Robust E-values for gapped local alignments.

We examine a Poisson heuristic for judging the significance of local sequence alignments with gaps. Model parameters are estimated directly from the sequences to be aligned, so that laborious prior simulation studies or database comparisons for the estimation of parameters describing the connection between score and E-value are unnecessary. Simulation studies give evidence that this method gives reasonable results even when the usual assumptions like the independence of sequence positions are violated.     

Accurate formula for P-values of gapped local sequence and profile alignments

A simple general approximation for the distribution of gapped local alignment scores is presented, suitable for assessing significance of comparisons between two protein sequences or a sequence and a profile. The approximation takes account of the scoring scheme (i.e. gap penalty and substitution matrix or profile), sequence composition and length. Use of this formula means it is unnecessary to fit an extreme-value distribution to simulations or to the results of databank searches. The method is based on the theoretical ideas introduced by R. Mott and R. Tribe in 1999. Extensive simulation studies show that score-thresholds produced by the method are accurate to within +/-5 % 95 % of the time. We also investigate factors which effect the accuracy of alignment statistics, and show that any method based on asymptotic theory is limited because asymptotic behaviour is not strictly achieved for many real protein sequences, due to extreme composition effects. Consequently, it may not be practicable to find a general formula that is significantly more accurate until the sub-asymptotic behaviour of alignments is better understood.     

Toward an accurate statistics of gapped alignments

Sequence alignment has been an invaluable tool for finding homologous sequences. The significance of the homology found is often quantified statistically by p-values. Theory for computing p-values exists for gapless alignments [Karlin, S., Altschul, S.F., 1990. Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. Proc. Natl. Acad. Sci. USA 87, 2264–2268; Karlin, S., Dembo A., 1992. Limit distributions of maximal segmental score among Markov-dependent partial sums. Adv. Appl. Probab. 24, 13–140], but a full generalization to alignments with gaps is not yet complete. We present a unified statistical analysis of two common sequence comparison algorithms: maximum-score (Smith-Waterman) alignments and their generalized probabilistic counterparts, including maximum-likelihood alignments and hidden Markov models. The most important statistical characteristic of these algorithms is the distribution function of the maximum score S _max, resp. the maximum free energy F _max, for mutually uncorrelated random sequences. This distribution is known empirically to be of the Gumbel form with an exponential tail P(S _max > x) ∼ exp(−λx) for maximum-score alignment and P(F _max > x) ∼ exp(−λx) for some classes of probabilistic alignment. We derive an exact expression for λ for particular probabilistic alignments. This result is then used to obtain accurate λ values for generic probabilistic and maximum-score alignments. Although the result demonstrated uses a simple match-mismatch scoring system, it is expected to be a good starting point for more general scoring functions.     

Remote homology detection: a motif based approach

MOTIVATION: Remote homology detection is the problem of detecting homology in cases of low sequence similarity. It is a hard computational problem with no approach that works well in all cases. RESULTS: We present a method for detecting remote homology that is based on the presence of discrete sequence motifs. The motif content of a pair of sequences is used to define a similarity that is used as a kernel for a Support Vector Machine (SVM) classifier. We test the method on two remote homology detection tasks: prediction of a previously unseen SCOP family and prediction of an enzyme class given other enzymes that have a similar function on other substrates. We find that it performs significantly better than an SVM method that uses BLAST or Smith-Waterman similarity scores as features.     

Statistics of local multiple alignments

SUMMARY: BLAST statistics have been shown to be extremely useful for searching for significant similarity hits, for amino acid and nucleotide sequences. Although these statistics are well understood for pairwise comparisons, there has been little success developing statistical scores for multiple alignments. In particular, there is no score for multiple alignment that is well founded and treated as a standard. We extend the BLAST theory to multiple alignments. Following some simple assumptions, we present and justify a significance score for multiple segments of a local multiple alignment. We demonstrate its usefulness in distinguishing high and moderate quality multiple alignments from low quality ones, with supporting experiments on orthologous vertebrate promoter sequences.     

Approximate p-values for local sequence alignments: numerical studies.

Siegmund and Yakir (2000) have given an approximate p-value when two independent, identically distributed sequences from a finite alphabet are optimally aligned based on a scoring system that rewards similarities according to a general scoring matrix and penalizes gaps (insertions and deletions). The approximation involves an infinite sequence of difficult-to-compute parameters. In this paper, it is shown by numerical studies that these reduce to essentially two numerically distinct parameters, which can be computed as one-dimensional numerical integrals. For an arbitrary scoring matrix and affine gap penalty, this modified approximation is easily evaluated. Comparison with published numerical results show that it is reasonably accurate.     

ddbRNA: detection of conserved secondary structures in multiple alignments

MOTIVATION: Structured non-coding RNAs (ncRNAs) have a very important functional role in the cell. No distinctive general features common to all ncRNA have yet been discovered. This makes it difficult to design computational tools able to detect novel ncRNAs in the genomic sequence. RESULTS: We devised an algorithm able to detect conserved secondary structures in both pairwise and multiple DNA sequence alignments with computational time proportional to the square of the sequence length. We implemented the algorithm for the case of pairwise and three-way alignments and tested it on ncRNAs obtained from public databases. On the test sets, the pairwise algorithm has a specificity greater than 97% with a sensitivity varying from 22.26% for Blast alignments to 56.35% for structural alignments. The three-way algorithm behaves similarly. Our algorithm is able to efficiently detect a conserved secondary structure in multiple alignments.     

Datamonkey: rapid detection of selective pressure on individual sites of codon alignments

Datamonkey is a web interface to a suite of cutting edge maximum likelihood-based tools for identification of sites subject to positive or negative selection. The methods range from very fast data exploration to the some of the most complex models available in public domain software, and are implemented to run in parallel on a cluster of computers. AVAILABILITY: http://www.datamonkey.org. In the future, we plan to expand the collection of available analytic tools, and provide a package for installation on other systems.     

A novel approach to local reliability of sequence alignments

MOTIVATION: The pairwise alignment of biological sequences obtained from an algorithm will in general contain both correct and incorrect parts. Hence, to allow for a valid interpretation of the alignment, the local trustworthiness of the alignment has to be quantified. RESULTS: We present a novel approach that attributes a reliability index to every pair of residues, including gapped regions, in the optimal alignment of two protein sequences. The method is based on a fuzzy recast of the dynamic programming algorithm for sequence alignment in terms of mean field annealing. An extensive evaluation with structural reference alignments not only shows that the probability for a pair of residues to be correctly aligned grows consistently with increasing reliability index, but moreover demonstrates that the value of the reliability index can directly be translated into an estimate of the probability for a correct alignment.     

TOPAL 2.0: improved detection of mosaic sequences within multiple alignments

MOTIVATION: The Dss statistic was proposed by McGuire et al. (Mol. Biol. Evol., 14, 1125-1131, 1997) for scanning data sets for the presence of recombination, an important step in some phylogenetic analyses. The statistic, however, could not distinguish well between among-site rate variation and recombination, and had no statistical test for significant values. This paper addresses these shortfalls. RESULTS: A modification to the Dss statistic is proposed which accounts for rate variation to a large extent. A statistical test, based on parametric bootstrapping, is also suggested. AVAILABILITY: The TOPAL package (version 2) may be accessed from http:/ /www.bioss.sari.ac.uk/frank/Genetics and by anonymous ftp from typ://ftp.bioss.sari.ac.uk in the directory pub/phylogeny/topal. CONTACT: frank@bioss.sari.ac.uk     

ProfDistS: (profile-) distance based phylogeny on sequence--structure alignments

MOTIVATION: The Profile Neighbor Joining (PNJ) algorithm as implemented in the software ProfDist is computationally efficient in reconstructing very large trees. Besides the huge amount of sequence data the structure is important in RNA alignment analysis and phylogenetic reconstruction. RESULTS: For this ProfDistS provides a phylogenetic workflow that uses individual RNA secondary structures in reconstructing phylogenies based on sequence-structure alignments-using PNJ with manual or iterative and automatic profile definition. Moreover, ProfDistS can deal also with protein sequences.     

Stepwise detection of recombination breakpoints in sequence alignments

MOTIVATION: We propose a stepwise approach to identify recombination breakpoints in a sequence alignment. The approach can be applied to any recombination detection method that uses a permutation test and provides estimates of breakpoints. RESULTS: We illustrate the approach by analyses of a simulated dataset and alignments of real data from HIV-1 and human chromosome 7. The presented simulation results compare the statistical properties of one-step and two-step procedures. More breakpoints are found with a two-step procedure than with a single application of a given method, particularly for higher recombination rates. At higher recombination rates, the additional breakpoints were located at the cost of only a slight increase in the number of falsely declared breakpoints. However, a large proportion of breakpoints still go undetected. AVAILABILITY: A makefile and C source code for phylogenetic profiling and the maximum chi2 method, tested with the gcc compiler on Linux and WindowsXP, are available at http://stat-db.stat.sfu.ca/stepwise/ CONTACT: jgraham@stat.sfu.ca.     

A biresonant plasma source based on a gapped linear microwave vibrator

The operating principle of a novel microwave plasma source—a linear microwave vibrator with a gap—is discussed. The source is placed on a microwave-transparent window of a chamber filled with a plasma-forming gas (argon or methane). The device operation is based on the combination of two resonances—geometric and plasma ones. The results of experimental tests of the source are presented. For a microwave frequency of 2.45 GHz, microwave power of ≤1 kW, and plasma-forming gas pressure in the range 5 × 10⁻²–10⁻¹ Torr, the source is capable of filling the reactor volume with a plasma having an electron density of about 10¹² cm⁻³ and electron temperature of a few electronvolts.     

Analysis of chimpanzee history based on genome sequence alignments

Population geneticists often study small numbers of carefully chosen loci, but it has become possible to obtain orders of magnitude for more data from overlaps of genome sequences. Here, we generate tens of millions of base pairs of multiple sequence alignments from combinations of three western chimpanzees, three central chimpanzees, an eastern chimpanzee, a bonobo, a human, an orangutan, and a macaque. Analysis provides a more precise understanding of demographic history than was previously available. We show that bonobos and common chimpanzees were separated ~1,290,000 years ago, western and other common chimpanzees ~510,000 years ago, and eastern and central chimpanzees at least 50,000 years ago. We infer that the central chimpanzee population size increased by at least a factor of 4 since its separation from western chimpanzees, while the western chimpanzee effective population size decreased. Surprisingly, in about one percent of the genome, the genetic relationships between humans, chimpanzees, and bonobos appear to be different from the species relationships. We used PCR-based resequencing to confirm 11 regions where chimpanzees and bonobos are not most closely related. Study of such loci should provide information about the period of time 5–7 million years ago when the ancestors of humans separated from those of the chimpanzees.     

A novel approach to remote homology detection: jumping alignments.

We describe a new algorithm for protein classification and the detection of remote homologs. The rationale is to exploit both vertical and horizontal information of a multiple alignment in a well-balanced manner. This is in contrast to established methods such as profiles and profile hidden Markov models which focus on vertical information as they model the columns of the alignment independently and to family pairwise search which focuses on horizontal information as it treats given sequences separately. In our setting, we want to select from a given database of "candidate sequences" those proteins that belong to a given superfamily. In order to do so, each candidate sequence is separately tested against a multiple alignment of the known members of the superfamily by means of a new jumping alignment algorithm. This algorithm is an extension of the Smith-Waterman algorithm and computes a local alignment of a single sequence and a multiple alignment. In contrast to traditional methods, however, this alignment is not based on a summary of the individual columns of the multiple alignment. Rather, the candidate sequence is at each position aligned to one sequence of the multiple alignment, called the "reference sequence." In addition, the reference sequence may change within the alignment, while each such jump is penalized. To evaluate the discriminative quality of the jumping alignment algorithm, we compare it to profiles, profile hidden Markov models, and family pairwise search on a subset of the SCOP database of protein domains. The discriminative quality is assessed by median false positive counts (med-FP-counts). For moderate med-FP-counts, the number of successful searches with our method is considerably higher than with the competing methods.     

Biological network motif detection: principles and practice

Network motifs are statistically overrepresented sub-structures (sub-graphs) in a network, and have been recognized as 'the simple building blocks of complex networks'. Study of biological network motifs may reveal answers to many important biological questions. The main difficulty in detecting larger network motifs in biological networks lies in the facts that the number of possible sub-graphs increases exponentially with the network or motif size (node counts, in general), and that no known polynomial-time algorithm exists in deciding if two graphs are topologically equivalent. This article discusses the biological significance of network motifs, the motivation behind solving the motif-finding problem, and strategies to solve the various aspects of this problem. A simple classification scheme is designed to analyze the strengths and weaknesses of several existing algorithms. Experimental results derived from a few comparative studies in the literature are discussed, with conclusions that lead to future research directions.     

Pfam: A comprehensive database of protein domain families based on seed alignments

Databases of multiple sequence alignments are a valuable aid to protein sequence classification and analysis. One of the main challenges when constructing such a database is to simultaneously satisfy the conflicting demands of completeness on the one hand and quality of alignment and domain definitions on the other. The latter properties are best dealt with by manual approaches, whereas completeness in practice is only amenable to automatic methods. Herein we present a database based on hidden Markov model profiles (HMMs), which combines high quality and completeness. Our database, Pfam, consists of parts A and B. Pfam-A is curated and contains well-characterized protein domain families with high quality alignments, which are maintained by using manually checked seed alignments and HMMs to find and align all members. Pfam-B contains sequence families that were generated automatically by applying the Domainer algorithm to cluster and align the remaining protein sequences after removal of Pfam-A domains. By using Pfam, a large number of previously unannotated proteins from the Caenorhabditis elegans genome project were classified. We have also identified many novel family memberships in known proteins, including new kazal, Fibronectin type III, and response regulator receiver domains. Pfam-A families have permanent accession numbers and form a library of HMMs available for searching and automatic annotation of new protein sequences. Proteins: 28:405–420, 1997. © 1997 Wiley-Liss, Inc.