The correlation error and finite-size correction in an ungapped sequence alignment

MOTIVATION: The BLAST program for comparing two sequences assumes independent sequences in its random model. The resulting random alignment matrices have correlations across their diagonals. Analytic formulas for the BLAST p-value essentially neglect these correlations and are equivalent to a random model with independent diagonals. Progress on the independent diagonals model has been surprisingly rapid, but the practical magnitude of the correlations it neglects remains unknown. In addition, BLAST uses a finite-size correction that is particularly important when either of the sequences being compared is short. Several formulas for the finite-size correction have now been given, but the corresponding errors in the BLAST p-values have not been quantified. As the lengths of compared sequences tend to infinity, it is also theoretically unknown whether the neglected correlations vanish faster than the finite-size correction. RESULTS: Because we required certain analytic formulas, our study restricted its computer experiments to ungapped sequence alignment. We expect some of our conclusions to extend qualitatively to gapped sequence alignment, however. With this caveat, the finite-size correction appeared to vanish faster than the neglected correlations. Although the finite-size correction underestimated the BLAST p-value, it improved the approximation substantially for all but very short sequences. In practice, the Altschul-Gish finite-size correction was superior to Spouge's. The independent diagonals model was always within a factor of 2 of the true BLAST p-value, although fitting p-value parameters from it probably is unwise. CONTACT: spouge@ncbi.nlm.nih.gov     

JAE

One of the most basic methods of understanding the biological significance of a sequence is to produce an alignment with related sequences. A vital aspect of correctly aligning sequences is to apply biological intuition through manual editing of an alignment produced by multiple-sequence alignment software. As part of the European Molecular Biology Open Source Software Suite (EMBOSS), a new alignment editor in the Jemboss package is freely available for download. The Jemboss Alignment Editor (JAE) incorporates standard methods of editing, and colouring residues and nucleotides to highlight important regions of interest. JAE also makes use of scoring matrices (PAM and BLOSUM), selected by the user, to display regions of high degrees of similarity and identity. Other tools include the ability to calculate a consensus, a consensus plot (using a selected scoring matrix) and pairwise identities. AVAILABILITY: The JAE can be launched from the webpage (http://emboss.sourceforge.net/Jemboss/).     

BCL::Align—Sequence alignment and fold recognition with a custom scoring function online

BCL::Align is a multiple sequence alignment tool that utilizes the dynamic programming method in combination with a customizable scoring function for sequence alignment and fold recognition. The scoring function is a weighted sum of the traditional PAM and BLOSUM scoring matrices, position-specific scoring matrices output by PSI-BLAST, secondary structure predicted by a variety of methods, chemical properties, and gap penalties. By adjusting the weights, the method can be tailored for fold recognition or sequence alignment tasks at different levels of sequence identity. A Monte Carlo algorithm was used to determine optimized weight sets for sequence alignment and fold recognition that most accurately reproduced the SABmark reference alignment test set. In an evaluation of sequence alignment performance, BCL::Align ranked best in alignment accuracy (Cline score of 22.90 for sequences in the Twilight Zone) when compared with Align-m, ClustalW, T-Coffee, and MUSCLE. ROC curve analysis indicates BCL::Align's ability to correctly recognize protein folds with over 80% accuracy. The flexibility of the program allows it to be optimized for specific classes of proteins (e.g. membrane proteins) or fold families (e.g. TIM-barrel proteins). BCL::Align is free for academic use and available online at http://www.meilerlab.org/.     

BCL::Align-sequence alignment and fold recognition with a custom scoring function online

BCL::Align is a multiple sequence alignment tool that utilizes the dynamic programming method in combination with a customizable scoring function for sequence alignment and fold recognition. The scoring function is a weighted sum of the traditional PAM and BLOSUM scoring matrices, position-specific scoring matrices output by PSI-BLAST, secondary structure predicted by a variety of methods, chemical properties, and gap penalties. By adjusting the weights, the method can be tailored for fold recognition or sequence alignment tasks at different levels of sequence identity. A Monte Carlo algorithm was used to determine optimized weight sets for sequence alignment and fold recognition that most accurately reproduced the SABmark reference alignment test set. In an evaluation of sequence alignment performance, BCL::Align ranked best in alignment accuracy (Cline score of 22.90 for sequences in the Twilight Zone) when compared with Align-m, ClustalW, T-Coffee, and MUSCLE. ROC curve analysis indicates BCL::Align's ability to correctly recognize protein folds with over 80% accuracy. The flexibility of the program allows it to be optimized for specific classes of proteins (e.g. membrane proteins) or fold families (e.g. TIM-barrel proteins). BCL::Align is free for academic use and available online at http://www.meilerlab.org/.     

Estimating and evaluating the statistics of gapped local-alignment scores.

We present a novel maximum-likelihood-based algorithm for estimating the distribution of alignment scores from the scores of unrelated sequences in a database search. Using a new method for measuring the accuracy of p-values, we show that our maximum-likelihood-based algorithm is more accurate than existing regression-based and lookup table methods. We explore a more sophisticated way of modeling and estimating the score distributions (using a two-component mixture model and expectation maximization), but conclude that this does not improve significantly over simply ignoring scores with small E-values during estimation. Finally, we measure the classification accuracy of p-values estimated in different ways and observe that inaccurate p-values can, somewhat paradoxically, lead to higher classification accuracy. We explain this paradox and argue that statistical accuracy, not classification accuracy, should be the primary criterion in comparisons of similarity search methods that return p-values that adjust for target sequence length.     

A comparison of scoring functions for protein sequence profile alignment

MOTIVATION: In recent years, several methods have been proposed for aligning two protein sequence profiles, with reported improvements in alignment accuracy and homolog discrimination versus sequence-sequence methods (e.g. BLAST) and profile-sequence methods (e.g. PSI-BLAST). Profile-profile alignment is also the iterated step in progressive multiple sequence alignment algorithms such as CLUSTALW. However, little is known about the relative performance of different profile-profile scoring functions. In this work, we evaluate the alignment accuracy of 23 different profile-profile scoring functions by comparing alignments of 488 pairs of sequences with identity < or =30% against structural alignments. We optimize parameters for all scoring functions on the same training set and use profiles of alignments from both PSI-BLAST and SAM-T99. Structural alignments are constructed from a consensus between the FSSP database and CE structural aligner. We compare the results with sequence-sequence and sequence-profile methods, including BLAST and PSI-BLAST. RESULTS: We find that profile-profile alignment gives an average improvement over our test set of typically 2-3% over profile-sequence alignment and approximately 40% over sequence-sequence alignment. No statistically significant difference is seen in the relative performance of most of the scoring functions tested. Significantly better results are obtained with profiles constructed from SAM-T99 alignments than from PSI-BLAST alignments. AVAILABILITY: Source code, reference alignments and more detailed results are freely available at http://phylogenomics.berkeley.edu/profilealignment/     

Detection of homologous proteins by an intermediate sequence search

We developed a variant of the intermediate sequence search method (ISS(new)) for detection and alignment of weakly similar pairs of protein sequences. ISS(new) relates two query sequences by an intermediate sequence that is potentially homologous to both queries. The improvement was achieved by a more robust overlap score for a match between the queries through an intermediate. The approach was benchmarked on a data set of 2369 sequences of known structure with insignificant sequence similarity to each other (BLAST E-value larger than 0.001); 2050 of these sequences had a related structure in the set. ISS(new) performed significantly better than both PSI-BLAST and a previously described intermediate sequence search method. PSI-BLAST could not detect correct homologs for 1619 of the 2369 sequences. In contrast, ISS(new) assigned a correct homolog as the top hit for 121 of these 1619 sequences, while incorrectly assigning homologs for only nine targets; it did not assign homologs for the remainder of the sequences. By estimate, ISS(new) may be able to assign the folds of domains in approximately 29,000 of the approximately 500,000 sequences unassigned by PSI-BLAST, with 90% specificity (1 - false positives fraction). In addition, we show that the 15 alignments with the most significant BLAST E-values include the nearly best alignments constructed by ISS(new).     

Composition-modified matrices improve identification of homologs of saccharomyces cerevisiae low-complexity glycoproteins

Yeast glycoproteins are representative of low-complexity sequences, those sequences rich in a few types of amino acids. Low-complexity protein sequences comprise more than 10% of the proteome but are poorly aligned by existing methods. Under default conditions, BLAST and FASTA use the scoring matrix BLOSUM62, which is optimized for sequences with diverse amino acid compositions. Because low-complexity sequences are rich in a few amino acids, these tools tend to align the most common residues in nonhomologous positions, thereby generating anomalously high scores, deviations from the expected extreme value distribution, and small e values. This anomalous scoring prevents BLOSUM62-based BLAST and FASTA from identifying correct homologs for proteins with low-complexity sequences, including Saccharomyces cerevisiae wall proteins. We have devised and empirically tested scoring matrices that compensate for the overrepresentation of some amino acids in any query sequence in different ways. These matrices were tested for sensitivity in finding true homologs, discrimination against nonhomologous and random sequences, conformance to the extreme value distribution, and accuracy of e values. Of the tested matrices, the two best matrices (called E and gtQ) gave reliable alignments in BLAST and FASTA searches, identified a consistent set of paralogs of the yeast cell wall test set proteins, and improved the consistency of secondary structure predictions for cell wall proteins.     

New finite-size correction for local alignment score distributions

ABSTRACT: BACKGROUND: Local alignment programs often calculate the probability that a match occurred by chance. The calculation of this probability may require a "finite-size" correction to the lengths of the sequences, as an alignment that starts near the end of either sequence may run out of sequence before achieving a significant score. FINDINGS: We present an improved finite-size correction that considers the distribution of sequence lengths rather than simply the corresponding means. This approach improves sensitivity and avoids substituting an ad hoc length for short sequences that can underestimate the significance of a match. We use a test set derived from ASTRAL to show improved ROC scores, especially for shorter sequences. CONCLUSIONS: The new finite-size correction improves the calculation of probabilities for a local alignment. It is now used in the BLAST + package and at the NCBI BLAST web site (http://blast.ncbi.nlm.nih.gov).     

双序列比对基础和应用实例

首先介绍序列比对的分子生物学基础,即核酸序列基本单元核苷酸和蛋白质序列基本单元氨基酸。文中以精心设计的图表列出四种核苷酸和二十种氨基酸的名称、性质和分类。第2节简述序列比对基础,包括相似性和同源性基本概念、整体比对和局部比对、点阵图方法、动态规划和启发式算法、计分矩阵和空位罚分,以及常用软件和分析平台。第3节介绍核酸序列比对中常用计分矩阵DNAfull,蛋白质序列比对中常用计分矩阵BLOSUM62和PAM250。第4-8节则以血红蛋白、多肽毒素、植物转录因子、癌胚抗原和唾液酸酶为例,介绍双序列比对的具体应用。通过这些实例,说明如何选择分析平台和比对程序、如何设置计分矩阵和空位罚分,如何分析比对结果及其生物学意义。文末进行简要总结。     

Increased detection of structural templates using alignments of designed sequences

Protein structure prediction by comparative modeling benefits greatly from the use of multiple sequence alignment information to improve the accuracy of structural template identification and the alignment of target sequences to structural templates. Unfortunately, this benefit is limited to those protein sequences for which at least several natural sequence homologues exist. We show here that the use of large diverse alignments of computationally designed protein sequences confers many of the same benefits as natural sequences in identifying structural templates for comparative modeling targets. A large-scale massively parallelized application of an all-atom protein design algorithm, including a simple model of peptide backbone flexibility, has allowed us to generate 500 diverse, non-native, high-quality sequences for each of 264 protein structures in our test set. PSI-BLAST searches using the sequence profiles generated from the designed sequences ("reverse" BLAST searches) give near-perfect accuracy in identifying true structural homologues of the parent structure, with 54% coverage. In 41 of 49 genomes scanned using reverse BLAST searches, at least one novel structural template (not found by the standard method of PSI-BLAST against PDB) is identified. Further improvements in coverage, through optimizing the scoring function used to design sequences and continued application to new protein structures beyond the test set, will allow this method to mature into a useful strategy for identifying distantly related structural templates.     

Use of residue pairs in protein sequence-sequence and sequence-structure alignments

Two new sets of scoring matrices are introduced: H2 for the protein sequence comparison and T2 for the protein sequence-structure correlation. Each element of H2 or T2 measures the frequency with which a pair of amino acid types in one protein, k-residues apart in the sequence, is aligned with another pair of residues, of given amino acid types (for H2) or in given structural states (for T2), in other structurally homologous proteins. There are four types, corresponding to the k-values of 1 to 4, for both H2 and T2. These matrices were set up using a large number of structurally homologous protein pairs, with little sequence homology between the pair, that were recently generated using the structure comparison program SHEBA. The two scoring matrices were incorporated into the main body of the sequence alignment program SSEARCH in the FASTA package and tested in a fold recognition setting in which a set of 107 test sequences were aligned to each of a panel of 3,539 domains that represent all known protein structures. Six procedures were tested; the straight Smith-Waterman (SW) and FASTA procedures, which used the Blosum62 single residue type substitution matrix; BLAST and PSI-BLAST procedures, which also used the Blosum62 matrix; PASH, which used Blosum62 and H2 matrices; and PASSC, which used Blosum62, H2, and T2 matrices. All procedures gave similar results when the probe and target sequences had greater than 30% sequence identity. However, when the sequence identity was below 30%, a similar structure could be found for more sequences using PASSC than using any other procedure. PASH and PSI-BLAST gave the next best results.     

Simple is beautiful: a straightforward approach to improve the delineation of true and false positives in PSI-BLAST searches

MOTIVATION: The deluge of biological information from different genomic initiatives and the rapid advancement in biotechnologies have made bioinformatics tools an integral part of modern biology. Among the widely used sequence alignment tools, BLAST and PSI-BLAST are arguably the most popular. PSI-BLAST, which uses an iterative profile position specific score matrix (PSSM)-based search strategy, is more sensitive than BLAST in detecting weak homologies, thus making it suitable for remote homolog detection. Many refinements have been made to improve PSI-BLAST, and its computational efficiency and high specificity have been much touted. Nevertheless, corruption of its profile via the incorporation of false positive sequences remains a major challenge. RESULTS: We have developed a simple and elegant approach to resolve the problem of model corruption in PSI-BLAST searches. We hypothesized that combining results from the first (least-corrupted) profile with results from later (most sensitive) iterations of PSI-BLAST provides a better discriminator for true and false hits. Accordingly, we have derived a formula that utilizes the E-values from these two PSI-BLAST iterations to obtain a figure of merit for rank-ordering the hits. Our verification results based on a 'gold-standard' test set indicate that this figure of merit does indeed delineate true positives from false positives better than PSI-BLAST E-values. Perhaps what is most notable about this strategy is that it is simple and straightforward to implement.     

Use of multiple profiles corresponding to a sequence alignment enables effective detection of remote homologues

MOTIVATION: Position specific scoring matrices (PSSMs) corresponding to aligned sequences of homologous proteins are commonly used in homology detection. A PSSM is generated on the basis of one of the homologues as a reference sequence, which is the query in the case of PSI-BLAST searches. The reference sequence is chosen arbitrarily while generating PSSMs for reverse BLAST searches. In this work we demonstrate that the use of multiple PSSMs corresponding to a given alignment and variable reference sequences is more effective than using traditional single PSSMs and hidden Markov models. RESULTS: Searches for proteins with known 3-D structures have been made against three databases of protein family profiles corresponding to known structures: (1) One PSSM per family; (2) multiple PSSMs corresponding to an alignment and variable reference sequences for every family; and (3) hidden Markov models. A comparison of the performances of these three approaches suggests that the use of multiple PSSMs is most effective. CONTACT: ns@mbu.iisc.ernet.in.     

Protein database searches using compositionally adjusted substitution matrices

Almost all protein database search methods use amino acid substitution matrices for scoring, optimizing, and assessing the statistical significance of sequence alignments. Much care and effort has therefore gone into constructing substitution matrices, and the quality of search results can depend strongly upon the choice of the proper matrix. A long-standing problem has been the comparison of sequences with biased amino acid compositions, for which standard substitution matrices are not optimal. To address this problem, we have recently developed a general procedure for transforming a standard matrix into one appropriate for the comparison of two sequences with arbitrary, and possibly differing compositions. Such adjusted matrices yield, on average, improved alignments and alignment scores when applied to the comparison of proteins with markedly biased compositions. Here we review the application of compositionally adjusted matrices and consider whether they may also be applied fruitfully to general purpose protein sequence database searches, in which related sequence pairs do not necessarily have strong compositional biases. Although it is not advisable to apply compositional adjustment indiscriminately, we describe several simple criteria under which invoking such adjustment is on average beneficial. In a typical database search, at least one of these criteria is satisfied by over half the related sequence pairs. Compositional substitution matrix adjustment is now available in NCBI's protein-protein version of blast.     

Large-scale comparison of protein sequence alignment algorithms with structure alignments

Sequence alignment programs such as BLAST and PSI-BLAST are used routinely in pairwise, profile-based, or intermediate-sequence-search (ISS) methods to detect remote homologies for the purposes of fold assignment and comparative modeling. Yet, the sequence alignment quality of these methods at low sequence identity is not known. We have used the CE structure alignment program (Shindyalov and Bourne, Prot Eng 1998;11:739) to derive sequence alignments for all superfamily and family-level related proteins in the SCOP domain database. CE aligns structures and their sequences based on distances within each protein, rather than on interprotein distances. We compared BLAST, PSI-BLAST, CLUSTALW, and ISS alignments with the CE structural alignments. We found that global alignments with CLUSTALW were very poor at low sequence identity (<25%), as judged by the CE alignments. We used PSI-BLAST to search the nonredundant sequence database (nr) with every sequence in SCOP using up to four iterations. The resulting matrix was used to search a database of SCOP sequences. PSI-BLAST is only slightly better than BLAST in alignment accuracy on a per-residue basis, but PSI-BLAST matrix alignments are much longer than BLAST's, and so align correctly a larger fraction of the total number of aligned residues in the structure alignments. Any two SCOP sequences in the same superfamily that shared a hit or hits in the nr PSI-BLAST searches were identified as linked by the shared intermediate sequence. We examined the quality of the longest SCOP-query/ SCOP-hit alignment via an intermediate sequence, and found that ISS produced longer alignments than PSI-BLAST searches alone, of nearly comparable per-residue quality. At 10-15% sequence identity, BLAST correctly aligns 28%, PSI-BLAST 40%, and ISS 46% of residues according to the structure alignments. We also compared CE structure alignments with FSSP structure alignments generated by the DALI program. In contrast to the sequence methods, CE and structure alignments from the FSSP database identically align 75% of residue pairs at the 10-15% level of sequence identity, indicating that there is substantial room for improvement in these sequence alignment methods. BLAST produced alignments for 8% of the 10,665 nonimmunoglobulin SCOP superfamily sequence pairs (nearly all <25% sequence identity), PSI-BLAST matched 17% and the double-PSI-BLAST ISS method aligned 38% with E-values <10.0. The results indicate that intermediate sequences may be useful not only in fold assignment but also in achieving more complete sequence alignments for comparative modeling.     

ProViDE: A software tool for accurate estimation of viral diversity in metagenomic samples

Given the absence of universal marker genes in the viral kingdom, researchers typically use BLAST (with stringent E-values) for taxonomic classification of viral metagenomic sequences. Since majority of metagenomic sequences originate from hitherto unknown viral groups, using stringent e-values results in most sequences remaining unclassified. Furthermore, using less stringent e-values results in a high number of incorrect taxonomic assignments. The SOrt-ITEMS algorithm provides an approach to address the above issues. Based on alignment parameters, SOrt-ITEMS follows an elaborate work-flow for assigning reads originating from hitherto unknown archaeal/bacterial genomes. In SOrt-ITEMS, alignment parameter thresholds were generated by observing patterns of sequence divergence within and across various taxonomic groups belonging to bacterial and archaeal kingdoms. However, many taxonomic groups within the viral kingdom lack a typical Linnean-like taxonomic hierarchy. In this paper, we present ProViDE (Program for Viral Diversity Estimation), an algorithm that uses a customized set of alignment parameter thresholds, specifically suited for viral metagenomic sequences. These thresholds capture the pattern of sequence divergence and the non-uniform taxonomic hierarchy observed within/across various taxonomic groups of the viral kingdom. Validation results indicate that the percentage of 'correct' assignments by ProViDE is around 1.7 to 3 times higher than that by the widely used similarity based method MEGAN. The misclassification rate of ProViDE is around 3 to 19% (as compared to 5 to 42% by MEGAN) indicating significantly better assignment accuracy. ProViDE software and a supplementary file (containing supplementary figures and tables referred to in this article) is available for download from http://metagenomics.atc.tcs.com/binning/ProViDE/     

Saturated BLAST: an automated multiple intermediate sequence search used to detect distant homology

MOTIVATION: Two proteins can have a similar 3-dimensional structure and biological function, but have sequences sufficiently different that traditional protein sequence comparison algorithms do not identify their relationship. The desire to identify such relations has led to the development of more sensitive sequence alignment strategies. One such strategy is the Intermediate Sequence Search (ISS), which connects two proteins through one or more intermediate sequences. In its brute-force implementation, ISS is a strategy that repetitively uses the results of the previous query as new search seeds, making it time-consuming and difficult to analyze. RESULTS: Saturated BLAST is a package that performs ISS in an efficient and automated manner. It was developed using Perl and Perl/Tk and implemented on the LINUX operating system. Starting with a protein sequence, Saturated BLAST runs a BLAST search and identifies representative sequences for the next generation of searches. The procedure is run until convergence or until some predefined criteria are met. Saturated BLAST has a friendly graphic user interface, a built-in BLAST result parser, several multiple alignment tools, clustering algorithms and various filters for the elimination of false positives, thereby providing an easy way to edit, visualize, analyze, monitor and control the search. Besides detecting remote homologies, Saturated BLAST can be used to maintain protein family databases and to search for new genes in genomic databases.     

Optimizing amino acid substitution matrices with a local alignment kernel

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.