A local algorithm for DNA sequence alignment with inversions

A dynamic programming algorithm to find all optimal alignments of DNA subsequences is described. The alignments use not only substitutions, insertions and deletions of nucleotides but also inversions (reversed complements) of substrings of the sequences. The inversion alignments themselves contain substitutions, insertions and deletions of nucleotides. We study the problem of alignment with non-intersecting inversions. To provide a computationally efficient algorithm we restrict candidate inversions to theK highest scoring inversions. An algorithm to find theJ best non-intersecting alignments with inversions is also described. The new algorithm is applied to the regions of mitochondrial DNA ofDrosophila yakuba and mouse coding for URF6 and cytochrome b and the inversion of the URF6 gene is found. The open problem of intersecting inversions is discussed.     

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.     

Thermodynamic criteria for high hit rate antisense oligonucleotide design

Antisense oligonucleotides are used for therapeutic applications and in functional genomic studies. In practice, however, many of the oligonucleotides complementary to an mRNA have little or no antisense activity. Theoretical strategies to improve the ‘hit rate’ in antisense screens will reduce the cost of discovery and may lead to identification of antisense oligonucleotides with increased potency. Statistical analysis performed on data collected from more than 1000 experiments with phosphorothioate-modified oligonucleotides revealed that the oligo-probes, which form stable duplexes with RNA (ΔG^o₃₇ ≤ –30 kcal/mol) and have small self-interaction potential, are more frequently efficient than molecules that form less stable oligonucleotide–RNA hybrids or more stable self-structures. To achieve optimal statistical preference, the values for self-interaction should be (ΔG^o₃₇) ≥ –8 kcal/mol for inter-oligonucleotide pairing and (ΔG^o₃₇) ≥ –1.1 kcal/mol for intra-molecular pairing. Selection of oligonucleotides with these thermodynamic values in the analyzed experiments would have increased the ‘hit rate’ by as much as 6-fold.     

Improved alignment of nucleosome DNA sequences using a mixture model

DNA sequences that are present in nucleosomes have a preferential approximately 10 bp periodicity of certain dinucleotide signals, but the overall sequence similarity of the nucleosomal DNA is weak, and traditional multiple sequence alignment tools fail to yield meaningful alignments. We develop a mixture model that characterizes the known dinucleotide periodicity probabilistically to improve the alignment of nucleosomal DNAs. We assume that a periodic dinucleotide signal of any type emits according to a probability distribution around a series of 'hot spots' that are equally spaced along nucleosomal DNA with 10 bp period, but with a 1 bp phase shift across the middle of the nucleosome. We model the three statistically most significant dinucleotide signals, AA/TT, GC and TA, simultaneously, while allowing phase shifts between the signals. The alignment is obtained by maximizing the likelihood of both Watson and Crick strands simultaneously. The resulting alignment of 177 chicken nucleosomal DNA sequences revealed that all 10 distinct dinucleotides are periodic, however, with only two distinct phases and varying intensity. By Fourier analysis, we show that our new alignment has enhanced periodicity and sequence identity compared with center alignment. The significance of the nucleosomal DNA sequence alignment is evaluated by comparing it with that obtained using the same model on non-nucleosomal sequences.     

Improved statistical methods for hit selection in high-throughput screening

High-throughput screening (HTS) plays a central role in modern drug discovery, allowing the rapid screening of large compound collections against a variety of putative drug targets. HTS is an industrial-scale process, relying on sophisticated automation, control, and state-of-the art detection technologies to organize, test, and measure hundreds of thousands to millions of compounds in nano- to microliter volumes. Despite this high technology, hit selection for HTS is still typically done using simple data analysis and basic statistical methods. The authors discuss in this article some shortcomings of these methods and present alternatives based on modern methods of statistical data analysis. Most important, they describe and show numerous real examples from the biologist-friendly Stat Server HTS application (SHS), a custom-developed software tool built on the commercially available S-PLUS and StatServer statistical analysis and server software. This system remotely processes HTS data using powerful and sophisticated statistical methodology but insulates users from the technical details by outputting results in a variety of readily interpretable graphs and tables.     

New finite-size correction for local alignment score distributions

ABSTRACT: BACKGROUND: Local alignment programs often calculate the probability that a match occurred by chance. The calculation of this probability may require a "finite-size" correction to the lengths of the sequences, as an alignment that starts near the end of either sequence may run out of sequence before achieving a significant score. FINDINGS: We present an improved finite-size correction that considers the distribution of sequence lengths rather than simply the corresponding means. This approach improves sensitivity and avoids substituting an ad hoc length for short sequences that can underestimate the significance of a match. We use a test set derived from ASTRAL to show improved ROC scores, especially for shorter sequences. CONCLUSIONS: The new finite-size correction improves the calculation of probabilities for a local alignment. It is now used in the BLAST + package and at the NCBI BLAST web site (http://blast.ncbi.nlm.nih.gov).     

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.     

Basic local alignment search tool

A new approach to rapid sequence comparison, basic local alignment search tool (BLAST), directly approximates alignments that optimize a measure of local similarity, the maximal segment pair (MSP) score. Recent mathematical results on the stochastic properties of MSP scores allow an analysis of the performance of this method as well as the statistical significance of alignments it generates. The basic algorithm is simple and robust; it can be implemented in a number of ways and applied in a variety of contexts including straightforward DNA and protein sequence database searches, motif searches, gene identification searches, and in the analysis of multiple regions of similarity in long DNA sequences. In addition to its flexibility and tractability to mathematical analysis, BLAST is an order of magnitude faster than existing sequence comparison tools of comparable sensitivity.     

Improved magnetization alignment schemes for spin-lock relaxation experiments

A pair of pulse schemes that spin-lock magnetization efficiently are presented. The design of the sequences benefited from a particularly simple relation that is derived describing to first order the evolution of any magnetization component due to the application of an off-resonance 90° pulse. The sequences are shown theoretically and experimentally to significantly outperform the 90°-delay-90° element that is often used in current applications. It is shown that alignment of magnetization to within 1° of the effective field can be obtained over a bandwidth extending between [−ω_SL, ω_SL], where ω_SL is the strength of the spin-lock field using a simple scheme that is an order of magnitude shorter than an adiabatic pulse that might also be used for a similar purpose. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Improved gapped alignment in BLAST

Homology search is a key tool for understanding the role, structure, and biochemical function of genomic sequences. The most popular technique for rapid homology search is BLAST, which has been in widespread use within universities, research centers, and commercial enterprises since the early 1990s. We propose a new step in the BLAST algorithm to reduce the computational cost of searching with negligible effect on accuracy. This new step - semigapped alignment - compromises between the efficiency of ungapped alignment and the accuracy of gapped alignment, allowing BLAST to accurately filter sequences with lower computational cost. In addition, we propose a heuristic - restricted insertion alignment - that avoids unlikely evolutionary paths with the aim of reducing gapped alignment cost with negligible effect on accuracy. Together, after including an optimization of the local alignment recursion, our two techniques more than double the speed of the gapped alignment stages in blast. We conclude that our techniques are an important improvement to the BLAST algorithm. Source code for the alignment algorithms is available for download at http://www.bsg.rmit.edu.au/iga/.     

Image correlation method for DNA sequence alignment

The complexity of searches and the volume of genomic data make sequence alignment one of bioinformatics most active research areas. New alignment approaches have incorporated digital signal processing techniques. Among these, correlation methods are highly sensitive. This paper proposes a novel sequence alignment method based on 2-dimensional images, where each nucleic acid base is represented as a fixed gray intensity pixel. Query and known database sequences are coded to their pixel representation and sequence alignment is handled as object recognition in a scene problem. Query and database become object and scene, respectively. An image correlation process is carried out in order to search for the best match between them. Given that this procedure can be implemented in an optical correlator, the correlation could eventually be accomplished at light speed. This paper shows an initial research stage where results were "digitally" obtained by simulating an optical correlation of DNA sequences represented as images. A total of 303 queries (variable lengths from 50 to 4500 base pairs) and 100 scenes represented by 100 x 100 images each (in total, one million base pair database) were considered for the image correlation analysis. The results showed that correlations reached very high sensitivity (99.01%), specificity (98.99%) and outperformed BLAST when mutation numbers increased. However, digital correlation processes were hundred times slower than BLAST. We are currently starting an initiative to evaluate the correlation speed process of a real experimental optical correlator. By doing this, we expect to fully exploit optical correlation light properties. As the optical correlator works jointly with the computer, digital algorithms should also be optimized. The results presented in this paper are encouraging and support the study of image correlation methods on sequence alignment.     

Tsukuba BB: a branch and bound algorithm for local multiple alignment of DNA and protein sequences.

In this paper we present a branch and bound algorithm for local gapless multiple sequence alignment (motif alignment) and its implementation. The algorithm uses both score-based bounding and a novel bounding technique based on the "consistency" of the alignment. A sequence order independent search tree is used in conjunction with a technique for avoiding redundant calculations inherent in the structure of the tree. This is the first program to exploit the fact that the motif alignment problem is easier for short motifs. Indeed, for a short fixed motif width, the running time of the algorithm is asymptotically linear in the size of the input. We tested the performance of the program on a dataset of 300 E. coli promoter sequences and a dataset of 85 lipocalin protein sequences. For a motif width of 4, the optimal alignment of the entire set of sequences can be found. For the more natural motif width of 6, the program can align 21 sequences of length 100, more than twice the number of sequences which can be aligned by the best previous exact algorithm. The algorithm can relax the constraint of requiring each sequence to be aligned, and align 105 of the 300 promoter sequences with a motif width of 6. For the lipocalin dataset, we introduce a technique for reducing the effective alphabet size with a minimal loss of useful information. With this technique, we show that the program can find meaningful motifs in a reasonable amount of time by optimizing the score over three motif positions.     

Biclustering as a method for RNA local multiple sequence alignment

Motivations: Biclustering is a clustering method that simultaneously clusters both the domain and range of a relation. A challenge in multiple sequence alignment (MSA) is that the alignment of sequences is often intended to reveal groups of conserved functional subsequences. Simultaneously, the grouping of the sequences can impact the alignment; precisely the kind of dual situation biclustering is intended to address. RESULTS: We define a representation of the MSA problem enabling the application of biclustering algorithms. We develop a computer program for local MSA, BlockMSA, that combines biclustering with divide-and-conquer. BlockMSA simultaneously finds groups of similar sequences and locally aligns subsequences within them. Further alignment is accomplished by dividing both the set of sequences and their contents. The net result is both a multiple sequence alignment and a hierarchical clustering of the sequences. BlockMSA was tested on the subsets of the BRAliBase 2.1 benchmark suite that display high variability and on an extension to that suite to larger problem sizes. Also, alignments were evaluated of two large datasets of current biological interest, T box sequences and Group IC1 Introns. The results were compared with alignments computed by ClustalW, MAFFT, MUCLE and PROBCONS alignment programs using Sum of Pairs (SPS) and Consensus Count. Results for the benchmark suite are sensitive to problem size. On problems of 15 or greater sequences, BlockMSA is consistently the best. On none of the problems in the test suite are there appreciable differences in scores among BlockMSA, MAFFT and PROBCONS. On the T box sequences, BlockMSA does the most faithful job of reproducing known annotations. MAFFT and PROBCONS do not. On the Intron sequences, BlockMSA, MAFFT and MUSCLE are comparable at identifying conserved regions. AVAILABILITY: BlockMSA is implemented in Java. Source code and supplementary datasets are available at http://aug.csres.utexas.edu/msa/     

PLAST: parallel local alignment search tool for database comparison

Background  

Sequence similarity searching is an important and challenging task in molecular biology and next-generation sequencing should further strengthen the need for faster algorithms to process such vast amounts of data. At the same time, the internal architecture of current microprocessors is tending towards more parallelism, leading to the use of chips with two, four and more cores integrated on the same die. The main purpose of this work was to design an effective algorithm to fit with the parallel capabilities of modern microprocessors.     

The estimation of statistical parameters for local alignment score distributions

The distribution of optimal local alignment scores of random sequences plays a vital role in evaluating the statistical significance of sequence alignments. These scores can be well described by an extreme-value distribution. The distribution’s parameters depend upon the scoring system employed and the random letter frequencies; in general they cannot be derived analytically, but must be estimated by curve fitting. For obtaining accurate parameter estimates, a form of the recently described ‘island’ method has several advantages. We describe this method in detail, and use it to investigate the functional dependence of these parameters on finite-length edge effects.     

The Gumbel pre-factor k for gapped local alignment can be estimated from simulations of global alignment

The optimal gapped local alignment score of two random sequences follows a Gumbel distribution. The Gumbel distribution has two parameters, the scale parameter λ and the pre-factor k. Presently, the basic local alignment search tool (BLAST) programs (BLASTP (BLAST for proteins), PSI-BLAST, etc.) use all time-consuming computer simulations to determine the Gumbel parameters. Because the simulations must be done offline, BLAST users are restricted in their choice of alignment scoring schemes. The ultimate aim of this paper is to speed the simulations, to determine the Gumbel parameters online, and to remove the corresponding restrictions on BLAST users. Simulations for the scale parameter λ can be as much as five times faster, if they use global instead of local alignment [R. Bundschuh (2002) J. Comput. Biol., 9, 243–260]. Unfortunately, the acceleration does not extend in determining the Gumbel pre-factor k, because k has no known mathematical relationship to global alignment. This paper relates k to global alignment and exploits the relationship to show that for the BLASTP defaults, 10000 realizations with sequences of average length 140 suffice to estimate both Gumbel parameters λ and k within the errors required (λ, 0.8%; k, 10%). For the BLASTP defaults, simulations for both Gumbel parameters now take less than 30 s on a 2.8 GHz Pentium 4 processor.     

A local alignment metric for accelerating biosequence database search.

We introduce a metric for local sequence alignments that has utility for accelerating optimal alignment searches without loss of sensitivity. The metric's triangle inequality property permits identification of redundant database entries guaranteed to have optimal alignments to the query sequence that fall below a specified score threshold, thereby permitting comparisons to these entries to be skipped. We prove the existence of the metric for a variety of scoring systems, including the most commonly used ones, and show that a triangle inequality can be established as well for nucleotide-to-protein sequence comparisons. We discuss a database clustering and search strategy that takes advantage of the triangle inequality. The strategy permits moderate but significant acceleration of searches against the widely used "nr" protein database. It also provides a theoretically based method for database clustering in general and provides a standard against which to compare heuristic clustering strategies.     

Spreadsheet-based program for alignment of overlapping DNA sequences.

Molecular biology laboratories frequently face the challenge of aligning small overlapping DNA sequences derived from a long DNA segment. Here, we present a short program that can be used to adapt Excel spreadsheets as a tool for aligning DNA sequences, regardless of their orientation. The program runs on any Windows or Macintosh operating system computer with Excel 97 or Excel 98. The program is available for use as an Excel file, which can be downloaded from the BioTechniques Web site. Upon execution, the program opens a specially designed customized workbook and is capable of identifying overlapping regions between two sequence fragments and displaying the sequence alignment. It also performs a number of specialized functions such as recognition of restriction enzyme cutting sites and CpG island mapping without costly specialized software.     

Benchmarking tools for the alignment of functional noncoding DNA

Background

Numerous tools have been developed to align genomic sequences. However, their relative performance in specific applications remains poorly characterized. Alignments of protein-coding sequences typically have been benchmarked against "correct" alignments inferred from structural data. For noncoding sequences, where such independent validation is lacking, simulation provides an effective means to generate "correct" alignments with which to benchmark alignment tools.

Results

Using rates of noncoding sequence evolution estimated from the genus Drosophila, we simulated alignments over a range of divergence times under varying models incorporating point substitution, insertion/deletion events, and short blocks of constrained sequences such as those found in cis-regulatory regions. We then compared "correct" alignments generated by a modified version of the ROSE simulation platform to alignments of the simulated derived sequences produced by eight pairwise alignment tools (Avid, BlastZ, Chaos, ClustalW, DiAlign, Lagan, Needle, and WABA) to determine the off-the-shelf performance of each tool. As expected, the ability to align noncoding sequences accurately decreases with increasing divergence for all tools, and declines faster in the presence of insertion/deletion evolution. Global alignment tools (Avid, ClustalW, Lagan, and Needle) typically have higher sensitivity over entire noncoding sequences as well as in constrained sequences. Local tools (BlastZ, Chaos, and WABA) have lower overall sensitivity as a consequence of incomplete coverage, but have high specificity to detect constrained sequences as well as high sensitivity within the subset of sequences they align. Tools such as DiAlign, which generate both local and global outputs, produce alignments of constrained sequences with both high sensitivity and specificity for divergence distances in the range of 1.25–3.0 substitutions per site.

Conclusion

For species with genomic properties similar to Drosophila, we conclude that a single pair of optimally diverged species analyzed with a high performance alignment tool can yield accurate and specific alignments of functionally constrained noncoding sequences. Further algorithm development, optimization of alignment parameters, and benchmarking studies will be necessary to extract the maximal biological information from alignments of functional noncoding DNA.