Comparative analysis of primary structure of nucleic acids and proteins

The review considers the original works on the primary structure of biopolymers, which were carried out from 1983 to 2003. Most works were supported by the Russian program Human Genome and earlier similar Russian programs. Little-known publications of 1983-1993 and recent unpublished results are described in detail. In the field of genome comparisons, these concern the OWEN hierarchic algorithm aligning syntenic regions of two genome sequences. The resulting global alignment is obtained as an ordered chain of local similarities. Alignment of sequences sized about 10(6) nucleotides takes several minutes. The concept of local similarity conflicts is generalized to multiple comparisons. New algorithms aligning protein sequences are described and compared with the Smith-Waterman algorithm, which is now most accurate. The ANCHOR hierarchic algorithm generates alignments of much the same accuracy and is twice as rapid as the Smith-Waterman one. The STRSWer algorithm takes an account of the secondary structures of proteins under study. With the secondary structures predicted using the PSI-PRED software for pairs of proteins having 10-30% similarity, the average accuracy of alignments generated by STRSWer is 15% higher than that achieved with the Smith-Waterman algorithm.     

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.     

A new algorithm for best subsequence alignments with application to tRNA-rRNA comparisons

The algorithm of Smith & Waterman for identification of maximally similar subsequences is extended to allow identification of all non-intersecting similar subsequences with similarity score at or above some preset level. The resulting alignments are found in order of score, with the highest scoring alignment first. In the case of single gaps or multiple gaps weighted linear with gap length, the algorithm is extremely efficient, taking very little time beyond that of the initial calculation of the matrix. The algorithm is applied to comparisons of tRNA-rRNA sequences from Escherichia coli. A statistical analysis is important for proper evaluation of the results, which differ substantially from the results of an earlier analysis of the same sequences by Bloch and colleagues.     

Post-processing long pairwise alignments

MOTIVATION: The local alignment problem for two sequences requires determining similar regions, one from each sequence, and aligning those regions. For alignments computed by dynamic programming, current approaches for selecting similar regions may have potential flaws. For instance, the criterion of Smith and Waterman can lead to inclusion of an arbitrarily poor internal segment. Other approaches can generate an alignment scoring less than some of its internal segments. RESULTS: We develop an algorithm that decomposes a long alignment into sub-alignments that avoid these potential imperfections. Our algorithm runs in time proportional to the original alignment's length. Practical applications to alignments of genomic DNA sequences are described.     

On comparing two structured RNA multiple alignments

We present a method, called BlockMatch, for aligning two blocks, where a block is an RNA multiple sequence alignment with the consensus secondary structure of the alignment in Stockholm format. The method employs a quadratic-time dynamic programming algorithm for aligning columns and column pairs of the multiple alignments in the blocks. Unlike many other tools that can perform pairwise alignment of either single sequences or structures only, BlockMatch takes into account the characteristics of all the sequences in the blocks along with their consensus structures during the alignment process, thus being able to achieve a high-quality alignment result. We apply BlockMatch to phylogeny reconstruction on a set of 5S rRNA sequences taken from fifteen bacteria species. Experimental results showed that the phylogenetic tree generated by our method is more accurate than the tree constructed based on the widely used ClustalW tool. The BlockMatch algorithm is implemented into a web server, accessible at http://bioinformatics.njit.edu/blockmatch. A jar file of the program is also available for download from the web server.     

Information about the protein secondary structure improves quality of an alignment of protein sequences

All popular algorithms of pair-wise alignment of protein primary structures (e.g. Smith-Waterman (SW), FASTA, BLAST, et al.) utilize only amino acid sequences. The SW-algorithm is the most accurate among them, i.e. it produces alignments that are most similar to the alignments obtained by superposition of protein 3D-structures. But even the SW-algorithm is unable to restore the 3D-based alignment if similarity of amino acid sequences (%id) is below 30%. We have proposed a novel alignment method that explicitly takes into account the secondary structure of the compared proteins. We have shown that it creates significantly more accurate alignments compared to SW-algorithm. In particular, for sequences with %id < 30% the average accuracy of the new method is 58% compared to 35% for SW-algorithm (the accuracy of an algorithmic sequence alignment is the part of restored position of a "golden standard" alignment obtained by superposition of corresponding 3D-structures). The accuracy of the proposed method is approximately identical both for experimental, and for theoretically predicted secondary structures. Thus the method can be applied for alignment of protein sequences even if protein 3D-structure is unknown. The program is available at ftp://194.149.64.196/STRUSWER/.     

A platform for biological sequence comparison on parallel computers

We have written two programs for searching biological sequencedatabases that run on Intel hypercube computers. PSCANLJB comparesa single sequence against a sequence library, and PCOMPLIB comparesall the entries in one sequence library against a second library.The programs provide a general framework for similarity searching;they include functions for reading in query sequences, searchparameters and library entries, and reporting the results ofa search. We have isolated the code for the specific functionthat calculates the similarity score between the query and librarysequence; alternative searching algorithms can be implementedby editing two files. We have implemented the rapid FASTA sequencecomparison algorithm and the more rigorous Smith — Watermanalgorithm within this framework. The PSCANLIB program on a 16node iPSC/2 80386-based hypercube can compare a 229 amino acidprotein sequence with a 3.4 million residue sequence libraryin {small tilde}16s with the FASTA algorithm. Using the Smith— Waterman algorithm, the same search takes 35 min. ThePCOMPUB program can compare a 0.8 millon amino acid proteinsequence library with itself in 5.3 min with FASTA on a third-generation32 node Intel iPSC/860 hypercube. Received on September 8, 1990; accepted on December 15, 1990     

SCARNA: fast and accurate structural alignment of RNA sequences by matching fixed-length stem fragments

MOTIVATION: The functions of non-coding RNAs are strongly related to their secondary structures, but it is known that a secondary structure prediction of a single sequence is not reliable. Therefore, we have to collect similar RNA sequences with a common secondary structure for the analyses of a new non-coding RNA without knowing the exact secondary structure itself. Therefore, the sequence comparison in searching similar RNAs should consider not only their sequence similarities but also their potential secondary structures. Sankoff's algorithm predicts the common secondary structures of the sequences, but it is computationally too expensive to apply to large-scale analyses. Because we often want to compare a large number of cDNA sequences or to search similar RNAs in the whole genome sequences, much faster algorithms are required. RESULTS: We propose a new method of comparing RNA sequences based on the structural alignments of the fixed-length fragments of the stem candidates. The implemented software, SCARNA (Stem Candidate Aligner for RNAs), is fast enough to apply to the long sequences in the large-scale analyses. The accuracy of the alignments is better or comparable with the much slower existing algorithms. AVAILABILITY: The web server of SCARNA with graphical structural alignment viewer is available at http://www.scarna.org/.     

Multiple sequence alignment

A method has been developed for aligning segments of several sequences at once. The number of search steps depends only polynomially on the number of sequences, instead of exponentially, because most alignments are rejected without being evaluated explicitly. A data structure herein called the "heap" facilitates this process. For a set of n sequence segments, the overall similarity is taken to be the sum of all the constituent segment pair similarities, which are in turn sums of corresponding residue similarity scores from a Table. The statistical models that test alignments for significance make it possible to group sequences objectively, even when most or all of the interrelationships are weak. These tests are very sensitive, while remaining quite conservative, and discourage the addition of "misfit" sequences to an existing set. The new techniques are applied to a set of five DNA-binding proteins, to a group of three enzymes that employ the coenzyme FAD, and to a control set. The alignment previously proposed for the DNA-binding proteins on the basis of structural comparisons and inspection of sequences is supported quite dramatically, and a highly significant alignment is found for the FAD-binding proteins.     

MARNA: multiple alignment and consensus structure prediction of RNAs based on sequence structure comparisons

MOTIVATION: Due to the importance of considering secondary structures in aligning functional RNAs, several pairwise sequence-structure alignment methods have been developed. They use extended alignment scores that evaluate secondary structure information in addition to sequence information. However, two problems for the multiple alignment step remain. First, how to combine pairwise sequence-structure alignments into a multiple alignment and second, how to generate secondary structure information for sequences whose explicit structural information is missing. RESULTS: We describe a novel approach for multiple alignment of RNAs (MARNA) taking into consideration both the primary and the secondary structures. It is based on pairwise sequence-structure comparisons of RNAs. From these sequence-structure alignments, libraries of weighted alignment edges are generated. The weights reflect the sequential and structural conservation. For sequences whose secondary structures are missing, the libraries are generated by sampling low energy conformations. The libraries are then processed by the T-Coffee system, which is a consistency based multiple alignment method. Furthermore, we are able to extract a consensus-sequence and -structure from a multiple alignment. We have successfully tested MARNA on several datasets taken from the Rfam database.     

Self-consistently optimized statistical mechanical energy functions for sequence structure alignment.

A quantitative form of the principle of minimal frustration is used to obtain from a database analysis statistical mechanical energy functions and gap parameters for aligning sequences to three-dimensional structures. The analysis that partially takes into account correlations in the energy landscape improves upon the previous approximations of Goldstein et al. (1994, 1995) (Goldstein R, Luthey-Schulten Z, Wolynes P, 1994, Proceedings of the 27th Hawaii International Conference on System Sciences. Los Alamitos, California: IEEE Computer Society Press. pp 306-315; Goldstein R, Luthey-Schulten Z, Wolynes P, 1995, In: Elber R, ed. New developments in theoretical studies of proteins. Singapore: World Scientific). The energy function allows for ordering of alignments based on the compatibility of a sequence to be in a given structure (i.e., lowest energy) and therefore removes the necessity of using percent identity or similarity as scoring parameters. The alignments produced by the energy function on distant homologues with low percent identity (less than 21%) are generally better than those generated with evolutionary information. The lowest energy alignment generated with the energy function for sequences containing prosite signatures but unknown structures is a structure containing the same prosite signature, providing a check on the robustness of the algorithm. Finally, the energy function can make use of known experimental evidence as constraints within the alignment algorithm to aid in finding the correct structural alignment.     

Fast, optimal alignment of three sequences using linear gap costs

Alignment algorithms can be used to infer a relationship between sequences when the true relationship is unknown. Simple alignment algorithms use a cost function that gives a fixed cost to each possible point mutation-mismatch, deletion, insertion. These algorithms tend to find optimal alignments that have many small gaps. It is more biologically plausible to have fewer longer gaps rather than many small gaps in an alignment. To address this issue, linear gap cost algorithms are in common use for aligning biological sequence data. More reliable inferences are obtained by aligning more than two sequences at a time. The obvious dynamic programming algorithm for optimally aligning k sequences of length n runs in O(n(k)) time. This is impractical if k>/=3 and n is of any reasonable length. Thus, for this problem there are many heuristics for aligning k sequences, however, they are not guaranteed to find an optimal alignment. In this paper, we present a new algorithm guaranteed to find the optimal alignment for three sequences using linear gap costs. This gives the same results as the dynamic programming algorithm for three sequences, but typically does so much more quickly. It is particularly fast when the (three-way) edit distance is small. Our algorithm uses a speed-up technique based on Ukkonen's greedy algorithm (Ukkonen, 1983) which he presented for two sequences and simple costs.     

SW-ARRAY: a dynamic programming solution for the identification of copy-number changes in genomic DNA using array comparative genome hybridization data

Comparative genome hybridization (CGH) to DNA microarrays (array CGH) is a technique capable of detecting deletions and duplications in genomes at high resolution. However, array CGH studies of the human genome noting false negative and false positive results using large insert clones as probes have raised important concerns regarding the suitability of this approach for clinical diagnostic applications. Here, we adapt the Smith–Waterman dynamic-programming algorithm to provide a sensitive and robust analytic approach (SW-ARRAY) for detecting copy-number changes in array CGH data. In a blind series of hybridizations to arrays consisting of the entire tiling path for the terminal 2 Mb of human chromosome 16p, the method identified all monosomies between 267 and 1567 kb with a high degree of statistical significance and accurately located the boundaries of deletions in the range 267–1052 kb. The approach is unique in offering both a nonparametric segmentation procedure and a nonparametric test of significance. It is scalable and well-suited to high resolution whole genome array CGH studies that use array probes derived from large insert clones as well as PCR products and oligonucleotides.     

STRAL: progressive alignment of non-coding RNA using base pairing probability vectors in quadratic time

MOTIVATION: Alignment of RNA has a wide range of applications, for example in phylogeny inference, consensus structure prediction and homology searches. Yet aligning structural or non-coding RNAs (ncRNAs) correctly is notoriously difficult as these RNA sequences may evolve by compensatory mutations, which maintain base pairing but destroy sequence homology. Ideally, alignment programs would take RNA structure into account. The Sankoff algorithm for the simultaneous solution of RNA structure prediction and RNA sequence alignment was proposed 20 years ago but suffers from its exponential complexity. A number of programs implement lightweight versions of the Sankoff algorithm by restricting its application to a limited type of structure and/or only pairwise alignment. Thus, despite recent advances, the proper alignment of multiple structural RNA sequences remains a problem. RESULTS: Here we present StrAl, a heuristic method for alignment of ncRNA that reduces sequence-structure alignment to a two-dimensional problem similar to standard multiple sequence alignment. The scoring function takes into account sequence similarity as well as up- and downstream pairing probability. To test the robustness of the algorithm and the performance of the program, we scored alignments produced by StrAl against a large set of published reference alignments. The quality of alignments predicted by StrAl is far better than that obtained by standard sequence alignment programs, especially when sequence homologies drop below approximately 65%; nevertheless StrAl's runtime is comparable to that of ClustalW.     

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.     

Alignment of Escherichia coli K12 DNA sequences to a genomic restriction map.

We use the extensive published information describing the genome of Escherichia coli and new restriction map alignment software to align DNA sequence, genetic, and physical maps. Restriction map alignment software is used which considers restriction maps as strings analogous to DNA or protein sequences except that two values, enzyme name and DNA base address, are associated with each position on the string. The resulting alignments reveal a nearly linear relationship between the physical and genetic maps of the E. coli chromosome. Physical map comparisons with the 1976, 1980, and 1983 genetic maps demonstrate a better fit with the more recent maps. The results of these alignments are genomic kilobase coordinates, orientation and rank of the alignment that best fits the genetic data. A statistical measure based on extreme value distribution is applied to the alignments. Additional computer analyses allow us to estimate the accuracy of the published E. coli genomic restriction map, simulate rearrangements of the bacterial chromosome, and search for repetitive DNA. The procedures we used are general enough to be applicable to other genome mapping projects.     

Compressed indexing and local alignment of DNA

MOTIVATION: Recent experimental studies on compressed indexes (BWT, CSA, FM-index) have confirmed their practicality for indexing very long strings such as the human genome in the main memory. For example, a BWT index for the human genome (with about 3 billion characters) occupies just around 1 G bytes. However, these indexes are designed for exact pattern matching, which is too stringent for biological applications. The demand is often on finding local alignments (pairs of similar substrings with gaps allowed). Without indexing, one can use dynamic programming to find all the local alignments between a text T and a pattern P in O(|T||P|) time, but this would be too slow when the text is of genome scale (e.g. aligning a gene with the human genome would take tens to hundreds of hours). In practice, biologists use heuristic-based software such as BLAST, which is very efficient but does not guarantee to find all local alignments. RESULTS: In this article, we show how to build a software called BWT-SW that exploits a BWT index of a text T to speed up the dynamic programming for finding all local alignments. Experiments reveal that BWT-SW is very efficient (e.g. aligning a pattern of length 3 000 with the human genome takes less than a minute). We have also analyzed BWT-SW mathematically for a simpler similarity model (with gaps disallowed), and we show that the expected running time is O(/T/(0.628)/P/) for random strings. As far as we know, BWT-SW is the first practical tool that can find all local alignments. Yet BWT-SW is not meant to be a replacement of BLAST, as BLAST is still several times faster than BWT-SW for long patterns and BLAST is indeed accurate enough in most cases (we have used BWT-SW to check against the accuracy of BLAST and found that only rarely BLAST would miss some significant alignments). AVAILABILITY: www.cs.hku.hk/~ckwong3/bwtsw CONTACT: twlam@cs.hku.hk.     

A general method for fast multiple sequence alignment

We have developed a fast heuristic algorithm for multiple sequence alignment which provides near-to-optimal results for sufficiently homologous sequences. The algorithm makes use of the standard dynamic programming procedure by applying it to all pairs of sequences. The resulting score matrices for pair-wise alignment give rise to secondary matrices containing the additional charges imposed by forcing the alignment path to run through a particular vertex. Such a constraint corresponds to slicing the sequences at the positions defining that vertex, and aligning the remaining pairs of prefix and suffix sequences separately. From these secondary matrices, one can compute - for any given family of sequences - suitable positions for cutting all of these sequences simultaneously, thus reducing the problem of aligning a family of n sequences of average length l in a Divide and Conquer fashion to aligning two families of n sequences of approximately half that length.In this paper, we explain the method for the case of 3 sequences in detail, and we demonstrate its potential and its limits by discussing its behaviour for several test families. A generalization for aligning more than 3 sequences is lined out, and some actual alignments constructed by our algorithm for various user-defined parameters are presented.     

PROMALS: towards accurate multiple sequence alignments of distantly related proteins

MOTIVATION: Accurate multiple sequence alignments are essential in protein structure modeling, functional prediction and efficient planning of experiments. Although the alignment problem has attracted considerable attention, preparation of high-quality alignments for distantly related sequences remains a difficult task. RESULTS: We developed PROMALS, a multiple alignment method that shows promising results for protein homologs with sequence identity below 10%, aligning close to half of the amino acid residues correctly on average. This is about three times more accurate than traditional pairwise sequence alignment methods. PROMALS algorithm derives its strength from several sources: (i) sequence database searches to retrieve additional homologs; (ii) accurate secondary structure prediction; (iii) a hidden Markov model that uses a novel combined scoring of amino acids and secondary structures; (iv) probabilistic consistency-based scoring applied to progressive alignment of profiles. Compared to the best alignment methods that do not use secondary structure prediction and database searches (e.g. MUMMALS, ProbCons and MAFFT), PROMALS is up to 30% more accurate, with improvement being most prominent for highly divergent homologs. Compared to SPEM and HHalign, which also employ database searches and secondary structure prediction, PROMALS shows an accuracy improvement of several percent. AVAILABILITY: The PROMALS web server is available at: http://prodata.swmed.edu/promals/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

From analysis of protein structural alignments toward a novel approach to align protein sequences

Alignment of protein sequences is a key step in most computational methods for prediction of protein function and homology-based modeling of three-dimensional (3D)-structure. We investigated correspondence between "gold standard" alignments of 3D protein structures and the sequence alignments produced by the Smith-Waterman algorithm, currently the most sensitive method for pair-wise alignment of sequences. The results of this analysis enabled development of a novel method to align a pair of protein sequences. The comparison of the Smith-Waterman and structure alignments focused on their inner structure and especially on the continuous ungapped alignment segments, "islands" between gaps. Approximately one third of the islands in the gold standard alignments have negative or low positive score, and their recognition is below the sensitivity limit of the Smith-Waterman algorithm. From the alignment accuracy perspective, the time spent by the algorithm while working in these unalignable regions is unnecessary. We considered features of the standard similarity scoring function responsible for this phenomenon and suggested an alternative hierarchical algorithm, which explicitly addresses high scoring regions. This algorithm is considerably faster than the Smith-Waterman algorithm, whereas resulting alignments are in average of the same quality with respect to the gold standard. This finding shows that the decrease of alignment accuracy is not necessarily a price for the computational efficiency.