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1.  The Construction and Use of Log-Odds Substitution Scores for Multiple Sequence Alignment 
PLoS Computational Biology  2010;6(7):e1000852.
Most pairwise and multiple sequence alignment programs seek alignments with optimal scores. Central to defining such scores is selecting a set of substitution scores for aligned amino acids or nucleotides. For local pairwise alignment, substitution scores are implicitly of log-odds form. We now extend the log-odds formalism to multiple alignments, using Bayesian methods to construct “BILD” (“Bayesian Integral Log-odds”) substitution scores from prior distributions describing columns of related letters. This approach has been used previously only to define scores for aligning individual sequences to sequence profiles, but it has much broader applicability. We describe how to calculate BILD scores efficiently, and illustrate their uses in Gibbs sampling optimization procedures, gapped alignment, and the construction of hidden Markov model profiles. BILD scores enable automated selection of optimal motif and domain model widths, and can inform the decision of whether to include a sequence in a multiple alignment, and the selection of insertion and deletion locations. Other applications include the classification of related sequences into subfamilies, and the definition of profile-profile alignment scores. Although a fully realized multiple alignment program must rely upon more than substitution scores, many existing multiple alignment programs can be modified to employ BILD scores. We illustrate how simple BILD score based strategies can enhance the recognition of DNA binding domains, including the Api-AP2 domain in Toxoplasma gondii and Plasmodium falciparum.
Author Summary
Multiple sequence alignment is a fundamental tool of biological research, widely used to identify important regions of DNA or protein molecules, to infer their biological functions, to reconstruct ancestries, and in numerous other applications. The effectiveness and accuracy of sequence comparison programs depends crucially upon the quality of the scoring systems they use to measure sequence similarity. To compare pairs of DNA or protein sequences, the best strategy for constructing similarity measures has long been understood, but there has been a lack of consensus about how to measure similarity among multiple (i.e. more than two) sequences. In this paper, we describe a natural generalization to multiple alignment of the accepted measure of pairwise similarity. A large variety of methods that are used to compare and analyze DNA or protein molecules, or to model protein domain families, could be rendered more sensitive and precise by adopting this similarity measure. We illustrate how our measure can enhance the recognition of important DNA binding domains.
doi:10.1371/journal.pcbi.1000852
PMCID: PMC2904766  PMID: 20657661
2.  Genomic multiple sequence alignments: refinement using a genetic algorithm 
BMC Bioinformatics  2005;6:200.
Background
Genomic sequence data cannot be fully appreciated in isolation. Comparative genomics – the practice of comparing genomic sequences from different species – plays an increasingly important role in understanding the genotypic differences between species that result in phenotypic differences as well as in revealing patterns of evolutionary relationships. One of the major challenges in comparative genomics is producing a high-quality alignment between two or more related genomic sequences. In recent years, a number of tools have been developed for aligning large genomic sequences. Most utilize heuristic strategies to identify a series of strong sequence similarities, which are then used as anchors to align the regions between the anchor points. The resulting alignment is globally correct, but in many cases is suboptimal locally. We describe a new program, GenAlignRefine, which improves the overall quality of global multiple alignments by using a genetic algorithm to improve local regions of alignment. Regions of low quality are identified, realigned using the program T-Coffee, and then refined using a genetic algorithm. Because a better COFFEE (Consistency based Objective Function For alignmEnt Evaluation) score generally reflects greater alignment quality, the algorithm searches for an alignment that yields a better COFFEE score. To improve the intrinsic slowness of the genetic algorithm, GenAlignRefine was implemented as a parallel, cluster-based program.
Results
We tested the GenAlignRefine algorithm by running it on a Linux cluster to refine sequences from a simulation, as well as refine a multiple alignment of 15 Orthopoxvirus genomic sequences approximately 260,000 nucleotides in length that initially had been aligned by Multi-LAGAN. It took approximately 150 minutes for a 40-processor Linux cluster to optimize some 200 fuzzy (poorly aligned) regions of the orthopoxvirus alignment. Overall sequence identity increased only slightly; but significantly, this occurred at the same time that the overall alignment length decreased – through the removal of gaps – by approximately 200 gapped regions representing roughly 1,300 gaps.
Conclusion
We have implemented a genetic algorithm in parallel mode to optimize multiple genomic sequence alignments initially generated by various alignment tools. Benchmarking experiments showed that the refinement algorithm improved genomic sequence alignments within a reasonable period of time.
doi:10.1186/1471-2105-6-200
PMCID: PMC1208854  PMID: 16086841
3.  Local alignment of generalized k-base encoded DNA sequence 
BMC Bioinformatics  2010;11:347.
Background
DNA sequence comparison is a well-studied problem, in which two DNA sequences are compared using a weighted edit distance. Recent DNA sequencing technologies however observe an encoded form of the sequence, rather than each DNA base individually. The encoded DNA sequence may contain technical errors, and therefore encoded sequencing errors must be incorporated when comparing an encoded DNA sequence to a reference DNA sequence.
Results
Although two-base encoding is currently used in practice, many other encoding schemes are possible, whereby two ore more bases are encoded at a time. A generalized k-base encoding scheme is presented, whereby feasible higher order encodings are better able to differentiate errors in the encoded sequence from true DNA sequence variants. A generalized version of the previous two-base encoding DNA sequence comparison algorithm is used to compare a k-base encoded sequence to a DNA reference sequence. Finally, simulations are performed to evaluate the power, the false positive and false negative SNP discovery rates, and the performance time of k-base encoding compared to previous methods as well as to the standard DNA sequence comparison algorithm.
Conclusions
The novel generalized k-base encoding scheme and resulting local alignment algorithm permits the development of higher fidelity ligation-based next generation sequencing technology. This bioinformatic solution affords greater robustness to errors, as well as lower false SNP discovery rates, only at the cost of computational time.
doi:10.1186/1471-2105-11-347
PMCID: PMC2911458  PMID: 20576157
4.  ReformAlign: improved multiple sequence alignments using a profile-based meta-alignment approach 
BMC Bioinformatics  2014;15(1):265.
Background
Obtaining an accurate sequence alignment is fundamental for consistently analyzing biological data. Although this problem may be efficiently solved when only two sequences are considered, the exact inference of the optimal alignment easily gets computationally intractable for the multiple sequence alignment case. To cope with the high computational expenses, approximate heuristic methods have been proposed that address the problem indirectly by progressively aligning the sequences in pairs according to their relatedness. These methods however are not flexible to change the alignment of an already aligned group of sequences in the view of new data, resulting thus in compromises on the quality of the deriving alignment. In this paper we present ReformAlign, a novel meta-alignment approach that may significantly improve on the quality of the deriving alignments from popular aligners. We call ReformAlign a meta-aligner as it requires an initial alignment, for which a variety of alignment programs can be used. The main idea behind ReformAlign is quite straightforward: at first, an existing alignment is used to construct a standard profile which summarizes the initial alignment and then all sequences are individually re-aligned against the formed profile. From each sequence-profile comparison, the alignment of each sequence against the profile is recorded and the final alignment is indirectly inferred by merging all the individual sub-alignments into a unified set. The employment of ReformAlign may often result in alignments which are significantly more accurate than the starting alignments.
Results
We evaluated the effect of ReformAlign on the generated alignments from ten leading alignment methods using real data of variable size and sequence identity. The experimental results suggest that the proposed meta-aligner approach may often lead to statistically significant more accurate alignments. Furthermore, we show that ReformAlign results in more substantial improvement in cases where the starting alignment is of relatively inferior quality or when the input sequences are harder to align.
Conclusions
The proposed profile-based meta-alignment approach seems to be a promising and computationally efficient method that can be combined with practically all popular alignment methods and may lead to significant improvements in the generated alignments.
Electronic supplementary material
The online version of this article (doi:10.1186/1471-2105-15-265) contains supplementary material, which is available to authorized users.
doi:10.1186/1471-2105-15-265
PMCID: PMC4133627  PMID: 25099134
Multiple sequence alignment; Iterative refinement; Dynamic programming
5.  Iterative refinement of structure-based sequence alignments by Seed Extension 
BMC Bioinformatics  2009;10:210.
Background
Accurate sequence alignment is required in many bioinformatics applications but, when sequence similarity is low, it is difficult to obtain accurate alignments based on sequence similarity alone. The accuracy improves when the structures are available, but current structure-based sequence alignment procedures still mis-align substantial numbers of residues. In order to correct such errors, we previously explored the possibility of replacing the residue-based dynamic programming algorithm in structure alignment procedures with the Seed Extension algorithm, which does not use a gap penalty. Here, we describe a new procedure called RSE (Refinement with Seed Extension) that iteratively refines a structure-based sequence alignment.
Results
RSE uses SE (Seed Extension) in its core, which is an algorithm that we reported recently for obtaining a sequence alignment from two superimposed structures. The RSE procedure was evaluated by comparing the correctly aligned fractions of residues before and after the refinement of the structure-based sequence alignments produced by popular programs. CE, DaliLite, FAST, LOCK2, MATRAS, MATT, TM-align, SHEBA and VAST were included in this analysis and the NCBI's CDD root node set was used as the reference alignments. RSE improved the average accuracy of sequence alignments for all programs tested when no shift error was allowed. The amount of improvement varied depending on the program. The average improvements were small for DaliLite and MATRAS but about 5% for CE and VAST. More substantial improvements have been seen in many individual cases. The additional computation times required for the refinements were negligible compared to the times taken by the structure alignment programs.
Conclusion
RSE is a computationally inexpensive way of improving the accuracy of a structure-based sequence alignment. It can be used as a standalone procedure following a regular structure-based sequence alignment or to replace the traditional iterative refinement procedures based on residue-level dynamic programming algorithm in many structure alignment programs.
doi:10.1186/1471-2105-10-210
PMCID: PMC2753854  PMID: 19589133
6.  Measuring Global Credibility with Application to Local Sequence Alignment 
PLoS Computational Biology  2008;4(5):e1000077.
Computational biology is replete with high-dimensional (high-D) discrete prediction and inference problems, including sequence alignment, RNA structure prediction, phylogenetic inference, motif finding, prediction of pathways, and model selection problems in statistical genetics. Even though prediction and inference in these settings are uncertain, little attention has been focused on the development of global measures of uncertainty. Regardless of the procedure employed to produce a prediction, when a procedure delivers a single answer, that answer is a point estimate selected from the solution ensemble, the set of all possible solutions. For high-D discrete space, these ensembles are immense, and thus there is considerable uncertainty. We recommend the use of Bayesian credibility limits to describe this uncertainty, where a (1−α)%, 0≤α≤1, credibility limit is the minimum Hamming distance radius of a hyper-sphere containing (1−α)% of the posterior distribution. Because sequence alignment is arguably the most extensively used procedure in computational biology, we employ it here to make these general concepts more concrete. The maximum similarity estimator (i.e., the alignment that maximizes the likelihood) and the centroid estimator (i.e., the alignment that minimizes the mean Hamming distance from the posterior weighted ensemble of alignments) are used to demonstrate the application of Bayesian credibility limits to alignment estimators. Application of Bayesian credibility limits to the alignment of 20 human/rodent orthologous sequence pairs and 125 orthologous sequence pairs from six Shewanella species shows that credibility limits of the alignments of promoter sequences of these species vary widely, and that centroid alignments dependably have tighter credibility limits than traditional maximum similarity alignments.
Author Summary
Sequence alignment is the cornerstone capability used by a multitude of computational biology applications, such as phylogeny reconstruction and identification of common regulatory mechanisms. Sequence alignment methods typically seek a high-scoring alignment between a pair of sequences, and assign a statistical significance to this single alignment. However, because a single alignment of two (or more) sequences is a point estimate, it may not be representative of the entire set (ensemble) of possible alignments of those sequences; thus, there may be considerable uncertainty associated with any one alignment among an immense ensemble of possibilities. To address the uncertainty of a proposed alignment, we used a Bayesian probabilistic approach to assess an alignment's reliability in the context of the entire ensemble of possible alignments. Our approach performs a global assessment of the degree to which the members of the ensemble depart from a selected alignment, thereby determining a credibility limit. In an evaluation of the popular maximum similarity alignment and the centroid alignment (i.e., the alignment that is in the center of the posterior distribution of alignments), we find that the centroid yields tighter credibility limits (on average) than the maximum similarity alignment. Beyond the usual interest in putting error limits on point estimates, our findings of substantial variability in credibility limits of alignments argue for wider adoption of these limits, so the degree of error is delineated prior to the subsequent use of the alignments.
doi:10.1371/journal.pcbi.1000077
PMCID: PMC2367447  PMID: 18464927
7.  Robust and accurate prediction of noncoding RNAs from aligned sequences 
BMC Bioinformatics  2010;11(Suppl 7):S3.
Background
Computational prediction of noncoding RNAs (ncRNAs) is an important task in the post-genomic era. One common approach is to utilize the profile information contained in alignment data rather than single sequences. However, this strategy involves the possibility that the quality of input alignments can influence the performance of prediction methods. Therefore, the evaluation of the robustness against alignment errors is necessary as well as the development of accurate prediction methods.
Results
We describe a new method, called Profile BPLA kernel, which predicts ncRNAs from alignment data in combination with support vector machines (SVMs). Profile BPLA kernel is an extension of base-pairing profile local alignment (BPLA) kernel which we previously developed for the prediction from single sequences. By utilizing the profile information of alignment data, the proposed kernel can achieve better accuracy than the original BPLA kernel. We show that Profile BPLA kernel outperforms the existing prediction methods which also utilize the profile information using the high-quality structural alignment dataset. In addition to these standard benchmark tests, we extensively evaluate the robustness of Profile BPLA kernel against errors in input alignments. We consider two different types of error: first, that all sequences in an alignment are actually ncRNAs but are aligned ignoring their secondary structures; second, that an alignment contains unrelated sequences which are not ncRNAs but still aligned. In both cases, the effects on the performance of Profile BPLA kernel are surprisingly small. Especially for the latter case, we demonstrate that Profile BPLA kernel is more robust compared to the existing prediction methods.
Conclusions
Profile BPLA kernel provides a promising way for identifying ncRNAs from alignment data. It is more accurate than the existing prediction methods, and can keep its performance under the practical situations in which the quality of input alignments is not necessarily high.
doi:10.1186/1471-2105-11-S7-S3
PMCID: PMC2957686  PMID: 21106125
8.  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
9.  Sigma: multiple alignment of weakly-conserved non-coding DNA sequence 
BMC Bioinformatics  2006;7:143.
Background
Existing tools for multiple-sequence alignment focus on aligning protein sequence or protein-coding DNA sequence, and are often based on extensions to Needleman-Wunsch-like pairwise alignment methods. We introduce a new tool, Sigma, with a new algorithm and scoring scheme designed specifically for non-coding DNA sequence. This problem acquires importance with the increasing number of published sequences of closely-related species. In particular, studies of gene regulation seek to take advantage of comparative genomics, and recent algorithms for finding regulatory sites in phylogenetically-related intergenic sequence require alignment as a preprocessing step. Much can also be learned about evolution from intergenic DNA, which tends to evolve faster than coding DNA. Sigma uses a strategy of seeking the best possible gapless local alignments (a strategy earlier used by DiAlign), at each step making the best possible alignment consistent with existing alignments, and scores the significance of the alignment based on the lengths of the aligned fragments and a background model which may be supplied or estimated from an auxiliary file of intergenic DNA.
Results
Comparative tests of sigma with five earlier algorithms on synthetic data generated to mimic real data show excellent performance, with Sigma balancing high "sensitivity" (more bases aligned) with effective filtering of "incorrect" alignments. With real data, while "correctness" can't be directly quantified for the alignment, running the PhyloGibbs motif finder on pre-aligned sequence suggests that Sigma's alignments are superior.
Conclusion
By taking into account the peculiarities of non-coding DNA, Sigma fills a gap in the toolbox of bioinformatics.
doi:10.1186/1471-2105-7-143
PMCID: PMC1468434  PMID: 16542424
10.  Matt: Local Flexibility Aids Protein Multiple Structure Alignment 
PLoS Computational Biology  2008;4(1):e10.
Even when there is agreement on what measure a protein multiple structure alignment should be optimizing, finding the optimal alignment is computationally prohibitive. One approach used by many previous methods is aligned fragment pair chaining, where short structural fragments from all the proteins are aligned against each other optimally, and the final alignment chains these together in geometrically consistent ways. Ye and Godzik have recently suggested that adding geometric flexibility may help better model protein structures in a variety of contexts. We introduce the program Matt (Multiple Alignment with Translations and Twists), an aligned fragment pair chaining algorithm that, in intermediate steps, allows local flexibility between fragments: small translations and rotations are temporarily allowed to bring sets of aligned fragments closer, even if they are physically impossible under rigid body transformations. After a dynamic programming assembly guided by these “bent” alignments, geometric consistency is restored in the final step before the alignment is output. Matt is tested against other recent multiple protein structure alignment programs on the popular Homstrad and SABmark benchmark datasets. Matt's global performance is competitive with the other programs on Homstrad, but outperforms the other programs on SABmark, a benchmark of multiple structure alignments of proteins with more distant homology. On both datasets, Matt demonstrates an ability to better align the ends of α-helices and β-strands, an important characteristic of any structure alignment program intended to help construct a structural template library for threading approaches to the inverse protein-folding problem. The related question of whether Matt alignments can be used to distinguish distantly homologous structure pairs from pairs of proteins that are not homologous is also considered. For this purpose, a p-value score based on the length of the common core and average root mean squared deviation (RMSD) of Matt alignments is shown to largely separate decoys from homologous protein structures in the SABmark benchmark dataset. We postulate that Matt's strong performance comes from its ability to model proteins in different conformational states and, perhaps even more important, its ability to model backbone distortions in more distantly related proteins.
Author Summary
Proteins fold into complicated highly asymmetrical 3-D shapes. When a protein is found to fold in a shape that is sufficiently similar to other proteins whose functional roles are known, this can significantly aid in predicting function in the new protein. In addition, the areas where structure is highly conserved in a set of such similar proteins may indicate functional or structural importance of the conserved region. Given a set of protein structures, the protein structural alignment problem is to determine the superimposition of the backbones of these protein structures that places as much of the structures as possible into close spatial alignment. We introduce an algorithm that allows local flexibility in the structures when it brings them into closer alignment. The algorithm performs as well as its competitors when the structures to be aligned are highly similar, and outperforms them by a larger and larger margin as similarity decreases. In addition, for the related classification problem that asks if the degree of structural similarity between two proteins implies if they likely evolved from a common ancestor, a scoring function assesses, based on the best alignment generated for each pair of protein structures, whether they should be declared sufficiently structurally similar or not. This score can be used to predict when two proteins have sufficiently similar shapes to likely share functional characteristics.
doi:10.1371/journal.pcbi.0040010
PMCID: PMC2186361  PMID: 18193941
11.  Structure alignment based on coding of local geometric measures 
BMC Bioinformatics  2006;7:346.
Background
A structure alignment method based on a local geometric property is presented and its performance is tested in pairwise and multiple structure alignments. In this approach, the writhing number, a quantity originating from integral formulas of Vassiliev knot invariants, is used as a local geometric measure. This measure is used in a sliding window to calculate the local writhe down the length of the protein chain. By encoding the distribution of writhing numbers across all the structures in the protein databank (PDB), protein geometries are represented in a 20-letter alphabet. This encoding transforms the structure alignment problem into a sequence alignment problem and allows the well-established algorithms of sequence alignment to be employed. Such geometric alignments offer distinct advantages over structural alignments in Cartesian coordinates as it better handles structural subtleties associated with slight twists and bends that distort one structure relative to another.
Results
The performance of programs for pairwise local alignment (TLOCAL) and multiple alignment (TCLUSTALW) are readily adapted from existing code for Smith-Waterman pairwise alignment and for multiple sequence alignment using CLUSTALW. The alignment algorithms employed a blocked scoring matrix (TBLOSUM) generated using the frequency of changes in the geometric alphabet of a block of protein structures. TLOCAL was tested on a set of 10 difficult proteins and found to give high quality alignments that compare favorably to those generated by existing pairwise alignment programs. A set of protein comparison involving hinged structures was also analyzed and TLOCAL was seen to compare favorably to other alignment methods. TCLUSTALW was tested on a family of protein kinases and reveal conserved regions similar to those previously identified by a hand alignment.
Conclusion
These results show that the encoding of the writhing number as a geometric measure allow high quality structure alignments to be generated using standard algorithms of sequence alignment. This approach provides computationally efficient algorithms that allow fast database searching and multiple structure alignment. Because the geometric measure can employ different window sizes, the method allows the exploration of alignments on different, well-defined length scales.
doi:10.1186/1471-2105-7-346
PMCID: PMC1559724  PMID: 16842622
12.  Comparative analysis of the quality of a global algorithm and a local algorithm for alignment of two sequences 
Background
Algorithms of sequence alignment are the key instruments for computer-assisted studies of biopolymers. Obviously, it is important to take into account the "quality" of the obtained alignments, i.e. how closely the algorithms manage to restore the "gold standard" alignment (GS-alignment), which superimposes positions originating from the same position in the common ancestor of the compared sequences. As an approximation of the GS-alignment, a 3D-alignment is commonly used not quite reasonably. Among the currently used algorithms of a pair-wise alignment, the best quality is achieved by using the algorithm of optimal alignment based on affine penalties for deletions (the Smith-Waterman algorithm). Nevertheless, the expedience of using local or global versions of the algorithm has not been studied.
Results
Using model series of amino acid sequence pairs, we studied the relative "quality" of results produced by local and global alignments versus (1) the relative length of similar parts of the sequences (their "cores") and their nonhomologous parts, and (2) relative positions of the core regions in the compared sequences. We obtained numerical values of the average quality (measured as accuracy and confidence) of the global alignment method and the local alignment method for evolutionary distances between homologous sequence parts from 30 to 240 PAM and for the core length making from 10% to 70% of the total length of the sequences for all possible positions of homologous sequence parts relative to the centers of the sequences.
Conclusion
We revealed criteria allowing to specify conditions of preferred applicability for the local and the global alignment algorithms depending on positions and relative lengths of the cores and nonhomologous parts of the sequences to be aligned. It was demonstrated that when the core part of one sequence was positioned above the core of the other sequence, the global algorithm was more stable at longer evolutionary distances and larger nonhomologous parts than the local algorithm. On the contrary, when the cores were positioned asymmetrically, the local algorithm was more stable at longer evolutionary distances and larger nonhomologous parts than the global algorithm. This opens a possibility for creation of a combined method allowing generation of more accurate alignments.
doi:10.1186/1748-7188-6-25
PMCID: PMC3223492  PMID: 22032267
13.  Parameters for accurate genome alignment 
BMC Bioinformatics  2010;11:80.
Background
Genome sequence alignments form the basis of much research. Genome alignment depends on various mundane but critical choices, such as how to mask repeats and which score parameters to use. Surprisingly, there has been no large-scale assessment of these choices using real genomic data. Moreover, rigorous procedures to control the rate of spurious alignment have not been employed.
Results
We have assessed 495 combinations of score parameters for alignment of animal, plant, and fungal genomes. As our gold-standard of accuracy, we used genome alignments implied by multiple alignments of proteins and of structural RNAs. We found the HOXD scoring schemes underlying alignments in the UCSC genome database to be far from optimal, and suggest better parameters. Higher values of the X-drop parameter are not always better. E-values accurately indicate the rate of spurious alignment, but only if tandem repeats are masked in a non-standard way. Finally, we show that γ-centroid (probabilistic) alignment can find highly reliable subsets of aligned bases.
Conclusions
These results enable more accurate genome alignment, with reliability measures for local alignments and for individual aligned bases. This study was made possible by our new software, LAST, which can align vertebrate genomes in a few hours http://last.cbrc.jp/.
doi:10.1186/1471-2105-11-80
PMCID: PMC2829014  PMID: 20144198
14.  Simultaneous identification of long similar substrings in large sets of sequences 
BMC Bioinformatics  2007;8(Suppl 5):S7.
Background
Sequence comparison faces new challenges today, with many complete genomes and large libraries of transcripts known. Gene annotation pipelines match these sequences in order to identify genes and their alternative splice forms. However, the software currently available cannot simultaneously compare sets of sequences as large as necessary especially if errors must be considered.
Results
We therefore present a new algorithm for the identification of almost perfectly matching substrings in very large sets of sequences. Its implementation, called ClustDB, is considerably faster and can handle 16 times more data than VMATCH, the most memory efficient exact program known today. ClustDB simultaneously generates large sets of exactly matching substrings of a given minimum length as seeds for a novel method of match extension with errors. It generates alignments of maximum length with a considered maximum number of errors within each overlapping window of a given size. Such alignments are not optimal in the usual sense but faster to calculate and often more appropriate than traditional alignments for genomic sequence comparisons, EST and full-length cDNA matching, and genomic sequence assembly. The method is used to check the overlaps and to reveal possible assembly errors for 1377 Medicago truncatula BAC-size sequences published at .
Conclusion
The program ClustDB proves that window alignment is an efficient way to find long sequence sections of homogenous alignment quality, as expected in case of random errors, and to detect systematic errors resulting from sequence contaminations. Such inserts are systematically overlooked in long alignments controlled by only tuning penalties for mismatches and gaps.
ClustDB is freely available for academic use.
doi:10.1186/1471-2105-8-S5-S7
PMCID: PMC1892095  PMID: 17570866
15.  Improving the Alignment Quality of Consistency Based Aligners with an Evaluation Function Using Synonymous Protein Words 
PLoS ONE  2011;6(12):e27872.
Most sequence alignment tools can successfully align protein sequences with higher levels of sequence identity. The accuracy of corresponding structure alignment, however, decreases rapidly when considering distantly related sequences (<20% identity). In this range of identity, alignments optimized so as to maximize sequence similarity are often inaccurate from a structural point of view. Over the last two decades, most multiple protein aligners have been optimized for their capacity to reproduce structure-based alignments while using sequence information. Methods currently available differ essentially in the similarity measurement between aligned residues using substitution matrices, Fourier transform, sophisticated profile-profile functions, or consistency-based approaches, more recently.
In this paper, we present a flexible similarity measure for residue pairs to improve the quality of protein sequence alignment. Our approach, called SymAlign, relies on the identification of conserved words found across a sizeable fraction of the considered dataset, and supported by evolutionary analysis. These words are then used to define a position specific substitution matrix that better reflects the biological significance of local similarity. The experiment results show that the SymAlign scoring scheme can be incorporated within T-Coffee to improve sequence alignment accuracy. We also demonstrate that SymAlign is less sensitive to the presence of structurally non-similar proteins. In the analysis of the relationship between sequence identity and structure similarity, SymAlign can better differentiate structurally similar proteins from non- similar proteins.
We show that protein sequence alignments can be significantly improved using a similarity estimation based on weighted n-grams. In our analysis of the alignments thus produced, sequence conservation becomes a better indicator of structural similarity. SymAlign also provides alignment visualization that can display sub-optimal alignments on dot-matrices. The visualization makes it easy to identify well-supported alternative alignments that may not have been identified by dynamic programming. SymAlign is available at http://bio-cluster.iis.sinica.edu.tw/SymAlign/.
doi:10.1371/journal.pone.0027872
PMCID: PMC3229492  PMID: 22163274
16.  SE: an algorithm for deriving sequence alignment from a pair of superimposed structures 
BMC Bioinformatics  2009;10(Suppl 1):S4.
Background
Generating sequence alignments from superimposed structures is an important part of many structure comparison programs. The accuracy of the alignment affects structure recognition, classification and possibly function prediction. Many programs use a dynamic programming algorithm to generate the sequence alignment from superimposed structures. However, this procedure requires using a gap penalty and, depending on the value of the penalty used, can introduce spurious gaps and misalignments. Here we present a new algorithm, Seed Extension (SE), for generating the sequence alignment from a pair of superimposed structures. The SE algorithm first finds "seeds", which are the pairs of residues, one from each structure, that meet certain stringent criteria for being structurally equivalent. Three consecutive seeds form a seed segment, which is extended along the diagonal of the alignment matrix in both directions. Distance and the amino acid type similarity between the residues are used to resolve conflicts that arise during extension of more than one diagonal. The manually curated alignments in the Conserved Domain Database were used as the standard to assess the quality of the sequence alignments.
Results
SE gave an average accuracy of 95.9% over 582 pairs of superimposed proteins tested, while CHIMERA, LSQMAN, and DP extracted from SHEBA, which all use a dynamic programming algorithm, yielded 89.9%, 90.2% and 91.0%, respectively. For pairs of proteins with low sequence or structural similarity, SE produced alignments up to 18% more accurate on average than the next best scoring program. Improvement was most pronounced when the two superimposed structures contained equivalent helices or beta-strands that crossed at an angle. When the SE algorithm was implemented in SHEBA to replace the dynamic programming routine, the alignment accuracy improved by 10% on average for structure pairs with RMSD between 2 and 4 Å. SE also used considerably less CPU time than DP.
Conclusion
The Seed Extension algorithm is fast and, without using a gap penalty, produces more accurate sequence alignments from superimposed structures than three other programs tested that use dynamic programming algorithm.
doi:10.1186/1471-2105-10-S1-S4
PMCID: PMC2648757  PMID: 19208141
17.  Highly improved homopolymer aware nucleotide-protein alignments with 454 data 
BMC Bioinformatics  2012;13:230.
Background
Roche 454 sequencing is the leading sequencing technology for producing long read high throughput sequence data. Unlike most methods where sequencing errors translate to base uncertainties, 454 sequencing inaccuracies create nucleotide gaps. These gaps are particularly troublesome for translated search tools such as BLASTx where they introduce frame-shifts and result in regions of decreased identity and/or terminated alignments, which affect further analysis.
Results
To address this issue, the Homopolymer Aware Cross Alignment Tool (HAXAT) was developed. HAXAT uses a novel dynamic programming algorithm for solving the optimal local alignment between a 454 nucleotide and a protein sequence by allowing frame-shifts, guided by 454 flowpeak values. The algorithm is an efficient minimal extension of the Smith-Waterman-Gotoh algorithm that easily fits in into other tools. Experiments using HAXAT demonstrate, through the introduction of 454 specific frame-shift penalties, significantly increased accuracy of alignments spanning homopolymer sequence errors. The full effect of the new parameters introduced with this novel alignment model is explored. Experimental results evaluating homopolymer inaccuracy through alignments show a two to five-fold increase in Matthews Correlation Coefficient over previous algorithms, for 454-derived data.
Conclusions
This increased accuracy provided by HAXAT does not only result in improved homologue estimations, but also provides un-interrupted reading-frames, which greatly facilitate further analysis of protein space, for example phylogenetic analysis. The alignment tool is available at http://bioinfo.ifm.liu.se/454tools/haxat.
doi:10.1186/1471-2105-13-230
PMCID: PMC3568017  PMID: 22971057
18.  Sequence Alignment, Mutual Information, and Dissimilarity Measures for Constructing Phylogenies 
PLoS ONE  2011;6(1):e14373.
Background
Existing sequence alignment algorithms use heuristic scoring schemes based on biological expertise, which cannot be used as objective distance metrics. As a result one relies on crude measures, like the p- or log-det distances, or makes explicit, and often too simplistic, a priori assumptions about sequence evolution. Information theory provides an alternative, in the form of mutual information (MI). MI is, in principle, an objective and model independent similarity measure, but it is not widely used in this context and no algorithm for extracting MI from a given alignment (without assuming an evolutionary model) is known. MI can be estimated without alignments, by concatenating and zipping sequences, but so far this has only produced estimates with uncontrolled errors, despite the fact that the normalized compression distance based on it has shown promising results.
Results
We describe a simple approach to get robust estimates of MI from global pairwise alignments. Our main result uses algorithmic (Kolmogorov) information theory, but we show that similar results can also be obtained from Shannon theory. For animal mitochondrial DNA our approach uses the alignments made by popular global alignment algorithms to produce MI estimates that are strikingly close to estimates obtained from the alignment free methods mentioned above. We point out that, due to the fact that it is not additive, normalized compression distance is not an optimal metric for phylogenetics but we propose a simple modification that overcomes the issue of additivity. We test several versions of our MI based distance measures on a large number of randomly chosen quartets and demonstrate that they all perform better than traditional measures like the Kimura or log-det (resp. paralinear) distances.
Conclusions
Several versions of MI based distances outperform conventional distances in distance-based phylogeny. Even a simplified version based on single letter Shannon entropies, which can be easily incorporated in existing software packages, gave superior results throughout the entire animal kingdom. But we see the main virtue of our approach in a more general way. For example, it can also help to judge the relative merits of different alignment algorithms, by estimating the significance of specific alignments. It strongly suggests that information theory concepts can be exploited further in sequence analysis.
doi:10.1371/journal.pone.0014373
PMCID: PMC3014950  PMID: 21245917
19.  Predicting and improving the protein sequence alignment quality by support vector regression 
BMC Bioinformatics  2007;8:471.
Background
For successful protein structure prediction by comparative modeling, in addition to identifying a good template protein with known structure, obtaining an accurate sequence alignment between a query protein and a template protein is critical. It has been known that the alignment accuracy can vary significantly depending on our choice of various alignment parameters such as gap opening penalty and gap extension penalty. Because the accuracy of sequence alignment is typically measured by comparing it with its corresponding structure alignment, there is no good way of evaluating alignment accuracy without knowing the structure of a query protein, which is obviously not available at the time of structure prediction. Moreover, there is no universal alignment parameter option that would always yield the optimal alignment.
Results
In this work, we develop a method to predict the quality of the alignment between a query and a template. We train the support vector regression (SVR) models to predict the MaxSub scores as a measure of alignment quality. The alignment between a query protein and a template of length n is transformed into a (n + 1)-dimensional feature vector, then it is used as an input to predict the alignment quality by the trained SVR model. Performance of our work is evaluated by various measures including Pearson correlation coefficient between the observed and predicted MaxSub scores. Result shows high correlation coefficient of 0.945. For a pair of query and template, 48 alignments are generated by changing alignment options. Trained SVR models are then applied to predict the MaxSub scores of those and to select the best alignment option which is chosen specifically to the query-template pair. This adaptive selection procedure results in 7.4% improvement of MaxSub scores, compared to those when the single best parameter option is used for all query-template pairs.
Conclusion
The present work demonstrates that the alignment quality can be predicted with reasonable accuracy. Our method is useful not only for selecting the optimal alignment parameters for a chosen template based on predicted alignment quality, but also for filtering out problematic templates that are not suitable for structure prediction due to poor alignment accuracy. This is implemented as a part in FORECAST, the server for fold-recognition and is freely available on the web at
doi:10.1186/1471-2105-8-471
PMCID: PMC2222655  PMID: 18053160
20.  Evolutionary rates at codon sites may be used to align sequences and infer protein domain function 
BMC Bioinformatics  2010;11:151.
Background
Sequence alignments form part of many investigations in molecular biology, including the determination of phylogenetic relationships, the prediction of protein structure and function, and the measurement of evolutionary rates. However, to obtain meaningful results, a significant degree of sequence similarity is required to ensure that the alignments are accurate and the inferences correct. Limitations arise when sequence similarity is low, which is particularly problematic when working with fast-evolving genes, evolutionary distant taxa, genomes with nucleotide biases, and cases of convergent evolution.
Results
A novel approach was conceptualized to address the "low sequence similarity" alignment problem. We developed an alignment algorithm termed FIRE (Functional Inference using the Rates of Evolution), which aligns sequences using the evolutionary rate at codon sites, as measured by the dN/dS ratio, rather than nucleotide or amino acid residues. FIRE was used to test the hypotheses that evolutionary rates can be used to align sequences and that the alignments may be used to infer protein domain function. Using a range of test data, we found that aligning domains based on evolutionary rates was possible even when sequence similarity was very low (for example, antibody variable regions). Furthermore, the alignment has the potential to infer protein domain function, indicating that domains with similar functions are subject to similar evolutionary constraints. These data suggest that an evolutionary rate-based approach to sequence analysis (particularly when combined with structural data) may be used to study cases of convergent evolution or when sequences have very low similarity. However, when aligning homologous gene sets with sequence similarity, FIRE did not perform as well as the best traditional alignment algorithms indicating that the conventional approach of aligning residues as opposed to evolutionary rates remains the method of choice in these cases.
Conclusions
FIRE provides proof of concept that it is possible to align sequences and infer domain function by using evolutionary rates rather than residue similarity. This represents a new approach to sequence analysis with a wide range of potential applications in molecular biology.
doi:10.1186/1471-2105-11-151
PMCID: PMC2851608  PMID: 20334658
21.  Parametric and non-parametric masking of randomness in sequence alignments can be improved and leads to better resolved trees 
Frontiers in Zoology  2010;7:10.
Background
Methods of alignment masking, which refers to the technique of excluding alignment blocks prior to tree reconstructions, have been successful in improving the signal-to-noise ratio in sequence alignments. However, the lack of formally well defined methods to identify randomness in sequence alignments has prevented a routine application of alignment masking. In this study, we compared the effects on tree reconstructions of the most commonly used profiling method (GBLOCKS) which uses a predefined set of rules in combination with alignment masking, with a new profiling approach (ALISCORE) based on Monte Carlo resampling within a sliding window, using different data sets and alignment methods. While the GBLOCKS approach excludes variable sections above a certain threshold which choice is left arbitrary, the ALISCORE algorithm is free of a priori rating of parameter space and therefore more objective.
Results
ALISCORE was successfully extended to amino acids using a proportional model and empirical substitution matrices to score randomness in multiple sequence alignments. A complex bootstrap resampling leads to an even distribution of scores of randomly similar sequences to assess randomness of the observed sequence similarity. Testing performance on real data, both masking methods, GBLOCKS and ALISCORE, helped to improve tree resolution. The sliding window approach was less sensitive to different alignments of identical data sets and performed equally well on all data sets. Concurrently, ALISCORE is capable of dealing with different substitution patterns and heterogeneous base composition. ALISCORE and the most relaxed GBLOCKS gap parameter setting performed best on all data sets. Correspondingly, Neighbor-Net analyses showed the most decrease in conflict.
Conclusions
Alignment masking improves signal-to-noise ratio in multiple sequence alignments prior to phylogenetic reconstruction. Given the robust performance of alignment profiling, alignment masking should routinely be used to improve tree reconstructions. Parametric methods of alignment profiling can be easily extended to more complex likelihood based models of sequence evolution which opens the possibility of further improvements.
doi:10.1186/1742-9994-7-10
PMCID: PMC2867768  PMID: 20356385
22.  The tree alignment problem 
BMC Bioinformatics  2012;13:293.
Background
The inference of homologies among DNA sequences, that is, positions in multiple genomes that share a common evolutionary origin, is a crucial, yet difficult task facing biologists. Its computational counterpart is known as the multiple sequence alignment problem. There are various criteria and methods available to perform multiple sequence alignments, and among these, the minimization of the overall cost of the alignment on a phylogenetic tree is known in combinatorial optimization as the Tree Alignment Problem. This problem typically occurs as a subproblem of the Generalized Tree Alignment Problem, which looks for the tree with the lowest alignment cost among all possible trees. This is equivalent to the Maximum Parsimony problem when the input sequences are not aligned, that is, when phylogeny and alignments are simultaneously inferred.
Results
For large data sets, a popular heuristic is Direct Optimization (DO). DO provides a good tradeoff between speed, scalability, and competitive scores, and is implemented in the computer program POY. All other (competitive) algorithms have greater time complexities compared to DO. Here, we introduce and present experiments a new algorithm Affine-DO to accommodate the indel (alignment gap) models commonly used in phylogenetic analysis of molecular sequence data. Affine-DO has the same time complexity as DO, but is correctly suited for the affine gap edit distance. We demonstrate its performance with more than 330,000 experimental tests. These experiments show that the solutions of Affine-DO are close to the lower bound inferred from a linear programming solution. Moreover, iterating over a solution produced using Affine-DO shows little improvement.
Conclusions
Our results show that Affine-DO is likely producing near-optimal solutions, with approximations within 10% for sequences with small divergence, and within 30% for random sequences, for which Affine-DO produced the worst solutions. The Affine-DO algorithm has the necessary scalability and optimality to be a significant improvement in the real-world phylogenetic analysis of sequence data.
doi:10.1186/1471-2105-13-293
PMCID: PMC3605350  PMID: 23140486
Tree alignment; Tree search; Phylogeny; Sequence alignment; Direct optimization
23.  Using Structure to Explore the Sequence Alignment Space of Remote Homologs 
PLoS Computational Biology  2011;7(10):e1002175.
Protein structure modeling by homology requires an accurate sequence alignment between the query protein and its structural template. However, sequence alignment methods based on dynamic programming (DP) are typically unable to generate accurate alignments for remote sequence homologs, thus limiting the applicability of modeling methods. A central problem is that the alignment that is “optimal” in terms of the DP score does not necessarily correspond to the alignment that produces the most accurate structural model. That is, the correct alignment based on structural superposition will generally have a lower score than the optimal alignment obtained from sequence. Variations of the DP algorithm have been developed that generate alternative alignments that are “suboptimal” in terms of the DP score, but these still encounter difficulties in detecting the correct structural alignment. We present here a new alternative sequence alignment method that relies heavily on the structure of the template. By initially aligning the query sequence to individual fragments in secondary structure elements and combining high-scoring fragments that pass basic tests for “modelability”, we can generate accurate alignments within a small ensemble. Our results suggest that the set of sequences that can currently be modeled by homology can be greatly extended.
Author Summary
It has been suggested that, for nearly every protein sequence, there is already a protein with a similar structure in current protein structure databases. However, with poor or undetectable sequence relationships, it is expected that accurate alignments and models cannot be generated. Here we show that this is not the case, and that whenever structural relationship exists, there are usually local sequence relationships that can be used to generate an accurate alignment, no matter what the global sequence identity. However, this requires an alternative to the traditional dynamic programming algorithm and the consideration of a small ensemble of alignments. We present an algorithm, S4, and demonstrate that it is capable of generating accurate alignments in nearly all cases where a structural relationship exists between two proteins. Our results thus constitute an important advance in the full exploitation of the information in structural databases. That is, the expectation of an accurate alignment suggests that a meaningful model can be generated for nearly every sequence for which a suitable template exists.
doi:10.1371/journal.pcbi.1002175
PMCID: PMC3188491  PMID: 21998567
24.  Protein sequence alignment with family-specific amino acid similarity matrices 
BMC Research Notes  2011;4:296.
Background
Alignment of amino acid sequences by means of dynamic programming is a cornerstone sequence comparison method. The quality of alignments produced by dynamic programming critically depends on the choice of the alignment scoring function. Therefore, for a specific alignment problem one needs a way of selecting the best performing scoring function. This work is focused on the issue of finding optimized protein family- and fold-specific scoring functions for global similarity matrix-based sequence alignment.
Findings
I utilize a comprehensive set of reference alignments obtained from structural superposition of homologous and analogous proteins to design a quantitative statistical framework for evaluating the performance of alignment scoring functions in global pairwise sequence alignment. This framework is applied to study how existing general-purpose amino acid similarity matrices perform on individual protein families and structural folds, and to compare them to family-specific and fold-specific matrices derived in this work. I describe an adaptive alignment procedure that automatically selects an appropriate similarity matrix and optimized gap penalties based on the properties of the sequences being aligned.
Conclusions
The results of this work indicate that using family-specific similarity matrices significantly improves the quality of the alignment of homologous sequences over the traditional sequence alignment based on a single general-purpose similarity matrix. However, using fold-specific similarity matrices can only marginally improve sequence alignment of proteins that share the same structural fold but do not share a common evolutionary origin. The family-specific matrices derived in this work and the optimized gap penalties are available at http://taurus.crc.albany.edu/fsm.
doi:10.1186/1756-0500-4-296
PMCID: PMC3201029  PMID: 21846354
25.  Searching for evolutionary distant RNA homologs within genomic sequences using partition function posterior probabilities 
BMC Bioinformatics  2008;9:61.
Background
Identification of RNA homologs within genomic stretches is difficult when pairwise sequence identity is low or unalignable flanking residues are present. In both cases structure-sequence or profile/family-sequence alignment programs become difficult to apply because of unreliable RNA structures or family alignments. As such, local sequence-sequence alignment programs are frequently used instead. We have recently demonstrated that maximal expected accuracy alignments using partition function match probabilities (implemented in Probalign) are significantly better than contemporary methods on heterogeneous length protein sequence datasets, thus suggesting an affinity for local alignment.
Results
We create a pairwise RNA-genome alignment benchmark from RFAM families with average pairwise sequence identity up to 60%. Each dataset contains a query RNA aligned to a target RNA (of the same family) embedded in a genomic sequence at least 5K nucleotides long. To simulate common conditions when exact ends of an ncRNA are unknown, each query RNA has 5' and 3' genomic flanks of size 50, 100, and 150 nucleotides. We subsequently compare the error of the Probalign program (adjusted for local alignment) to the commonly used local alignment programs HMMER, SSEARCH, and BLAST, and the popular ClustalW program with zero end-gap penalties. Parameters were optimized for each program on a small subset of the benchmark. Probalign has overall highest accuracies on the full benchmark. It leads by 10% accuracy over SSEARCH (the next best method) on 5 out of 22 families. On datasets restricted to maximum of 30% sequence identity, Probalign's overall median error is 71.2% vs. 83.4% for SSEARCH (P-value < 0.05). Furthermore, on these datasets Probalign leads SSEARCH by at least 10% on five families; SSEARCH leads Probalign by the same margin on two of the fourteen families. We also demonstrate that the Probalign mean posterior probability, compared to the normalized SSEARCH Z-score, is a better discriminator of alignment quality. All datasets and software are available online.
Conclusion
We demonstrate, for the first time, that partition function match probabilities used for expected accuracy alignment, as done in Probalign, provide statistically significant improvement over current approaches for identifying distantly related RNA sequences in larger genomic segments.
doi:10.1186/1471-2105-9-61
PMCID: PMC2248559  PMID: 18226231

Results 1-25 (1472020)