Increasing the accuracy of the global alignment of amino acid sequences by constructing a set of alignment candidates

The accuracy of the global Smith-Waterman alignments and Pareto-optimal alignments depending on the degree of sequence similarity (percent of coincidence, % id, and the number of remote fragments NGap) has been examined. An algorithm for constructing a set of three to six alignments has been developed of which the accuracy of the best alignment exceeds on the average the accuracy of the best alignment that can be constructed using the Smith-Waterman algorithm. For weakly homologous sequences (% id 15, NGap 20), the increase in the accuracy is on the average about 8%, with the average accuracy of the global Smith-Waterman alignments being about 38% (the accuracy was estimated on model test sets).     

ReformAlign: improved multiple sequence alignments using a profile-based meta-alignment approach

Background

Obtaining an accurate sequence alignment is fundamental for consistently analyzing biological data. Although this problem may be efficiently solved when only two sequences are considered, the exact inference of the optimal alignment easily gets computationally intractable for the multiple sequence alignment case. To cope with the high computational expenses, approximate heuristic methods have been proposed that address the problem indirectly by progressively aligning the sequences in pairs according to their relatedness. These methods however are not flexible to change the alignment of an already aligned group of sequences in the view of new data, resulting thus in compromises on the quality of the deriving alignment. In this paper we present ReformAlign, a novel meta-alignment approach that may significantly improve on the quality of the deriving alignments from popular aligners. We call ReformAlign a meta-aligner as it requires an initial alignment, for which a variety of alignment programs can be used. The main idea behind ReformAlign is quite straightforward: at first, an existing alignment is used to construct a standard profile which summarizes the initial alignment and then all sequences are individually re-aligned against the formed profile. From each sequence-profile comparison, the alignment of each sequence against the profile is recorded and the final alignment is indirectly inferred by merging all the individual sub-alignments into a unified set. The employment of ReformAlign may often result in alignments which are significantly more accurate than the starting alignments.

Results

We evaluated the effect of ReformAlign on the generated alignments from ten leading alignment methods using real data of variable size and sequence identity. The experimental results suggest that the proposed meta-aligner approach may often lead to statistically significant more accurate alignments. Furthermore, we show that ReformAlign results in more substantial improvement in cases where the starting alignment is of relatively inferior quality or when the input sequences are harder to align.

Conclusions

The proposed profile-based meta-alignment approach seems to be a promising and computationally efficient method that can be combined with practically all popular alignment methods and may lead to significant improvements in the generated alignments.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-265) contains supplementary material, which is available to authorized users.     

Increasing the accuracy of global alignment of amino acid sequences by constructing a set of alignment candidates

The accuracy of global Smith-Waterman alignments and Pareto-optimal alignments depending on the degree of sequence similarity (percent of coincidence, %id, and the number of removed fragments NGap) has been examined. An algorithm for constructing a set of three to six alignments has been developed of which the best alignment on the average exceeds in accuracy the best alignment that can be constructed using the Smith-Waterman algorithm. For weakly homologous sequences (%id 15, NGap 20), the increase in accuracy is on the average about 8%, with the average accuracy of the global Smith-Waterman alignments being about 38% (the accuracy was estimated on model test sets).     

PALMA: mRNA to genome alignments using large margin algorithms

MOTIVATION: Despite many years of research on how to properly align sequences in the presence of sequencing errors, alternative splicing and micro-exons, the correct alignment of mRNA sequences to genomic DNA is still a challenging task. RESULTS: We present a novel approach based on large margin learning that combines accurate splice site predictions with common sequence alignment techniques. By solving a convex optimization problem, our algorithm-called PALMA-tunes the parameters of the model such that true alignments score higher than other alignments. We study the accuracy of alignments of mRNAs containing artificially generated micro-exons to genomic DNA. In a carefully designed experiment, we show that our algorithm accurately identifies the intron boundaries as well as boundaries of the optimal local alignment. It outperforms all other methods: for 5702 artificially shortened EST sequences from Caenorhabditis elegans and human, it correctly identifies the intron boundaries in all except two cases. The best other method is a recently proposed method called exalin which misaligns 37 of the sequences. Our method also demonstrates robustness to mutations, insertions and deletions, retaining accuracy even at high noise levels. AVAILABILITY: Datasets for training, evaluation and testing, additional results and a stand-alone alignment tool implemented in C++ and python are available at http://www.fml.mpg.de/raetsch/projects/palma     

Optimal sum-of-pairs multiple sequence alignment using incremental Carrillo and Lipman bounds.

Alignment of sequences is an important routine in various areas of science, notably molecular biology. Multiple sequence alignment is a computationally hard optimization problem which involves the consideration of different possible alignments in order to find an optimal one, given a measure of goodness of alignments. Dynamic programming algorithms are generally well suited for the search of optimal alignments, but are constrained by unwieldy space requirements for large numbers of sequences. Carrillo and Lipman devised a method that helps to reduce the search space for an optimal alignment under a sum-of-pairs measure using bounds on the scores of its pairwise projections. In this paper, we generalize Carrillo and Lipman bounds and demonstrate a novel approach for finding optimal sum-of-pairs multiple alignments that allows incremental pruning of the optimal alignment search space. This approach can result in a drastic pruning of the final search space polytope (where we search for the optimal alignment) when compared to Carrillo and Lipman's approach and hence allows many runs that are not feasible with the original method.     

Aligning amino acid sequences: comparison of commonly used methods

We examined two extensive families of protein sequences using four different alignment schemes that employ various degrees of "weighting" in order to determine which approach is most sensitive in establishing relationships. All alignments used a similarity approach based on a general algorithm devised by Needleman and Wunsch. The approaches included a simple program, UM (unitary matrix), whereby only identities are scored; a scheme in which the genetic code is used as a basis for weighting (GC); another that employs a matrix based on structural similarity of amino acids taken together with the genetic basis of mutation (SG); and a fourth that uses the empirical log-odds matrix (LOM) developed by Dayhoff on the basis of observed amino acid replacements. The two sequence families examined were (a) nine different globins and (b) nine different tyrosine kinase-like proteins. It was assumed a priori that all members of a family share common ancestry. In cases where two sequences were more than 30% identical, alignments by all four methods were almost always the same. In cases where the percentage identity was less than 20%, however, there were often significant differences in the alignments. On the average, the Dayhoff LOM approach was the most effective in verifying distant relationships, as judged by an empirical "jumbling test." This was not universally the case, however, and in some instances the simple UM was actually as good or better. Trees constructed on the basis of the various alignments differed with regard to their limb lengths, but had essentially the same branching orders. We suggest some reasons for the different effectivenesses of the four approaches in the two different sequence settings, and offer some rules of thumb for assessing the significance of sequence relationships.     

Towards an automatic method of predicting protein structure by homology: an evaluation of suboptimal sequence alignments.

A major problem in predicting protein structure by homology modelling is that the sequence alignment from which the model is built may not be the best one in terms of the correct equivalencing of residues assessed by structural or functional criteria. A useful strategy is to generate and examine a number of suboptimal alignments as better alignments can often be found away from the optimal. A procedure to filter rapidly suboptimal alignments based on measurement of core volumes and packing pair potentials is investigated. The approach is benchmarked on three pairs of sequences which are non-trivial to align correctly, namely two immunoglobulin domains, plastocyanin with azurin and two distant globin sequences. It is shown to be useful to reduce a large ensemble of possible alignments down to a few which correspond more closely to the correct (structure based) alignment.     

Suboptimal sequence alignment in molecular biology. Alignment with error analysis

A molecular sequence alignment algorithm based on dynamic programming has been extended to allow the computation of all pairs of residues that can be part of optimal and suboptimal sequence alignments. The uncertainties inherent in sequence alignment can be displayed using a new form of dot plot. The method allows the qualitative assessment of whether or not two sequences are related, and can reveal what parts of the alignment are better determined than others. It also permits the computation of representative optimal and suboptimal alignments. The relation between alignment reliability and alignment parameters is discussed. Other applications are to cyclical permutations of sequences and the detection of self-similarity. An application to multiple sequence alignment is noted.     

A strategy for the rapid multiple alignment of protein sequences. Confidence levels from tertiary structure comparisons

An algorithm is presented for the multiple alignment of protein sequences that is both accurate and rapid computationally. The approach is based on the conventional dynamic-programming method of pairwise alignment. Initially, two sequences are aligned, then the third sequence is aligned against the alignment of both sequences one and two. Similarly, the fourth sequence is aligned against one, two and three. This is repeated until all sequences have been aligned. Iteration is then performed to yield a final alignment. The accuracy of sequence alignment is evaluated from alignment of the secondary structures in a family of proteins. For the globins, the multiple alignment was on average 99% accurate compared to 90% for pairwise comparison of sequences. For the alignment of immunoglobulin constant and variable domains, the use of many sequences yielded an alignment of 63% average accuracy compared to 41% average for individual variable/constant alignments. The multiple alignment algorithm yields an assignment of disulphide connectivity in mammalian serotransferrin that is consistent with crystallographic data, whereas pairwise alignments give an alternative assignment.     

Learning scoring schemes for sequence alignment from partial examples

When aligning biological sequences, the choice of parameter values for the alignment scoring function is critical. Small changes in gap penalties, for example, can yield radically different alignments. A rigorous way to compute parameter values that are appropriate for aligning biological sequences is through inverse parametric sequence alignment. Given a collection of examples of biologically correct alignments, this is the problem of finding parameter values that make the scores of the example alignments close to those of optimal alignments for their sequences. We extend prior work on inverse parametric alignment to partial examples, which contain regions where the alignment is left unspecified, and to an improved formulation based on minimizing the average error between the score of an example and the score of an optimal alignment. Experiments on benchmark biological alignments show we can find parameters that generalize across protein families and that boost the accuracy of multiple sequence alignment by as much as 25%.     

Reconstruction of genuine pair-wise sequence alignment.

In many applications, the algorithmically obtained alignment ideally should restore the "golden standard" (GS) alignment, which superimposes positions originating from the same position of the common ancestor of the compared sequences. The average similarity between the algorithmically obtained and GS alignments ("the quality") is an important characteristic of an alignment algorithm. We proposed to determine the quality of an algorithm, using sequences that were artificially generated in accordance with an appropriate evolution model; the approach was applied to the global version of the Smith-Waterman algorithm (SWA). The quality of SWA is between 97% (for a PAM distance of 60) and 70% (for a PAM distance of 300). The percentage of identical aligned residues is the same for algorithmic and GS alignments. The total length of indels in algorithmic alignments is less than in the GS-mainly due to a substantial decrease in the number of indels in algorithmic alignments.     

Heads or tails: a simple reliability check for multiple sequence alignments

The question of multiple sequence alignment quality has received much attention from developers of alignment methods. Less forthcoming, however, are practical measures for addressing alignment quality issues in real life settings. Here, we present a simple methodology to help identify and quantify the uncertainties in multiple sequence alignments and their effects on subsequent analyses. The proposed methodology is based upon the a priori expectation that sequence alignment results should be independent of the orientation of the input sequences. Thus, for totally unambiguous cases, reversing residue order prior to alignment should yield an exact reversed alignment of that obtained by using the unreversed sequences. Such "ideal" alignments, however, are the exception in real life settings, and the two alignments, which we term the heads and tails alignments, are usually different to a greater or lesser degree. The degree of agreement or discrepancy between these two alignments may be used to assess the reliability of the sequence alignment. Furthermore, any alignment dependent sequence analysis protocol can be carried out separately for each of the two alignments, and the two sets of results may be compared with each other, providing us with valuable information regarding the robustness of the whole analytical process. The heads-or-tails (HoT) methodology can be easily implemented for any choice of alignment method and for any subsequent analytical protocol. We demonstrate the utility of HoT for phylogenetic reconstruction for the case of 130 sequences belonging to the chemoreceptor superfamily in Drosophila melanogaster, and by analysis of the BaliBASE alignment database. Surprisingly, Neighbor-Joining methods of phylogenetic reconstruction turned out to be less affected by alignment errors than maximum likelihood and Bayesian methods.     

Optimal classification of protein sequences and selection of representative sets from multiple alignments: application to homologous families and lessons for structural genomics

Hierarchical classification is probably the most popular approach to group related proteins. However, there are a number of problems associated with its use for this purpose. One is that the resulting tree showing a nested sequence of groups may not be the most suitable representation of the data. Another is that visual inspection is the most common method to decide the most appropriate number of subsets from a tree. In fact, classification of proteins in general is bedevilled with the need for subjective thresholds to define group membership (e.g., 'significant' sequence identity for homologous families). Such arbitrariness is not only intellectually unsatisfying but also has important practical consequences. For instance, it hinders meaningful identification of protein targets for structural genomics. I describe an alternative approach to cluster related proteins without the need for an a priori threshold: one, through its use of dynamic programming, which is guaranteed to produce globally optimal solutions at all levels of partition granularity. Grouping proteins according to weights assigned to their aligned sequences makes it possible to delineate dynamically a 'core-periphery' structure within families. The 'core' of a protein family comprises the most typical sequences while the 'periphery' consists of the atypical ones. Further, a new sequence weighting scheme that combines the information in all the multiply aligned positions of an alignment in a novel way is put forward. Instead of averaging over all positions, this procedure takes into account directly the distribution of sequence variability along an alignment. The relationships between sequence weights and sequence identity are investigated for 168 families taken from HOMSTRAD, a database of protein structure alignments for homologous families. An exact solution is presented for the problem of how to select the most representative pair of sequences for a protein family. Extension of this approach by a greedy algorithm allows automatic identification of a minimal set of aligned sequences. The results of this analysis are available on the Web at http://mathbio.nimr.mrc.ac.uk/~amay.     

A polynomial time solvable formulation of multiple sequence alignment.

Since traditional multiple alignment formulations are NP-hard, heuristics are commonly employed to find acceptable alignments with no guaranteed performance bound. This causes a substantial difficulty in understanding what the resulting alignment means and in assessing the quality of these alignments. We propose an alternative formulation of multiple alignment based on the idea of finding a multiple alignment of k sequences which preserves k - 1 pairwise alignments as specified by edges of a given tree. Although it is well known that such a preserving alignment always exists, it did not become a mainstream method for multiple alignment since it seems that a lot of information is lost from ignoring pairwise similarities outside the tree. In contrast, by using pairwise alignments that incorporate consistency information from other sequences, we show that it is possible to obtain very good accuracy with the preserving alignment formulation. We show that a reasonable objective function to use is to find the shortest preserving alignment, and, by a reduction to a graph-theoretic problem, that the problem of finding the shortest preserving multiple alignment can be solved in polynomial time. We demonstrate the success of this approach on three sets of benchmark multiple alignments by using consistency-based pairwise alignments from the first stage of two of the best performing progressive alignment algorithms TCoffee and ProbCons and replace the second heuristic progressive step of these algorithms by the exact preserving alignment step. We apply this strategy to TCoffee and show that our approach outperforms TCoffee on two of the three test sets. We apply the strategy to a variant of ProbCons with no iterative refinements and show that our approach achieves similar or better accuracy except on one test set. We also compare our performance to ProbCons with iterative refinements and show that our approach achieves similar or better accuracy on many subcategories even without further refinements. The most important advantage of the preserving alignment formulation is that we are certain that we can solve the problem in polynomial time without using a heuristic. A software program implementing this approach (PSAlign) is available at http://faculty.cs.tamu.edu/shsze/psalign.     

A pairwise alignment algorithm which favors clusters of blocks.

Pairwise sequence alignments aim to decide whether two sequences are related and, if so, to exhibit their related domains. Recent works have pointed out that a significant number of true homologous sequences are missed when using classical comparison algorithms. This is the case when two homologous sequences share several little blocks of homology, too small to lead to a significant score. On the other hand, classical alignment algorithms, when detecting homologies, may fail to recognize all the significant biological signals. The aim of the paper is to give a solution to these two problems. We propose a new scoring method which tends to increase the score of an alignment when "blocks" are detected. This so-called Block-Scoring algorithm, which makes use of dynamic programming, is worth being used as a complementary tool to classical exact alignments methods. We validate our approach by applying it on a large set of biological data. Finally, we give a limit theorem for the score statistics of the algorithm.     

A method for the simultaneous alignment of three or more amino acid sequences

Summary We describe an algorithm for the concurrent comparison of three or more amino acid sequences. The basis of the approach is a progressive evaluation of selected segments from each sequence. Only a small subset of all possible segments from each sequence is compared, and a minimum of information is retained for the trace-back of the alignment. As a result, this method has the advantage of being both rapid and minimally consumptive of computer memory when constructing an alignment. This being the case, there are no practical limits on the length of sequences that may be aligned. A computer program for the alignment of three sequences is described, and this method is compared with two three-sequence extensions of the Needleman and Wunsch variety, including a recently published approach. In addition, we have made simultaneous alignments of sets of four and five sequences with this selected-segment method.     

Using structure to explore the sequence alignment space of remote homologs

Protein structure modeling by homology requires an accurate sequence alignment between the query protein and its structural template. However, sequence alignment methods based on dynamic programming (DP) are typically unable to generate accurate alignments for remote sequence homologs, thus limiting the applicability of modeling methods. A central problem is that the alignment that is "optimal" in terms of the DP score does not necessarily correspond to the alignment that produces the most accurate structural model. That is, the correct alignment based on structural superposition will generally have a lower score than the optimal alignment obtained from sequence. Variations of the DP algorithm have been developed that generate alternative alignments that are "suboptimal" in terms of the DP score, but these still encounter difficulties in detecting the correct structural alignment. We present here a new alternative sequence alignment method that relies heavily on the structure of the template. By initially aligning the query sequence to individual fragments in secondary structure elements and combining high-scoring fragments that pass basic tests for "modelability", we can generate accurate alignments within a small ensemble. Our results suggest that the set of sequences that can currently be modeled by homology can be greatly extended.     

Gap costs for multiple sequence alignment

Standard methods for aligning pairs of biological sequences charge for the most common mutations, which are substitutions, deletions and insertions. Because a single mutation may insert or delete several nucleotides, gap costs that are not directly proportional to gap length are usually the most effective. How to extend such gap costs to alignments of three or more sequences is not immediately obvious, and a variety of approaches have been taken. This paper argues that, since gap and substitution costs together specify optimal alignments, they should be defined using a common rationale. Specifically, a new definition of gap costs for multiple alignments is proposed and compared with previous ones. Since the new definition links a multiple alignment's cost to that of its pairwise projections, it allows knowledge gained about two-sequence alignments to bear on the multiple alignment problem. Also, such linkage is a key element of recent algorithms that have rendered practical the simultaneous alignment of as many as six sequences.     

Efficient methods for multiple sequence alignment with guaranteed error bounds

Multiple string (sequence) alignment is a difficult and important problem in computational biology, where it is central in two related tasks: finding highly conserved subregions or embedded patterns of a set of biological sequences (strings of DNA, RNA or amino acids), and inferring the evolutionary history of a set of taxa from their associated biological sequences. Several precise measures have been proposed for evaluating the goodness of a multiple alignment, but no efficient methods are known which compute the optimal alignment for any of these measures in any but small cases. In this paper, we consider two previously proposed measures, and given two computationaly efficient multiple alignment methods (one for each measure) whose deviation from the optimal value isguaranteed to be less than a factor of two. This is the novel feature of these methods, but the methods have additional virtues as well. For both methods, the guaranteed bounds are much smaller than two when the number of strings is small (1.33 for three strings of any length); for one of the methods we give a related randomized method which is much faster and which gives, with high probability, multiple alignments with fairly small error bounds; and for the other measure, the method given yields a non-obviouslower bound on the value of the optimal alignment.