Provably sensitive indexing strategies for biosequence similarity search.

Fast algorithms for pairwise biosequence similarity search frequently use filtering and indexing strategies to identify potential matches between a query sequence and a database. For the most part, these strategies are not informed by the substitution score matrices commonly used by comparison algorithms to assign numerical scores to pairs of aligned residues. Consequently, although many filtering strategies offer strong formal guarantees about their ability to detect pairs of sequences differing by few substitutions, these methods can make no guarantee of detecting pairs with high similarity scores. We describe a general technique, score simulation, to help resolve the tension between existing filtering techniques and the use of score matrices. Score simulation, using score matrices, maps ungapped similarity search problems to the simpler problem of finding pairs of strings that differ by few substitutions. Score simulation leads to indexing schemes for biosequences that permit efficient ungapped similarity search with arbitrary score matrices while maintaining strong formal guarantees of sensitivity. We introduce the LSH-ALL-PAIRS-SIM algorithm for finding local similarities in large biosequence collections and show that it is both computationally feasible and sensitive in practice.     

Minimal-risk scoring matrices for sequence analysis.

We introduce a minimal-risk method for estimating the frequencies of amino acids at conserved positions in a protein family. Our method, called minimal-risk estimation, finds the optimal weighting between a set of observed amino acid counts and a set of pseudofrequencies, which represent prior information about the frequencies. We compute the optimal weighting by minimizing the expected distance between the estimated frequencies and the true population frequencies, measured by either a squared-error or a relative-entropy metric. Our method accounts for the source of the pseudofrequencies, which arise either from the background distribution of amino acids or from applying a substitution matrix to the observed data. Our frequency estimates therefore depend on the size and composition of the observed data as well as the source of the pseudofrequencies. We convert our frequency estimates into minimal-risk scoring matrices for sequence analysis. A large-scale cross-validation study, involving 48 variants of seven methods, shows that the best performing method is minimal-risk estimation using the squared-error metric. Our method is implemented in the package EMATRIX, which is available on the Internet at http://motif.stanford.edu/ematrix.     

Three-dimensional cluster analysis identifies interfaces and functional residue clusters in proteins

Three-dimensional cluster analysis offers a method for the prediction of functional residue clusters in proteins. This method requires a representative structure and a multiple sequence alignment as input data. Individual residues are represented in terms of regional alignments that reflect both their structural environment and their evolutionary variation, as defined by the alignment of homologous sequences. From the overall (global) and the residue-specific (regional) alignments, we calculate the global and regional similarity matrices, containing scores for all pairwise sequence comparisons in the respective alignments. Comparing the matrices yields two scores for each residue. The regional conservation score (C(R)(x)) defines the conservation of each residue x and its neighbors in 3D space relative to the protein as a whole. The similarity deviation score (S(x)) detects residue clusters with sequence similarities that deviate from the similarities suggested by the full-length sequences. We evaluated 3D cluster analysis on a set of 35 families of proteins with available cocrystal structures, showing small ligand interfaces, nucleic acid interfaces and two types of protein-protein interfaces (transient and stable). We present two examples in detail: fructose-1,6-bisphosphate aldolase and the mitogen-activated protein kinase ERK2. We found that the regional conservation score (C(R)(x)) identifies functional residue clusters better than a scoring scheme that does not take 3D information into account. C(R)(x) is particularly useful for the prediction of poorly conserved, transient protein-protein interfaces. Many of the proteins studied contained residue clusters with elevated similarity deviation scores. These residue clusters correlate with specificity-conferring regions: 3D cluster analysis therefore represents an easily applied method for the prediction of functionally relevant spatial clusters of residues in proteins.     

Pairwise alignment incorporating dipeptide covariation

MOTIVATION: Standard algorithms for pairwise protein sequence alignment make the simplifying assumption that amino acid substitutions at neighboring sites are uncorrelated. This assumption allows implementation of fast algorithms for pairwise sequence alignment, but it ignores information that could conceivably increase the power of remote homolog detection. We examine the validity of this assumption by constructing extended substitution matrices that encapsulate the observed correlations between neighboring sites, by developing an efficient and rigorous algorithm for pairwise protein sequence alignment that incorporates these local substitution correlations and by assessing the ability of this algorithm to detect remote homologies. RESULTS: Our analysis indicates that local correlations between substitutions are not strong on the average. Furthermore, incorporating local substitution correlations into pairwise alignment did not lead to a statistically significant improvement in remote homology detection. Therefore, the standard assumption that individual residues within protein sequences evolve independently of neighboring positions appears to be an efficient and appropriate approximation.     

Estimation of amino acid residue substitution rates at local spatial regions and application in protein function inference: a Bayesian Monte Carlo approach

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent-exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.     

A novel knowledge-based approach to design inorganic-binding peptides

MOTIVATION: The discovery of solid-binding peptide sequences is accelerating along with their practical applications in biotechnology and materials sciences. A better understanding of the relationships between the peptide sequences and their binding affinities or specificities will enable further design of novel peptides with selected properties of interest both in engineering and medicine. RESULTS: A bioinformatics approach was developed to classify peptides selected by in vivo techniques according to their inorganic solid-binding properties. Our approach performs all-against-all comparisons of experimentally selected peptides with short amino acid sequences that were categorized for their binding affinity and scores the alignments using sequence similarity scoring matrices. We generated novel scoring matrices that optimize the similarities within the strong-binding peptide sequences and the differences between the strong- and weak-binding peptide sequences. Using the scoring matrices thus generated, a given peptide is classified based on the sequence similarity to a set of experimentally selected peptides. We demonstrate the new approach by classifying experimentally characterized quartz-binding peptides and computationally designing new sequences with specific affinities. Experimental verifications of binding of these computationally designed peptides confirm our predictions with high accuracy. We further show that our approach is a general one and can be used to design new sequences that bind to a given inorganic solid with predictable and enhanced affinity.     

On the significance of sequence alignments when using multiple scoring matrices

MOTIVATION: Pairwise local sequence alignment is commonly used to search data bases for sequences related to some query sequence. Alignments are obtained using a scoring matrix that takes into account the different frequencies of occurrence of the various types of amino acid substitutions. Software like BLAST provides the user with a set of scoring matrices available to choose from, and in the literature it is sometimes recommended to try several scoring matrices on the sequences of interest. The significance of an alignment is usually assessed by looking at E-values and p-values. While sequence lengths and data base sizes enter the standard calculations of significance, it is much less common to take the use of several scoring matrices on the same sequences into account. Altschul proposed corrections of the p-value that account for the simultaneous use of an infinite number of PAM matrices. Here we consider the more realistic situation where the user may choose from a finite set of popular PAM and BLOSUM matrices, in particular the ones available in BLAST. It turns out that the significance of a result can be considerably overestimated, if a set of substitution matrices is used in an alignment problem and the most significant alignment is then quoted. RESULTS: Based on extensive simulations, we study the multiple testing problem that occurs when several scoring matrices for local sequence alignment are used. We consider a simple Bonferroni correction of the p-values and investigate its accuracy. Finally, we propose a more accurate correction based on extreme value distributions fitted to the maximum of the normalized scores obtained from different scoring matrices. For various sets of matrices we provide correction factors which can be easily applied to adjust p- and E-values reported by software packages.     

Embedding strategies for effective use of information from multiple sequence alignments.

We describe a new strategy for utilizing multiple sequence alignment information to detect distant relationships in searches of sequence databases. A single sequence representing a protein family is enriched by replacing conserved regions with position-specific scoring matrices (PSSMs) or consensus residues derived from multiple alignments of family members. In comprehensive tests of these and other family representations, PSSM-embedded queries produced the best results overall when used with a special version of the Smith-Waterman searching algorithm. Moreover, embedding consensus residues instead of PSSMs improved performance with readily available single sequence query searching programs, such as BLAST and FASTA. Embedding PSSMs or consensus residues into a representative sequence improves searching performance by extracting multiple alignment information from motif regions while retaining single sequence information where alignment is uncertain.     

PRALINETM: a strategy for improved multiple alignment of transmembrane proteins

MOTIVATION: Membrane-bound proteins are a special class of proteins. The regions that insert into the cell-membrane have a profoundly different hydrophobicity pattern compared with soluble proteins. Multiple alignment techniques use scoring schemes tailored for sequences of soluble proteins and are therefore in principle not optimal to align membrane-bound proteins. RESULTS: Transmembrane (TM) regions in protein sequences can be reliably recognized using state-of-the-art sequence prediction techniques. Furthermore, membrane-specific scoring matrices are available. We have developed a new alignment method, called PRALINETM, which integrates these two features to enhance multiple sequence alignment. We tested our algorithm on the TM alignment benchmark set by Bahr et al. (2001), and showed that the quality of TM alignments can be significantly improved compared with the quality produced by a standard multiple alignment technique. The results clearly indicate that the incorporation of these new elements into current state-of-the-art alignment methods is crucial for optimizing the alignment of TM proteins. AVAILABILITY: A webserver is available at http://www.ibi.vu.nl/programs/pralinewww.     

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/.     

Bayesian adaptive sequence alignment algorithms

The selection of a scoring matrix and gap penalty parameters continues to be an important problem in sequence alignment. We describe here an algorithm, the 'Bayes block aligner, which bypasses this requirement. Instead of requiring a fixed set of parameter settings, this algorithm returns the Bayesian posterior probability for the number of gaps and for the scoring matrices in any series of interest. Furthermore, instead of returning the single best alignment for the chosen parameter settings, this algorithm returns the posterior distribution of all alignments considering the full range of gapping and scoring matrices selected, weighing each in proportion to its probability based on the data. We compared the Bayes aligner with the popular Smith-Waterman algorithm with parameter settings from the literature which had been optimized for the identification of structural neighbors, and found that the Bayes aligner correctly identified more structural neighbors. In a detailed examination of the alignment of a pair of kinase and a pair of GTPase sequences, we illustrate the algorithm's potential to identify subsequences that are conserved to different degrees. In addition, this example shows that the Bayes aligner returns an alignment-free assessment of the distance between a pair of sequences.      

A transition probability model for amino acid substitutions from blocks.

Substitution matrices have been useful for sequence alignment and protein sequence comparisons. The BLOSUM series of matrices, which had been derived from a database of alignments of protein blocks, improved the accuracy of alignments previously obtained from the PAM-type matrices estimated from only closely related sequences. Although BLOSUM matrices are scoring matrices now widely used for protein sequence alignments, they do not describe an evolutionary model. BLOSUM matrices do not permit the estimation of the actual number of amino acid substitutions between sequences by correcting for multiple hits. The method presented here uses the Blocks database of protein alignments, along with the additivity of evolutionary distances, to approximate the amino acid substitution probabilities as a function of actual evolutionary distance. The PMB (Probability Matrix from Blocks) defines a new evolutionary model for protein evolution that can be used for evolutionary analyses of protein sequences. Our model is directly derived from, and thus compatible with, the BLOSUM matrices. The model has the additional advantage of being easily implemented.     

Comparison of methods for searching protein sequence databases.

We have compared commonly used sequence comparison algorithms, scoring matrices, and gap penalties using a method that identifies statistically significant differences in performance. Search sensitivity with either the Smith-Waterman algorithm or FASTA is significantly improved by using modern scoring matrices, such as BLOSUM45-55, and optimized gap penalties instead of the conventional PAM250 matrix. More dramatic improvement can be obtained by scaling similarity scores by the logarithm of the length of the library sequence (In()-scaling). With the best modern scoring matrix (BLOSUM55 or JO93) and optimal gap penalties (-12 for the first residue in the gap and -2 for additional residues), Smith-Waterman and FASTA performed significantly better than BLASTP. With In()-scaling and optimal scoring matrices (BLOSUM45 or Gonnet92) and gap penalties (-12, -1), the rigorous Smith-Waterman algorithm performs better than either BLASTP and FASTA, although with the Gonnet92 matrix the difference with FASTA was not significant. Ln()-scaling performed better than normalization based on other simple functions of library sequence length. Ln()-scaling also performed better than scores based on normalized variance, but the differences were not statistically significant for the BLOSUM50 and Gonnet92 matrices. Optimal scoring matrices and gap penalties are reported for Smith-Waterman and FASTA, using conventional or In()-scaled similarity scores. Searches with no penalty for gap extension, or no penalty for gap opening, or an infinite penalty for gaps performed significantly worse than the best methods. Differences in performance between FASTA and Smith-Waterman were not significant when partial query sequences were used. However, the best performance with complete query sequences was obtained with the Smith-Waterman algorithm and In()-scaling.     

Residue-residue contact substitution probabilities derived from aligned three-dimensional structures and the identification of common folds.

We report the derivation of scores that are based on the analysis of residue-residue contact matrices from 443 3-dimensional structures aligned structurally as 96 families, which can be used to evaluate sequence-structure matches. Residue-residue contacts and the more than 3 x 10(6) amino acid substitutions that take place between pairs of these contacts at aligned positions within each family of structures have been tabulated and segregated according to the solvent accessibility of the residues involved. Contact maps within a family of structures are shown to be highly conserved (approximately 75%) even when the sequence identity is approaching 10%. In a comparison involving a globin structure and the search of a sequence databank (> 21,000 sequences), the contact probability scores are shown to provide a very powerful secondary screen for the top scoring sequence-structure matches, where between 69% and 84% of the unrelated matches are eliminated. The search of an aligned set of 2 globins against a sequence databank and the subsequent residue contact-based evaluation of matches locates all 618 globin sequences before the first non-globin match. From a single bacterial serine proteinase structure, the structural template approach coupled with residue-residue contact substitution data lead to the detection of the mammalian serine proteinase family among the top matches in the search of a sequence databank.     

FIMO: scanning for occurrences of a given motif

A motif is a short DNA or protein sequence that contributes to the biological function of the sequence in which it resides. Over the past several decades, many computational methods have been described for identifying, characterizing and searching with sequence motifs. Critical to nearly any motif-based sequence analysis pipeline is the ability to scan a sequence database for occurrences of a given motif described by a position-specific frequency matrix. RESULTS: We describe Find Individual Motif Occurrences (FIMO), a software tool for scanning DNA or protein sequences with motifs described as position-specific scoring matrices. The program computes a log-likelihood ratio score for each position in a given sequence database, uses established dynamic programming methods to convert this score to a P-value and then applies false discovery rate analysis to estimate a q-value for each position in the given sequence. FIMO provides output in a variety of formats, including HTML, XML and several Santa Cruz Genome Browser formats. The program is efficient, allowing for the scanning of DNA sequences at a rate of 3.5 Mb/s on a single CPU. Availability and Implementation: FIMO is part of the MEME Suite software toolkit. A web server and source code are available at http://meme.sdsc.edu.     

A score matrix to reveal the hidden links in glycans

MOTIVATION: Glycans are the third major class of biomolecules following DNA and proteins. They are extremely vital for the functioning of multicellular organisms. However, comparing the fast development of sequence analysis techniques, informatics work on glycans have a long way to go. Alignment algorithms for glycan tree structures are one of the foremost concerns. In addition, the statistical analysis of these algorithms in terms of biological significance needs to be addressed. RESULTS: We developed a tree-structure alignment algorithm for glycans and performed a statistical analysis of these alignment scores such that biologically interesting features could be captured into a score matrix for glycans. We generated our score matrix in a manner similar to BLOSUM, but with slight variations to accomodate our glycan data, including the incorporation of linkage information. We verified the effectiveness of our new glycan score matrix by illustrating how well the resulting score matrix entries correspond with biological knowledge. Future work for even better improvements with the use of a variety of score matrices for different subclasses of glycans due to their complexity is also discussed. CONTACT: mami@kuicr.kyoto-u.ac.jp SUPPLEMENTARY INFORMATION: The glycan score matrix can be downloaded from http://kanehisa.kuicr.kyoto-u.ac.jp/Paper/kcam/glycanMatrix0.1.txt.     

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.     

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.