Sequence alignment with an appropriate substitution matrix.

A widely used algorithm for computing an optimal local alignment between two sequences requires a parameter set with a substitution matrix and gap penalties. It is recognized that a proper parameter set should be selected to suit the level of conservation between sequences. We describe an algorithm for selecting an appropriate substitution matrix at given gap penalties for computing an optimal local alignment between two sequences. In the algorithm, a substitution matrix that leads to the maximum alignment similarity score is selected among substitution matrices at various evolutionary distances. The evolutionary distance of the selected substitution matrix is defined as the distance of the computed alignment. To show the effects of gap penalties on alignments and their distances and help select appropriate gap penalties, alignments and their distances are computed at various gap penalties. The algorithm has been implemented as a computer program named SimDist. The SimDist program was compared with an existing local alignment program named SIM for finding reciprocally best-matching pairs (RBPs) of sequences in each of 100 protein families, where RBPs are commonly used as an operational definition of orthologous sequences. SimDist produced more accurate results than SIM on 50 of the 100 families, whereas both programs produced the same results on the other 50 families. SimDist was also used to compare three types of substitution matrices in scoring 444,461 pairs of homologous sequences from the 100 families.     

Optimization of a new score function for the generation of accurate alignments

The accuracy of the alignments of protein sequences depends on the score matrix and gap penalties used in performing the alignment. Most score functions are designed to find homologs in the various databases rather than to generate accurate alignments between known homologs. We describe the optimization of a score function for the purpose of generating accurate alignments, as evaluated by using a coordinate root-mean-square deviation (RMSD)-based merit function. We show that the resulting score matrix, which we call STROMA, generates more accurate alignments than other commonly used score matrices, and this difference is not due to differences in the gap penalties. In fact, in contrast to most of the other matrices, the alignment accuracies with STROMA are relatively insensitive to the choice of gap penalty parameters.     

SSALN: an alignment algorithm using structure-dependent substitution matrices and gap penalties learned from structurally aligned protein pairs

In template-based modeling of protein structures, the generation of the alignment between the target and the template is a critical step that significantly affects the accuracy of the final model. This paper proposes an alignment algorithm SSALN that learns substitution matrices and position-specific gap penalties from a database of structurally aligned protein pairs. In addition to the amino acid sequence information, secondary structure and solvent accessibility information of a position are used to derive substitution scores and position-specific gap penalties. In a test set of CASP5 targets, SSALN outperforms sequence alignment methods such as a Smith-Waterman algorithm with BLOSUM50 and PSI_BLAST. SSALN also generates better alignments than PSI_BLAST in the CASP6 test set. LOOPP server prediction based on an SSALN alignment is ranked the best for target T0280_1 in CASP6. SSALN is also compared with several threading methods and sequence alignment methods on the ProSup benchmark. SSALN has the highest alignment accuracy among the methods compared. On the Fischer's benchmark, SSALN performs better than CLUSTALW and GenTHREADER, and generates more alignments with accuracy >50%, >60% or >70% than FUGUE, but fewer alignments with accuracy >80% than FUGUE. All the supplemental materials can be found at http://www.cs.cornell.edu/ approximately jianq/research.htm.     

Empirical codon substitution matrix

Background  

Codon substitution probabilities are used in many types of molecular evolution studies such as determining Ka/Ks ratios, creating ancestral DNA sequences or aligning coding DNA. Until the recent dramatic increase in genomic data enabled construction of empirical matrices, researchers relied on parameterized models of codon evolution. Here we present the first empirical codon substitution matrix entirely built from alignments of coding sequences from vertebrate DNA and thus provide an alternative to parameterized models of codon evolution.     

A class frequency mixture model that adjusts for site-specific amino acid frequencies and improves inference of protein phylogeny

Background  

Widely used substitution models for proteins, such as the Jones-Taylor-Thornton (JTT) or Whelan and Goldman (WAG) models, are based on empirical amino acid interchange matrices estimated from databases of protein alignments that incorporate the average amino acid frequencies of the data set under examination (e.g JTT + F). Variation in the evolutionary process between sites is typically modelled by a rates-across-sites distribution such as the gamma (Γ) distribution. However, sites in proteins also vary in the kinds of amino acid interchanges that are favoured, a feature that is ignored by standard empirical substitution matrices. Here we examine the degree to which the pattern of evolution at sites differs from that expected based on empirical amino acid substitution models and evaluate the impact of these deviations on phylogenetic estimation.     

BALSA: Bayesian algorithm for local sequence alignment

The Smith–Waterman algorithm yields a single alignment, which, albeit optimal, can be strongly affected by the choice of the scoring matrix and the gap penalties. Additionally, the scores obtained are dependent upon the lengths of the aligned sequences, requiring a post-analysis conversion. To overcome some of these shortcomings, we developed a Bayesian algorithm for local sequence alignment (BALSA), that takes into account the uncertainty associated with all unknown variables by incorporating in its forward sums a series of scoring matrices, gap parameters and all possible alignments. The algorithm can return both the joint and the marginal optimal alignments, samples of alignments drawn from the posterior distribution and the posterior probabilities of gap penalties and scoring matrices. Furthermore, it automatically adjusts for variations in sequence lengths. BALSA was compared with SSEARCH, to date the best performing dynamic programming algorithm in the detection of structural neighbors. Using the SCOP databases PDB40D-B and PDB90D-B, BALSA detected 19.8 and 41.3% of remote homologs whereas SSEARCH detected 18.4 and 38% at an error rate of 1% errors per query over the databases, respectively.     

CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice.

The sensitivity of the commonly used progressive multiple sequence alignment method has been greatly improved for the alignment of divergent protein sequences. Firstly, individual weights are assigned to each sequence in a partial alignment in order to down-weight near-duplicate sequences and up-weight the most divergent ones. Secondly, amino acid substitution matrices are varied at different alignment stages according to the divergence of the sequences to be aligned. Thirdly, residue-specific gap penalties and locally reduced gap penalties in hydrophilic regions encourage new gaps in potential loop regions rather than regular secondary structure. Fourthly, positions in early alignments where gaps have been opened receive locally reduced gap penalties to encourage the opening up of new gaps at these positions. These modifications are incorporated into a new program, CLUSTAL W which is freely available.     

Empirical determination of effective gap penalties for sequence comparison

MOTIVATION: No general theory guides the selection of gap penalties for local sequence alignment. We empirically determined the most effective gap penalties for protein sequence similarity searches with substitution matrices over a range of target evolutionary distances from 20 to 200 Point Accepted Mutations (PAMs). RESULTS: We embedded real and simulated homologs of protein sequences into a database and searched the database to determine the gap penalties that produced the best statistical significance for the distant homologs. The most effective penalty for the first residue in a gap (q+r) changes as a function of evolutionary distance, while the gap extension penalty for additional residues (r) does not. For these data, the optimal gap penalties for a given matrix scaled in 1/3 bit units (e.g. BLOSUM50, PAM200) are q=25-0.1 * (target PAM distance), r=5. Our results provide an empirical basis for selection of gap penalties and demonstrate how optimal gap penalties behave as a function of the target evolutionary distance of the substitution matrix. These gap penalties can improve expectation values by at least one order of magnitude when searching with short sequences, and improve the alignment of proteins containing short sequences repeated in tandem.     

Alignment of Helical Membrane Protein Sequences Using AlignMe

Few sequence alignment methods have been designed specifically for integral membrane proteins, even though these important proteins have distinct evolutionary and structural properties that might affect their alignments. Existing approaches typically consider membrane-related information either by using membrane-specific substitution matrices or by assigning distinct penalties for gap creation in transmembrane and non-transmembrane regions. Here, we ask whether favoring matching of predicted transmembrane segments within a standard dynamic programming algorithm can improve the accuracy of pairwise membrane protein sequence alignments. We tested various strategies using a specifically designed program called AlignMe. An updated set of homologous membrane protein structures, called HOMEP2, was used as a reference for optimizing the gap penalties. The best of the membrane-protein optimized approaches were then tested on an independent reference set of membrane protein sequence alignments from the BAliBASE collection. When secondary structure (S) matching was combined with evolutionary information (using a position-specific substitution matrix (P)), in an approach we called AlignMePS, the resultant pairwise alignments were typically among the most accurate over a broad range of sequence similarities when compared to available methods. Matching transmembrane predictions (T), in addition to evolutionary information, and secondary-structure predictions, in an approach called AlignMePST, generally reduces the accuracy of the alignments of closely-related proteins in the BAliBASE set relative to AlignMePS, but may be useful in cases of extremely distantly related proteins for which sequence information is less informative. The open source AlignMe code is available at https://sourceforge.net/projects/alignme/, and at http://www.forrestlab.org, along with an online server and the HOMEP2 data set.     

Comparing sequences without using alignments: application to HIV/SIV subtyping

Background  

In general, the construction of trees is based on sequence alignments. This procedure, however, leads to loss of informationwhen parts of sequence alignments (for instance ambiguous regions) are deleted before tree building. To overcome this difficulty, one of us previously introduced a new and rapid algorithm that calculates dissimilarity matrices between sequences without preliminary alignment.     

Statistical distributions of optimal global alignment scores of random protein sequences

Background  

The inference of homology from statistically significant sequence similarity is a central issue in sequence alignments. So far the statistical distribution function underlying the optimal global alignments has not been completely determined.     

Local sequence alignments with monotonic gap penalties.

MOTIVATION: Sequence alignments obtained using affine gap penalties are not always biologically correct, because the insertion of long gaps is over-penalised. There is a need for an efficient algorithm which can find local alignments using non-linear gap penalties. RESULTS: A dynamic programming algorithm is described which computes optimal local sequence alignments for arbitrary, monotonically increasing gap penalties, i.e. where the cost g(k) of inserting a gap of k symbols is such that g(k) >/= g(k-1). The running time of the algorithm is dependent on the scoring scheme; if the expected score of an alignment between random, unrelated sequences of lengths m, n is proportional to log mn, then with one exception, the algorithm has expected running time O(mn). Elsewhere, the running time is no greater than O(mn(m+n)). Optimisations are described which appear to reduce the worst-case run-time to O(mn) in many cases. We show how using a non-affine gap penalty can dramatically increase the probability of detecting a similarity containing a long gap. AVAILABILITY: The source code is available to academic collaborators under licence.     

<Emphasis Type="Italic">Scoredist</Emphasis>: A simple and robust protein sequence distance estimator

Background  

Distance-based methods are popular for reconstructing evolutionary trees thanks to their speed and generality. A number of methods exist for estimating distances from sequence alignments, which often involves some sort of correction for multiple substitutions. The problem is to accurately estimate the number of true substitutions given an observed alignment. So far, the most accurate protein distance estimators have looked for the optimal matrix in a series of transition probability matrices, e.g. the Dayhoff series. The evolutionary distance between two aligned sequences is here estimated as the evolutionary distance of the optimal matrix. The optimal matrix can be found either by an iterative search for the Maximum Likelihood matrix, or by integration to find the Expected Distance. As a consequence, these methods are more complex to implement and computationally heavier than correction-based methods. Another problem is that the result may vary substantially depending on the evolutionary model used for the matrices. An ideal distance estimator should produce consistent and accurate distances independent of the evolutionary model used.     

Improving pairwise sequence alignment accuracy using near-optimal protein sequence alignments

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.     

Contact-based sequence alignment

This paper introduces the novel method of contact-based protein sequence alignment, where structural information in the form of contact mutation probabilities is incorporated into an alignment routine using contact-mutation matrices (CAO: Contact Accepted mutatiOn). The contact-based alignment routine optimizes the score of matched contacts, which involves four (two per contact) instead of two residues per match in pairwise alignments. The first contact refers to a real side-chain contact in a template sequence with known structure, and the second contact is the equivalent putative contact of a homologous query sequence with unknown structure. An algorithm has been devised to perform a pairwise sequence alignment based on contact information. The contact scores were combined with PAM-type (Point Accepted Mutation) substitution scores after parameterization of gap penalties and score weights by means of a genetic algorithm. We show that owing to the structural information contained in the CAO matrices, significantly improved alignments of distantly related sequences can be obtained. This has allowed us to annotate eight putative Drosophila IGF sequences. Contact-based sequence alignment should therefore prove useful in comparative modelling and fold recognition.     

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.     

SABERTOOTH: protein structural alignment based on a vectorial structure representation

Background  

The task of computing highly accurate structural alignments of proteins in very short computation time is still challenging. This is partly due to the complexity of protein structures. Therefore, instead of manipulating coordinates directly, matrices of inter-atomic distances, sets of vectors between protein backbone atoms, and other reduced representations are used. These decrease the effort of comparing large sets of coordinates, but protein structural alignment still remains computationally expensive.     

Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail

Background  

The optimal score for ungapped local alignments of infinitely long random sequences is known to follow a Gumbel extreme value distribution. Less is known about the important case, where gaps are allowed. For this case, the distribution is only known empirically in the high-probability region, which is biologically less relevant.