Locality and gaps in RNA comparison.

Locality is an important and well-studied notion in comparative analysis of biological sequences. Similarly, taking into account affine gap penalties when calculating biological sequence alignments is a well-accepted technique for obtaining better alignments. When dealing with RNA, one has to take into consideration not only sequential features, but also structural features of the inspected molecule. This makes the computation more challenging, and usually prohibits the comparison only to small RNAs. In this paper we introduce two local metrics for comparing RNAs that extend the Smith-Waterman metric and its normalized version used for string comparison. We also present a global RNA alignment algorithm which handles affine gap penalties. Our global algorithm runs in O(m(2)n(1 + lg n/m)) time, while our local algorithms run in O(m(2)n(1 + lg n/m)) and O(n(2)m) time, respectively, where m 相似文献   

Improving the quality of twilight-zone alignments

Several recent publications illustrated advantages of using sequence profiles in recognizing distant homologies between proteins. At the same time, the practical usefulness of distant homology recognition depends not only on the sensitivity of the algorithm, but also on the quality of the alignment between a prediction target and the template from the database of known proteins. Here, we study this question for several supersensitive protein algorithms that were previously compared in their recognition sensitivity (Rychlewski et al., 2000). A database of protein pairs with similar structures, but low sequence similarity is used to rate the alignments obtained with several different methods, which included sequence-sequence, sequence-profile, and profile-profile alignment methods. We show that incorporation of evolutionary information encoded in sequence profiles into alignment calculation methods significantly increases the alignment accuracy, bringing them closer to the alignments obtained from structure comparison. In general, alignment quality is correlated with recognition and alignment score significance. For every alignment method, alignments with statistically significant scores correlate with both correct structural templates and good quality alignments. At the same time, average alignment lengths differ in various methods, making the comparison between them difficult. For instance, the alignments obtained by FFAS, the profile-profile alignment algorithm developed in our group are always longer that the alignments obtained with the PSI-BLAST algorithms. To address this problem, we develop methods to truncate or extend alignments to cover a specified percentage of protein lengths. In most cases, the elongation of the alignment by profile-profile methods is reasonable, adding fragments of similar structure. The examples of erroneous alignment are examined and it is shown that they can be identified based on the model quality.     

Structure alignment based on coding of local geometric measures

Background  

A structure alignment method based on a local geometric property is presented and its performance is tested in pairwise and multiple structure alignments. In this approach, the writhing number, a quantity originating from integral formulas of Vassiliev knot invariants, is used as a local geometric measure. This measure is used in a sliding window to calculate the local writhe down the length of the protein chain. By encoding the distribution of writhing numbers across all the structures in the protein databank (PDB), protein geometries are represented in a 20-letter alphabet. This encoding transforms the structure alignment problem into a sequence alignment problem and allows the well-established algorithms of sequence alignment to be employed. Such geometric alignments offer distinct advantages over structural alignments in Cartesian coordinates as it better handles structural subtleties associated with slight twists and bends that distort one structure relative to another.     

Local sequence alignments with monotonic gap penalties.

MOTIVATION: Sequence alignments obtained using affine gap penalties are not always biologically correct, because the insertion of long gaps is over-penalised. There is a need for an efficient algorithm which can find local alignments using non-linear gap penalties. RESULTS: A dynamic programming algorithm is described which computes optimal local sequence alignments for arbitrary, monotonically increasing gap penalties, i.e. where the cost g(k) of inserting a gap of k symbols is such that g(k) >/= g(k-1). The running time of the algorithm is dependent on the scoring scheme; if the expected score of an alignment between random, unrelated sequences of lengths m, n is proportional to log mn, then with one exception, the algorithm has expected running time O(mn). Elsewhere, the running time is no greater than O(mn(m+n)). Optimisations are described which appear to reduce the worst-case run-time to O(mn) in many cases. We show how using a non-affine gap penalty can dramatically increase the probability of detecting a similarity containing a long gap. AVAILABILITY: The source code is available to academic collaborators under licence.     

A method to recognize distant repeats in protein sequences

An automated algorithm is presented that delineates protein sequence fragments which display similarity. The method incorporates a selection of a number of local nonoverlapping sequence alignments with the highest similarity scores and a graphtheoretical approach to elucidate the consistent start and end points of the fragments comprising one or more ensembles of related subsequences. The procedure allows the simultaneous identification of different types of repeats within one sequence. A multiple alignment of the resulting fragments is performed and a consensus sequence derived from the ensemble(s). Finally, a profile is constructed form the multiple alignment to detect possible and more distant members within the sequence. The method tolerates mutations in the repeats as well as insertions and deletions. The sequence spans between the various repeats or repeat clusters may be of different lengths. The technique has been applied to a number of proteins where the repeating fragments have been derived from information additional to the protein sequences. © 1993 Wiley-Liss, Inc.     

CLUSTAL: a package for performing multiple sequence alignment on a microcomputer

An approach for performing multiple alignments of large numbers of amino acid or nucleotide sequences is described. The method is based on first deriving a phylogenetic tree from a matrix of all pairwise sequence similarity scores, obtained using a fast pairwise alignment algorithm. Then the multiple alignment is achieved from a series of pairwise alignments of clusters of sequences, following the order of branching in the tree. The method is sufficiently fast and economical with memory to be easily implemented on a microcomputer, and yet the results obtained are comparable to those from packages requiring mainframe computer facilities.     

Scoring profile-to-profile sequence alignments

Sequence alignment profiles have been shown to be very powerful in creating accurate sequence alignments. Profiles are often used to search a sequence database with a local alignment algorithm. More accurate and longer alignments have been obtained with profile-to-profile comparison. There are several steps that must be performed in creating profile-profile alignments, and each involves choices in parameters and algorithms. These steps include (1) what sequences to include in a multiple alignment used to build each profile, (2) how to weight similar sequences in the multiple alignment and how to determine amino acid frequencies from the weighted alignment, (3) how to score a column from one profile aligned to a column of the other profile, (4) how to score gaps in the profile-profile alignment, and (5) how to include structural information. Large-scale benchmarks consisting of pairs of homologous proteins with structurally determined sequence alignments are necessary for evaluating the efficacy of each scoring scheme. With such a benchmark, we have investigated the properties of profile-profile alignments and found that (1) with optimized gap penalties, most column-column scoring functions behave similarly to one another in alignment accuracy; (2) some functions, however, have much higher search sensitivity and specificity; (3) position-specific weighting schemes in determining amino acid counts in columns of multiple sequence alignments are better than sequence-specific schemes; (4) removing positions in the profile with gaps in the query sequence results in better alignments; and (5) adding predicted and known secondary structure information improves alignments.     

Rapid significance estimation in local sequence alignment with gaps.

In order to assess the significance of sequence alignments, it is crucial to know the distribution of alignment scores of pairs of random sequences. For gapped local alignment, it is empirically known that the shape of this distribution is of the Gumbel form. However, the determination of the parameters of this distribution is a computationally very expensive task. We present a new algorithmic approach which allows estimation of the more important of the Gumbel parameters at least five times faster than the traditional methods. Actual runtimes of our algorithm between less than a second and a few minutes on a workstation bring significance estimation into the realm of interactive applications.     

Local sequence-structure motifs in RNA

Ribonuclic acid (RNA) enjoys increasing interest in molecular biology; despite this interest fundamental algorithms are lacking, e.g. for identifying local motifs. As proteins, RNA molecules have a distinctive structure. Therefore, in addition to sequence information, structure plays an important part in assessing the similarity of RNAs. Furthermore, common sequence-structure features in two or several RNA molecules are often only spatially local, where possibly large parts of the molecules are dissimilar. Consequently, we address the problem of comparing RNA molecules by computing an optimal local alignment with respect to sequence and structure information. While local alignment is superior to global alignment for identifying local similarities, no general local sequence-structure alignment algorithms are currently known. We suggest a new general definition of locality for sequence-structure alignments that is biologically motivated and efficiently tractable. To show the former, we discuss locality of RNA and prove that the defined locality means connectivity by atomic and non-atomic bonds. To show the latter, we present an efficient algorithm for the newly defined pairwise local sequence-structure alignment (lssa) problem for RNA. For molecules of lengthes n and m, the algorithm has worst-case time complexity of O(n2 x m2 x max(n,m)) and a space complexity of only O(n x m). An implementation of our algorithm is available at http://www.bio.inf.uni-jena.de. Its runtime is competitive with global sequence-structure alignment.     

Aligning gene expression time series with time warping algorithms

motivation: Increasingly, biological processes are being studied through time series of RNA expression data collected for large numbers of genes. Because common processes may unfold at varying rates in different experiments or individuals, methods are needed that will allow corresponding expression states in different time series to be mapped to one another. Results: We present implementations of time warping algorithms applicable to RNA and protein expression data and demonstrate their application to published yeast RNA expression time series. Programs executing two warping algorithms are described, a simple warping algorithm and an interpolative algorithm, along with programs that generate graphics that visually present alignment information. We show time warping to be superior to simple clustering at mapping corresponding time states. We document the impact of statistical measurement noise and sample size on the quality of time alignments, and present issues related to statistical assessment of alignment quality through alignment scores. We also discuss directions for algorithm improvement including development of multiple time series alignments and possible applications to causality searches and non-temporal processes ('concentration warping').     

Iterative pass optimization of sequence data

The problem of determining the minimum-cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete. This "tree alignment" problem has motivated the considerable effort placed in multiple sequence alignment procedures. Wheeler in 1996 proposed a heuristic method, direct optimization, to calculate cladogram costs without the intervention of multiple sequence alignment. This method, though more efficient in time and more effective in cladogram length than many alignment-based procedures, greedily optimizes nodes based on descendent information only. In their proposal of an exact multiple alignment solution, Sankoff et al. in 1976 described a heuristic procedure--the iterative improvement method--to create alignments at internal nodes by solving a series of median problems. The combination of a three-sequence direct optimization with iterative improvement and a branch-length-based cladogram cost procedure, provides an algorithm that frequently results in superior (i.e., lower) cladogram costs. This iterative pass optimization is both computation and memory intensive, but economies can be made to reduce this burden. An example in arthropod systematics is discussed.     

The Construction and Use of Log-Odds Substitution Scores for Multiple Sequence Alignment

Most pairwise and multiple sequence alignment programs seek alignments with optimal scores. Central to defining such scores is selecting a set of substitution scores for aligned amino acids or nucleotides. For local pairwise alignment, substitution scores are implicitly of log-odds form. We now extend the log-odds formalism to multiple alignments, using Bayesian methods to construct “BILD” (“Bayesian Integral Log-odds”) substitution scores from prior distributions describing columns of related letters. This approach has been used previously only to define scores for aligning individual sequences to sequence profiles, but it has much broader applicability. We describe how to calculate BILD scores efficiently, and illustrate their uses in Gibbs sampling optimization procedures, gapped alignment, and the construction of hidden Markov model profiles. BILD scores enable automated selection of optimal motif and domain model widths, and can inform the decision of whether to include a sequence in a multiple alignment, and the selection of insertion and deletion locations. Other applications include the classification of related sequences into subfamilies, and the definition of profile-profile alignment scores. Although a fully realized multiple alignment program must rely upon more than substitution scores, many existing multiple alignment programs can be modified to employ BILD scores. We illustrate how simple BILD score based strategies can enhance the recognition of DNA binding domains, including the Api-AP2 domain in Toxoplasma gondii and Plasmodium falciparum.     

A hidden Markov model for progressive multiple alignment

MOTIVATION: Progressive algorithms are widely used heuristics for the production of alignments among multiple nucleic-acid or protein sequences. Probabilistic approaches providing measures of global and/or local reliability of individual solutions would constitute valuable developments. RESULTS: We present here a new method for multiple sequence alignment that combines an HMM approach, a progressive alignment algorithm, and a probabilistic evolution model describing the character substitution process. Our method works by iterating pairwise alignments according to a guide tree and defining each ancestral sequence from the pairwise alignment of its child nodes, thus, progressively constructing a multiple alignment. Our method allows for the computation of each column minimum posterior probability and we show that this value correlates with the correctness of the result, hence, providing an efficient mean by which unreliably aligned columns can be filtered out from a multiple alignment.     

SQUARE--determining reliable regions in sequence alignments

The Server for Quick Alignment Reliability Evaluation (SQUARE) is a Web-based version of the method we developed to predict regions of reliably aligned residues in sequence alignments. Given an alignment between a query sequence and a sequence of known structure, SQUARE is able to predict which residues are reliably aligned. The server accesses a database of profiles of sequences of known three-dimensional structures in order to calculate the scores for each residue in the alignment. SQUARE produces a graphical output of the residue profile-derived alignment scores along with an indication of the reliability of the alignment. In addition, the scores can be compared against template secondary structure, conserved residues and important sites.     

A workbench for multiple alignment construction and analysis

Multiple sequence alignment can be a useful technique for studying molecular evolution, as well as for analyzing relationships between structure or function and primary sequence. We have developed for this purpose an interactive program, MACAW (Multiple Alignment Construction and Analysis Workbench), that allows the user to construct multiple alignments by locating, analyzing, editing, and combining "blocks" of aligned sequence segments. MACAW incorporates several novel features. (1) Regions of local similarity are located by a new search algorithm that avoids many of the limitations of previous techniques. (2) The statistical significance of blocks of similarity is evaluated using a recently developed mathematical theory. (3) Candidate blocks may be evaluated for potential inclusion in a multiple alignment using a variety of visualization tools. (4) A user interface permits each block to be edited by moving its boundaries or by eliminating particular segments, and blocks may be linked to form a composite multiple alignment. No completely automatic program is likely to deal effectively with all the complexities of the multiple alignment problem; by combining a powerful similarity search algorithm with flexible editing, analysis and display tools, MACAW allows the alignment strategy to be tailored to the problem at hand.     

MINRMS: an efficient algorithm for determining protein structure similarity using root-mean-squared-distance

MOTIVATION: Existing algorithms for automated protein structure alignment generate contradictory results and are difficult to interpret. An algorithm which can provide a context for interpreting the alignment and uses a simple method to characterize protein structure similarity is needed. RESULTS: We describe a heuristic for limiting the search space for structure alignment comparisons between two proteins, and an algorithm for finding minimal root-mean-squared-distance (RMSD) alignments as a function of the number of matching residue pairs within this limited search space. Our alignment algorithm uses coordinates of alpha-carbon atoms to represent each amino acid residue and requires a total computation time of O(m(3) n(2)), where m and n denote the lengths of the protein sequences. This makes our method fast enough for comparisons of moderate-size proteins (fewer than approximately 800 residues) on current workstation-class computers and therefore addresses the need for a systematic analysis of multiple plausible shape similarities between two proteins using a widely accepted comparison metric.     

Similarity queries for temporal toxicogenomic expression profiles

We present an approach for answering similarity queries about gene expression time series that is motivated by the task of characterizing the potential toxicity of various chemicals. Our approach involves two key aspects. First, our method employs a novel alignment algorithm based on time warping. Our time warping algorithm has several advantages over previous approaches. It allows the user to impose fairly strong biases on the form that the alignments can take, and it permits a type of local alignment in which the entirety of only one series has to be aligned. Second, our method employs a relaxed spline interpolation to predict expression responses for unmeasured time points, such that the spline does not necessarily exactly fit every observed point. We evaluate our approach using expression time series from the Edge toxicology database. Our experiments show the value of using spline representations for sparse time series. More significantly, they show that our time warping method provides more accurate alignments and classifications than previous standard alignment methods for time series.     

Optimal sequence alignment allowing for long gaps

A new algorithm for optimal sequence alignment allowing for long insertions and deletions is developed. The algorithm requires O((L+C)MN) computational steps, O(LN) primary memory and O(MN) secondary memory storage, whereM andN(M≥N) are sequence lengths,L (typicallyL≤3) is the number of segment specifying the gap weighting function, andC is a constant. We have also modified our earlier traceback algorithm so that it finds all and only the optimal alignments in a compact form of a directed graph. The current versions accept a set of aligned sequences as input, which facilitates multiple sequence alignment by some iterative procedures. Dedicated to Professor Akiyoshi Wada on the occasion of his 60th birthday.     

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.     

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.