Statistical significance of probabilistic sequence alignment and related local hidden Markov models.

The score statistics of probabilistic gapped local alignment of random sequences is investigated both analytically and numerically. The full probabilistic algorithm (e.g., the "local" version of maximum-likelihood or hidden Markov model method) is found to have anomalous statistics. A modified "semi-probabilistic" alignment consisting of a hybrid of Smith-Waterman and probabilistic alignment is then proposed and studied in detail. It is predicted that the score statistics of the hybrid algorithm is of the Gumbel universal form, with the key Gumbel parameter lambda taking on a fixed asymptotic value for a wide variety of scoring systems and parameters. A simple recipe for the computation of the "relative entropy," and from it the finite size correction to lambda, is also given. These predictions compare well with direct numerical simulations for sequences of lengths between 100 and 1,000 examined using various PAM substitution scores and affine gap functions. The sensitivity of the hybrid method in the detection of sequence homology is also studied using correlated sequences generated from toy mutation models. It is found to be comparable to that of the Smith-Waterman alignment and significantly better than the Viterbi version of the probabilistic alignment.     

Performance evaluation of a new algorithm for the detection of remote homologs with sequence comparison

A detailed analysis of the performance of hybrid, a new sequence alignment algorithm developed by Yu and coworkers that combines Smith Waterman local dynamic programming with a local version of the maximum-likelihood approach, was made to access the applicability of this algorithm to the detection of distant homologs by sequence comparison. We analyzed the statistics of hybrid with a set of nonhomologous protein sequences from the SCOP database and found that the statistics of the scores from hybrid algorithm follows an Extreme Value Distribution with lambda approximately 1, as previously shown by Yu et al. for the case of artificially generated sequences. Local dynamic programming was compared to the hybrid algorithm by using two different test data sets of distant homologs from the PFAM and COGs protein sequence databases. The studies were made with several score functions in current use including OPTIMA, a new score function originally developed to detect remote homologs with the Smith Waterman algorithm. We found OPTIMA to be the best score function for both both dynamic programming and the hybrid algorithms. The ability of dynamic programming to discriminate between homologs and nonhomologs in the two sets of distantly related sequences is slightly better than that of hybrid algorithm. The advantage of producing accurate score statistics with only a few simulations may overcome the small differences in performance and make this new algorithm suitable for detection of homologs in conjunction with a wide range of score functions and gap penalties.     

Pandit: a database of protein and associated nucleotide domains with inferred trees

MOTIVATION: A large, high-quality database of homologous sequence alignments with good estimates of their corresponding phylogenetic trees will be a valuable resource to those studying phylogenetics. It will allow researchers to compare current and new models of sequence evolution across a large variety of sequences. The large quantity of data may provide inspiration for new models and methodology to study sequence evolution and may allow general statements about the relative effect of different molecular processes on evolution. RESULTS: The Pandit 7.6 database contains 4341 families of sequences derived from the seed alignments of the Pfam database of amino acid alignments of families of homologous protein domains (Bateman et al., 2002). Each family in Pandit includes an alignment of amino acid sequences that matches the corresponding Pfam family seed alignment, an alignment of DNA sequences that contain the coding sequence of the Pfam alignment when they can be recovered (overall, 82.9% of sequences taken from Pfam) and the alignment of amino acid sequences restricted to only those sequences for which a DNA sequence could be recovered. Each of the alignments has an estimate of the phylogenetic tree associated with it. The tree topologies were obtained using the neighbor joining method based on maximum likelihood estimates of the evolutionary distances, with branch lengths then calculated using a standard maximum likelihood approach.     

HOMSTRAD: adding sequence information to structure-based alignments of homologous protein families

summary: We describe an extension to the Homologous Structure Alignment Database (HOMSTRAD; Mizuguchi et al., Protein Sci., 7, 2469-2471, 1998a) to include homologous sequences derived from the protein families database Pfam (Bateman et al., Nucleic Acids Res., 28, 263-266, 2000). HOMSTRAD is integrated with the server FUGUE (Shi et al., submitted, 2001) for recognition and alignment of homologues, benefitting from the combination of abundant sequence information and accurate structure-based alignments. AVAILABILITY The HOMSTRAD database is available at: http://www-cryst.bioc.cam.ac.uk/homstrad/. Query sequences can be submitted to the homology recognition/alignment server FUGUE at: http://www-cryst.bioc.cam.ac.uk/fugue/.     

Functional annotation by sequence-weighted structure alignments: statistical analysis and case studies from the Protein 3000 structural genomics project in Japan

A method to functionally annotate structural genomics targets, based on a novel structural alignment scoring function, is proposed. In the proposed score, position-specific scoring matrices are used to weight structurally aligned residue pairs to highlight evolutionarily conserved motifs. The functional form of the score is first optimized for discriminating domains belonging to the same Pfam family from domains belonging to different families but the same CATH or SCOP superfamily. In the optimization stage, we consider four standard weighting functions as well as our own, the "maximum substitution probability," and combinations of these functions. The optimized score achieves an area of 0.87 under the receiver-operating characteristic curve with respect to identifying Pfam families within a sequence-unique benchmark set of domain pairs. Confidence measures are then derived from the benchmark distribution of true-positive scores. The alignment method is next applied to the task of functionally annotating 230 query proteins released to the public as part of the Protein 3000 structural genomics project in Japan. Of these queries, 78 were found to align to templates with the same Pfam family as the query or had sequence identities > or = 30%. Another 49 queries were found to match more distantly related templates. Within this group, the template predicted by our method to be the closest functional relative was often not the most structurally similar. Several nontrivial cases are discussed in detail. Finally, 103 queries matched templates at the fold level, but not the family or superfamily level, and remain functionally uncharacterized.     

Family pairwise search with embedded motif models.

MOTIVATION: Statistical models of protein families, such as position-specific scoring matrices, profiles and hidden Markov models, have been used effectively to find remote homologs when given a set of known protein family members. Unfortunately, training these models typically requires a relatively large set of training sequences. Recent work (Grundy, J. Comput. Biol., 5,<479-492, 1998) has shown that, when only a few family members are known, several theoretically justified statistical modeling techniques fail to provide homology detection performance on a par with Family Pairwise Search (FPS), an algorithm that combines scores from a pairwise sequence similarity algorithm such as BLAST. RESULTS: The present paper provides a model-based algorithm that improves FPS by incorporating hybrid motif-based models of the form generated by Cobbler (Henikoff and Henikoff, Protein Sci., 6, 698-705, 1997). For the 73 protein families investigated here, this cobbled FPS algorithm provides better homology detection performance than either Cobbler or FPS alone. This improvement is maintained when BLAST is replaced with the full Smith-Waterman algorithm. AVAILABILITY: http://fps.sdsc.edu     

A probabilistic model of local sequence alignment that simplifies statistical significance estimation

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (λ) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (“Forward” scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (“Viterbi” scores) are Gumbel-distributed with constant λ=log 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments.     

Improving the quality of twilight-zone alignments

Several recent publications illustrated advantages of using sequence profiles in recognizing distant homologies between proteins. At the same time, the practical usefulness of distant homology recognition depends not only on the sensitivity of the algorithm, but also on the quality of the alignment between a prediction target and the template from the database of known proteins. Here, we study this question for several supersensitive protein algorithms that were previously compared in their recognition sensitivity (Rychlewski et al., 2000). A database of protein pairs with similar structures, but low sequence similarity is used to rate the alignments obtained with several different methods, which included sequence-sequence, sequence-profile, and profile-profile alignment methods. We show that incorporation of evolutionary information encoded in sequence profiles into alignment calculation methods significantly increases the alignment accuracy, bringing them closer to the alignments obtained from structure comparison. In general, alignment quality is correlated with recognition and alignment score significance. For every alignment method, alignments with statistically significant scores correlate with both correct structural templates and good quality alignments. At the same time, average alignment lengths differ in various methods, making the comparison between them difficult. For instance, the alignments obtained by FFAS, the profile-profile alignment algorithm developed in our group are always longer that the alignments obtained with the PSI-BLAST algorithms. To address this problem, we develop methods to truncate or extend alignments to cover a specified percentage of protein lengths. In most cases, the elongation of the alignment by profile-profile methods is reasonable, adding fragments of similar structure. The examples of erroneous alignment are examined and it is shown that they can be identified based on the model quality.     

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/.     

A new scoring function and associated statistical significance for structure alignment by CE.

A new scoring function for assessing the statistical significance of protein structure alignment has been developed. The new scores were tested empirically using the combinatorial extension (CE) algorithm. The significance of a given score was given a p-value by curve-fitting the distribution of the scores generated by a random comparison of proteins taken from the PDB_SELECT database and the structural classification of proteins (SCOP) database. Although the scoring function was developed based on the CE algorithm, it is portable to any other protein structure alignment algorithm. The new scoring function is examined by sensitivity, specificity, and ROC curves.     

Convergent Island Statistics: a fast method for determining local alignment score significance

MOTIVATION: Background distribution statistics for profile-based sequence alignment algorithms cannot be calculated analytically, and hence such algorithms must resort to measuring the significance of an alignment score by assessing its location among a distribution of background alignment scores. The Gumbel parameters that describe this background distribution are usually pre-computed for a limited number of scoring systems, gap schemes, and sequence lengths and compositions. The use of such look-ups is known to introduce errors, which compromise the significance assessment of a remote homology relationship. One solution is to estimate the background distribution for each pair of interest by generating a large number of sequence shuffles and use the distribution of their scores to approximate the parameters of the underlying extreme value distribution. This is computationally very expensive, as a large number of shuffles are needed to precisely estimate the score statistics. RESULTS: Convergent Island Statistics (CIS) is a computationally efficient solution to the problem of calculating the Gumbel distribution parameters for an arbitrary pair of sequences and an arbitrary set of gap and scoring schemes. The basic idea behind our method is to recognize the lack of similarity for any pair of sequences early in the shuffling process and thus save on the search time. The method is particularly useful in the context of profile-profile alignment algorithms where the normalization of alignment scores has traditionally been a challenging task. CONTACT: aleksandar@eidogen.com SUPPLEMENTARY INFORMATION: http://www.eidogen-sertanty.com/Documents/convergent_island_stats_sup.pdf.     

A comparison of position-specific score matrices based on sequence and structure alignments

Sequence comparison methods based on position-specific score matrices (PSSMs) have proven a useful tool for recognition of the divergent members of a protein family and for annotation of functional sites. Here we investigate one of the factors that affects overall performance of PSSMs in a PSI-BLAST search, the algorithm used to construct the seed alignment upon which the PSSM is based. We compare PSSMs based on alignments constructed by global sequence similarity (ClustalW and ClustalW-pairwise), local sequence similarity (BLAST), and local structure similarity (VAST). To assess performance with respect to identification of conserved functional or structural sites, we examine the accuracy of the three-dimensional molecular models predicted by PSSM-sequence alignments. Using the known structures of those sequences as the standard of truth, we find that model accuracy varies with the algorithm used for seed alignment construction in the pattern local-structure (VAST) > local-sequence (BLAST) > global-sequence (ClustalW). Using structural similarity of query and database proteins as the standard of truth, we find that PSSM recognition sensitivity depends primarily on the diversity of the sequences included in the alignment, with an optimum around 30-50% average pairwise identity. We discuss these observations, and suggest a strategy for constructing seed alignments that optimize PSSM-sequence alignment accuracy and recognition sensitivity.     

Scoring profile-to-profile sequence alignments

Sequence alignment profiles have been shown to be very powerful in creating accurate sequence alignments. Profiles are often used to search a sequence database with a local alignment algorithm. More accurate and longer alignments have been obtained with profile-to-profile comparison. There are several steps that must be performed in creating profile-profile alignments, and each involves choices in parameters and algorithms. These steps include (1) what sequences to include in a multiple alignment used to build each profile, (2) how to weight similar sequences in the multiple alignment and how to determine amino acid frequencies from the weighted alignment, (3) how to score a column from one profile aligned to a column of the other profile, (4) how to score gaps in the profile-profile alignment, and (5) how to include structural information. Large-scale benchmarks consisting of pairs of homologous proteins with structurally determined sequence alignments are necessary for evaluating the efficacy of each scoring scheme. With such a benchmark, we have investigated the properties of profile-profile alignments and found that (1) with optimized gap penalties, most column-column scoring functions behave similarly to one another in alignment accuracy; (2) some functions, however, have much higher search sensitivity and specificity; (3) position-specific weighting schemes in determining amino acid counts in columns of multiple sequence alignments are better than sequence-specific schemes; (4) removing positions in the profile with gaps in the query sequence results in better alignments; and (5) adding predicted and known secondary structure information improves alignments.     

A scheme for multiple sequence alignment optimization—an improvement based on family representative mechanics features

As a basic tool of modern biology, sequence alignment can provide us useful information in fold, function, and active site of protein. For many cases, the increased quality of sequence alignment means a better performance. The motivation of present work is to increase ability of the existing scoring scheme/algorithm by considering residue-residue correlations better. Based on a coarse-grained approach, the hydrophobic force between each pair of residues is written out from protein sequence. It results in the construction of an intramolecular hydrophobic force network that describes the whole residue-residue interactions of each protein molecule, and characterizes protein's biological properties in the hydrophobic aspect. A former work has suggested that such network can characterize the top weighted feature regarding hydrophobicity. Moreover, for each homologous protein of a family, the corresponding network shares some common and representative family characters that eventually govern the conservation of biological properties during protein evolution. In present work, we score such family representative characters of a protein by the deviation of its intramolecular hydrophobic force network from that of background. Such score can assist the existing scoring schemes/algorithms, and boost up the ability of multiple sequences alignment, e.g. achieving a prominent increase (∼50%) in searching the structurally alike residue segments at a low identity level. As the theoretical basis is different, the present scheme can assist most existing algorithms, and improve their efficiency remarkably.     

An expectation maximization algorithm for training hidden substitution models

We derive an expectation maximization algorithm for maximum-likelihood training of substitution rate matrices from multiple sequence alignments. The algorithm can be used to train hidden substitution models, where the structural context of a residue is treated as a hidden variable that can evolve over time. We used the algorithm to train hidden substitution matrices on protein alignments in the Pfam database. Measuring the accuracy of multiple alignment algorithms with reference to BAliBASE (a database of structural reference alignments) our substitution matrices consistently outperform the PAM series, with the improvement steadily increasing as up to four hidden site classes are added. We discuss several applications of this algorithm in bioinformatics.     

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.     

Evolutionary HMMs: a Bayesian approach to multiple alignment

MOTIVATION: We review proposed syntheses of probabilistic sequence alignment, profiling and phylogeny. We develop a multiple alignment algorithm for Bayesian inference in the links model proposed by Thorne et al. (1991, J. Mol. Evol., 33, 114-124). The algorithm, described in detail in Section 3, samples from and/or maximizes the posterior distribution over multiple alignments for any number of DNA or protein sequences, conditioned on a phylogenetic tree. The individual sampling and maximization steps of the algorithm require no more computational resources than pairwise alignment. METHODS: We present a software implementation (Handel) of our algorithm and report test results on (i) simulated data sets and (ii) the structurally informed protein alignments of BAliBASE (Thompson et al., 1999, Nucleic Acids Res., 27, 2682-2690). RESULTS: We find that the mean sum-of-pairs score (a measure of residue-pair correspondence) for the BAliBASE alignments is only 13% lower for Handelthan for CLUSTALW(Thompson et al., 1994, Nucleic Acids Res., 22, 4673-4680), despite the relative simplicity of the links model (CLUSTALW uses affine gap scores and increased penalties for indels in hydrophobic regions). With reference to these benchmarks, we discuss potential improvements to the links model and implications for Bayesian multiple alignment and phylogenetic profiling. AVAILABILITY: The source code to Handelis freely distributed on the Internet at http://www.biowiki.org/Handel under the terms of the GNU Public License (GPL, 2000, http://www.fsf.org./copyleft/gpl.html).     

MatAlign: precise protein structure comparison by matrix alignment

We propose a detailed protein structure alignment method named "MatAlign". It is a two-step algorithm. Firstly, we represent 3D protein structures as 2D distance matrices, and align these matrices by means of dynamic programming in order to find the initially aligned residue pairs. Secondly, we refine the initial alignment iteratively into the optimal one according to an objective scoring function. We compare our method against DALI and CE, which are among the most accurate and the most widely used of the existing structural comparison tools. On the benchmark set of 68 protein structure pairs by Fischer et al., MatAlign provides better alignment results, according to four different criteria, than both DALI and CE in a majority of cases. MatAlign also performs as well in structural database search as DALI does, and much better than CE does. MatAlign is about two to three times faster than DALI, and has about the same speed as CE. The software and the supplementary information for this paper are available at http://xena1.ddns.comp.nus.edu.sg/~genesis/MatAlign/.     

Derivative-free neural network for optimizing the scoring functions associated with dynamic programming of pairwise-profile alignment

Background

A profile-comparison method with position-specific scoring matrix (PSSM) is among the most accurate alignment methods. Currently, cosine similarity and correlation coefficients are used as scoring functions of dynamic programming to calculate similarity between PSSMs. However, it is unclear whether these functions are optimal for profile alignment methods. By definition, these functions cannot capture nonlinear relationships between profiles. Therefore, we attempted to discover a novel scoring function, which was more suitable for the profile-comparison method than existing functions, using neural networks.

Results

Although neural networks required derivative-of-cost functions, the problem being addressed in this study lacked them. Therefore, we implemented a novel derivative-free neural network by combining a conventional neural network with an evolutionary strategy optimization method used as a solver. Using this novel neural network system, we optimized the scoring function to align remote sequence pairs. Our results showed that the pairwise-profile aligner using the novel scoring function significantly improved both alignment sensitivity and precision relative to aligners using existing functions.

Conclusions

We developed and implemented a novel derivative-free neural network and aligner (Nepal) for optimizing sequence alignments. Nepal improved alignment quality by adapting to remote sequence alignments and increasing the expressiveness of similarity scores. Additionally, this novel scoring function can be realized using a simple matrix operation and easily incorporated into other aligners. Moreover our scoring function could potentially improve the performance of homology detection and/or multiple-sequence alignment of remote homologous sequences. The goal of the study was to provide a novel scoring function for profile alignment method and develop a novel learning system capable of addressing derivative-free problems. Our system is capable of optimizing the performance of other sophisticated methods and solving problems without derivative-of-cost functions, which do not always exist in practical problems. Our results demonstrated the usefulness of this optimization method for derivative-free problems.