perform a very rapid computation of the exact optimal ungapped alignment score for all diagonals in the alignment matrix. Then, a novel heuristic is employed to compute an approximate score of a gapped alignment by combining the scores of several diagonals. This approximate score is used to select the most interesting database sequences for a subsequent Smith-Waterman alignment, which is also parallelised. The resulting method represents a substantial improvement compared to existing heuristics. The sensitivity and specificity of ParAlign was found to be as good as Smith-Waterman implementations when the same method for computing the statistical significance of the matches was used. In terms of speed, only the significantly less sensitive NCBI BLAST 2 program was found to outperform the new approach. Online searches are available at http://dna.uio.no/search/     

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.     

An alternative view of protein fold space

Comparing and subsequently classifying protein structures information has received significant attention concurrent with the increase in the number of experimentally derived 3-dimensional structures. Classification schemes have focused on biological function found within protein domains and on structure classification based on topology. Here an alternative view is presented that groups substructures. Substructures are long (50-150 residue) highly repetitive near-contiguous pieces of polypeptide chain that occur frequently in a set of proteins from the PDB defined as structurally non-redundant over the complete polypeptide chain. The substructure classification is based on a previously reported Combinatorial Extension (CE) algorithm that provides a significantly different set of structure alignments than those previously described, having, for example, only a 40% overlap with FSSP. Qualitatively the algorithm provides longer contiguous aligned segments at the price of a slightly higher root-mean-square deviation (rmsd). Clustering these alignments gives a discreet and highly repetitive set of substructures not detectable by sequence similarity alone. In some cases different substructures represent all or different parts of well known folds indicative of the Russian doll effect--the continuity of protein fold space. In other cases they fall into different structure and functional classifications. It is too early to determine whether these newly classified substructures represent new insights into the evolution of a structural framework important to many proteins. What is apparent from on-going work is that these substructures have the potential to be useful probes in finding remote sequence homology and in structure prediction studies. The characteristics of the complete all-by-all comparison of the polypeptide chains present in the PDB and details of the filtering procedure by pair-wise structure alignment that led to the emergent substructure gallery are discussed. Substructure classification, alignments, and tools to analyze them are available at http://cl.sdsc.edu/ce.html.     

Aligning two RNA secondary structures with l-block

RNA sequences can form structures which are conserved throughout evolution and the question of aligning two RNA secondary structures has been extensively studied. Most of the previous alignment algorithms require the input of gap opening and gap extension penalty parameters. The choice of appropriate parameter values is controversial as there is little biological information to guide their assignment. In this paper, we present an algorithm which circumvents this problem. Instead of finding an optimal alignment with predefined gap opening penalty, the algorithm finds the optimal alignment with exact number of aligned blocks.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

Pair stochastic tree adjoining grammars for aligning and predicting pseudoknot RNA structures

MOTIVATION: Since the whole genome sequences of many species have been determined, computational prediction of RNA secondary structures and computational identification of those non-coding RNA regions by comparative genomics become important. Therefore, more advanced alignment methods are required. Recently, an approach of structural alignment for RNA sequences has been introduced to solve these problems. Pair hidden Markov models on tree structures (PHMMTSs) proposed by Sakakibara are efficient automata-theoretic models for structural alignment of RNA secondary structures, although PHMMTSs are incapable of handling pseudoknots. On the other hand, tree adjoining grammars (TAGs), a subclass of context-sensitive grammars, are suitable for modeling pseudoknots. Our goal is to extend PHMMTSs by incorporating TAGs to be able to handle pseudoknots. RESULTS: We propose pair stochastic TAGs (PSTAGs) for aligning and predicting RNA secondary structures including a simple type of pseudoknot which can represent most known pseudoknot structures. First, we extend PHMMTSs defined on alignment of 'trees' to PSTAGs defined on alignment of 'TAG trees' which represent derivation processes of TAGs and are functionally equivalent to derived trees of TAGs. Then, we develop an efficient dynamic programming algorithm of PSTAGs for obtaining an optimal structural alignment including pseudoknots. We implement the PSTAG algorithm and demonstrate the properties of the algorithm by using it to align and predict several small pseudoknot structures. We believe that our implemented program based on PSTAGs is the first grammar-based and practically executable software for comparative analyses of RNA pseudoknot structures, and, further, non-coding RNAs.