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1.  Memory-efficient dynamic programming backtrace and pairwise local sequence alignment 
Bioinformatics (Oxford, England)  2008;24(16):1772-1778.
Motivation
A backtrace through a dynamic programming algorithm’s intermediate results in search of an optimal path, or to sample paths according to an implied probability distribution, or as the second stage of a forward–backward algorithm, is a task of fundamental importance in computational biology. When there is insufficient space to store all intermediate results in high-speed memory (e.g. cache) existing approaches store selected stages of the computation, and recompute missing values from these checkpoints on an as-needed basis.
Results
Here we present an optimal checkpointing strategy, and demonstrate its utility with pairwise local sequence alignment of sequences of length 10 000.
Availability
Sample C++-code for optimal backtrace is available in the Supplementary Materials.
doi:10.1093/bioinformatics/btn308
PMCID: PMC2668612  PMID: 18558620
2.  Versatile and declarative dynamic programming using pair algebras 
BMC Bioinformatics  2005;6:224.
Background
Dynamic programming is a widely used programming technique in bioinformatics. In sharp contrast to the simplicity of textbook examples, implementing a dynamic programming algorithm for a novel and non-trivial application is a tedious and error prone task. The algebraic dynamic programming approach seeks to alleviate this situation by clearly separating the dynamic programming recurrences and scoring schemes.
Results
Based on this programming style, we introduce a generic product operation of scoring schemes. This leads to a remarkable variety of applications, allowing us to achieve optimizations under multiple objective functions, alternative solutions and backtracing, holistic search space analysis, ambiguity checking, and more, without additional programming effort. We demonstrate the method on several applications for RNA secondary structure prediction.
Conclusion
The product operation as introduced here adds a significant amount of flexibility to dynamic programming. It provides a versatile testbed for the development of new algorithmic ideas, which can immediately be put to practice.
doi:10.1186/1471-2105-6-224
PMCID: PMC1261154  PMID: 16156887
3.  AGE: defining breakpoints of genomic structural variants at single-nucleotide resolution, through optimal alignments with gap excision 
Bioinformatics  2011;27(5):595-603.
Motivation: Defining the precise location of structural variations (SVs) at single-nucleotide breakpoint resolution is an important problem, as it is a prerequisite for classifying SVs, evaluating their functional impact and reconstructing personal genome sequences. Given approximate breakpoint locations and a bridging assembly or split read, the problem essentially reduces to finding a correct sequence alignment. Classical algorithms for alignment and their generalizations guarantee finding the optimal (in terms of scoring) global or local alignment of two sequences. However, they cannot generally be applied to finding the biologically correct alignment of genomic sequences containing SVs because of the need to simultaneously span the SV (e.g. make a large gap) and perform precise local alignments at the flanking ends.
Results: Here, we formulate the computations involved in this problem and describe a dynamic-programming algorithm for its solution. Specifically, our algorithm, called AGE for Alignment with Gap Excision, finds the optimal solution by simultaneously aligning the 5′ and 3′ ends of two given sequences and introducing a ‘large-gap jump’ between the local end alignments to maximize the total alignment score. We also describe extensions allowing the application of AGE to tandem duplications, inversions and complex events involving two large gaps. We develop a memory-efficient implementation of AGE (allowing application to long contigs) and make it available as a downloadable software package. Finally, we applied AGE for breakpoint determination and standardization in the 1000 Genomes Project by aligning locally assembled contigs to the human genome.
Availability and Implementation: AGE is freely available at http://sv.gersteinlab.org/age.
Contact: pi@gersteinlab.org
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btq713
PMCID: PMC3042181  PMID: 21233167
4.  SW#–GPU-enabled exact alignments on genome scale 
Bioinformatics  2013;29(19):2494-2495.
Summary: We propose SW#, a new CUDA graphical processor unit-enabled and memory-efficient implementation of dynamic programming algorithm, for local alignment. It can be used as either a stand-alone application or a library. Although there are other graphical processor unit implementations of the Smith–Waterman algorithm, SW# is the only one publicly available that can produce sequence alignments on genome-wide scale. For long sequences, it is at least a few hundred times faster than a CPU version of the same algorithm.
Availability: Source code and installation instructions freely available for download at http://complex.zesoi.fer.hr/SW.html.
Contact: mile.sikic@fer.hr
Supplementary information: Supplementary results are available at Bioinformatics online.
doi:10.1093/bioinformatics/btt410
PMCID: PMC3777108  PMID: 23864730
5.  Visualization of near-optimal sequence alignments 
Bioinformatics (Oxford, England)  2004;20(6):953-958.
Motivation
Mathematically optimal alignments do not always properly align active site residues or well-recognized structural elements. Most near-optimal sequence alignment algorithms display alternative alignment paths, rather than the conventional residue-by-residue pairwise alignment. Typically, these methods do not provide mechanisms for finding effectively the most biologically meaningful alignment in the potentially large set of options.
Results
We have developed Web-based software that displays near optimal or alternative alignments of two protein or DNA sequences as a continuous moving picture. A WWW interface to a C++ program generates near optimal alignments, which are sent to a Java Applet, which displays them in a series of alignment frames. The Applet aligns residues so that consistently aligned regions remain at a fixed position on the display, while variable regions move. The display can be stopped to examine alignment details.
Availability
Available at http://fasta.bioch.virginia.edu/ noptalign. For source code contact the authors at wrp@virginia.edu
Contact
wrp@virginia.edu
doi:10.1093/bioinformatics/bth013
PMCID: PMC2836811  PMID: 14751975
6.  Optimizing a global alignment of protein interaction networks 
Bioinformatics  2013;29(21):2765-2773.
Motivation: The global alignment of protein interaction networks is a widely studied problem. It is an important first step in understanding the relationship between the proteins in different species and identifying functional orthologs. Furthermore, it can provide useful insights into the species’ evolution.
Results: We propose a novel algorithm, PISwap, for optimizing global pairwise alignments of protein interaction networks, based on a local optimization heuristic that has previously demonstrated its effectiveness for a variety of other intractable problems. PISwap can begin with different types of network alignment approaches and then iteratively adjust the initial alignments by incorporating network topology information, trading it off for sequence information. In practice, our algorithm efficiently refines other well-studied alignment techniques with almost no additional time cost. We also show the robustness of the algorithm to noise in protein interaction data. In addition, the flexible nature of this algorithm makes it suitable for different applications of network alignment. This algorithm can yield interesting insights into the evolutionary dynamics of related species.
Availability: Our software is freely available for non-commercial purposes from our Web site, http://piswap.csail.mit.edu/.
Contact: bab@csail.mit.edu or csliao@ie.nthu.edu.tw
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btt486
PMCID: PMC3799479  PMID: 24048352
7.  Multilign: an algorithm to predict secondary structures conserved in multiple RNA sequences 
Bioinformatics  2010;27(5):626-632.
Motivation: With recent advances in sequencing, structural and functional studies of RNA lag behind the discovery of sequences. Computational analysis of RNA is increasingly important to reveal structure–function relationships with low cost and speed. The purpose of this study is to use multiple homologous sequences to infer a conserved RNA structure.
Results: A new algorithm, called Multilign, is presented to find the lowest free energy RNA secondary structure common to multiple sequences. Multilign is based on Dynalign, which is a program that simultaneously aligns and folds two sequences to find the lowest free energy conserved structure. For Multilign, Dynalign is used to progressively construct a conserved structure from multiple pairwise calculations, with one sequence used in all pairwise calculations. A base pair is predicted only if it is contained in the set of low free energy structures predicted by all Dynalign calculations. In this way, Multilign improves prediction accuracy by keeping the genuine base pairs and excluding competing false base pairs. Multilign has computational complexity that scales linearly in the number of sequences. Multilign was tested on extensive datasets of sequences with known structure and its prediction accuracy is among the best of available algorithms. Multilign can run on long sequences (> 1500 nt) and an arbitrarily large number of sequences.
Availability: The algorithm is implemented in ANSI C++ and can be downloaded as part of the RNAstructure package at: http://rna.urmc.rochester.edu
Contact: david_mathews@urmc.rochester.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btq726
PMCID: PMC3042186  PMID: 21193521
8.  A practical algorithm for finding maximal exact matches in large sequence datasets using sparse suffix arrays 
Bioinformatics  2009;25(13):1609-1616.
Motivation: High-throughput sequencing technologies place ever increasing demands on existing algorithms for sequence analysis. Algorithms for computing maximal exact matches (MEMs) between sequences appear in two contexts where high-throughput sequencing will vastly increase the volume of sequence data: (i) seeding alignments of high-throughput reads for genome assembly and (ii) designating anchor points for genome–genome comparisons.
Results: We introduce a new algorithm for finding MEMs. The algorithm leverages a sparse suffix array (SA), a text index that stores every K-th position of the text. In contrast to a full text index that stores every position of the text, a sparse SA occupies much less memory. Even though we use a sparse index, the output of our algorithm is the same as a full text index algorithm as long as the space between the indexed suffixes is not greater than a minimum length of a MEM. By relying on partial matches and additional text scanning between indexed positions, the algorithm trades memory for extra computation. The reduced memory usage makes it possible to determine MEMs between significantly longer sequences.
Availability: Source code for the algorithm is available under a BSD open source license at http://compbio.cs.princeton.edu/mems. The implementation can serve as a drop-in replacement for the MEMs algorithm in MUMmer 3.
Contact: zkhan@cs.princeton.edu;mona@cs.princeton.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btp275
PMCID: PMC2732316  PMID: 19389736
9.  Optimal contact map alignment of protein–protein interfaces 
Bioinformatics  2008;24(20):2324-2328.
The long-standing problem of constructing protein structure alignments is of central importance in computational biology. The main goal is to provide an alignment of residue correspondences, in order to identify homologous residues across chains. A critical next step of this is the alignment of protein complexes and their interfaces. Here, we introduce the program CMAPi, a two-dimensional dynamic programming algorithm that, given a pair of protein complexes, optimally aligns the contact maps of their interfaces: it produces polynomial-time near-optimal alignments in the case of multiple complexes. We demonstrate the efficacy of our algorithm on complexes from PPI families listed in the SCOPPI database and from highly divergent cytokine families. In comparison to existing techniques, CMAPi generates more accurate alignments of interacting residues within families of interacting proteins, especially for sequences with low similarity. While previous methods that use an all-atom based representation of the interface have been successful, CMAPi's use of a contact map representation allows it to be more tolerant to conformational changes and thus to align more of the interaction surface. These improved interface alignments should enhance homology modeling and threading methods for predicting PPIs by providing a basis for generating template profiles for sequence–structure alignment.
Contact: bab@mit.edu; jbienkowska@gmail.com
Supplementary information: Supplementary data are available at http://theory.csail.mit.edu/cmapi
doi:10.1093/bioinformatics/btn432
PMCID: PMC2562013  PMID: 18710876
10.  A Parallel Computing Approach to Genetic Sequence Comparison: The Master-Worker Paradigm 
We have implemented a parallel computer version of a dynamic programming biological sequence comparison algorithm to study the potential applicability of using parallel computers for genetic sequence comparisons. Our parallel program is built using C-Linda ®, a machine-independent parallel programming language, and currently runs on a Sequent Symmetry ® parallel computer. C-Linda implements a shared associative memory model, “tuple space”, through which multiple processes can communicate and coordinate control. In our master-worker (MW) parallel implementation, a master process creates several worker processes, extracts a target sequence and multiple test sequences from a database and stores them in tuple space. Each worker reads the target and then repeatedly extracts test strings from tuple space, performs pairwise sequence comparisons using a local comparison algorithm to generate a similarity score, and returns the similarity scores to tuple space. The master collects the scores from tuple space and identifies the best match over all test sequences. The entire program is constructed so that alternative sequence comparison algorithms can be substituted quite easily. Comparisons of the total run-time, speedup, and efficiency were made for the MW parallel implementation and a sequential version.
PMCID: PMC2245566
11.  DIAL: a web server for the pairwise alignment of two RNA three-dimensional structures using nucleotide, dihedral angle and base-pairing similarities 
Nucleic Acids Research  2007;35(Web Server issue):W659-W668.
DIAL (dihedral alignment) is a web server that provides public access to a new dynamic programming algorithm for pairwise 3D structural alignment of RNA. DIAL achieves quadratic time by performing an alignment that accounts for (i) pseudo-dihedral and/or dihedral angle similarity, (ii) nucleotide sequence similarity and (iii) nucleotide base-pairing similarity.
DIAL provides access to three alignment algorithms: global (Needleman–Wunsch), local (Smith–Waterman) and semiglobal (modified to yield motif search). Suboptimal alignments are optionally returned, and also Boltzmann pair probabilities Pr(ai,bj) for aligned positions ai , bj from the optimal alignment. If a non-zero suboptimal alignment score ratio is entered, then the semiglobal alignment algorithm may be used to detect structurally similar occurrences of a user-specified 3D motif. The query motif may be contiguous in the linear chain or fragmented in a number of noncontiguous regions.
The DIAL web server provides graphical output which allows the user to view, rotate and enlarge the 3D superposition for the optimal (and suboptimal) alignment of query to target. Although graphical output is available for all three algorithms, the semiglobal motif search may be of most interest in attempts to identify RNA motifs. DIAL is available at http://bioinformatics.bc.edu/clotelab/DIAL.
doi:10.1093/nar/gkm334
PMCID: PMC1933154  PMID: 17567620
12.  Rapid identification of non-human sequences in high-throughput sequencing datasets 
Bioinformatics  2012;28(8):1174-1175.
Summary: Rapid identification of non-human sequences (RINS) is an intersection-based pathogen detection workflow that utilizes a user-provided custom reference genome set for identification of non-human sequences in deep sequencing datasets. In <2 h, RINS correctly identified the known virus in the dataset SRR73726 and is compatible with any computer capable of running the prerequisite alignment and assembly programs. RINS accurately identifies sequencing reads from intact or mutated non-human genomes in a dataset and robustly generates contigs with these non-human sequences (Supplementary Material).
Availability: RINS is available for free download at http://khavarilab.stanford.edu/resources.html
Contact: abhaduri@stanford.edu or kqu@stanford.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/bts100
PMCID: PMC3324519  PMID: 22377895
13.  Progressive multiple sequence alignments from triplets 
BMC Bioinformatics  2007;8:254.
Background
The quality of progressive sequence alignments strongly depends on the accuracy of the individual pairwise alignment steps since gaps that are introduced at one step cannot be removed at later aggregation steps. Adjacent insertions and deletions necessarily appear in arbitrary order in pairwise alignments and hence form an unavoidable source of errors.
Research
Here we present a modified variant of progressive sequence alignments that addresses both issues. Instead of pairwise alignments we use exact dynamic programming to align sequence or profile triples. This avoids a large fractions of the ambiguities arising in pairwise alignments. In the subsequent aggregation steps we follow the logic of the Neighbor-Net algorithm, which constructs a phylogenetic network by step-wisely replacing triples by pairs instead of combining pairs to singletons. To this end the three-way alignments are subdivided into two partial alignments, at which stage all-gap columns are naturally removed. This alleviates the "once a gap, always a gap" problem of progressive alignment procedures.
Conclusion
The three-way Neighbor-Net based alignment program aln3nn is shown to compare favorably on both protein sequences and nucleic acids sequences to other progressive alignment tools. In the latter case one easily can include scoring terms that consider secondary structure features. Overall, the quality of resulting alignments in general exceeds that of clustalw or other multiple alignments tools even though our software does not included heuristics for context dependent (mis)match scores.
doi:10.1186/1471-2105-8-254
PMCID: PMC1948021  PMID: 17631683
14.  Computing folding pathways between RNA secondary structures 
Nucleic Acids Research  2009;38(5):1711-1722.
Given an RNA sequence and two designated secondary structures A, B, we describe a new algorithm that computes a nearly optimal folding pathway from A to B. The algorithm, RNAtabupath, employs a tabu semi-greedy heuristic, known to be an effective search strategy in combinatorial optimization. Folding pathways, sometimes called routes or trajectories, are computed by RNAtabupath in a fraction of the time required by the barriers program of Vienna RNA Package. We benchmark RNAtabupath with other algorithms to compute low energy folding pathways between experimentally known structures of several conformational switches. The RNApathfinder web server, source code for algorithms to compute and analyze pathways and supplementary data are available at http://bioinformatics.bc.edu/clotelab/RNApathfinder.
doi:10.1093/nar/gkp1054
PMCID: PMC2836545  PMID: 20044352
15.  Comprehensive comparison of graph based multiple protein sequence alignment strategies 
BMC Bioinformatics  2012;13:64.
Background
Alignment of protein sequences (MPSA) is the starting point for a multitude of applications in molecular biology. Here, we present a novel MPSA program based on the SeqAn sequence alignment library. Our implementation has a strict modular structure, which allows to swap different components of the alignment process and, thus, to investigate their contribution to the alignment quality and computation time. We systematically varied information sources, guiding trees, score transformations and iterative refinement options, and evaluated the resulting alignments on BAliBASE and SABmark.
Results
Our results indicate the optimal alignment strategy based on the choices compared. First, we show that pairwise global and local alignments contain sufficient information to construct a high quality multiple alignment. Second, single linkage clustering is almost invariably the best algorithm to build a guiding tree for progressive alignment. Third, triplet library extension, with introduction of new edges, is the most efficient consistency transformation of those compared. Alternatively, one can apply tree dependent partitioning as a post processing step, which was shown to be comparable with the best consistency transformation in both time and accuracy. Finally, propagating information beyond four transitive links introduces more noise than signal.
Conclusions
This is the first time multiple protein alignment strategies are comprehensively and clearly compared using a single implementation platform. In particular, we showed which of the existing consistency transformations and iterative refinement techniques are the most valid. Our implementation is freely available at http://ekhidna.biocenter.helsinki.fi/MMSA and as a supplementary file attached to this article (see Additional file 1).
doi:10.1186/1471-2105-13-64
PMCID: PMC3375188  PMID: 22540977
16.  Dynamic use of multiple parameter sets in sequence alignment 
Nucleic Acids Research  2006;35(2):678-686.
The level of conservation between two homologous sequences often varies among sequence regions; functionally important domains are more conserved than the remaining regions. Thus, multiple parameter sets should be used in alignment of homologous sequences with a stringent parameter set for highly conserved regions and a moderate parameter set for weakly conserved regions. We describe an alignment algorithm to allow dynamic use of multiple parameter sets with different levels of stringency in computation of an optimal alignment of two sequences. The algorithm dynamically considers various candidate alignments, partitions each candidate alignment into sections, and determines the most appropriate set of parameter values for each section of the alignment. The algorithm and its local alignment version are implemented in a computer program named GAP4. The local alignment algorithm in GAP4, that in its predecessor GAP3, and an ordinary local alignment program SIM were evaluated on 257 716 pairs of homologous sequences from 100 protein families. On 168 475 of the 257 716 pairs (a rate of 65.4%), alignments from GAP4 were more statistically significant than alignments from GAP3 and SIM.
doi:10.1093/nar/gkl1063
PMCID: PMC1802605  PMID: 17182633
17.  HPC-CLUST: distributed hierarchical clustering for large sets of nucleotide sequences 
Bioinformatics  2013;30(2):287-288.
Motivation: Nucleotide sequence data are being produced at an ever increasing rate. Clustering such sequences by similarity is often an essential first step in their analysis—intended to reduce redundancy, define gene families or suggest taxonomic units. Exact clustering algorithms, such as hierarchical clustering, scale relatively poorly in terms of run time and memory usage, yet they are desirable because heuristic shortcuts taken during clustering might have unintended consequences in later analysis steps.
Results: Here we present HPC-CLUST, a highly optimized software pipeline that can cluster large numbers of pre-aligned DNA sequences by running on distributed computing hardware. It allocates both memory and computing resources efficiently, and can process more than a million sequences in a few hours on a small cluster.
Availability and implementation: Source code and binaries are freely available at http://meringlab.org/software/hpc-clust/; the pipeline is implemented in C++ and uses the Message Passing Interface (MPI) standard for distributed computing.
Contact: mering@imls.uzh.ch
Supplementary Information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btt657
PMCID: PMC3892691  PMID: 24215029
18.  A max-margin model for efficient simultaneous alignment and folding of RNA sequences 
Bioinformatics  2008;24(13):i68-i76.
Motivation: The need for accurate and efficient tools for computational RNA structure analysis has become increasingly apparent over the last several years: RNA folding algorithms underlie numerous applications in bioinformatics, ranging from microarray probe selection to de novo non-coding RNA gene prediction.
In this work, we present RAF (RNA Alignment and Folding), an efficient algorithm for simultaneous alignment and consensus folding of unaligned RNA sequences. Algorithmically, RAF exploits sparsity in the set of likely pairing and alignment candidates for each nucleotide (as identified by the CONTRAfold or CONTRAlign programs) to achieve an effectively quadratic running time for simultaneous pairwise alignment and folding. RAF's fast sparse dynamic programming, in turn, serves as the inference engine within a discriminative machine learning algorithm for parameter estimation.
Results: In cross-validated benchmark tests, RAF achieves accuracies equaling or surpassing the current best approaches for RNA multiple sequence secondary structure prediction. However, RAF requires nearly an order of magnitude less time than other simultaneous folding and alignment methods, thus making it especially appropriate for high-throughput studies.
Availability: Source code for RAF is available at:http://contra.stanford.edu/contrafold/
Contact: chuongdo@cs.stanford.edu
doi:10.1093/bioinformatics/btn177
PMCID: PMC2718655  PMID: 18586747
19.  A fast, lock-free approach for efficient parallel counting of occurrences of k-mers 
Bioinformatics  2011;27(6):764-770.
Motivation: Counting the number of occurrences of every k-mer (substring of length k) in a long string is a central subproblem in many applications, including genome assembly, error correction of sequencing reads, fast multiple sequence alignment and repeat detection. Recently, the deep sequence coverage generated by next-generation sequencing technologies has caused the amount of sequence to be processed during a genome project to grow rapidly, and has rendered current k-mer counting tools too slow and memory intensive. At the same time, large multicore computers have become commonplace in research facilities allowing for a new parallel computational paradigm.
Results: We propose a new k-mer counting algorithm and associated implementation, called Jellyfish, which is fast and memory efficient. It is based on a multithreaded, lock-free hash table optimized for counting k-mers up to 31 bases in length. Due to their flexibility, suffix arrays have been the data structure of choice for solving many string problems. For the task of k-mer counting, important in many biological applications, Jellyfish offers a much faster and more memory-efficient solution.
Availability: The Jellyfish software is written in C++ and is GPL licensed. It is available for download at http://www.cbcb.umd.edu/software/jellyfish.
Contact: gmarcais@umd.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btr011
PMCID: PMC3051319  PMID: 21217122
20.  Fast and accurate search for non-coding RNA pseudoknot structures in genomes 
Bioinformatics  2008;24(20):2281-2287.
Motivation: Searching genomes for non-coding RNAs (ncRNAs) by their secondary structure has become an important goal for bioinformatics. For pseudoknot-free structures, ncRNA search can be effective based on the covariance model and CYK-type dynamic programming. However, the computational difficulty in aligning an RNA sequence to a pseudoknot has prohibited fast and accurate search of arbitrary RNA structures. Our previous work introduced a graph model for RNA pseudoknots and proposed to solve the structure–sequence alignment by graph optimization. Given k candidate regions in the target sequence for each of the n stems in the structure, we could compute a best alignment in time O(ktn) based upon a tree width t decomposition of the structure graph. However, to implement this method to programs that can routinely perform fast yet accurate RNA pseudoknot searches, we need novel heuristics to ensure that, without degrading the accuracy, only a small number of stem candidates need to be examined and a tree decomposition of a small tree width can always be found for the structure graph.
Results: The current work builds on the previous one with newly developed preprocessing algorithms to reduce the values for parameters k and t and to implement the search method into a practical program, called RNATOPS, for RNA pseudoknot search. In particular, we introduce techniques, based on probabilistic profiling and distance penalty functions, which can identify for every stem just a small number k (e.g. k ≤ 10) of plausible regions in the target sequence to which the stem needs to align. We also devised a specialized tree decomposition algorithm that can yield tree decomposition of small tree width t (e.g. t ≤ 4) for almost all RNA structure graphs. Our experiments show that with RNATOPS it is possible to routinely search prokaryotic and eukaryotic genomes for specific RNA structures of medium to large sizes, including pseudoknots, with high sensitivity and high specificity, and in a reasonable amount of time.
Availability: The source code in C++ for RNATOPS is available at www.uga.edu/RNA-Informatics/software/rnatops/
Contact: cai@cs.uga.edu
Supplementary information: The online Supplementary Material contains all illustrative figures and tables referenced by this article.
doi:10.1093/bioinformatics/btn393
PMCID: PMC2562014  PMID: 18687694
21.  Finding the most significant common sequence and structure motifs in a set of RNA sequences. 
Nucleic Acids Research  1997;25(18):3724-3732.
We present a computational scheme to locally align a collection of RNA sequences using sequence and structure constraints. In addition, the method searches for the resulting alignments with the most significant common motifs, among all possible collections. The first part utilizes a simplified version of the Sankoff algorithm for simultaneous folding and alignment of RNA sequences, but maintains tractability by constructing multi-sequence alignments from pairwise comparisons. The algorithm finds the multiple alignments using a greedy approach and has similarities to both CLUSTAL and CONSENSUS, but the core algorithm assures that the pairwise alignments are optimized for both sequence and structure conservation. The choice of scoring system and the method of progressively constructing the final solution are important considerations that are discussed. Example solutions, and comparisons with other approaches, are provided. The solutions include finding consensus structures identical to published ones.
PMCID: PMC146942  PMID: 9278497
22.  Improving pairwise sequence alignment accuracy using near-optimal protein sequence alignments 
BMC Bioinformatics  2010;11:146.
Background
While the pairwise alignments produced by sequence similarity searches are a powerful tool for identifying homologous proteins - proteins that share a common ancestor and a similar structure; pairwise sequence alignments often fail to represent accurately the structural alignments inferred from three-dimensional coordinates. Since sequence alignment algorithms produce optimal alignments, the best structural alignments must reflect suboptimal sequence alignment scores. Thus, we have examined a range of suboptimal sequence alignments and a range of scoring parameters to understand better which sequence alignments are likely to be more structurally accurate.
Results
We compared near-optimal protein sequence alignments produced by the Zuker algorithm and a set of probabilistic alignments produced by the probA program with structural alignments produced by four different structure alignment algorithms. There is significant overlap between the solution spaces of structural alignments and both the near-optimal sequence alignments produced by commonly used scoring parameters for sequences that share significant sequence similarity (E-values < 10-5) and the ensemble of probA alignments. We constructed a logistic regression model incorporating three input variables derived from sets of near-optimal alignments: robustness, edge frequency, and maximum bits-per-position. A ROC analysis shows that this model more accurately classifies amino acid pairs (edges in the alignment path graph) according to the likelihood of appearance in structural alignments than the robustness score alone. We investigated various trimming protocols for removing incorrect edges from the optimal sequence alignment; the most effective protocol is to remove matches from the semi-global optimal alignment that are outside the boundaries of the local alignment, although trimming according to the model-generated probabilities achieves a similar level of improvement. The model can also be used to generate novel alignments by using the probabilities in lieu of a scoring matrix. These alignments are typically better than the optimal sequence alignment, and include novel correct structural edges. We find that the probA alignments sample a larger variety of alignments than the Zuker set, which more frequently results in alignments that are closer to the structural alignments, but that using the probA alignments as input to the regression model does not increase performance.
Conclusions
The pool of suboptimal pairwise protein sequence alignments substantially overlaps structure-based alignments for pairs with statistically significant similarity, and a regression model based on information contained in this alignment pool improves the accuracy of pairwise alignments with respect to structure-based alignments.
doi:10.1186/1471-2105-11-146
PMCID: PMC2850363  PMID: 20307279
23.  Pairagon: a highly accurate, HMM-based cDNA-to-genome aligner 
Bioinformatics  2009;25(13):1587-1593.
Motivation: The most accurate way to determine the intron–exon structures in a genome is to align spliced cDNA sequences to the genome. Thus, cDNA-to-genome alignment programs are a key component of most annotation pipelines. The scoring system used to choose the best alignment is a primary determinant of alignment accuracy, while heuristics that prevent consideration of certain alignments are a primary determinant of runtime and memory usage. Both accuracy and speed are important considerations in choosing an alignment algorithm, but scoring systems have received much less attention than heuristics.
Results: We present Pairagon, a pair hidden Markov model based cDNA-to-genome alignment program, as the most accurate aligner for sequences with high- and low-identity levels. We conducted a series of experiments testing alignment accuracy with varying sequence identity. We first created ‘perfect’ simulated cDNA sequences by splicing the sequences of exons in the reference genome sequences of fly and human. The complete reference genome sequences were then mutated to various degrees using a realistic mutation simulator and the perfect cDNAs were aligned to them using Pairagon and 12 other aligners. To validate these results with natural sequences, we performed cross-species alignment using orthologous transcripts from human, mouse and rat.
We found that aligner accuracy is heavily dependent on sequence identity. For sequences with 100% identity, Pairagon achieved accuracy levels of >99.6%, with one quarter of the errors of any other aligner. Furthermore, for human/mouse alignments, which are only 85% identical, Pairagon achieved 87% accuracy, higher than any other aligner.
Availability: Pairagon source and executables are freely available at http://mblab.wustl.edu/software/pairagon/
Contact: davidlu@wustl.edu; brent@cse.wustl.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btp273
PMCID: PMC2732315  PMID: 19414532
24.  Accelerated large-scale multiple sequence alignment 
BMC Bioinformatics  2011;12:466.
Background
Multiple sequence alignment (MSA) is a fundamental analysis method used in bioinformatics and many comparative genomic applications. Prior MSA acceleration attempts with reconfigurable computing have only addressed the first stage of progressive alignment and consequently exhibit performance limitations according to Amdahl's Law. This work is the first known to accelerate the third stage of progressive alignment on reconfigurable hardware.
Results
We reduce subgroups of aligned sequences into discrete profiles before they are pairwise aligned on the accelerator. Using an FPGA accelerator, an overall speedup of up to 150 has been demonstrated on a large data set when compared to a 2.4 GHz Core2 processor.
Conclusions
Our parallel algorithm and architecture accelerates large-scale MSA with reconfigurable computing and allows researchers to solve the larger problems that confront biologists today. Program source is available from http://dna.cs.byu.edu/msa/.
doi:10.1186/1471-2105-12-466
PMCID: PMC3310909  PMID: 22151470
25.  Optimizing amino acid substitution matrices with a local alignment kernel 
BMC Bioinformatics  2006;7:246.
Background
Detecting remote homologies by direct comparison of protein sequences remains a challenging task. We had previously developed a similarity score between sequences, called a local alignment kernel, that exhibits good performance for this task in combination with a support vector machine. The local alignment kernel depends on an amino acid substitution matrix. Since commonly used BLOSUM or PAM matrices for scoring amino acid matches have been optimized to be used in combination with the Smith-Waterman algorithm, the matrices optimal for the local alignment kernel can be different.
Results
Contrary to the local alignment score computed by the Smith-Waterman algorithm, the local alignment kernel is differentiable with respect to the amino acid substitution and its derivative can be computed efficiently by dynamic programming. We optimized the substitution matrix by classical gradient descent by setting an objective function that measures how well the local alignment kernel discriminates homologs from non-homologs in the COG database. The local alignment kernel exhibits better performance when it uses the matrices and gap parameters optimized by this procedure than when it uses the matrices optimized for the Smith-Waterman algorithm. Furthermore, the matrices and gap parameters optimized for the local alignment kernel can also be used successfully by the Smith-Waterman algorithm.
Conclusion
This optimization procedure leads to useful substitution matrices, both for the local alignment kernel and the Smith-Waterman algorithm. The best performance for homology detection is obtained by the local alignment kernel.
doi:10.1186/1471-2105-7-246
PMCID: PMC1513605  PMID: 16677385

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