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.     

An iterative method for faster sum-of-pairs multiple sequence alignment

MOTIVATION: Multiple sequence alignment is an important tool in computational biology. In order to solve the task of computing multiple alignments in affordable time, the most commonly used multiple alignment methods have to use heuristics. Nevertheless, the computation of optimal multiple alignments is important in its own right, and it provides a means of evaluating heuristic approaches or serves as a subprocedure of heuristic alignment methods. RESULTS: We present an algorithm that uses the divide-and-conquer alignment approach together with recent results on search space reduction to speed up the computation of multiple sequence alignments. The method is adaptive in that depending on the time one wants to spend on the alignment, a better, up to optimal alignment can be obtained. To speed up the computation in the optimal alignment step, we apply the alpha(*) algorithm which leads to a procedure provably more efficient than previous exact algorithms. We also describe our implementation of the algorithm and present results showing the effectiveness and limitations of the procedure.     

Multiple protein structure alignment.

A method was developed to compare protein structures and to combine them into a multiple structure consensus. Previous methods of multiple structure comparison have only concatenated pairwise alignments or produced a consensus structure by averaging coordinate sets. The current method is a fusion of the fast structure comparison program SSAP and the multiple sequence alignment program MULTAL. As in MULTAL, structures are progressively combined, producing intermediate consensus structures that are compared directly to each other and all remaining single structures. This leads to a hierarchic "condensation," continually evaluated in the light of the emerging conserved core regions. Following the SSAP approach, all interatomic vectors were retained with well-conserved regions distinguished by coherent vector bundles (the structural equivalent of a conserved sequence position). Each bundle of vectors is summarized by a resultant, whereas vector coherence is captured in an error term, which is the only distinction between conserved and variable positions. Resultant vectors are used directly in the comparison, which is weighted by their error values, giving greater importance to the matching of conserved positions. The resultant vectors and their errors can also be used directly in molecular modeling. Applications of the method were assessed by the quality of the resulting sequence alignments, phylogenetic tree construction, and databank scanning with the consensus. Visual assessment of the structural superpositions and consensus structure for various well-characterized families confirmed that the consensus had identified a reasonable core.     

Matt: local flexibility aids protein multiple structure alignment

Even when there is agreement on what measure a protein multiple structure alignment should be optimizing, finding the optimal alignment is computationally prohibitive. One approach used by many previous methods is aligned fragment pair chaining, where short structural fragments from all the proteins are aligned against each other optimally, and the final alignment chains these together in geometrically consistent ways. Ye and Godzik have recently suggested that adding geometric flexibility may help better model protein structures in a variety of contexts. We introduce the program Matt (Multiple Alignment with Translations and Twists), an aligned fragment pair chaining algorithm that, in intermediate steps, allows local flexibility between fragments: small translations and rotations are temporarily allowed to bring sets of aligned fragments closer, even if they are physically impossible under rigid body transformations. After a dynamic programming assembly guided by these “bent” alignments, geometric consistency is restored in the final step before the alignment is output. Matt is tested against other recent multiple protein structure alignment programs on the popular Homstrad and SABmark benchmark datasets. Matt's global performance is competitive with the other programs on Homstrad, but outperforms the other programs on SABmark, a benchmark of multiple structure alignments of proteins with more distant homology. On both datasets, Matt demonstrates an ability to better align the ends of α-helices and β-strands, an important characteristic of any structure alignment program intended to help construct a structural template library for threading approaches to the inverse protein-folding problem. The related question of whether Matt alignments can be used to distinguish distantly homologous structure pairs from pairs of proteins that are not homologous is also considered. For this purpose, a p-value score based on the length of the common core and average root mean squared deviation (RMSD) of Matt alignments is shown to largely separate decoys from homologous protein structures in the SABmark benchmark dataset. We postulate that Matt's strong performance comes from its ability to model proteins in different conformational states and, perhaps even more important, its ability to model backbone distortions in more distantly related proteins.     

Grammar-based distance in progressive multiple sequence alignment

Background  

We propose a multiple sequence alignment (MSA) algorithm and compare the alignment-quality and execution-time of the proposed algorithm with that of existing algorithms. The proposed progressive alignment algorithm uses a grammar-based distance metric to determine the order in which biological sequences are to be pairwise aligned. The progressive alignment occurs via pairwise aligning new sequences with an ensemble of the sequences previously aligned.     

Protein local structure alignment under the discrete Fréchet distance.

Protein structure alignment is a fundamental problem in computational and structural biology. While there has been lots of experimental/heuristic methods and empirical results, very few results are known regarding the algorithmic/complexity aspects of the problem, especially on protein local structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the famous Fréchet distance, and with the application of protein-related research, a related discrete Fréchet distance has been used recently. In this paper, following the recent work of Jiang et al. we investigate the protein local structural alignment problem using bounded discrete Fréchet distance. Given m proteins (or protein backbones, which are 3D polygonal chains), each of length O(n), our main results are summarized as follows: * If the number of proteins, m, is not part of the input, then the problem is NP-complete; moreover, under bounded discrete Fréchet distance it is NP-hard to approximate the maximum size common local structure within a factor of n(1-epsilon). These results hold both when all the proteins are static and when translation/rotation are allowed. * If the number of proteins, m, is a constant, then there is a polynomial time solution for the problem.     

Improving the accuracy of protein secondary structure prediction using structural alignment

Background  

The accuracy of protein secondary structure prediction has steadily improved over the past 30 years. Now many secondary structure prediction methods routinely achieve an accuracy (Q3) of about 75%. We believe this accuracy could be further improved by including structure (as opposed to sequence) database comparisons as part of the prediction process. Indeed, given the large size of the Protein Data Bank (>35,000 sequences), the probability of a newly identified sequence having a structural homologue is actually quite high.     

Evaluation of protein multiple alignments by SAM-T99 using the BAliBASE multiple alignment test set

MOTIVATION: SAM-T99 is an iterative hidden Markov model-based method for finding proteins similar to a single target sequence and aligning them. One of its main uses is to produce multiple alignments of homologs of the target sequence. Previous tests of SAM-T99 and its predecessors have concentrated on the quality of the searches performed, not on the quality of the multiple alignment. In this paper we report on tests of multiple alignment quality, comparing SAM-T99 to the standard multiple aligner, CLUSTALW. RESULTS: The paper evaluates the multiple-alignment aspect of the SAM-T99 protocol, using the BAliBASE benchmark alignment database. On these benchmarks, SAM-T99 is comparable in accuracy with ClustalW. AVAILABILITY: The SAM-T99 protocol can be run on the web at http://www.cse.ucsc.edu/research/compbio/HMM-apps/T99-query.html and the alignment tune-up option described here can be run at http://www.cse.ucsc.edu/research/compbio/HMM-apps/T99-tuneup.html. The protocol is also part of the standard SAM suite of tools. http://www.cse.ucsc.edu/research/compbio/sam/     

MSACompro: protein multiple sequence alignment using predicted secondary structure, solvent accessibility, and residue-residue contacts

Background

Estimation of allele frequency is of fundamental importance in population genetic analyses and in association mapping. In most studies using next-generation sequencing, a cost effective approach is to use medium or low-coverage data (e.g., < 15X). However, SNP calling and allele frequency estimation in such studies is associated with substantial statistical uncertainty because of varying coverage and high error rates.

Results

We evaluate a new maximum likelihood method for estimating allele frequencies in low and medium coverage next-generation sequencing data. The method is based on integrating over uncertainty in the data for each individual rather than first calling genotypes. This method can be applied to directly test for associations in case/control studies. We use simulations to compare the likelihood method to methods based on genotype calling, and show that the likelihood method outperforms the genotype calling methods in terms of: (1) accuracy of allele frequency estimation, (2) accuracy of the estimation of the distribution of allele frequencies across neutrally evolving sites, and (3) statistical power in association mapping studies. Using real re-sequencing data from 200 individuals obtained from an exon-capture experiment, we show that the patterns observed in the simulations are also found in real data.

Conclusions

Overall, our results suggest that association mapping and estimation of allele frequencies should not be based on genotype calling in low to medium coverage data. Furthermore, if genotype calling methods are used, it is usually better not to filter genotypes based on the call confidence score.     

A parameterized algorithm for protein structure alignment.

This paper proposes a parameterized polynomial time approximation scheme (PTAS) for aligning two protein structures, in the case where one protein structure is represented by a contact map graph and the other by a contact map graph or a distance matrix. If the sequential order of alignment is not required, the time complexity is polynomial in the protein size and exponential with respect to two parameters D(u)/D(l) and D(c)/D(l), which usually can be treated as constants. In particular, D(u) is the distance threshold determining if two residues are in contact or not, D(c) is the maximally allowed distance between two matched residues after two proteins are superimposed, and D(l) is the minimum inter-residue distance in a typical protein. This result clearly demonstrates that the computational hardness of the contact map based protein structure alignment problem is related not to protein size but to several parameters modeling the problem. The result is achieved by decomposing the protein structure using tree decomposition and discretizing the rigid-body transformation space. Preliminary experimental results indicate that on a Linux PC, it takes from ten minutes to one hour to align two proteins with approximately 100 residues.     

Fast structure alignment for protein databank searching.

A fast method is described for searching and analyzing the protein structure databank. It uses secondary structure followed by residue matching to compare protein structures and is developed from a previous structural alignment method based on dynamic programming. Linear representations of secondary structures are derived and their features compared to identify equivalent elements in two proteins. The secondary structure alignment then constrains the residue alignment, which compares only residues within aligned secondary structures and with similar buried areas and torsional angles. The initial secondary structure alignment improves accuracy and provides a means of filtering out unrelated proteins before the slower residue alignment stage. It is possible to search or sort the protein structure databank very quickly using just secondary structure comparisons. A search through 720 structures with a probe protein of 10 secondary structures required 1.7 CPU hours on a Sun 4/280. Alternatively, combined secondary structure and residue alignments, with a cutoff on the secondary structure score to remove pairs of unrelated proteins from further analysis, took 10.1 CPU hours. The method was applied in searches on different classes of proteins and to cluster a subset of the databank into structurally related groups. Relationships were consistent with known families of protein structure.     

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.     

Application of multiple sequence alignment profiles to improve protein secondary structure prediction

The effect of training a neural network secondary structure prediction algorithm with different types of multiple sequence alignment profiles derived from the same sequences, is shown to provide a range of accuracy from 70.5% to 76.4%. The best accuracy of 76.4% (standard deviation 8.4%), is 3.1% (Q(3)) and 4.4% (SOV2) better than the PHD algorithm run on the same set of 406 sequence non-redundant proteins that were not used to train either method. Residues predicted by the new method with a confidence value of 5 or greater, have an average Q(3) accuracy of 84%, and cover 68% of the residues. Relative solvent accessibility based on a two state model, for 25, 5, and 0% accessibility are predicted at 76.2, 79.8, and 86. 6% accuracy respectively. The source of the improvements obtained from training with different representations of the same alignment data are described in detail. The new Jnet prediction method resulting from this study is available in the Jpred secondary structure prediction server, and as a stand-alone computer program from: http://barton.ebi.ac.uk/. Proteins 2000;40:502-511.     

Protein multiple alignment incorporating primary and secondary structure information.

Identifying common local segments, also called motifs, in multiple protein sequences plays an important role for establishing homology between proteins. Homology is easy to establish when sequences are similar (sharing an identity > 25%). However, for distant proteins, it is much more difficult to align motifs that are not similar in sequences but still share common structures or functions. This paper is a first attempt to align multiple protein sequences using both primary and secondary structure information. A new sequence model is proposed so that the model assigns high probabilities not only to motifs that contain conserved amino acids but also to motifs that present common secondary structures. The proposed method is tested in a structural alignment database BAliBASE. We show that information brought by the predicted secondary structures greatly improves motif identification. A website of this program is available at www.stat.purdue.edu/~junxie/2ndmodel/sov.html.     

A multiple alignment program for protein sequences

A program for the multiple alignment of protein sequences ispresented. The program is an extension of the fast alignmentprogram by Wilbur et al. (1984) into higher dimensions. Theuse of hash procedures on fragments of the protein sequencesincreases the speed of calculation. Thereby we also take intoaccount fragments which are present in some, but not in all,sequences considered. The results of some multiple alignmentsare given. Received on September 11, 1986; accepted on March 18, 1987     

MASTR: multiple alignment and structure prediction of non-coding RNAs using simulated annealing

MOTIVATION: As more non-coding RNAs are discovered, the importance of methods for RNA analysis increases. Since the structure of ncRNA is intimately tied to the function of the molecule, programs for RNA structure prediction are necessary tools in this growing field of research. Furthermore, it is known that RNA structure is often evolutionarily more conserved than sequence. However, few existing methods are capable of simultaneously considering multiple sequence alignment and structure prediction. RESULT: We present a novel solution to the problem of simultaneous structure prediction and multiple alignment of RNA sequences. Using Markov chain Monte Carlo in a simulated annealing framework, the algorithm MASTR (Multiple Alignment of STructural RNAs) iteratively improves both sequence alignment and structure prediction for a set of RNA sequences. This is done by minimizing a combined cost function that considers sequence conservation, covariation and basepairing probabilities. The results show that the method is very competitive to similar programs available today, both in terms of accuracy and computational efficiency. AVAILABILITY: Source code available from http://mastr.binf.ku.dk/     

Arby: automatic protein structure prediction using profile-profile alignment and confidence measures

MOTIVATION: Arby is a new server for protein structure prediction that combines several homology-based methods for predicting the three-dimensional structure of a protein, given its sequence. The methods used include a threading approach, which makes use of structural information, and a profile-profile alignment approach that incorporates secondary structure predictions. The combination of the different methods with the help of empirically derived confidence measures affords reliable template selection. RESULTS: According to the recent CAFASP3 experiment, the server is one of the most sensitive methods for predicting the structure of single domain proteins. The quality of template selection is assessed using a fold-recognition experiment. AVAILABILITY: The Arby server is available through the portal of the Helmholtz Network for Bioinformatics at http://www.hnbioinfo.de under the protein structure category.     

Automatic 3D protein structure classification without structural alignment.

In this paper, we present a new scheme named ProtClass for automatic classification of three-dimensional (3D) protein structures. It is a dedicated and unified multiclass classification scheme. Neither detailed structural alignment nor multiple binary classifications are required in this scheme. We adopt a nearest neighbor-based classification strategy. We use a filter-and-refine scheme. In the first step, we filter out the improbable answers using the precalculated parameters from the training data. In the second, we perform a relatively more detailed nearest neighbor search on the remaining answers. We use very concise and effective encoding schemes of the 3D protein structures in both steps. We compare our proposed method against two other dedicated protein structure classification schemes, namely SGM and CPMine. The experimental results show that ProtClass is slightly better in accuracy than SGM and much faster. In comparison with CPMine, ProtClass is much more accurate, while their running times are about the same. We also compare ProtClass against a structural alignment-based classification scheme named DALI, which is found to be more accurate, but extremely slow. The software is available upon request from the authors. The supplementary information on ProtClass method can be found at: http://xena1.ddns.comp.nus.edu.sg/ approximately genesis/PClass.htm.     

Prediction of protein secondary structure and active sites using the alignment of homologous sequences

The prediction of protein secondary structure (alpha-helices, beta-sheets and coil) is improved by 9% to 66% using the information available from a family of homologous sequences. The approach is based both on averaging the Garnier et al. (1978) secondary structure propensities for aligned residues and on the observation that insertions and high sequence variability tend to occur in loop regions between secondary structures. Accordingly, an algorithm first aligns a family of sequences and a value for the extent of sequence conservation at each position is obtained. This value modifies a Garnier et al. prediction on the averaged sequence to yield the improved prediction. In addition, from the sequence conservation and the predicted secondary structure, many active site regions of enzymes can be located (26 out of 43) with limited over-prediction (8 extra). The entire algorithm is fully automatic and is applicable to all structural classes of globular proteins.     

Local multiple sequence alignment using dead-end elimination

MOTIVATION: Local multiple sequence alignment is a basic tool for extracting functionally important regions shared by a family of protein sequences. We present an effectively polynomial-time algorithm for rigorously solving the local multiple alignment problem. RESULTS: The algorithm is based on the dead-end elimination procedure that makes it possible to avoid an exhaustive search. In the framework of the sum-of-pairs scoring system, certain rejection criteria are derived in order to eliminate those sequence segments and segment pairs that can be mathematically shown to be inconsistent (dead-ending) with the globally optimal alignment. Iterative application of the elimination criteria results in a rapid reduction of combinatorial possibilities without considering them explicitly. In the vast majority of cases, the procedure converges to a unique globally optimal solution. In contrast to the exhaustive search, whose computational complexity is combinatorial, the algorithm is computationally feasible because the number of operations required to eliminate the dead-ending segments and segment pairs grows quadratically and cubically, respectively, with the total number of sequence elements. The method is illustrated on a set of protein families for which the globally optimal alignments are well recognized. AVAILABILITY: The source code of the program implementing the algorithm is available upon request from the authors. CONTACT: alex_lukashin@biogen.com.